I'm not sure very many people will actually be helped by reading the linked discussion, which appears both too technical to be clear for newcomers to Quantum mechanics while also not providing any interesting detail for the more experienced reader.
This seems to be entire argument:
> But the wave function is a wave in the space of possibilities, and not in physical space.
Which is fair enough as an initial claim, but it doesn't really get motivated further, or at least not before I got bored reading and started skimming.
For a single particle they are easy to confuse. A wave function ψ(t,x) for a single particle gives a probability amplitude to find the particle at coordinate x at time t. In this case one can imagine an amplitude at each point in space and time, like a field. This interpretation however completely breaks down once you introduce a second particle: the wave function ψ(t,x1,x2) gives a probability amplitude to find particle 1 at x1 and particle 2 at x2 at time t. This no longer admits an interpretation of assigning some value to locations in space. Intuitively one might think you get one amplitude for each particle at some location but that's not how QM works, so we shouldn't think of the wave function as living in physical space.
Yes, which is exactly the point. The main difference is that the wave function has a complex value with norm <= 1, while a probability distribution function has a real value <= 1.
But if you aren't trying to map the wave function to physical space somehow you are essentially saying that the central construct of your theory has no direct relation to the actual physical processes happening "underneath".
This reduces to a kind of "shut up and calculate" attitude, so it seems poor starting point from which to write an interpretation text.
Space is a part of the wavefunction, as the article explains clearly. The wave function describes where the particles can be in physical space. And, the wave function has the same shape as the wave equations for traditional mechanical waves, like a sound wave or a sea wave.
However, if a classical three-dimensional wave equation describes how matter osciallates in three-dimensional physical space, a quantum wavefunction doesn't do that. Quantum particles don't oscillate in physical space like that. A three-dimensional wavefunction might describe three particles' positions along a one-dimensional line, and it's oscillations are oscillations of probability, not position. The particles don't move, say, up and down. Their probability to be here or there on that 1-d line waxes and wanes.
This is what the article is trying to explain: the basic mathematics of quantum mechanics, the definition of the wavefunction. The value of a wavefunction for the position of three particles is not a position in space at a moment in time. It is a (complex) probability for the position of every particle at that moment.
This only seems confusing when looking at wavefunctions that describe positions. But wavefunctions often have many more observables, such as spin or polarization. A wavefunctions for two electrons moving around on a plane will not be a two-dimensional wave. It will be a wave in a six-dimensional space, whose axis may be "particle 1 has spin up/down, particle 2 has spin up/down, particle 1 position along x axis, particle 2 position along x axis, particle 1 position along y axis, particle two position along y axis".
I'm honestly confused; it's fine to say the wave function lives in some high dimensional phase space and that it's not actually describing some vibration of spacetime. But I don't recall ever imagining the wave function being a vibration of spacetime, is that really something people think?
If I were to express some sort of wave-function-in-spacetime theory, I'd invoke lots of classical fields filling space and have those wiggle.
In any case, the whole bit about the proper two-particle wave function living in a higher dimensional space is somewhat spoiled by the fact that you can factorise it into normal 3-space pieces (so long as you don't have your particles interacting), it doesn't seem such an alien space to me.
Before the wavefunction, we used to explain the double slit experiment (the version without detectors at a slit) as light being an EM wave in physical space, essentially equivalent to a sound wave propagating through the EM field, which breaks on the wall and essentially transforms into two separate waves, each originating from one slit, which are then in phase and so they constructively interfere, forming the final pattern on the screen.
Lots of people think that this is the same picture that the wavefunction gives, but this is wrong. In the QM picture, the emitter emits one photon, which is a quantum of energy described by a four-dimensional wavefunction which assigns some probability of a detection event at the slits, at the screen, etc. In this picture, there is no physical EM wave, any interaction with the light will happen at a single localized point in space. Of course, if you add more particles, especially those carrying charges, the picture changes, and you'll see probabilities that roughly correspond to a picture of an oscillating EM field. But the wavefunction, which is the "bedrock" physical theory, is separate from those waves in the EM field, which are just an approximate picture of the probabilities dictated by the wavefunciton.
I morally agree, but not quite: think of the wave function as not more than a bookkeeping device. It does get the job done but be careful to ascribe it too high an ontological status! The path integral formulation seems a lot more natural to me and it does not need a wave function, instead you can derive it and treat it as a bookkeeping device. The way I think about it is that it's an attempt to deterministically model non-deterministic behavior: you "pretend" that the system is deterministic by keeping track of all the possible ways it could have evolved in time. sure enough, once you make a measurement this probability distribution "collapses" and you find out what is actually the case.
I think you are agreeing with my point that declaring the wave function to be mere bookkeeping is a poor foundation for writing about the interpretation of quantum mechanics?
Can't really get any other sense out of your reply, but I'm not entirely sure.
Also not sure I'm understanding you right :)
My view is this: the wave function is mere bookkeeping and not anything ontologically fundamental. However the fact that such a seemingly bizarre concept lets you do quantum physics (even if it's not the only way) points to some fundamental questions about the nature of...well, nature.
Of course this is not the only valid view...just one that makes sense to me. Thinking about these sorts of questions is a very fun endeavour.
My view is that OP's text about whether the wavefunction goes through both slits is overly long if the premise is that the wavefunction is only for bookkeeping.
Considering a particle is an excitation of a quantum field, the space of possibilities could be seen as the only space there is. At least that’s what I think (but don’t know for sure) that the mathematical universe hypothesis people posit.
I had the same reaction. If you make it to the end he concludes with:
> The wave function’s pattern can travel across regions of possibility space that are associated with the slits.
Which to me conflicts with his emphatic “no” at the beginning of the article because this implies you can define some mapping between the physical and probability space. And of course you can because if you couldn’t the theory would not be physically predictive.
His point from the beginning is this: the particle described by the wavefunction can't be said to move through both slits at once, because ψ(t, x, y) has a single value for a particular x and y at a particular time. The particle has non-0 probability for both x, y1, t and for x, y2, t, of course - but that just means the particle has non-0 probability to pass through either slit.
And as for saying that the wave moves through both slits, that also doesn't make sense, by the very definition of the wave function - it's a wave in probability space, not in space, so it just doesn't move through space.
I’m with you on point 1, (I think this is also obvious from experiment because you will never measure a particle at both slits).
for point 2 it seems you can define a mapping from the physical space to probability space. Saying that the wave doesn’t “move through” space might be technically correct but also seems like semantics on the definition of the phrase “move through” ?
Of course it is to some extent semantics. But the important point is that the wavefunction is not something like a sound wave, or even something like a classical EM wave. Those are all waves defined over 3-dimensional physical space.
In the original QM model, light is not a wave in the classical electrical theory sense. Light is made up entirely of photons, which are particles just like electrons or billiard balls, and they are described by a wavefunction. That wavefunction gives them various probabilities of being in various states at a certain time, and those probabilities can increase or decrease when more particles come into the mix. The states can represent position, momentum, charge, spin, energy levels, etc.
> And as for saying that the wave moves through both slits, that also doesn't make sense, by the very definition of the wave function - it's a wave in probability space, not in space, so it just doesn't move through space.
I don't think that's a valid argument. Imagine a regular water wave, i.e. a wavefunction h = h(x, y, t) describing the height of the water at position (x, y) at time t. You could say "this is a wave in height space, not in space, so it just doesn't move through space" and in a certain sense that's true. But obviously there is something that does "move" through "space" to the extent that anything can ever be said to do so.
I’ve always wondered, has there ever been a definitive experiment where one photon hits a slit and on the other side two photons come out, but then when you add a photon observer, it immediately only comes out on one side? Or has the proof always been mathematical rather than a live experiment?
Edit: Thank you all for the responses, it has been very educational. It appears I was misunderstanding the most important aspect of the double slit experiment. A photon is a wave function when unobserved, it literally goes through both slits and creates an interference pattern like how waves in water would. However, when observed at the slit, or at the detector screen, the wave function collapses and only one photon(billiard like particle) will be detected.
Are you referring to the double-slit experiment? If so, yes: It has always been an experiment. The experiment came before any theory explaining the behavior AFAIK. https://en.m.wikipedia.org/wiki/Double-slit_experiment
One photon hits the slit and one photon comes out. It is only if you repeat the experiment many times that you start to see a strange wawe-like pattern in where the photons hit.
It is as if every photon that went through the slit is somehow aware of all other photons that did so too so each photon can choose the (random) position where it hits on the wall behind the slit such that together they look like as if a WAWE went through the slit.
That is (one reason) why they call it "Quantum Weirdness". God is playing dice with us
> It is as if every photon that went through the slit is somehow aware of all other photons that did so too
Why isn't it just that there's a probability density function that describes the aggregate outcomes of a large number of samples from a random process? Why is "memory" involved?
I think because instead of two clusters like you'd expect from random BBs being shot, you get multiple bands like you'd see with interfered waves. Even when shot one at a time.
No. The same photon is aware of all alternative paths it can take, without creating or interacting with any other photon.
There's no photon multiplication, and no "all other photons" changing their path.
There is some inter-photon interaction because they are bosons. But it's not significant enough to impact the multi-slit experiment. And the experiment works exactly the same way if you send only one photon at a time.
Double slit experiment did happen and totally reproducible even then photons/electrons are sent by one at a time.
"two photons come out" part makes no sense though. On a target side, there's always single hit after single photon/electron, but distribution of theses hits as if said electron got through both slits and interfered with itself
P.S. the funny thing is - this works on any small thingy, measured up to 2000 atoms-big, as if it's the property of the universe itself
I would love to try this experiment with something basketball sized out in space. Like we build an enormous basketball detector behind a double slit inside an unobservable black box. If thr basketball started acting like a wave I would be sooo freaked out
> The largest entities for which the double-slit experiment has been performed were molecules that each comprised 2000 atoms (whose total mass was 25,000 atomic mass units).[19]
The entanglement theory would imply that if you build a detector that turns the gravity interaction into a finite piece of data observable by an (amplified) system, then gravity will act as an observer and collapse the waveform when it reaches that point. That's my take on the whole thing... It's almost like information theory. If the information is lost to the sands of time (below noise floor if you will) then the entanglement can continue.
The experiment working on clusters of atoms is news to me and I loved getting to know about that. But the thing that really breaks my mind is the experiment that proves that the behavior depends on the possibility of getting information from which slit the particle went through. So we can rule out the act of measurement itself interfering with the behavior of the particle.
They did it by splitting a beam of particles into a pair of entangled particles and then setting up a way to measure the polarity of one of them after the point in time where it even hits the final screen. If you measure the polarity then, after the other stream of particles from the beam had already had time to make the pattern, the pattern will be two clusters. If you don't, it goes back to an interference pattern.
That one really cemented the notion in my head that this is just how the Universe is and not some local weirdness with particles and measurements.
I think Sabine explained this social effect few years ago. I know she's a little controversial, but the key thing in the video (as opposed to all other videos about DSE on the internet) was that you don't get "two clusters" actually. They are both statistical parts of a single [non-]interference pattern. "||" is a lie. I'm not in a physics rebel camp and don't prefer Sabine either, but after that I sort of lost trust in the interpretations that can't even get the resulting picture right. I even suspect that showing dumbed results amplifies "wow" effect and monetizes better.
This is the video if you're interested. Again, I'm no physicist and don't know if explanations are legit or statistically correct. But that little || trick that all other popsci videos play on you, that's a true concern.
> Here, we report interference of a molecular library of functionalized oligoporphyrins with masses beyond 25,000 Da and consisting of up to 2,000 atoms, by far the heaviest objects shown to exhibit matter-wave interference to date.
It would be awkward to say that the 2000 atom molecule comes out of both sides... but it does, until you look.
The double slit experiment is not a duplication cheat of reality... it's weirder than that.
Am I misunderstanding the significant of the double slit experiment?
I thought the takeaway wasn’t that the particle comes out both sides, the implication is that the behavior of a single particle is the same as the behavior of multiple particles - that is to say, it appears to be an interference pattern, even when there should be no other particles to interferes with the single one.
No you're understanding correctly (I think), the behaviour of a single detected particle depends on all possible paths it could take to get to the detection.
This is fundamental to 100 years of quantum mechanics and underlies most of physics including all semiconductors, materials science, chemistry, lasers, etc. The double slit experiment is just a very good illustration of the principle boiled down to its essentials, which is why it's everywhere in pop-sci. It makes for more accessible story than describing how a hydrogen atom works.
I think the problem is in insisting on referring to the photon as a particle.
In fact the photon may not actually exist. and I have questions as to what "single photon experiments" are actually measuring. let me explain.
The EM field is not quantized, or at least not quantized at the level of a photon, what we call a photon is the interaction of the EM field with matter, or more precisely with the electron shell of matter. it is the sound of the wave breaking on the shore, not the wave.
Now none of this actually matters as the only method we have of interacting with the EM field is through matter(electrons really) so we can only measure it in photon sized increments.
Just for sake of argument, when looking at it from this angle, EM particles could exist and we lack the ability to emit a single one? But then why would these "single photon" double slit problems not split the particle bunch further?
I honestly don't know, that is my question as well.
However note that we can only perturb the em field in photon sized energy levels, and we can only pick up disturbances of the em field in photon sized bunches as well. Not sure what this implies for how em field energy is accumulated on electrons in order for us to detect it.
Well, the EM field CAN be quantified. Just look up any textbook on quantum field theory. And the quanta of the EM field is called the photon.
But, to "solve" the wave /particle conundrum, I like to think of it as fields all the way down. A "particle" is then a localized and quantisized interaction of said field with another field.
If you think of particles as small billiard balls flying through space on some ballistic trajectory, you'll soon run into all kinds of trouble and the mental model breaks down.
> The EM field is not quantized, or at least not quantized at the level of a photon, what we call a photon is the interaction of the EM field with matter, or more precisely with the electron shell of matter.
I don't agree with this. You can absolutely consider a classical (non-quantized) EM field interacting with quantized matter. This semi-classical model can describe the photoelectric effect, but it cannot describe other experimental observations such as sub-poissonian photo-detections / photon anti-bunching.
Perhaps the closest thing would be some nuclear decays that spit out two gamma rays of equal energy in opposite directions. I'm struggling to remember which isotope does this.
I haven’t used it for my research, but it’s an incredible local probe of electric and magnetic fields in materials. There’s no other technique that I’m aware of that smuggles information about the chemical structure of a single coordination sphere into such clean, distinct emissions. The brief excited state of the isotope after the first emission event and before the second is sensitive to practically everything. It all shows up in the deconvoluted spectra.
