Another piece of widespread ignorance I've seen here on HN, is the treatment of conservation laws as if they're baked into the fabric of reality. This results in programmers making philosophical/cosmological arguments in ignorance. As far as we know, conservation laws are not baked into reality. Instead, they are very useful analysis tools which can take advantage of symmetries. (Or near-symmetries.) Any given conservation law can disappear if a given symmetry doesn't apply, but Noether's Theorem still remains.
If you want to see an example of how social media "bubbles" can impede the dissemination of knowledge, note that I've actually been flagged on HN for trying to explain this, apparently because someone misread this as advocacy for perpetual motion machines. It is not! (Also, because I used <facepalm> -- but when you're wrong, you're wrong, and when you're wrong and you think it's clever, it feels worse.)
Periodic, discrete symmetry holds, continuous is toast. Interesting.. Maybe there should be a rule of thumb (XKCD?) that says for any intuition one may hold, some researcher somewhere is, at ``this'' moment (in some measuring system) constructing a contrived situation that will break it via some contrivance that is strange in inverse proportion to the homeliness of the intuition? ....And some talky-site-poster (me in this case) is preparing to make it yak about it?
These don't break fundamental time translation symmetry, anymore than regular crystals break fundamental space translation symmetry (which is equivalent to conservation of momentum). The fundamental versions of these symmetries are that the laws of physics are unchanged under such changes.
These are merely systems such that the system itself lacks such a symmetry. This will indeed allow a change in the "effective" laws of physics (like electrons having different effective mass in metals or semiconductors than in free space, and quantized momenta), and give something interacting with the system the illusion that energy or momentum is not conserved. But this is only an illusion: momentum and energy of something interacting with the system are exchanged with the system.
This shouldn't be mysterious though -- a time changing potential already didn't preserve the energy of what it's interacting with, and a crystal can absorb momentum as a whole without any local disturbances that could be seen by a particle in it (e.g. Mossbauer effect). But the upshot is that what counts as a symmetry depends on what's fixed under your analysis vs what's part of the state space.
We already know that conservation of energy isn't absolute. It is, however, a very powerful analysis tool, just as Euclidian geometry is a very powerful powerful analysis tool. It's very accurate on certain scales, however, that's not how the universe works if you look closely enough.
> As far as we know, conservation laws are not baked into reality.
I think that's going too far. As far as we know, the symmetries could be baked into reality. And, via Noether's Theorem, so therefore are the conservation laws.
> I think that's going too far. As far as we know, the symmetries could be baked into reality.
Are you aware that the symmetries have been falling and that physicists been retreating? First, parity symmetry fell in 1956, resulting in a retreat to CP symmetry, which also fell. Now we're to CPT symmetry, which implies that there is no time symmetry, which in turn has been verified by physicists.
Well, it implies that charge symmetry, parity symmetry, and time-reversal symmetry are different aspects of the same thing. I'm not sure that's quite "falling", though.
You just admitted that charge symmetry, parity symmetry, and time-reversal symmetry are incomplete. I'm quite sure that the old mental models which held those to be absolute did "fall."
You seem to want to play "gotcha" games with my wording. I admitted far less than you seem to want to make my words say. And if you're going to try to manipulate what I said to make it fit the axe you're trying to grind, then I'm done talking to you.
You seem to want to play "gotcha" games with my wording.
It's not a game. You ironically committed the Map/Territory error, in a Map/Terriotry discussion. A condition of underlying reality where a given symmetry exists, or only appears to exist, can't fall. It either is or isn't. But the mental model -- the Map -- using symmetry can indeed be shown to be false and fall.
And if you're going to try to manipulate what I said to make it fit the axe you're trying to grind, then I'm done talking to you.
I did no such manipulation. I bet you can't substantiate that with reasoning and quotes. In any case, I am well satisfied to let 3rd parties read and decide for themselves.
(Ironic in the Alanis Morrisette sense, not the hipster sense.)
It is falling. The old theory was that these were 3 fundamental facts in the universe. The modern theory is that there is 1 fundamental "triangular" fact, not derivable from simpler facts. That makes the Universe more fundamentally complicated than previously thought.
And furthermore, it's not simply that any given random kind of particle is either "Yes or "No" on each of the 3 corners, while constrained to be "Yes" on the combination. There is a strong bias toward Yes in all three points -- which is even more asymmetry than was previously thought possible. (A fact that samples at 100% true or 50% true is far more symmetric than sampling at 98% true -- the bias needs a deeper explanation, or more fundamental parameters of the universe)
Completely unrelated to the original article which is just more multiverse bullocks of the stringy landscape variety. These scientists will die off and with it these articles.