Shame nearly all the isotopes that work for this are not ones that are super interesting for modern quantum materials. Perhaps that will change out of necessity.
You still do not understand what is happening, please READ the article, it shows that the wave function doesn't go through anything and the it certainly doesn't create the interference pattern.
I really don’t understand the topic much but this veritasium video is quite eye opening and goes into further depth than any layman explanation I’ve ever seen in the topic: https://youtu.be/qJZ1Ez28C-A?si=6gSQYcJPpaSIt1x1
> I’ve always wondered, has there ever been a definitive experiment where one photon hits a slit and on the other side two photons come out, but then when you add a photon observer, it immediately only comes out on one side? Or has the proof always been mathematical rather than a live experiment?
Only one photon comes out, but it can interfere with itself if it had the possibility of going through either slit.
That nuance aside, the Quantum Eraser Experiment is a real physical experiment that covers what I think you're asking about. If you send photons through double slits in a setup where you can tell which slit the photon went through, you don't get an interference pattern. If you can't tell, you do get the interference pattern.
> Figure 4: The wrong wave function! Even though it appears as though this wave function shows two particles, one trailing the other, similar to Fig. 3, it instead shows a single particle with definite speed but a superposition of two different locations (i.e. here OR there.)
I understand that if treat the act of adding two particles' wave functions as creating a new wave function for one particle, then we have this problem, essentially by definition. But it got me thinking - would it not make sense to treat the result as an expected value, such that we could then measure how many particles are likely to be to the right of the door at each point in time?
It isn't by definition, presuming the relationship between quantum mechanics and reality. You can have a _two particle_ state and a _one particle state_ with non-trivial probability of being in two places. They are distinct things. The key idea here (and really, in Quantum Mechanics generally) is that superpositions are important things in the theory. This is the statement that if you have a wave function for one situation and another wave function for another than the sum of the two is also, necessarily, a valid wave function for a physically realizable system.
This is different from a classical probability. Suppose we simply don't know whether the baseball was fired from HERE or from THERE. In a classical situation, we can carry forward our understanding of the situation in time by simply calculating what the classical particles would do independently. In quantum mechanics the mechanics are of the wave function itself, not of the things we measure. We cannot get the right answer by imagining first that we measure the particle in one location and calculate forward and then by imagining we measure the particle in another and calculating forward and then adding the results. It isn't how the theory works. We must time evolve the wave function to predict the statistical behavior of measurement in the future.
Particles don't exist. We just perceive waves with high decoherence rates as particles. Things we call objects effectively have a 100% decoherence rate. Things we call waves like light have low decoherence rates.
Decoherence is the process that makes it impractically difficult for an experiment to be designed that makes your observations the two interfering possibilities in some kind of double-slit experiment.
Interpreting this in the many-particle case is more difficult, but the basic idea is that due to single-particle uncertainty, you can't have a definite number of particles indexed by momentum and a definite number of particles indexed by position at the same time. If I had 100 particles that were definitely at x=0, in terms of momentum they'd be spread out over the range of possibilities unpredictably.
Not exactly. The Heisenburg uncertainty principle doesn't apply to knowledge (actual observations), it applies to observables (things that could affect interactions in principle). That is, Heisenburg uncertainty is not merely a limit on how fine our measurement instruments could get, or even how much information about an interaction we could conceive of and store. It's a limit on how strongly those properties can affect an interaction at all.
That is, the future direction and momentum of an interaction between two particles can't depend very strongly on both the position where the interaction happened, and on the momentum the particles had before the interaction. If the interaction is a direct collision, so the position is heavily constrained, then the momentum the particles had before the collision will not really matter a lot for what happens after they collide.
If you were to "put yourself in the shoes of" one of the particles, you could say that, because it "knows" where the other particle is at the time of the collision with high precision, it can't "know" the momentum the other particle had with any precision, so it's future movement can't depend strongly on that. But this stretches the definition of "knowledge" far beyond the normal understanding of the word.
> It happens outside QM, and even outside physics. It’s not a physical attribute, it’s statistical.
This is not true at all. In classical mechanics, particles have fully definite properties. In the theory, if two particles collide, the position and momentum they'll have after the collision depend on their exact position and exact momentum before the collision, with no bound on precision.
Of course, classical mechanics admits that we can't measure things to any level of precision, there is some practical bound below which noise in the measurement will drown out the signal. But the interaction itself has no such bound, it happens with infinite precision. If the speed of one of our particles were higher by just 10^-100 m/s, its trajectory might be completely different.
This is not possible in QM. In QM, if the particles collide (they meet at an exact point in space-time), then their trajectories afterwards wouldn't change even if one of their speeds were 10 times higher: if they have definite position, their speed is extremely fuzzy, and it can't significantly affect their trajectories after the event.
And QM turns out to be right abput this, when you measure things precisely enough.
I was making the point that the uncertainty principle is not about QM. And it is not. It occurs in a wide range of even classical systems.
As for your comment about them not having defined proporties; this is also just one interpretation. You argue for violation of realism. That’s fine, but unnecessary.
Violation of locality or realism is only needed in the context of Bell inequalities, and this assumes there is no superdeterminism and you are “free” to choose your experiment, which is of course a rather strange argument to have to begin with.
To spare your struggle with language: commutator of hermitian operators is a physical property of mathematical origin, inherited from linear algebra, because QM is described by linear algebra, so physics inherits all aspects of linear algebra as physical properties.
How frequently a wave would go through just 1 of the slits. If you threw a baseball at a wall with two baseball sized slits it would basically always go through just one of the slits. You would never see an interference pattern.
This is because a baseball is interacting with other matter on the way to the slit. A photon on the other hand might not interact with any matter and it stays as a wave and you can see an interference pattern on the other side.
Isn't it one of the 'does it matter if you didn't interact with it?' questions, and keep in mind 'observation' at quantum scales is to a good approximation synonymous to 'interaction'.
Rather than viewing wave functions as abstract mathematical objects in possibility space, we might understand them as describing the probabilistic nature of fundamental spinning energy entities whose rotational states generate wave-like behavior in measurement outcomes. Strassler's "possibilities" could be reinterpreted as different rotational configurations of spinning energy, with interference patterns emerging not from physical objects passing through slits but from how these spinning states evolve when constrained by sequential measurements.
To quote Cockshott, the Copenhagen Interpretation is an idealist recapitulation of Russian Machism/Bishop Berkley. The statement "nothing /is/ until it is observed" is not necessarily a Weird Quantum formulation but just a solipsistic attitude applicable towards all scientific observation in general.
If one tries to formulate QFT theory with Bohmian Mechanics the results are less than satisfying. Regular Quantum Mechanics in a Bohmian mode is, in addition to failing to be invariant, also pretty paltry if pressed to really serve, primarily in that it appears to be the case (for both theories) that one has quite a lot of freedom with respect to what precisely lives with the particle and what lives with the pilot wave function.
In another sense Bohmian mechanics just kicks the can down the road - we may decide to associate the specific thing we observe with a particle situated on the pilot wave, but in fact, as far as the theory goes, the particle can live at any point in the pilot wave it wishes and nothing about the dynamics of the pilot wave changes at all. Thus we simply place the non-determinism in the past rather than in the present.
Furthermore, Bohmian mechanics seems to break Newton's First Law, since the pilot particle, as hinted above, is influenced by the pilot wave but not vice versa. The appeal of Bohmian mechanics is obvious, but superficial. It does not dispense with the can of worms, just opens it from the other side, in my opinion.
Bohmian mechanics is based on the idea that we perceive stuff to be in a certain position in a single reality because there is a correspondence to stuff being actually there. That's nice. If the particles are surfing a wave and not impacting it, so be it.
It is also rather nice to think of the particles as just being points in space with nothing else associated with them; an electron is just an electron because the portion of the wave function that is relevant and guiding it is the electron portion; see a paper from 2004 entitled "Are all particles identical?" [1] (I am a coauthor on that). If one thinks about it, we only know about particles through their motion so having things like mass and charge linked to the object guiding the particle seems perfectly reasonable. Points are not only not labelled by numbers (particle 1, 2, etc) but also not labelled by mass and charge.
The nondeterminism of not knowing the initial conditions is fine; the point was to have a theory with well-defined objects that give some plausible story and connection to our experiences, such as stuff existing and being somewhere. The fact that non-relativistic Bohmian mechanics happens to be deterministic is just happenstance for many of its supporters. In some QFT versions, the dynamics of creation is not deterministic and there is no reason for that to be a problem. But it is well-specified without having to invoke some special magic action called "observation".
As for QFT, the biggest problem for Bohmian mecahnics is the need to have an actually well-defined evolution of the wave function. The idea of particles being created and annihilated is not particularly hard. And, in fact, recent work has shown that if one takes that seriously and respects probability leaking from n particle space to n+1 and n-1, then at least some of the divergence problems go away. See [2]
> Bohmian mechanics is based on the idea that we perceive stuff to be in a certain position in a single reality because there is a correspondence to stuff being actually there. That's nice. If the particles are surfing a wave and not impacting it, so be it.
At that point it's very obviously a violation of Occam's razor though. It's like positing that the content of my field of vision is an objectively real thing, that the reason the universe looks like a video projection is that there really is a video projection going on, even though that video projection has no physical effect.
> If one thinks about it, we only know about particles through their motion so having things like mass and charge linked to the object guiding the particle seems perfectly reasonable.
Indeed. But if one thinks a little more, what's the point of positing a particle at all, if all of the physics is in the pilot wave?
The definite positions of your brain states evolution is correlated to the other positions of all the stuff. The other particles do have an effect on your evolution and there is a "you" set of particles one can talk about. Remember the wave function is a function on configuration space so evaluating the guiding effect on the particles is to have to know what point in configuration space it is at; this is actually the troubling bit and leads to the nonlocality concerns, but that problem is common to any quantum theory with definite results happening.
The physics, therefore, is not all in the pilot wave. If you take as the point of a particle theory that there should be particles with positions changing in time, then that is what is being given in Bohmian mechanics.
Also, ask yourself, if the wave function is on configuration space, what constitutes a configuration? In Bohmian mechanics, it is clear, but if the wave function is all there is, then why are we talking about configuration space at all? It is just this abstract vector in Hilbert space evolving and many different representations can happen. Why do we not perceive reality in terms of these other representations?
If it helps, you can think of the wave function a bit like a dynamic law. In [1], the authors suggest thinking of log( psi) analogously to the Hamlitonian H on phase space in classical mechanics. There is no back action on H and most of it is irrelevant to the evolution of a particular particle system in that framework and yet everyone recognizes it as just a convenient way of describing the dynamics.
The difference is that psi evolves but even that may only be true on a subsystem point of view. It is theoretically possible to have a stateless universal wave function which, when particular particle positions of the environment are plugged in, nonetheless gives evolving subsystem wave functions.
Occam's razor is difficult to apply here without a prejudice. If you want to minimize the number of equations, then sure, "the wave function is everything" works, but it comes at the cost of there being what could be considered an infinite number of "you"s and everything else, all slightly different and whole existing other expressions of the universe with no connection to us. If you want collapse somewhere, then you have to posit that mechanism.
On the other hand, by adding in particles and the guiding equation, one gets a singular "you" and everything that we experience is, more or less, definite and singular. So the "existing" stuff is dramatically reduced.
Which one of this is truly simpler is a matter of taste, I would say. I think in terms of communicating with people, the Bohmian version of "there is this universal wave and the positions of stuff are guided by it" is pretty simple. The law itself is so trivially a part of the Schrodinger equation that it could easily be derived before the Schrodinger equation itself. Contrast this with other versions which is "reality collapses to a definite state when we look at it" or "there are infinitely many different universes". None of those seem as simple.
> there is a "you" set of particles one can talk about
We know that particles don't have identity though - exchange of identical particles is a symmetry and physics would be very different if it wasn't. I won't claim it's compelling, but to me that suggests that a particle is more like a pattern or a field excitation than a thing with its own concrete existence.
> Why do we not perceive reality in terms of these other representations?
What would be different if we did? I mean obviously at a macroscopic level particles moving through space is a model that gives a good approximation and is easy to think in, but that doesn't mean they're any more physically real than e.g. temperature.
In physics, particles not being labelled by anything other than their trajectories is a very natural starting point. When one uses the natural configuration space, one without labels in which a configuration is a set of n points in physical space rather than an ordered n-tuple, then the complex-valued wave functions on that space are exactly those of boson type. To get the fermions, one replaces the value space with a 1 dimensional complex bundle over the configuration space, one which twists in the right way. A paper I coauthored explores this in a general context: [1]
The "you" is then a rough set of particles whose trajectories roughly coincide with your macroscopic trajectory. Their identity is just given by where they are.
As for representations, I feel like I can easily understand how to get momentum or temperature from particles with their time evolution (trajectories), but I do not see how, say, to get positions of particle just from knowing what their momentums were and their time evolution.
But we don't have even a set of definite trajectories. If we see e.g. an electron coming towards a hydrogen atom and then an electron moving away from it, not only do we not know whether the incoming electron "bounced off" or whether it settled into the orbital and "kicked" the electron that was already there out, but in a fundamental physics sense what occurred is some weighted average of both (in the same way that we don't merely "not know" which of the two slits an electron went through but in an important physical sense it partially went through both).
It depends on the theory. The Bohmian theory, which is what I have been using, is one in which electrons have actual positions that change over time along trajectories. We may not have access to that data, but that is fine. Certainly in simulations one would be able to see which scenario happened. For some, it might be the same electron moving away, for others it would be kicking one out. One could definitively say which one is happening in the simulation. In experiments, we cannot say that because our access to the knowledge is limited by quantum equilibrium. The quantum formalism is very much like thermodynamics in that regard; the individual details are missing, but the larger picture can be computed. Nevertheless, in a Bohmian world, the electrons have their distinct identities as distinguished by, and only by, their trajectories.
I tend to think (as some others do) that it's also a much better way to reason about quantum computation. Should a factorization of a large semiprime number by Shor's algorithm be attributed to the semi-mystical power of The Observer collapsing the wave function (which is who by the way, the sensor, or the person reading that sensor?), or are we instead exploiting realism to do the work?
It's always seemed to me that these types of question only exist because we're considering a choice between two imperfect models. If we had a better model of what a "particle" really is, then there would be no dualing models nor paradox.
Do we really have to choose between wave and particle? What does the "particle" model bring to the table that a localized (wavelength-sized) wave/vibration could not?
We have a better model, but it's an ecuation so horrible that nobody want to solve it.
Luckly, sometimes the exact solution can be very accuately aproximated with a wave ecuation.
Luckly, sometimes the exact solution can be very accuately aproximated with a particle ecuation.
(Sometimes, the exact solution can be aproximated saying that the lowest energy state is an eigenvector of the Schoedinger equation. Is that a wave? It's not localized, but not very wavy.)
But neither are the exact solution, just aproximations that solve tpgether 99% of the experiment.
It's difficult to explain, because to explaing the detials you need like two years of algebra and calculus and then like another 2 years of physics, and now you get a degree in physics.
It's possible to solve the difficult ecuation only in very simple cases like electron-electron colissions, if you allow some cheating and a tiny error. For more complicated systems like electron-muon there are some problems. And for more complicated systems, you get more technical problems and more aproximations.
The photoelectric effect [0] can be explained if light behaves as discrete particles, but not when it's a wave since a higher amplitude does not imply a higher energy transfer.
If I emit a bass signal at a low amplitude, but then emit it at a higher amplitude, I can see the effect on a glass of water on the table. What’s happening here if amplitude does not carry power?
My understanding is that theoretically energy transfer is a function of wavelength.
Sorry, my last sentence wasn't formulated well. Yes, a wave with higher amplitude (or one could say "intensity") has a higher energy. The photoelectric effect happens when you shine light with "enough" energy on some material such that the atoms of the material are ionized, i. e. electrons are freed. You need a minimal energy for this and if you use dim light with a low frequency, you will not see the effect. Now, if you increase the frequency of the light, you can measure electrons. If, instead, you make the light brighter, that is, increase the amplitude of the wave (if it were a wave), you don't see electrons. So at least in this experiment, light does not function as a wave.
But once you've increased the light frequency (i.e. photon energy) above the required threshold, THEN making the light brighter (more photons) will increase the number of electrons emitted.
The point here is that the total displacement of water caused by a sound wave depends on both the amplitude of the wave, and its frequency, with no limit: if the wave has high enough amplitude, it will displace water even if the wave is very low frequency.
However, this is not true for EM interactions. If you shine infrared light on a solar panel, you'll see 0 current from it, even with an extremely powerful source of light (at some point the material might heat up enough it starts showing some thermo-electric effect, but that's a different thing). However, if you take even a very low intensity ultraviolet source, you'll see a measurable current right away. This is the unexpected behavior that quantized interactions have, which can't be reproduced with non-qunatized waves like sound waves.
OK - a bit like the fairground game of trying to knock coconuts off a stand by throwing a wooden ball at them. It doesn't matter how many balls you are throwing per minute (total energy being delivered) if the energy of each ball doesn't cross the threshold to knock the coconut off.
OTOH, the energy of a photon is such an abstract concept (not like the kinetic energy of a ball) that I'm not sure it really helps explain it.
Well, there is a saying about spin of an electron. Imagine that you have a ball and it's spinning. Except, it's not a ball. And it's not really spinning.
You can explain the photoelectric effect with classical light (i.e. as EM waves) as long as you properly quantize the atomic energy levels. This is often called s semi-classical model.
However, photo-detections with sub-poissonian statistics cannot be explained under this semi-classical model, but it can be explained with properly quantized EM field (i.e. with photons).
For reference, see Mandel and Wolf's Quantum Optics textbook.
I also don't understand this. AFAIK "particle" in this context means quantized unit rather than contiguous solid object. And I see no reason why a quantized unit of a wave can't propagate through two slits simultaneously. But my level of understanding here is YouTube level so if you know more please correct me.
The problem in these discussions is how to build an intuition about the underlying physical model.
I fail to have an intuition of how can a quantized unit of wave propagate through both slits.
I know that the equations say that the probability of finding the particle at a given location is given by the amplitude squared of the wave function (Born rule).
The image that a "quantized unit of wave propagates through two slits simultaneously" doesn't help me build any further intuition.
Do the two parts going through the two different paths carry half the unit? Clearly that's not the case otherwise they wouldn't be quanta anymore. So does it mean that the entire wavefront is "one unit" no matter how spread out? But in that case, "one unit" of what?
If one just sends photons through a narrow single slit, then the pattern that builds up on the screen (if you send multiple photons, and record their positions) will be a banded diffraction pattern.
If you have two slits, with a detector to determine which slit the photon went thru, then it'll behave as if it only went thru one of the two slits, at random, and what'll build up on the screen will be the two (slit A + slit B) overlayed diffraction patterns.
Finally, if you have two slits with NO detector, then what will build up on the screen is the interference pattern as if the photon had gone thru both slits simultaneously and the two resulting banded diffraction patterns interfered with each other. So, what SEEMS to be happening in this case is that the quantum state of the system post-slit is that of the photon simultaneously having gone thru both slits, each slit having diverted it per diffraction, and then these diffraction patterns (probabilities) interferering. Wave collapse can only be happening after this interference (if it was before then there would only be one diffraction pattern and no interference), presumably when quantum state interacts with the screen.
So, yeah, it seems that the "photon" does "go" through both slits, but this is a quantum representation, not a classical one.
Precisely. The question "is it a particle or a wave" is wrong. It's neither. It's a particle-wave. Something that behaves like a classical wave or particle depending on the situation, but it doesn't switch between them or anything like that. It's not a "particle that has interference" or a "wave with a location".
Being pedantic about the language, there is only one model, and effectively every physicist agrees on it.
What they differ about is the interpretation of that model. The equations are the same, but differ in what the variables refer to in the real world. It's really a matter of solving the equation for X vs Y, saying which one is independent and which is dependent.
The purpose is to take the fact that none of the variables correspond directly to anything we have any experience with. The best we can hope for is to isolate part of it and say "this much is like this thing we understand, but there's an additional thing that we'll treat as a correction".
We can try to take the whole thing seriously, and just call it "a quantum thingy" which is not like anything else. This is sometimes called "shut up and calculate", but even that makes assumptions about what things are feasible to calculate and which are hard. That skews your understanding even if you're trying to let it speak for itself.
There is one set of observations, and many many models to describe them: Schrödinger equation formulation, matrix mechanics (Heisenberg, Born, and Jordan), path integral formulation (Feynman), phase space formulation, density matrix formulation, QFT or second quantization, variational formulation, pilot wave theory aka de Broglie-Bohm theory, Hamilton-Jacobi formulation, PT-symmetric quantum mechanics, Dirac equation formulation (well, not really independent, just for spin 1/2 particles).
They all give the same results, and are therefore mathematically equivalent, but different models tend to be associated with different interpretations:
Schrödinger Equation : Copenhagen, Bohmian Mechanics, Many-Worlds
Matrix Mechanics : Copenhagen
Path Integral : Many-Worlds, Stochastic
Density Matrix: Ensemble, Decoherence-based
Second Quantization : Many-Worlds
Pilot Wave Theory : Bohmian Mechanics
Consistent Histories : Decoherence-based
Relational QM : Relational Interpretation
Stochastic Models : Stochastic Interpretations, GRW (Ghirardi–Rimini–Weber) Collapse
In video games that have procedural generation, there's often a seed function that predicts a continuous geometry.
But in order to track state changes from free agents, when you get close to that geometry the engine converts it to discrete units.
This duality of continuous foundation becoming discrete units around the point of observation/interaction is not the result of dueling models, but a unified system.
I sometimes wonder if we'd struggle with interpreting QM the same way if there wasn't a paradigm blindness with the interpretations all predating the advances in models in information systems.
> What does the "particle" model bring to the table that a localized (wavelength-sized) wave/vibration could not?
A lot of the article is about this. Start with the section "The Wave Function of Two Particles and a Single Door". The wave packet view can't explain why you don't for example see a "particle" (that is, a dot on a detector) show up simultaneously having gone through two different doors. You have to think about it in terms of a wave in the space of possible joint particle positions.
Particles are just standing waves, so to speak. They are not just an amorphous clay-like lump of matter. They are made of smaller things and those things are churning around. That in-place churning becomes a wave when the particles move at speeds that approach a significant fraction of c.
Observation is more important than model; if we take the model too seriously, we can be led astray. It's much like extending a metaphor too far.
We observe double-slit diffraction and model it with the wave-function. This doesn't preclude other models, and some of those models will be more intuitive than others. The model we use may only give us a slice of insight. We can model a roll of the dice with a function with 6 strong peaks and consider the state of the dice in superposition. The fact that the model is a continuous real function is an artifact of the model, a weakness not a strength. We are modeling a system who's concrete state is unknown between measurements (the dice is fundamentally "blurred"), and we keep expecting more from the model than it wants to give.
Programmers may have better models, actually. The world is a tree where the structure of a node births a certain number of discrete children at a certain probability, one to be determined "real" by some event (measurement), but it says little about "reality". The work of the scientist is to enumerate the children and their probabilities for ever more complex parent nodes. The foundations of quantum mechanics may be advanced by new experiments, but not, I think, by staring at the models hoping for inspiration.
Doesn't the difference between measurement and observation stem from an extension of the double slit experiment discussed in thus artucle?
It you place a detector on one of the two slits in the prior experiment, (so that you measure which slit each individual photon goes through) the interference pattern disappears.
If you leave the detector in place, but don't record the data that was measured, the interference pattern is back.
Hm, it says the observer-at-the-slit experiment hasn't been performed because it would absorb the photons. But it also says the experiment can be done with larger particles, so that shouldn't be a problem ...
I have heard similar things but this is THE most deeply weird result and I’ve never heard a good explanation for the setup.
A lot of people pose it as a question of pure information: do you record the data or not?
But what does that mean? The “detector” isn’t physically linked to anything else? Or we fully physically record the data and we look at it in one case vs deliberately not looking in the other? Or what if we construct a scenario where it is “recorded” but encrypted with keys we don’t have?
People are very quick to ascribe highly unintuitive, nearly mystical capabilities with respect to “information” to the experiment but exactly where in the setup they define “information” to begin to exist is unclear, although it should be plain to anyone who actually understands the math and experimental setup.
It's a little simpler than you're thinking: only fully matching configurations (of all particles etc) can interfere. If you have a setup where a particle can pass through one of two slits and then end up in the same location (with the same energy etc) afterward, so that all particles everywhere are in the same arrangement including the particle that passed through one of the slits, then these two configurations resulting from the possible paths can interfere. If anything is different between these two resulting configurations, such as a detector's particles differently jostled out of position, then the configurations won't be able to interfere with each other.
An interesting experiment to consider is the delayed-choice quantum eraser experiment, in which a special detector detects which path a particle went through, and then the full results of the detector are carefully fully stomped over so that the particles of the detector (and everything else) are in the same exact state no matter which path had been detected. The configurations are able to interfere once this erasure step happens and not if the erasure step isn't done.
Another fun consequence of this all is that we can basically check what configurations count as the same to reality by seeing if you still get interference patterns in the results. You can have a setup where two particles 1 and 2 of the same kind have a chance to end up in locations A and B respectively or in locations B and A, and then run it a bunch of times and see if you get the interference patterns in the results you'd expect if the configurations were able to interfere. Successful experiments like this have been done with many kinds of particles including photons, subatomic particles, and atoms of a given element and isotope, implying that the individual particles of these kinds have no unique internal structure or tracked identity and are basically fungible.
If anything is different between the two resulting configurations of possibly affected particles, such as the state of the particles of the detector, then interference can't happen. It's not just about whether the individual particle going through one of the slits is in an identical location.
An important thing to realize is that interference is a thing that happens between whole configurations of affected particles, not just between alternate versions of a single particle going through the slit.
> If you leave the detector in place, but don't record the data that was measured, the interference pattern is back.
This is not remotely true. It looks like you read an explanation of the quantum eraser experiment that was either flawed or very badly written, and you're now giving a mangled account of it.
That is true for classical probability, but the idea that unknown quantities are determining the outcomes in quantum mechanics has been disproven in the event of the speed of light being a true limit on communication speed. This is known as, "Bell's theorem."
My understanding is that it is not that simple, pilot-wave theories, are not the traditional hidden-variable theories. While some setups look very simple in pilot-wave compared to say the schrodinger equation, other setups are as unintuitive in pilot-wave as schrodinger equation is in some.
My lightly held conclusion is if it really was a full and more straight forward solution it would dominate the conversation more than it does now. This option was formed reading some primary sources but mostly reviews and comparisons of QM theories. Unlike other methodologies I have never working through a full QM example problem in pilot-wave theory.
I'm not sure what the point is you're trying to make. OP claimed
> the idea that unknown quantities are determining the outcomes in quantum mechanics has been disproven in the event of the speed of light being a true limit on communication speed.
and I provided an immediate counterexample. Yes, Bell's Theorem and its exact assumptions are not entirely straightforward but let's please stop propagating those falsehoods that die-hard proponents of the Copenhagen interpretation commonly propagate.
Let me throw in "Hydrodynamic Quantum Analogs" [1] as a fascinating review of how quantum effects emerge in experiments with bouncing oil drops on liquid. This is fully a pilot wave driven experiment and there has been a lot of academic work analyzing the system and trying to fit it into the de Broglie-Bohm formulations of quantum dynamics.
To quote section 10.2: "The [experimental] system represents a classical realization of wave–particle duality as envisaged by de Broglie, wherein a real object has both wave and particle components."
We've already got all those fields interacting in the real world, so I don't find it very far fetched that quantum mechanics emerges from their fully classically described interactions, probably expressed in some really gnarly 4D math.
Tim Maudlin's "Philosophy of Physics: Quantum Theory" makes for an excellent read! It addresses tons of questions which are rarely answered (let alone asked) in your run-of-the-mill university-level QM class.
Reality can be interpreted as non-local. There has been no conclusive proof it isn't.
c isn't a limit on the kind of non-locality that is required, because you can have a mechanism that appears to operate instantaneously - like wavefunction collapse in a huge region of space - but still doesn't allow useful FTL comms.
Bell's Theorem has no problem with this. Some of the Bohmian takes on non-locality have been experimentally disproven, but not all of them.
The Copenhagen POV is that particles do not necessarily exist between observations. Only probabilities exist between observations.
So there has to be some accounting mechanism somewhere which manages the probabilities and makes sure that particle-events are encouraged to happen in certain places/times and discouraged in others, according to what we call the wavefunction.
This mechanism is effectively metaphysical at the moment. It has real consequences and was originally derived by analogy from classical field theory, with a few twists. But it is clearly not the same kind of "object" as either a classical field or particle.
There may be no conclusive proof, but it's a philosophically tough pill to swallow.
Non-locality means things synchronise instantly across the universe, can go back in time in some reference frames, and yet reality _just so happens_ to censure these secret unobservable wave function components, trading quantum for classical probability so that it is impossible for us to observe the difference between a collapsed and uncollapsed state. Is this really tenable?
Strip back the metaphysical baggage and consider the basic purpose of science. We want a theoretical machine that is supplied a description about what is happening now and gives you a description of what will happen in the future. The "state" of a system is just that description. A good _scientific_ theory's description of state is minimal: it has no redundancy, and it has no extraneous unobservables.
The models of quantum mechanics have already withstood experiments to a dozen decimal places. You aren't going to find departures just by banging around in your garage; you just can't generate enough precision.
The only way forward at this point is to start with the model and design experiments focusing on some specific element that strikes you as promising. Unless you're staring at the model you're just guessing, and it's practically impossible that you're going to guess right.
>You aren't going to find departures just by banging around in your garage
This kind of rhetoric saddens me. Someone says "design an experiment" and you jump to the least charitable conclusion. That people do this is perhaps understandable, but to do it and not get pushback leads to it happening more and more, to the detriment of civil conversation.
No, the experiment I had in mind would take place near the Schwarzchild radius of a black hole. This would require an enormous effort, and (civilizational) luck to defy the expectations set by the Drake equation/Fermi paradox. It's something to look forward to, even if not in our lifetimes!
I mean you did just suggest that classical QM can be supplanted by your heavily underspecified finite(?)-state model for which you provide essentially no details, you must admit that's pretty crank-y behaviour.
This is one of the reasons I believe science and technology as a whole are on an S-curve. This is obviously not a precise statement and more of a general observation, but each step on the path is a little harder than the last.
Whenever a physics theory gets replaced it becomes even harder to make an even better theory. In technology low hanging fruit continues to get picked and the next fruit is a little higher up. Of course there are lots of fruits and sometimes you miss one and a solution turns out to be easier than expected but overall every phase of technology is a little harder and more expensive.
This actually coincides with science. Technology is finding useful configurations of science, and practically speaking there are only so many useful configurations for a given level of science. So the technology S-curve is built on the science S-curve.
It's just accelerated. AI is bound by physics just like everything else.
The S-curve is really about fundamental limits. Lets say ASI helps us make multiple big leaps ahead, I mean mind blowing stuff. That still doesn't change that there must be a limit somewhere. The idea that science and tech is infinite is pure science fiction.
The first turn in an S-curve can easily look like an exponential. ASI has physical limitations, so I don’t see why it wouldn’t take an S-curve as well, although at a much different rate than human intelligence.
I don't think this is strictly true. Rather it seems that the problem is that we, at some point, invariably assume the truth of something that is false, which then makes it really difficult to move beyond that because we're working off false premises, and relatively few people are going out of there way to go back in time and challenge/rework every single assumption, especially when those assumptions are supported by decades (if not centuries) of 'progress.'
An obvious example of this is the assumption of the geocentric universe. That rapidly leads to ever more mind-boggling complex phenomena like multitudes of epicycles, planets suddenly turning around mid-orbit, and much more. It turns out the actual physics are far more simple, but you have to get passed that flawed assumption.
In more modern times relativity was similar. Once it became clear that the luminiferous aether was wrong, and that the universe was really friggin weird, all sorts of new doors opened for easy access. The rapid decline in progress in modern times would seem most likely to suggest that something we are taking as a fundamental assumption is probably wrong, rather than that the next door is just unimaginably difficult to open. This is probably even more true given the vast numbers of open questions for which we have defacto answers, but yet they seem to defy every single test of their correctness.
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All that said, I don't disagree that technology may be on an s curve, but simply because I think the constraints on 'things' will be far greater than the constraints on knowledge. The most sophisticated naval vessel of modern times would look impressive but otherwise familiar to a seaman of hundreds or perhaps even thousands of years ago. Even things like the engines wouldn't be particularly hard to explain because they would have known full well that a boiling pot of water can push off its top, which is basically 90% of the way to understanding how an engine works.
> The rapid decline in progress in modern times would seem most likely to suggest that something we are taking as a fundamental assumption is probably wrong, rather than that the next door is just unimaginably difficult to open.
We actually know we have:
Bell’s inequality tells us that the universe is non-local or non-real. We originally preferred to retain locality (ie, Copenhagen interpretation) but were later forced to accept non-locality. But now we have a pedagogy and machinery built on this (incorrect) assumption — which people don’t personally benefit from re-writing.
Science appears trapped in something all too familiar to SDEs:
A technical design choice turned out to be wrong, but a re-write is too costly and risky for your career, so everyone just piles on more tech debt — or modern epicycles.
And perhaps that’s not a bad thing, in and of itself. Eg, geons were initially discarded because the math doesn’t work out — but with the huge asterisk that they might still be topologically stabilized. But the math there is hard and so it makes sense to continue piling onto the current model until enough advances in modeling (eg, 4D anyons) allow for exploring that idea again.
Similar to putting off moving tech stacks until someone else demonstrates it solves their problems.
But at least topological geons would explain one question: why does space look like geometry but particles look like algebra?
Because topological surgery looks like both!
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> clear that the luminiferous aether was wrong
Another interpretation is that the aether exists, but we’re also made of aether stuff — so we squish when we move, rather than rigidly moving through it (as per the theory tested by Michelson-Morley). That squishing cancels out the expected measurement in MM. LIGO (a scaled MM experiment) then works because waves in the aether squish and stretch us in a detectable way.
Modern theories are effectively this: everything is fields, which we believe to be low-energy parts of some unified field.
It's true that Ptolemaic cosmology stuck thinkers in a rut for a very long time; but what got us out of that rut was observation (and simplification). Copernicus saw that heliocentrism led to a simpler model that fit observation better (ironically he wanted to recover Ptolemy's perfectly circular orbits!). In turn, Kepler's perfectionism led him to ditch the circular orbit idea to yield the first accurate description of orbits as ellipses. Yes, transgression against long-held belief was necessary to move forward, but in every case the transgression explained observation. Transgression itself is undesirable. In fact, transgression unmotivated by observation is what powers the dark soul of the "crank", who is at best a time-waster and at worst a spreader of mental illness.
Even Einstein did not produce (e.g. special relativity) out of whole cloth. He provided a consistent conceptualization of Lorentz contraction, itself the result of observing descrepencies in the motion of Jupiter's moons. The same could be said of the photoelectric effect, the ultraviolet catastrophe, and QM.
All this to say that your statement "The rapid decline in progress in modern times would seem most likely to suggest that something we are taking as a fundamental assumption is probably wrong" is unsupported. Nothing could be more popular than questioning fundamental assumptions in science today!
It could very well be that, as Sean Carroll puts it, we really know how everything larger than the diameter of a nuetron works! Moreover, we know that even if we find strangeness at tiny scales, our current theories WILL remain valid approximations, just like Newtonian mechanics are valid approximations of special and general relativity. The path to progress will not happen because a rogue genius finds something everyone missed and boldly questions assumptions long-held. Scientific revolution first requires an observation inconsistent with known models, but even the LHC hasn't given us even one of those. There is reason to think that GR, QM, and the standard model are all there is...until we do some experiments near a black hole!
Heliocentrism from its earliest formulation was pretty bad for many reasons, including as you mentioned the desire to maintain circular orbits, as well as uniform velocities, epicycles, and more. You could easily pick a million holes in heliocentrism to 'disprove' it. And the geocentric view, as convoluted as it was, was observably accurate and predictive with 'holes' being plugged by simply having the entire dysfunctional model absorb them - e.g. by simply assuming retrograde motion as a natural phenomena, and otherwise - just add more epicycles.
Heliocentrism was most fundamentally driven by somebody, with extremely poor interpersonal skills (which is much more the reason he was left living his final days in house imprisonment, rather than his theory itself), moving forward on his own somewhat obsessive bias.
Similarly, with relativity. I have no idea what you mean by a 'consistent conceptualization' of Lorentz contraction, but length contraction was a completely ad hoc explanation for the Michelson Morley experiment. It's correctness was/is more incidental than anything else. Einstein did not cite Lorentz (or anybody for that matter), and I do not think that was unfair or egotistical of him.
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I'm also unsure of what you're referencing with Sean Carroll, but I'd offer a quote from Michelson of the Michelson-Morley experiment saying essentially the same, "The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.... Our future discoveries must be looked for in the sixth place of decimals."
So convinced was Michelson that the 'failure' of his experiment was just a measurement issue that he made that comment in 1894, near to a decade after his experiment and shortly before physics and our understanding of the universe was about to revolutionary explode thanks to a low ranking patent inspector.
>I have no idea what you mean by a 'consistent conceptualization' of Lorentz contraction, but length contraction was a completely ad hoc explanation for the Michelson Morley experiment. It's correctness was/is more incidental than anything else. Einstein did not cite Lorentz (or anybody for that matter), and I do not think that was unfair or egotistical of him.
In "On the Electrodynamics of Moving Bodies"[1] Einstein checks his derivation against Lorentz contraction. It's on page 20 of the referenced English translation. Lorentz' model was ad hoc, E derived it with only 2 postulates (equivalence principle; c invariance). Lorentz was indeed cited, and the cite is useful to connect E's theory to real-world observation. This is true whether or not you want to get pedantic about the meaning of "cite" vs "reference".
Max Planck famously said, "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is
familiar with it."
Now we know how to prevent it: popularize ideas like "physics is mathematics", "shut up and calculate", "it's useless philosophy not worth to think about", "nobody can understand it, so it's useless to even try". Also a nice excuse for ignorance.
> Copernicus saw that heliocentrism led to a simpler model that fit observation better.
That's not true, he didn't.
Geocentric model of the time was a better fit of the data than the Copernican model. What Copernican model had was simplicity (at some cost to observational data fidelity).
Making the heliocentric model approach (and breach) the accuracy obtained by the geocentric model took a lifetime of work by many people.
As a kinematic model (description of the geometry of motions) as observed from Earth's reference frame geocentric is still pretty darn accurate. There's a reason why it is so. Compositions of epicycles are a form of Fourier analysis -- they are universal approximators. They can fit any 'reasonably well behaved' function. The risk is, and it's the same risk with ML, deep neural nets, that one (i) could overfit and (ii) it could generate a model with high predictive accuracy without being a causal model that generalises.
Heliocentric model was proposed much much earlier than Copernicus but the counterarguments were non-ignorable. Reality, it turned out was very surprising and unintuitive.
Truth be told, I don't know much about Copernicus. He may indeed have been right but for the wrong reasons! If so, he's a very good example against my point that observation must precede successful revolution. It seems strange that the Catholic church took him so seriously if his claim was supported by his enthusiasm and not observation. It's definitely something I'd like to learn more about - any book recommendations?
This history is absolutely fascinating. Let me find a blog post by Baez that covers a lot of that history.
I don't think this history says anything against your point -- sometimes the time is just not right for the idea -- and even classical science can be very unintuitive and weird, so much so that common sense seems like very strong counter arguments against what eventually turn out to be better models.
I of course learned this over
many books, but the mind blanks out over which one to suggest. I think biographies of Copernicus and Kepler would be good places to start.
HN do you know what happened to John Baez's blog that listed his multiparty blog posts ? They are a treasure trove that I do not want to lose. Azimuthproject too seems to have disappeared
As a tangential hit on this issue, the relationship between the Catholic Church and science [1] is an interesting read. It's nowhere near as antagonistic as contemporary revisionary takes would suggest. In particular the most famed example of this is with Galileo (whose name is mentioned no less than 146 times on that fairly short page...) yet that was far more interpersonal issues than his concepts being an affront to theology. He wrote a book calling the Pope (at the time very much one of his supporters) through hardly veiled proxy, a simple minded idiot. Burning bridges is bad enough, but burning one you're standing on is lunacy.
If one does genuinely believe in a God then the existence of science need not pose a threat to that, since there's nothing preventing one from believing that God also then created the sciences and rationality of the universe. The classical 'gotchas' like 'Can God create a stone so heavy that he could not lift it?' were trivial to answer by simply accepting that omnipotence does not extend to things which are logically impossible, like a square circle.
Copernicus and Kepler did interpretations, not observations, they explained observations, but geocentrism explained observations too, so heliocentrism wasn't unquestionably superior.
I especially like your last paragraph. Even if our fundamental assumptions are wrong, current theories still work very well within appropriate bounds. And those bounds basically contain all practical scenarios here on earth. That's a big reason why it's hard to make progress on string theory, because we can't create scenarios extreme enough here on earth to test it.
So even if our fundamental assumptions are wrong and some new theory is able to explain a bunch of new stuff, chances are it won't impact the stuff we can practically do here on earth, because scientists have already been doing the most extreme experiments they can, and so far progress is still stalled on fundamental physics.
The trouble with QM is with it's interpretations, not with the accuracy of it's predictions. The latter informs interest in the former. QM works, but the models imply that nature is neither "local" - e.g. entanglement experiments undermine hidden-variables, nor "real" - e.g. a particle does not have a momentum (or position) until you measure it. These physical properties are not just hidden, they are undefined. These implications fly in the face of basic macroscale intuitions about what "physical reality" means, which makes it interesting. Inconsistency is a signal that we have discoveries yet to make. Note that "Many worlds people" think there is no inconsistency - my sketch of a model is fully consistent with that interpretation, if you wish, by simply assign a new universe to every child node in which the node is reached.
What you say doesn't quite correspond to quantum physics as it's known. Quantum physics is quantitative and precise, so it's difficult to say there's something undefined there. It doesn't suggest nonlocality, absence of hidden variables means only absence of hidden variables. It doesn't suggest antirealism, if only due to precision, you can say it doesn't work how you want, but at worst this makes it unintuitive. Conversely Dirac formalism works as if quantum state exists in itself in precise form, which has a good compatibility with basic macroscale intuitions about what "physical reality" means.
But quantum physics can't predict exactly where the individual dots on the detector will be, only their distribution. That does not sound totally quantitative and precise and defined. You would not accept such predictions for macroscopic objects :)
Would you be satisfied if the theory clearly states: "At the time of measurement, the position of the photon interaction is determined by randomly sampling from the quantum distribution"?
At least it shouldn't be nonlocal just because of the erroneous rumor that Bell proved that quantum physics is nonlocal or because randomness, nonlocality and retrocausality are just directly observed.
Your 6-sided dice example sort of brings some focus to his argument of 'its not a real wave it's a math wave ". The result of a 6-sided dice roll exists more in our minds as "math dice" because for most people, if you rolled and it fell in a sewer, lost etc, you wouldn't consider the roll complete until you grabbed a different dice and rolled it. More attached to the person rolling it and the resulting 'what does the number affect'.
>The fact that the model is a continuous real function is an artifact of the model, a weakness not a strength.
The wave function is the square root of a probability distribution. The wavefunction is a continuous real function of position because position is modeled as a continuous real variable. The idea of the wavefunction as a function of position is generally supported by the fact that it can be used to predict the measurement results of diffraction experiments like the double-slit experiment, but also practically the whole field of X-ray diffraction.
There is not just one experimental result that is explained by wavefunctions. There are widely used measurement techniques whose outcomes are calculated according to the quantum properties of matter — like X-ray diffraction and Raman scattering — which are widely considered to be extremely reliable. There is a good reason to explain the model of reality expressed by the equations as clearly as possible, because we want people to be able to use the equations.
Plenty of people (though certainly not all) expect quantum mechanics to be eventually modified to have a consistent theory of gravity. But physicists have experience with this. Special relativity and classical quantum mechanics were both more complex than Newtonian (classical) mechanics, and quantum field theory is more complicated than either. General relativity is substantially more involved than special relativity. It is likely that further extensions will continue to get worse.
The model of reality taught by Newtonian (classical) mechanics is also still widely discussed and used in introductory physics courses and many areas of physics (such as fluid dynamics) and engineering. This model also discusses position on the real line. Even though classical mechanics had to be modified, the use of Cartesian coordinates and real numbers turned out to be durable.
Usually the finitists will formally "rescue" countability by suggesting that the world could exist on the computable numbers, which are countable and invariant under computable rotations. But the computable numbers are a very unsatisfying model of reality, and have a lot of the same "weirdness" as the real numbers. Therefore they suggest that some other model must exist without giving a lot of specifics. Why this should be somehow helpful and not injurious to the pedagogy of physics is not clear.
> The foundations of quantum mechanics may be advanced by new experiments, but not, I think, by staring at the models hoping for inspiration.
To come up with new experiments that might shed light it certainly helps to spend time exploring the models to come up with new predictions that they might make. Sure, one can also come up with new experiments based only on existing observations, but it's most interesting when we can make predictions, as testing those advances some theories and crushes others.
There are no particles, only waves. I do not know how long it will take people to accept this because I think it effects their very psyche, realizing that there is no mass outside of our observations.
The wave went through the slits, not the "wave function". There is no "quantum" because there is nothing to measure so there is no quantum physics.
The fact that we are quantifying things is the problem. When we look at everything as a whole which is effected by waves we will find the solution.
Yes, you can reintroduce another beam splitter at the end and "lose" the path information, and provided you aren't measuring anywhere along the path, you get wave interference at the end even if you split the beam along two paths in the beginning. Look up the quantum eraser experiment.
No. Group movement of particles is one medium in which waves can occur, but the concept is more fundamental and general. The waves described in the article are not in particles.
Probably it's because I'm not a quantum physicist, but the argument boiling down to "the wavefunction is an object of a probability space not of physical space" seems to make the whole article moot. Can the "wavefunction" be anything else than a _representation_ of the particule(/wave)?... but then who could ever think that a representation would actually travel in space?
One thing I've thought about is whether observations in the present can influence past events. I'm thinking it must be so, though probably only on a microscopic level.
Choice of how to measure + physical system -> Observations -> Interpretation of observations -> History
The choice of what and how to measure will influence the history you conclude, but that is true of actual "Caesar and Napoleon" history too, and in that case it's definitely not that past events are being changed, instead it is your knowledge of them. A really interesting principle is that any philosophical question that can be phrased without referring to ideas that only exist in quantum mechanics can usually be answered without referring to them.
I always feel that we are inclined to ask this question because we want to treat the wavefunction as if it were a probability distribution. While they share some properties, fundamentally they are not the same thing.
In typical probability, we deal with an ensemble of fixed states, or at least phenomena that can be simulated as such.
In quantum physics, the wavefunction is fundamental. The question "what was the exact path?" is meaningless. In particular, if we take the approach of Feynman path integrals, we find that particles take many paths - including circular paths through each slit - before arriving somewhere else where they interact (i.e., become entangled) with, say, an electron in the screen.
Sure, we may consider different experiments (e.g., quantum erasers, see https://lab.quantumflytrap.com/lab/quantum-eraser), but analogies with deterministic particles are whimsical - sometimes they work, sometimes not.
So I only have a B.S. in physics but my impression is that the weird parts of quantum mechanics are fundamentally a measurement problem. At the quantum level, we are very very limited in what we can use to measure properties of a quantum system - which is why we resort to probabilities. Wave functions are just a mathematical representation of a physical property that are (only?) ever operated on using quantum operators which result in a statistical distribution. Because they are so closely tied to probabilities I struggle with interpretations that try to say that perhaps these wave functions are something physical and based in reality (i.e. they are in superposition so particles must take on every possible state at once). An analogy I use is its like when we talk about sample sizes of a population of people, what is an ‘average person’? An average person is not something physical we can pick out, it exists in abstract.
I’m curious if anyone with more experience in QM can shed light on how sound my thinking is here.
> Wave functions are just a mathematical representation of a physical property that are (only?) ever operated on using quantum operators which result in a statistical distribution.
It is not correct— at least not unless you subscribe to the Copenhagen interpretation. Yet, while this interpretation is a simple heuristic for interaction with big systems (e.g., a photon hits a CCD array), none of the quantum physicists I know treat it seriously (for that matter, I have a PhD in quantum optics theory).
I mean, at some certain level, everything is "just a mathematical representation" - in the spirit of "all models are wrong but some are useful". But the wavefunction is more fundamental than measurement. The other can be thought of as a particle entangling with a system so large that, for statistical reasons, it becomes irreversible - because of chaos, not fundamental rules.
The measurement, i.e. the Born rule, is just as fundamental as the wavefunction. The wavefunction doesn't mean anything on its own, it's not a measurable quantity that can be used to make any observable prediction whatsoever. If I claim that the wavefunction amplitude for some electron being at some location at some point in time is 1/2(1+i), how would you verify this prediction without invoking the Born rule?
You may say that nuclear fusion in stars does not mean anything; only what matters is that we see light. At a certain level it is true, but to simulate a system we need to simulate its inner workings, not only - the end effect.
The exact phase of a wavefunction does not matter - but it is an important phenomenon, giving raise to gauge invariance. The Born rule can be derived. In short, since we use unitary operators, length is preserved. For a derivation, see https://journals.aps.org/pra/abstract/10.1103/PhysRevA.71.05....
Also, to be nitpicky, we also never measure probabilities. Something (macroscopic) happened or not. It gives rise to quite fundamental and philosophical questions, including "what is (classical) probability" (I don't know an answer that fully satisfies me), many world interpretations (maybe all possible things just are), and in general what on indeterminism and free will.
I'm not a quantum physicist and so can't really comment on why, but it's clear that the paper you linked is not widely accepted, as the Born rule is still taught as a postulate of quantum mechanics, not a derived property of the wavefunction. I'd wager a guess that the paper ends up inventing some other postulate that is itself not derivable from the wavefunction, so it becomes at best a philosophical matter which postulate you actually prefer.
I also don't agree with your comparison of what I said to the nuclear reactions happening inside a star. The problem with the wavefunction without the Born rule is not that it's difficult to observe, it's that it's literally meaningless: knowing the value of the wavefunction for some state of a system doesn't tell you anything at all unless you apply the Born rule to this value.
And as for probabilities, certain kinds of probabilities at least have a very clear and simple definition (though they are rather narrow cases): if you repeat an experiment in exactly the same conditions N times, and an outcome O happens in p/N times and doesn't happen (1-p/N) times, then we define P(O), the probability of outcome O, as the value p/N. For systems where this applies, it is very much a measurable quantity (with some noise, of course, related to the fidelity with which you can reproduce the same experiment).
I do agree that this well-defined, measurable, concept of probability is rarely what we mean by "the probability of O", since (a) it's often hard or impossible to repeat (or even perform) the experiment, and (b) we often care about what will happen the next M times we repeat this experiment, and the measure P(O) I defined above does not tell us anything about future events.
Wavefunction has the Born rule, it's just not an independent postulate, but an emergent behavior from the Schrodinger equation. Also knowing the wavefunction does tell you everything, all properties are derived from it.
You say you need the Born rule to understand what's going on, for this you don't need it as a fundamental phenomenon, you only need to eventually observe the Born statistics, which is sufficient to provide understanding for you.
Again, the wavefunction just tells you "the amplitude of the state in which the photon is at location (x, y) on the screen at time t is sqrt(i); the amplitude of the state in which the particle is at position (x+2,y) at time t is sqrt(1+i/2)". Given these numbers, where do you expect to find the particle at time t?
Sure, but how specifically do you think it was checked?
Actually, I'll tell you how it was checked: they ran lots of experiments, and confirmed that the probability to find the particle in one state or the other is precisely equal to the norm of the wavefunction of the respective state. Also known as the Born rule.
So the amplitudes have no physical meaning directly, it's just that their norm represents the probability of the state being observed. That is, you have to take the Born rule as an additional postulate that is entirely separate from the wavefunction.
Now, you can dress this in other language. Some versions of MWI say that the universe splits into many literal worlds after any quantum event, and the number of worlds in which it has a certain outcome is proportional to the norm of the amplitude of the wavefunction of that outcome; based on this, they then derive the Born rule as P(stateA) = num_worlds(stateA) / num_total_worlds = norm(|stateA>). Of course, this is still the Born rule, and it is still not derivable from the wavefunction, still an additional postulate - just with extra steps.
And I don't know what you mean when you say that the Born rule is not statistics: it is exactly statistics (or at least probabilities, if you make a distinction). Sure it's possible to get a million tails in a row, that is always possible in statistics - by definition, any event with probability higher than 0 is possible.
What's observed is statistics, not the rule, and the goal of modelling is statistics. Once you have statistics, you don't need to assume the rule, because statistics tells you what you want to know - quantitative properties of the process. Also since statistics is quantitative, it can be just computed without interpretation, such quantitative properties don't depend on interpretation, simply because they are computable. Maybe you're confused by assumption that rule is identical to statistics, and thus believe statistics uncomputable merely because the Born rule is uncomputable? The fact is the Born rule allows to miscalculate statistics, because the probabilities are unintuitive, there is a precedent.
Amplitudes as quantitative properties are sufficient for calculation of statistics. Ironically classical theory of probabilities works the same way: first it assigns arbitrary weight to outcomes, then divides them by the weight of ensemble (usually >1 contrary to QM) to get statistical coefficients. The weights can be scaled by any constant factor, and the calculation still works.
It did that by checking whether an electron is found at a particular position relative to the nucleus lots and lots and lots of times, and building a heatmap of where the electron was actually found in ach individual experiment; the heatmap of course corresponded to the wavefunction model. So the experiment found that the probability of finding the electron at a certain position exactly corresponds to the square of the amplitude of the wavefunction at that position, i.e. the Born rule.
What the experiment did NOT do is directly detect the wavefunction of the electron, because that is, again, not a phsycially meaningful quantity.
Sounds like Einstein's hidden variables theory: below wave function picture there's more fundamental newtonian reality that produces the higher level wave function behavior, but is itself inaccessible due to insufficiently fine instruments, aka hidden variables. "God doesn't throw dice" is about that.
You're partially correct, but describing it in that way makes it sound like if you could "just look a little bit closer" the statistics would disappear, which doesn't happen. So it's more subtle than this. Fundamentally it's because QM doesn't use additive probabilities, but rather additive amplitudes which are complex numbers, and the probability is the square of the sum of these, so you can get interference between amplitudes. You can never get interference by adding probabilities.
In the dual slit experiment this is visible as you can't get the interference effects by summing the probabilities for "particle through slit 1" and "particle through slit 2" but rather you need to sum the amplitudes of the processes.
Working physicists (since 100 years) just do this, there is no practical need to interpret it further, but it would be cool if someone could figure out some prediction/experiment mismatch that does indeed require tweaking this!
There was a few lines on this, but I wish it clearer that everything it said is also true classically about particles for which we are uncertain.
IMO so much writing about quantum mechanics gets harder to follow by trying to jump classic -> quantum, and certain -> probabilistic at the same time. If one does the latter switch first, it cuts out the noise of easier-to-understand things to get to the second.
I'm enjoying this tutorial so far. Every sentence was carefully considered which I think is important for my level of understanding of quantum mechanics. I'm reading very slowly and carefully. It was really helpful to define the wave function as not existing in the physical world such as a water wave but exists as description in probability space.
Literally dim the light source until the probability of two showing up within the time scale of the measurement is low enough. This is not impractical. For instance there are many kinds of detectors that can be set up to discriminate single photons or particles.
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[ 5.4 ms ] story [ 353 ms ] threadThis seems to be entire argument:
> But the wave function is a wave in the space of possibilities, and not in physical space.
Which is fair enough as an initial claim, but it doesn't really get motivated further, or at least not before I got bored reading and started skimming.
This reduces to a kind of "shut up and calculate" attitude, so it seems poor starting point from which to write an interpretation text.
However, if a classical three-dimensional wave equation describes how matter osciallates in three-dimensional physical space, a quantum wavefunction doesn't do that. Quantum particles don't oscillate in physical space like that. A three-dimensional wavefunction might describe three particles' positions along a one-dimensional line, and it's oscillations are oscillations of probability, not position. The particles don't move, say, up and down. Their probability to be here or there on that 1-d line waxes and wanes.
This is what the article is trying to explain: the basic mathematics of quantum mechanics, the definition of the wavefunction. The value of a wavefunction for the position of three particles is not a position in space at a moment in time. It is a (complex) probability for the position of every particle at that moment.
This only seems confusing when looking at wavefunctions that describe positions. But wavefunctions often have many more observables, such as spin or polarization. A wavefunctions for two electrons moving around on a plane will not be a two-dimensional wave. It will be a wave in a six-dimensional space, whose axis may be "particle 1 has spin up/down, particle 2 has spin up/down, particle 1 position along x axis, particle 2 position along x axis, particle 1 position along y axis, particle two position along y axis".
If I were to express some sort of wave-function-in-spacetime theory, I'd invoke lots of classical fields filling space and have those wiggle.
In any case, the whole bit about the proper two-particle wave function living in a higher dimensional space is somewhat spoiled by the fact that you can factorise it into normal 3-space pieces (so long as you don't have your particles interacting), it doesn't seem such an alien space to me.
Lots of people think that this is the same picture that the wavefunction gives, but this is wrong. In the QM picture, the emitter emits one photon, which is a quantum of energy described by a four-dimensional wavefunction which assigns some probability of a detection event at the slits, at the screen, etc. In this picture, there is no physical EM wave, any interaction with the light will happen at a single localized point in space. Of course, if you add more particles, especially those carrying charges, the picture changes, and you'll see probabilities that roughly correspond to a picture of an oscillating EM field. But the wavefunction, which is the "bedrock" physical theory, is separate from those waves in the EM field, which are just an approximate picture of the probabilities dictated by the wavefunciton.
Can't really get any other sense out of your reply, but I'm not entirely sure.
Of course this is not the only valid view...just one that makes sense to me. Thinking about these sorts of questions is a very fun endeavour.
> The wave function’s pattern can travel across regions of possibility space that are associated with the slits.
Which to me conflicts with his emphatic “no” at the beginning of the article because this implies you can define some mapping between the physical and probability space. And of course you can because if you couldn’t the theory would not be physically predictive.
And as for saying that the wave moves through both slits, that also doesn't make sense, by the very definition of the wave function - it's a wave in probability space, not in space, so it just doesn't move through space.
for point 2 it seems you can define a mapping from the physical space to probability space. Saying that the wave doesn’t “move through” space might be technically correct but also seems like semantics on the definition of the phrase “move through” ?
In the original QM model, light is not a wave in the classical electrical theory sense. Light is made up entirely of photons, which are particles just like electrons or billiard balls, and they are described by a wavefunction. That wavefunction gives them various probabilities of being in various states at a certain time, and those probabilities can increase or decrease when more particles come into the mix. The states can represent position, momentum, charge, spin, energy levels, etc.
I don't think that's a valid argument. Imagine a regular water wave, i.e. a wavefunction h = h(x, y, t) describing the height of the water at position (x, y) at time t. You could say "this is a wave in height space, not in space, so it just doesn't move through space" and in a certain sense that's true. But obviously there is something that does "move" through "space" to the extent that anything can ever be said to do so.
Edit: Thank you all for the responses, it has been very educational. It appears I was misunderstanding the most important aspect of the double slit experiment. A photon is a wave function when unobserved, it literally goes through both slits and creates an interference pattern like how waves in water would. However, when observed at the slit, or at the detector screen, the wave function collapses and only one photon(billiard like particle) will be detected.
There is no photon multiplication happening on the double slit.
It is as if every photon that went through the slit is somehow aware of all other photons that did so too so each photon can choose the (random) position where it hits on the wall behind the slit such that together they look like as if a WAWE went through the slit.
That is (one reason) why they call it "Quantum Weirdness". God is playing dice with us
Why isn't it just that there's a probability density function that describes the aggregate outcomes of a large number of samples from a random process? Why is "memory" involved?
There's no photon multiplication, and no "all other photons" changing their path.
There is some inter-photon interaction because they are bosons. But it's not significant enough to impact the multi-slit experiment. And the experiment works exactly the same way if you send only one photon at a time.
"two photons come out" part makes no sense though. On a target side, there's always single hit after single photon/electron, but distribution of theses hits as if said electron got through both slits and interfered with itself
P.S. the funny thing is - this works on any small thingy, measured up to 2000 atoms-big, as if it's the property of the universe itself
https://iopscience.iop.org/article/10.1088/2058-7058/12/11/4
> The largest entities for which the double-slit experiment has been performed were molecules that each comprised 2000 atoms (whose total mass was 25,000 atomic mass units).[19]
https://en.m.wikipedia.org/wiki/Double-slit_experiment
The electron/proton entering a slit is affected by gravity!
Presumably a gravity based detector would have similar issues as these particles are affected by gravity (as can be seen around black holes)
They did it by splitting a beam of particles into a pair of entangled particles and then setting up a way to measure the polarity of one of them after the point in time where it even hits the final screen. If you measure the polarity then, after the other stream of particles from the beam had already had time to make the pattern, the pattern will be two clusters. If you don't, it goes back to an interference pattern.
That one really cemented the notion in my head that this is just how the Universe is and not some local weirdness with particles and measurements.
https://www.youtube.com/watch?v=RQv5CVELG3U
This is the video if you're interested. Again, I'm no physicist and don't know if explanations are legit or statistically correct. But that little || trick that all other popsci videos play on you, that's a true concern.
You can check it out here.
Summary https://www.stonybrook.edu/laser/_amarch/eraser/index.html
Paper https://www.stonybrook.edu/laser/_amarch/eraser/Walborn.pdf
My fascination with these experiments has never been due neat clusters of impacts, although popsci depictions have clearly tainted my memory.
https://www.nature.com/articles/s41567-019-0663-9
> Here, we report interference of a molecular library of functionalized oligoporphyrins with masses beyond 25,000 Da and consisting of up to 2,000 atoms, by far the heaviest objects shown to exhibit matter-wave interference to date.
It would be awkward to say that the 2000 atom molecule comes out of both sides... but it does, until you look.
The double slit experiment is not a duplication cheat of reality... it's weirder than that.
I thought the takeaway wasn’t that the particle comes out both sides, the implication is that the behavior of a single particle is the same as the behavior of multiple particles - that is to say, it appears to be an interference pattern, even when there should be no other particles to interferes with the single one.
This is fundamental to 100 years of quantum mechanics and underlies most of physics including all semiconductors, materials science, chemistry, lasers, etc. The double slit experiment is just a very good illustration of the principle boiled down to its essentials, which is why it's everywhere in pop-sci. It makes for more accessible story than describing how a hydrogen atom works.
In fact the photon may not actually exist. and I have questions as to what "single photon experiments" are actually measuring. let me explain.
The EM field is not quantized, or at least not quantized at the level of a photon, what we call a photon is the interaction of the EM field with matter, or more precisely with the electron shell of matter. it is the sound of the wave breaking on the shore, not the wave.
Now none of this actually matters as the only method we have of interacting with the EM field is through matter(electrons really) so we can only measure it in photon sized increments.
However note that we can only perturb the em field in photon sized energy levels, and we can only pick up disturbances of the em field in photon sized bunches as well. Not sure what this implies for how em field energy is accumulated on electrons in order for us to detect it.
But, to "solve" the wave /particle conundrum, I like to think of it as fields all the way down. A "particle" is then a localized and quantisized interaction of said field with another field.
If you think of particles as small billiard balls flying through space on some ballistic trajectory, you'll soon run into all kinds of trouble and the mental model breaks down.
Or in insisting on referring to the electron as a particle.
“We begin by throwing an ultra-microscopic object — perhaps a photon, or an electron, or a neutrino”
I don't agree with this. You can absolutely consider a classical (non-quantized) EM field interacting with quantized matter. This semi-classical model can describe the photoelectric effect, but it cannot describe other experimental observations such as sub-poissonian photo-detections / photon anti-bunching.
https://en.m.wikipedia.org/wiki/Perturbed_angular_correlatio...
I haven’t used it for my research, but it’s an incredible local probe of electric and magnetic fields in materials. There’s no other technique that I’m aware of that smuggles information about the chemical structure of a single coordination sphere into such clean, distinct emissions. The brief excited state of the isotope after the first emission event and before the second is sensitive to practically everything. It all shows up in the deconvoluted spectra.
Shame nearly all the isotopes that work for this are not ones that are super interesting for modern quantum materials. Perhaps that will change out of necessity.
You still do not understand what is happening, please READ the article, it shows that the wave function doesn't go through anything and the it certainly doesn't create the interference pattern.
Only one photon comes out, but it can interfere with itself if it had the possibility of going through either slit.
That nuance aside, the Quantum Eraser Experiment is a real physical experiment that covers what I think you're asking about. If you send photons through double slits in a setup where you can tell which slit the photon went through, you don't get an interference pattern. If you can't tell, you do get the interference pattern.
> Figure 4: The wrong wave function! Even though it appears as though this wave function shows two particles, one trailing the other, similar to Fig. 3, it instead shows a single particle with definite speed but a superposition of two different locations (i.e. here OR there.)
I understand that if treat the act of adding two particles' wave functions as creating a new wave function for one particle, then we have this problem, essentially by definition. But it got me thinking - would it not make sense to treat the result as an expected value, such that we could then measure how many particles are likely to be to the right of the door at each point in time?
This is different from a classical probability. Suppose we simply don't know whether the baseball was fired from HERE or from THERE. In a classical situation, we can carry forward our understanding of the situation in time by simply calculating what the classical particles would do independently. In quantum mechanics the mechanics are of the wave function itself, not of the things we measure. We cannot get the right answer by imagining first that we measure the particle in one location and calculate forward and then by imagining we measure the particle in another and calculating forward and then adding the results. It isn't how the theory works. We must time evolve the wave function to predict the statistical behavior of measurement in the future.
But underneath it is all quantum mechanics.
Interpreting this in the many-particle case is more difficult, but the basic idea is that due to single-particle uncertainty, you can't have a definite number of particles indexed by momentum and a definite number of particles indexed by position at the same time. If I had 100 particles that were definitely at x=0, in terms of momentum they'd be spread out over the range of possibilities unpredictably.
The Heisenberg uncertainty principle is not about particles. It’s about statistics and our knowledge about something.
That is, the future direction and momentum of an interaction between two particles can't depend very strongly on both the position where the interaction happened, and on the momentum the particles had before the interaction. If the interaction is a direct collision, so the position is heavily constrained, then the momentum the particles had before the collision will not really matter a lot for what happens after they collide.
If you were to "put yourself in the shoes of" one of the particles, you could say that, because it "knows" where the other particle is at the time of the collision with high precision, it can't "know" the momentum the other particle had with any precision, so it's future movement can't depend strongly on that. But this stretches the definition of "knowledge" far beyond the normal understanding of the word.
My point is that it’s not something special about quantum mechanics or particles or even positions and momentum.
It’s inherent in Fourier transform, conjugate variables and covariance matrices.
It happens outside QM, and even outside physics. It’s not a physical attribute, it’s statistical.
This is not true at all. In classical mechanics, particles have fully definite properties. In the theory, if two particles collide, the position and momentum they'll have after the collision depend on their exact position and exact momentum before the collision, with no bound on precision.
Of course, classical mechanics admits that we can't measure things to any level of precision, there is some practical bound below which noise in the measurement will drown out the signal. But the interaction itself has no such bound, it happens with infinite precision. If the speed of one of our particles were higher by just 10^-100 m/s, its trajectory might be completely different.
This is not possible in QM. In QM, if the particles collide (they meet at an exact point in space-time), then their trajectories afterwards wouldn't change even if one of their speeds were 10 times higher: if they have definite position, their speed is extremely fuzzy, and it can't significantly affect their trajectories after the event.
And QM turns out to be right abput this, when you measure things precisely enough.
As for your comment about them not having defined proporties; this is also just one interpretation. You argue for violation of realism. That’s fine, but unnecessary.
Violation of locality or realism is only needed in the context of Bell inequalities, and this assumes there is no superdeterminism and you are “free” to choose your experiment, which is of course a rather strange argument to have to begin with.
This is because a baseball is interacting with other matter on the way to the slit. A photon on the other hand might not interact with any matter and it stays as a wave and you can see an interference pattern on the other side.
Stop with the “wave particle duality”.
Stop with the “until it’s measured”.
Explain the experimental setup in grosse detail.
What do you mean by “a particle is emitted?”. What do you mean by “a particle is measured?”.
Even within the bounds of self described “double slit experiment”s there are numerous variations on how it is designed, constructed, and conducted.
Stop explaining the abstract notion of the experiment through a lens of your preconceived interpretation.
Show me data.
Show me numerical analysis.
https://iopscience.iop.org/article/10.1088/1367-2630/15/3/03...
One can only measure by interacting, there is no other way.
Three words, pilot wave theory
To quote Cockshott, the Copenhagen Interpretation is an idealist recapitulation of Russian Machism/Bishop Berkley. The statement "nothing /is/ until it is observed" is not necessarily a Weird Quantum formulation but just a solipsistic attitude applicable towards all scientific observation in general.
https://en.wikipedia.org/wiki/Pilot_wave_theory
In another sense Bohmian mechanics just kicks the can down the road - we may decide to associate the specific thing we observe with a particle situated on the pilot wave, but in fact, as far as the theory goes, the particle can live at any point in the pilot wave it wishes and nothing about the dynamics of the pilot wave changes at all. Thus we simply place the non-determinism in the past rather than in the present.
Furthermore, Bohmian mechanics seems to break Newton's First Law, since the pilot particle, as hinted above, is influenced by the pilot wave but not vice versa. The appeal of Bohmian mechanics is obvious, but superficial. It does not dispense with the can of worms, just opens it from the other side, in my opinion.
It is also rather nice to think of the particles as just being points in space with nothing else associated with them; an electron is just an electron because the portion of the wave function that is relevant and guiding it is the electron portion; see a paper from 2004 entitled "Are all particles identical?" [1] (I am a coauthor on that). If one thinks about it, we only know about particles through their motion so having things like mass and charge linked to the object guiding the particle seems perfectly reasonable. Points are not only not labelled by numbers (particle 1, 2, etc) but also not labelled by mass and charge.
The nondeterminism of not knowing the initial conditions is fine; the point was to have a theory with well-defined objects that give some plausible story and connection to our experiences, such as stuff existing and being somewhere. The fact that non-relativistic Bohmian mechanics happens to be deterministic is just happenstance for many of its supporters. In some QFT versions, the dynamics of creation is not deterministic and there is no reason for that to be a problem. But it is well-specified without having to invoke some special magic action called "observation".
As for QFT, the biggest problem for Bohmian mecahnics is the need to have an actually well-defined evolution of the wave function. The idea of particles being created and annihilated is not particularly hard. And, in fact, recent work has shown that if one takes that seriously and respects probability leaking from n particle space to n+1 and n-1, then at least some of the divergence problems go away. See [2]
1: https://arxiv.org/abs/quant-ph/0405039 2: https://arxiv.org/abs/1809.10235
At that point it's very obviously a violation of Occam's razor though. It's like positing that the content of my field of vision is an objectively real thing, that the reason the universe looks like a video projection is that there really is a video projection going on, even though that video projection has no physical effect.
> If one thinks about it, we only know about particles through their motion so having things like mass and charge linked to the object guiding the particle seems perfectly reasonable.
Indeed. But if one thinks a little more, what's the point of positing a particle at all, if all of the physics is in the pilot wave?
The physics, therefore, is not all in the pilot wave. If you take as the point of a particle theory that there should be particles with positions changing in time, then that is what is being given in Bohmian mechanics.
Also, ask yourself, if the wave function is on configuration space, what constitutes a configuration? In Bohmian mechanics, it is clear, but if the wave function is all there is, then why are we talking about configuration space at all? It is just this abstract vector in Hilbert space evolving and many different representations can happen. Why do we not perceive reality in terms of these other representations?
If it helps, you can think of the wave function a bit like a dynamic law. In [1], the authors suggest thinking of log( psi) analogously to the Hamlitonian H on phase space in classical mechanics. There is no back action on H and most of it is irrelevant to the evolution of a particular particle system in that framework and yet everyone recognizes it as just a convenient way of describing the dynamics.
The difference is that psi evolves but even that may only be true on a subsystem point of view. It is theoretically possible to have a stateless universal wave function which, when particular particle positions of the environment are plugged in, nonetheless gives evolving subsystem wave functions.
Occam's razor is difficult to apply here without a prejudice. If you want to minimize the number of equations, then sure, "the wave function is everything" works, but it comes at the cost of there being what could be considered an infinite number of "you"s and everything else, all slightly different and whole existing other expressions of the universe with no connection to us. If you want collapse somewhere, then you have to posit that mechanism.
On the other hand, by adding in particles and the guiding equation, one gets a singular "you" and everything that we experience is, more or less, definite and singular. So the "existing" stuff is dramatically reduced.
Which one of this is truly simpler is a matter of taste, I would say. I think in terms of communicating with people, the Bohmian version of "there is this universal wave and the positions of stuff are guided by it" is pretty simple. The law itself is so trivially a part of the Schrodinger equation that it could easily be derived before the Schrodinger equation itself. Contrast this with other versions which is "reality collapses to a definite state when we look at it" or "there are infinitely many different universes". None of those seem as simple.
1: https://arxiv.org/abs/1101.4575
We know that particles don't have identity though - exchange of identical particles is a symmetry and physics would be very different if it wasn't. I won't claim it's compelling, but to me that suggests that a particle is more like a pattern or a field excitation than a thing with its own concrete existence.
> Why do we not perceive reality in terms of these other representations?
What would be different if we did? I mean obviously at a macroscopic level particles moving through space is a model that gives a good approximation and is easy to think in, but that doesn't mean they're any more physically real than e.g. temperature.
The "you" is then a rough set of particles whose trajectories roughly coincide with your macroscopic trajectory. Their identity is just given by where they are.
As for representations, I feel like I can easily understand how to get momentum or temperature from particles with their time evolution (trajectories), but I do not see how, say, to get positions of particle just from knowing what their momentums were and their time evolution.
1: https://arxiv.org/abs/quant-ph/0601076
https://pubmed.ncbi.nlm.nih.gov/26989784/
I tend to think (as some others do) that it's also a much better way to reason about quantum computation. Should a factorization of a large semiprime number by Shor's algorithm be attributed to the semi-mystical power of The Observer collapsing the wave function (which is who by the way, the sensor, or the person reading that sensor?), or are we instead exploiting realism to do the work?
We are looking at a birds body calling it a particle but it has wings we don’t see which effect the direction the particle flies
Do we really have to choose between wave and particle? What does the "particle" model bring to the table that a localized (wavelength-sized) wave/vibration could not?
Luckly, sometimes the exact solution can be very accuately aproximated with a wave ecuation.
Luckly, sometimes the exact solution can be very accuately aproximated with a particle ecuation.
(Sometimes, the exact solution can be aproximated saying that the lowest energy state is an eigenvector of the Schoedinger equation. Is that a wave? It's not localized, but not very wavy.)
But neither are the exact solution, just aproximations that solve tpgether 99% of the experiment.
It's difficult to explain, because to explaing the detials you need like two years of algebra and calculus and then like another 2 years of physics, and now you get a degree in physics.
It's possible to solve the difficult ecuation only in very simple cases like electron-electron colissions, if you allow some cheating and a tiny error. For more complicated systems like electron-muon there are some problems. And for more complicated systems, you get more technical problems and more aproximations.
[0] https://en.m.wikipedia.org/wiki/Photoelectric_effect
My understanding is that theoretically energy transfer is a function of wavelength.
However, this is not true for EM interactions. If you shine infrared light on a solar panel, you'll see 0 current from it, even with an extremely powerful source of light (at some point the material might heat up enough it starts showing some thermo-electric effect, but that's a different thing). However, if you take even a very low intensity ultraviolet source, you'll see a measurable current right away. This is the unexpected behavior that quantized interactions have, which can't be reproduced with non-qunatized waves like sound waves.
OTOH, the energy of a photon is such an abstract concept (not like the kinetic energy of a ball) that I'm not sure it really helps explain it.
However, photo-detections with sub-poissonian statistics cannot be explained under this semi-classical model, but it can be explained with properly quantized EM field (i.e. with photons).
For reference, see Mandel and Wolf's Quantum Optics textbook.
The problem in these discussions is how to build an intuition about the underlying physical model.
I fail to have an intuition of how can a quantized unit of wave propagate through both slits.
I know that the equations say that the probability of finding the particle at a given location is given by the amplitude squared of the wave function (Born rule).
The image that a "quantized unit of wave propagates through two slits simultaneously" doesn't help me build any further intuition.
Do the two parts going through the two different paths carry half the unit? Clearly that's not the case otherwise they wouldn't be quanta anymore. So does it mean that the entire wavefront is "one unit" no matter how spread out? But in that case, "one unit" of what?
If you have two slits, with a detector to determine which slit the photon went thru, then it'll behave as if it only went thru one of the two slits, at random, and what'll build up on the screen will be the two (slit A + slit B) overlayed diffraction patterns.
Finally, if you have two slits with NO detector, then what will build up on the screen is the interference pattern as if the photon had gone thru both slits simultaneously and the two resulting banded diffraction patterns interfered with each other. So, what SEEMS to be happening in this case is that the quantum state of the system post-slit is that of the photon simultaneously having gone thru both slits, each slit having diverted it per diffraction, and then these diffraction patterns (probabilities) interferering. Wave collapse can only be happening after this interference (if it was before then there would only be one diffraction pattern and no interference), presumably when quantum state interacts with the screen.
So, yeah, it seems that the "photon" does "go" through both slits, but this is a quantum representation, not a classical one.
Classic labelling issue.
What they differ about is the interpretation of that model. The equations are the same, but differ in what the variables refer to in the real world. It's really a matter of solving the equation for X vs Y, saying which one is independent and which is dependent.
The purpose is to take the fact that none of the variables correspond directly to anything we have any experience with. The best we can hope for is to isolate part of it and say "this much is like this thing we understand, but there's an additional thing that we'll treat as a correction".
We can try to take the whole thing seriously, and just call it "a quantum thingy" which is not like anything else. This is sometimes called "shut up and calculate", but even that makes assumptions about what things are feasible to calculate and which are hard. That skews your understanding even if you're trying to let it speak for itself.
There is one set of observations, and many many models to describe them: Schrödinger equation formulation, matrix mechanics (Heisenberg, Born, and Jordan), path integral formulation (Feynman), phase space formulation, density matrix formulation, QFT or second quantization, variational formulation, pilot wave theory aka de Broglie-Bohm theory, Hamilton-Jacobi formulation, PT-symmetric quantum mechanics, Dirac equation formulation (well, not really independent, just for spin 1/2 particles).
They all give the same results, and are therefore mathematically equivalent, but different models tend to be associated with different interpretations:
But in order to track state changes from free agents, when you get close to that geometry the engine converts it to discrete units.
This duality of continuous foundation becoming discrete units around the point of observation/interaction is not the result of dueling models, but a unified system.
I sometimes wonder if we'd struggle with interpreting QM the same way if there wasn't a paradigm blindness with the interpretations all predating the advances in models in information systems.
A lot of the article is about this. Start with the section "The Wave Function of Two Particles and a Single Door". The wave packet view can't explain why you don't for example see a "particle" (that is, a dot on a detector) show up simultaneously having gone through two different doors. You have to think about it in terms of a wave in the space of possible joint particle positions.
Particles are just standing waves, so to speak. They are not just an amorphous clay-like lump of matter. They are made of smaller things and those things are churning around. That in-place churning becomes a wave when the particles move at speeds that approach a significant fraction of c.
We observe double-slit diffraction and model it with the wave-function. This doesn't preclude other models, and some of those models will be more intuitive than others. The model we use may only give us a slice of insight. We can model a roll of the dice with a function with 6 strong peaks and consider the state of the dice in superposition. The fact that the model is a continuous real function is an artifact of the model, a weakness not a strength. We are modeling a system who's concrete state is unknown between measurements (the dice is fundamentally "blurred"), and we keep expecting more from the model than it wants to give.
Programmers may have better models, actually. The world is a tree where the structure of a node births a certain number of discrete children at a certain probability, one to be determined "real" by some event (measurement), but it says little about "reality". The work of the scientist is to enumerate the children and their probabilities for ever more complex parent nodes. The foundations of quantum mechanics may be advanced by new experiments, but not, I think, by staring at the models hoping for inspiration.
This is how you get the tortured reasoning that views measurement and observation as somehow different. Even einstein struggled.
It you place a detector on one of the two slits in the prior experiment, (so that you measure which slit each individual photon goes through) the interference pattern disappears.
If you leave the detector in place, but don't record the data that was measured, the interference pattern is back.
https://en.wikipedia.org/wiki/Double-slit_experiment#Variati...
A lot of people pose it as a question of pure information: do you record the data or not?
But what does that mean? The “detector” isn’t physically linked to anything else? Or we fully physically record the data and we look at it in one case vs deliberately not looking in the other? Or what if we construct a scenario where it is “recorded” but encrypted with keys we don’t have?
People are very quick to ascribe highly unintuitive, nearly mystical capabilities with respect to “information” to the experiment but exactly where in the setup they define “information” to begin to exist is unclear, although it should be plain to anyone who actually understands the math and experimental setup.
An interesting experiment to consider is the delayed-choice quantum eraser experiment, in which a special detector detects which path a particle went through, and then the full results of the detector are carefully fully stomped over so that the particles of the detector (and everything else) are in the same exact state no matter which path had been detected. The configurations are able to interfere once this erasure step happens and not if the erasure step isn't done.
Another fun consequence of this all is that we can basically check what configurations count as the same to reality by seeing if you still get interference patterns in the results. You can have a setup where two particles 1 and 2 of the same kind have a chance to end up in locations A and B respectively or in locations B and A, and then run it a bunch of times and see if you get the interference patterns in the results you'd expect if the configurations were able to interfere. Successful experiments like this have been done with many kinds of particles including photons, subatomic particles, and atoms of a given element and isotope, implying that the individual particles of these kinds have no unique internal structure or tracked identity and are basically fungible.
An important thing to realize is that interference is a thing that happens between whole configurations of affected particles, not just between alternate versions of a single particle going through the slit.
This is not remotely true. It looks like you read an explanation of the quantum eraser experiment that was either flawed or very badly written, and you're now giving a mangled account of it.
My lightly held conclusion is if it really was a full and more straight forward solution it would dominate the conversation more than it does now. This option was formed reading some primary sources but mostly reviews and comparisons of QM theories. Unlike other methodologies I have never working through a full QM example problem in pilot-wave theory.
> the idea that unknown quantities are determining the outcomes in quantum mechanics has been disproven in the event of the speed of light being a true limit on communication speed.
and I provided an immediate counterexample. Yes, Bell's Theorem and its exact assumptions are not entirely straightforward but let's please stop propagating those falsehoods that die-hard proponents of the Copenhagen interpretation commonly propagate.
To quote section 10.2: "The [experimental] system represents a classical realization of wave–particle duality as envisaged by de Broglie, wherein a real object has both wave and particle components."
We've already got all those fields interacting in the real world, so I don't find it very far fetched that quantum mechanics emerges from their fully classically described interactions, probably expressed in some really gnarly 4D math.
[1] https://thales.mit.edu/bush/wp-content/uploads/2021/04/BushO...
Reality can be interpreted as non-local. There has been no conclusive proof it isn't.
c isn't a limit on the kind of non-locality that is required, because you can have a mechanism that appears to operate instantaneously - like wavefunction collapse in a huge region of space - but still doesn't allow useful FTL comms.
Bell's Theorem has no problem with this. Some of the Bohmian takes on non-locality have been experimentally disproven, but not all of them.
The Copenhagen POV is that particles do not necessarily exist between observations. Only probabilities exist between observations.
So there has to be some accounting mechanism somewhere which manages the probabilities and makes sure that particle-events are encouraged to happen in certain places/times and discouraged in others, according to what we call the wavefunction.
This mechanism is effectively metaphysical at the moment. It has real consequences and was originally derived by analogy from classical field theory, with a few twists. But it is clearly not the same kind of "object" as either a classical field or particle.
Non-locality means things synchronise instantly across the universe, can go back in time in some reference frames, and yet reality _just so happens_ to censure these secret unobservable wave function components, trading quantum for classical probability so that it is impossible for us to observe the difference between a collapsed and uncollapsed state. Is this really tenable?
Strip back the metaphysical baggage and consider the basic purpose of science. We want a theoretical machine that is supplied a description about what is happening now and gives you a description of what will happen in the future. The "state" of a system is just that description. A good _scientific_ theory's description of state is minimal: it has no redundancy, and it has no extraneous unobservables.
The only way forward at this point is to start with the model and design experiments focusing on some specific element that strikes you as promising. Unless you're staring at the model you're just guessing, and it's practically impossible that you're going to guess right.
This kind of rhetoric saddens me. Someone says "design an experiment" and you jump to the least charitable conclusion. That people do this is perhaps understandable, but to do it and not get pushback leads to it happening more and more, to the detriment of civil conversation.
No, the experiment I had in mind would take place near the Schwarzchild radius of a black hole. This would require an enormous effort, and (civilizational) luck to defy the expectations set by the Drake equation/Fermi paradox. It's something to look forward to, even if not in our lifetimes!
I think the GP was thinking of more practical experiments, not science fiction.
Now go look up how precise a prediction the same model makes for the muon g-factor.
Whenever a physics theory gets replaced it becomes even harder to make an even better theory. In technology low hanging fruit continues to get picked and the next fruit is a little higher up. Of course there are lots of fruits and sometimes you miss one and a solution turns out to be easier than expected but overall every phase of technology is a little harder and more expensive.
This actually coincides with science. Technology is finding useful configurations of science, and practically speaking there are only so many useful configurations for a given level of science. So the technology S-curve is built on the science S-curve.
The S-curve is really about fundamental limits. Lets say ASI helps us make multiple big leaps ahead, I mean mind blowing stuff. That still doesn't change that there must be a limit somewhere. The idea that science and tech is infinite is pure science fiction.
An obvious example of this is the assumption of the geocentric universe. That rapidly leads to ever more mind-boggling complex phenomena like multitudes of epicycles, planets suddenly turning around mid-orbit, and much more. It turns out the actual physics are far more simple, but you have to get passed that flawed assumption.
In more modern times relativity was similar. Once it became clear that the luminiferous aether was wrong, and that the universe was really friggin weird, all sorts of new doors opened for easy access. The rapid decline in progress in modern times would seem most likely to suggest that something we are taking as a fundamental assumption is probably wrong, rather than that the next door is just unimaginably difficult to open. This is probably even more true given the vast numbers of open questions for which we have defacto answers, but yet they seem to defy every single test of their correctness.
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All that said, I don't disagree that technology may be on an s curve, but simply because I think the constraints on 'things' will be far greater than the constraints on knowledge. The most sophisticated naval vessel of modern times would look impressive but otherwise familiar to a seaman of hundreds or perhaps even thousands of years ago. Even things like the engines wouldn't be particularly hard to explain because they would have known full well that a boiling pot of water can push off its top, which is basically 90% of the way to understanding how an engine works.
We actually know we have:
Bell’s inequality tells us that the universe is non-local or non-real. We originally preferred to retain locality (ie, Copenhagen interpretation) but were later forced to accept non-locality. But now we have a pedagogy and machinery built on this (incorrect) assumption — which people don’t personally benefit from re-writing.
Science appears trapped in something all too familiar to SDEs:
A technical design choice turned out to be wrong, but a re-write is too costly and risky for your career, so everyone just piles on more tech debt — or modern epicycles.
And perhaps that’s not a bad thing, in and of itself. Eg, geons were initially discarded because the math doesn’t work out — but with the huge asterisk that they might still be topologically stabilized. But the math there is hard and so it makes sense to continue piling onto the current model until enough advances in modeling (eg, 4D anyons) allow for exploring that idea again.
Similar to putting off moving tech stacks until someone else demonstrates it solves their problems.
But at least topological geons would explain one question: why does space look like geometry but particles look like algebra?
Because topological surgery looks like both!
- - - -
> clear that the luminiferous aether was wrong
Another interpretation is that the aether exists, but we’re also made of aether stuff — so we squish when we move, rather than rigidly moving through it (as per the theory tested by Michelson-Morley). That squishing cancels out the expected measurement in MM. LIGO (a scaled MM experiment) then works because waves in the aether squish and stretch us in a detectable way.
Modern theories are effectively this: everything is fields, which we believe to be low-energy parts of some unified field.
Even Einstein did not produce (e.g. special relativity) out of whole cloth. He provided a consistent conceptualization of Lorentz contraction, itself the result of observing descrepencies in the motion of Jupiter's moons. The same could be said of the photoelectric effect, the ultraviolet catastrophe, and QM.
All this to say that your statement "The rapid decline in progress in modern times would seem most likely to suggest that something we are taking as a fundamental assumption is probably wrong" is unsupported. Nothing could be more popular than questioning fundamental assumptions in science today!
It could very well be that, as Sean Carroll puts it, we really know how everything larger than the diameter of a nuetron works! Moreover, we know that even if we find strangeness at tiny scales, our current theories WILL remain valid approximations, just like Newtonian mechanics are valid approximations of special and general relativity. The path to progress will not happen because a rogue genius finds something everyone missed and boldly questions assumptions long-held. Scientific revolution first requires an observation inconsistent with known models, but even the LHC hasn't given us even one of those. There is reason to think that GR, QM, and the standard model are all there is...until we do some experiments near a black hole!
Heliocentrism was most fundamentally driven by somebody, with extremely poor interpersonal skills (which is much more the reason he was left living his final days in house imprisonment, rather than his theory itself), moving forward on his own somewhat obsessive bias.
Similarly, with relativity. I have no idea what you mean by a 'consistent conceptualization' of Lorentz contraction, but length contraction was a completely ad hoc explanation for the Michelson Morley experiment. It's correctness was/is more incidental than anything else. Einstein did not cite Lorentz (or anybody for that matter), and I do not think that was unfair or egotistical of him.
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I'm also unsure of what you're referencing with Sean Carroll, but I'd offer a quote from Michelson of the Michelson-Morley experiment saying essentially the same, "The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.... Our future discoveries must be looked for in the sixth place of decimals."
So convinced was Michelson that the 'failure' of his experiment was just a measurement issue that he made that comment in 1894, near to a decade after his experiment and shortly before physics and our understanding of the universe was about to revolutionary explode thanks to a low ranking patent inspector.
In "On the Electrodynamics of Moving Bodies"[1] Einstein checks his derivation against Lorentz contraction. It's on page 20 of the referenced English translation. Lorentz' model was ad hoc, E derived it with only 2 postulates (equivalence principle; c invariance). Lorentz was indeed cited, and the cite is useful to connect E's theory to real-world observation. This is true whether or not you want to get pedantic about the meaning of "cite" vs "reference".
1 - https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf Originally "Zur Elektrodynamik bewegter Koerper"
That's not true, he didn't.
Geocentric model of the time was a better fit of the data than the Copernican model. What Copernican model had was simplicity (at some cost to observational data fidelity).
Making the heliocentric model approach (and breach) the accuracy obtained by the geocentric model took a lifetime of work by many people.
As a kinematic model (description of the geometry of motions) as observed from Earth's reference frame geocentric is still pretty darn accurate. There's a reason why it is so. Compositions of epicycles are a form of Fourier analysis -- they are universal approximators. They can fit any 'reasonably well behaved' function. The risk is, and it's the same risk with ML, deep neural nets, that one (i) could overfit and (ii) it could generate a model with high predictive accuracy without being a causal model that generalises.
Heliocentric model was proposed much much earlier than Copernicus but the counterarguments were non-ignorable. Reality, it turned out was very surprising and unintuitive.
I don't think this history says anything against your point -- sometimes the time is just not right for the idea -- and even classical science can be very unintuitive and weird, so much so that common sense seems like very strong counter arguments against what eventually turn out to be better models.
I of course learned this over many books, but the mind blanks out over which one to suggest. I think biographies of Copernicus and Kepler would be good places to start.
Edit: you may find this interesting:
https://news.ycombinator.com/item?id=42347533
HN do you know what happened to John Baez's blog that listed his multiparty blog posts ? They are a treasure trove that I do not want to lose. Azimuthproject too seems to have disappeared
If one does genuinely believe in a God then the existence of science need not pose a threat to that, since there's nothing preventing one from believing that God also then created the sciences and rationality of the universe. The classical 'gotchas' like 'Can God create a stone so heavy that he could not lift it?' were trivial to answer by simply accepting that omnipotence does not extend to things which are logically impossible, like a square circle.
[1] - https://en.wikipedia.org/wiki/Science_and_the_Catholic_Churc...
So even if our fundamental assumptions are wrong and some new theory is able to explain a bunch of new stuff, chances are it won't impact the stuff we can practically do here on earth, because scientists have already been doing the most extreme experiments they can, and so far progress is still stalled on fundamental physics.
Or at least some clear statement how comes our reality is not like that.
The wave function is the square root of a probability distribution. The wavefunction is a continuous real function of position because position is modeled as a continuous real variable. The idea of the wavefunction as a function of position is generally supported by the fact that it can be used to predict the measurement results of diffraction experiments like the double-slit experiment, but also practically the whole field of X-ray diffraction.
There is not just one experimental result that is explained by wavefunctions. There are widely used measurement techniques whose outcomes are calculated according to the quantum properties of matter — like X-ray diffraction and Raman scattering — which are widely considered to be extremely reliable. There is a good reason to explain the model of reality expressed by the equations as clearly as possible, because we want people to be able to use the equations.
Plenty of people (though certainly not all) expect quantum mechanics to be eventually modified to have a consistent theory of gravity. But physicists have experience with this. Special relativity and classical quantum mechanics were both more complex than Newtonian (classical) mechanics, and quantum field theory is more complicated than either. General relativity is substantially more involved than special relativity. It is likely that further extensions will continue to get worse.
The model of reality taught by Newtonian (classical) mechanics is also still widely discussed and used in introductory physics courses and many areas of physics (such as fluid dynamics) and engineering. This model also discusses position on the real line. Even though classical mechanics had to be modified, the use of Cartesian coordinates and real numbers turned out to be durable.
Usually the finitists will formally "rescue" countability by suggesting that the world could exist on the computable numbers, which are countable and invariant under computable rotations. But the computable numbers are a very unsatisfying model of reality, and have a lot of the same "weirdness" as the real numbers. Therefore they suggest that some other model must exist without giving a lot of specifics. Why this should be somehow helpful and not injurious to the pedagogy of physics is not clear.
To come up with new experiments that might shed light it certainly helps to spend time exploring the models to come up with new predictions that they might make. Sure, one can also come up with new experiments based only on existing observations, but it's most interesting when we can make predictions, as testing those advances some theories and crushes others.
The wave went through the slits, not the "wave function". There is no "quantum" because there is nothing to measure so there is no quantum physics.
The fact that we are quantifying things is the problem. When we look at everything as a whole which is effected by waves we will find the solution.
No. Group movement of particles is one medium in which waves can occur, but the concept is more fundamental and general. The waves described in the article are not in particles.
Choice of how to measure -> History
it is,
Choice of how to measure + physical system -> Observations -> Interpretation of observations -> History
The choice of what and how to measure will influence the history you conclude, but that is true of actual "Caesar and Napoleon" history too, and in that case it's definitely not that past events are being changed, instead it is your knowledge of them. A really interesting principle is that any philosophical question that can be phrased without referring to ideas that only exist in quantum mechanics can usually be answered without referring to them.
In typical probability, we deal with an ensemble of fixed states, or at least phenomena that can be simulated as such.
In quantum physics, the wavefunction is fundamental. The question "what was the exact path?" is meaningless. In particular, if we take the approach of Feynman path integrals, we find that particles take many paths - including circular paths through each slit - before arriving somewhere else where they interact (i.e., become entangled) with, say, an electron in the screen.
Sure, we may consider different experiments (e.g., quantum erasers, see https://lab.quantumflytrap.com/lab/quantum-eraser), but analogies with deterministic particles are whimsical - sometimes they work, sometimes not.
It is not correct— at least not unless you subscribe to the Copenhagen interpretation. Yet, while this interpretation is a simple heuristic for interaction with big systems (e.g., a photon hits a CCD array), none of the quantum physicists I know treat it seriously (for that matter, I have a PhD in quantum optics theory).
I mean, at some certain level, everything is "just a mathematical representation" - in the spirit of "all models are wrong but some are useful". But the wavefunction is more fundamental than measurement. The other can be thought of as a particle entangling with a system so large that, for statistical reasons, it becomes irreversible - because of chaos, not fundamental rules.
For some materials, I recommend materials on decoherence by WH Zurek, e.g. https://arxiv.org/pdf/quant-ph/0105127. Some other references (here a shameless self ad) in https://www.spiedigitallibrary.org/journals/optical-engineer... - mostly in the introduction and, speaking about interpretations, section 3.7.
EDIT: or actually even simpler toy model of measurement, look at the Schrodinger cat in this one: https://arxiv.org/abs/2312.07840
The exact phase of a wavefunction does not matter - but it is an important phenomenon, giving raise to gauge invariance. The Born rule can be derived. In short, since we use unitary operators, length is preserved. For a derivation, see https://journals.aps.org/pra/abstract/10.1103/PhysRevA.71.05....
Also, to be nitpicky, we also never measure probabilities. Something (macroscopic) happened or not. It gives rise to quite fundamental and philosophical questions, including "what is (classical) probability" (I don't know an answer that fully satisfies me), many world interpretations (maybe all possible things just are), and in general what on indeterminism and free will.
I also don't agree with your comparison of what I said to the nuclear reactions happening inside a star. The problem with the wavefunction without the Born rule is not that it's difficult to observe, it's that it's literally meaningless: knowing the value of the wavefunction for some state of a system doesn't tell you anything at all unless you apply the Born rule to this value.
And as for probabilities, certain kinds of probabilities at least have a very clear and simple definition (though they are rather narrow cases): if you repeat an experiment in exactly the same conditions N times, and an outcome O happens in p/N times and doesn't happen (1-p/N) times, then we define P(O), the probability of outcome O, as the value p/N. For systems where this applies, it is very much a measurable quantity (with some noise, of course, related to the fidelity with which you can reproduce the same experiment).
I do agree that this well-defined, measurable, concept of probability is rarely what we mean by "the probability of O", since (a) it's often hard or impossible to repeat (or even perform) the experiment, and (b) we often care about what will happen the next M times we repeat this experiment, and the measure P(O) I defined above does not tell us anything about future events.
You say you need the Born rule to understand what's going on, for this you don't need it as a fundamental phenomenon, you only need to eventually observe the Born statistics, which is sufficient to provide understanding for you.
Actually, I'll tell you how it was checked: they ran lots of experiments, and confirmed that the probability to find the particle in one state or the other is precisely equal to the norm of the wavefunction of the respective state. Also known as the Born rule.
Now, you can dress this in other language. Some versions of MWI say that the universe splits into many literal worlds after any quantum event, and the number of worlds in which it has a certain outcome is proportional to the norm of the amplitude of the wavefunction of that outcome; based on this, they then derive the Born rule as P(stateA) = num_worlds(stateA) / num_total_worlds = norm(|stateA>). Of course, this is still the Born rule, and it is still not derivable from the wavefunction, still an additional postulate - just with extra steps.
And I don't know what you mean when you say that the Born rule is not statistics: it is exactly statistics (or at least probabilities, if you make a distinction). Sure it's possible to get a million tails in a row, that is always possible in statistics - by definition, any event with probability higher than 0 is possible.
Amplitudes as quantitative properties are sufficient for calculation of statistics. Ironically classical theory of probabilities works the same way: first it assigns arbitrary weight to outcomes, then divides them by the weight of ensemble (usually >1 contrary to QM) to get statistical coefficients. The weights can be scaled by any constant factor, and the calculation still works.
There was an experiment that measured and built a picture of electron orbitals in a water molecule.
What the experiment did NOT do is directly detect the wavefunction of the electron, because that is, again, not a phsycially meaningful quantity.
In the dual slit experiment this is visible as you can't get the interference effects by summing the probabilities for "particle through slit 1" and "particle through slit 2" but rather you need to sum the amplitudes of the processes.
Working physicists (since 100 years) just do this, there is no practical need to interpret it further, but it would be cool if someone could figure out some prediction/experiment mismatch that does indeed require tweaking this!
IMO so much writing about quantum mechanics gets harder to follow by trying to jump classic -> quantum, and certain -> probabilistic at the same time. If one does the latter switch first, it cuts out the noise of easier-to-understand things to get to the second.