I went to exactly the same post on Carroll's blog in response to the parent comment as well! Quite relevant I thought, given the comments about conservation laws and the especially the mention of dark energy that followed. -I elected not to post up there as I am studying GR - and not so confident with it! Thanks for dropping it in.
The map is the territory for belief about belief though, sometimes, if people choose to agree.
You can believe things about how people think and this can affect how people think. Sometimes precisely, such as in the case of a mental illness diagnosis a person may have been indoctrinated into believing is their identity, sometimes generally, chaotically, without direct transmission perfectly.
I'd compare Machiavellian motivations here, belief about belief with the intent to control comes from the desire to control and rule through thinking, but the domination of thought/behavior of individuals through one's thoughts alone... people eventually become aware of intents, if there's always that imbalance. The problem often stems from assuming one has earned the right to dominate and another must do X,Y,Z to earn respect. Quite frankly, humans from birth to death and every point in between are equivalently autonomous and worthy of being able to think the way they want to, without having to do anything to have earned such a right. Thinking otherwise is a good example of being wrong and clever in a way that can be quite haunting.
I think these kinds of validations get conflated with hard data. Often, it is a lot easier to just listen to people and let them believe what they want to. Gotta trust people to come to their own conclusions independently.
In the age of machine learning, behavior shaping, I think a lot of this is quite topical.
The map is the territory for belief about belief though, sometimes, if people choose to agree.
Let's say I build a theme park in the form of a giant map of the world. I could then print a map to my theme park.
Quite frankly, humans from birth to death and every point in between are equivalently autonomous and worthy of being able to think the way they want to, without having to do anything to have earned such a right.
You can think any way you want to, and I will respect your right to think that way. I can respect that you think, but that doesn't mean I have to respect what you think.
> You can think any way you want to, and I will respect your right to think that way. I can respect that you think, but that doesn't mean I have to respect what you think.
That's totally fine, just in my personal experience, stuff like that has a funny way of coming back in thought.
I find that no matter what words come out in reality, transmission through language, it never really tells you very much about how a person actually thinks. Kind of hard to know how another person thinks, because, that kind of seems like believing in telepathy.
Let's say that the mere act of me saying what I 'think' causes my thinking to change, instantly, perfectly flipping to a perfectly opposite perspective. What's there to respect at that point?
I've thought about it a lot. It just seems to loop, to find a way that allows me to believe I have done enough work such that I am allowed to have the thoughts I wanted to have from the beginning. There are all sorts of ways I seem to invent to do this. Doing differently, every single time, every new way of working through 'thought', what's the original point?
I think your experience of thought is worth a lot more than anything I could tell you about it. (Yes, I planned that out.)
Doing differently, every single time, every new way of working through 'thought', what's the original point?
Is it fun? If it's not fun, then don't do that. Also, as far as a "point" goes, that is up to you. Let me testify to you, as an atheist, that you can find meaning in life by living it "meaningfully." Do that enough, and you will find it. Physical and aesthetic activities with others help a lot. Sharing food and experiences with true friends is key.
I sort of find doing stuff with words fun, sometimes. It's a creative endeavor, but also fairly rigorous.
Otherwise, stare off into space, and wonder if the terrible things I don't want to happen have happened yet.
Food, experiences, aesthetics, pleasure, hedonism. I study Zen quite a bit. I don't find it fun. It's just a way to reveal truths to others because,they can't be revealed directly and accepted at face value, for some.
Words are memes. Ideas are baked in. Connections dance in patterns. Math and logic form the foundation. Mind tests for correctness. Self, universe, theory. Universe is infinite, self knowledge - finite (or is it?). Theory unites with self, universe serves as reality check. Theory united with self, is this equivalent to the universe?
What is mind? The experience of everything you've ever experienced, collapsing in on itself.
What happens after that? That, I find interesting. Post modernism, maybe. Where are the new words, new theories, new patterns? Dance on top of all that exists.
I used to be like that, but, life is too short to allow embarrassment to paralyze you. If you go through it often enough, you develop a sort of numbness to it. I'm sure I can still embarrass myself, but I try not to dwell in that micro blackhole. PTSD has taught me that if you are constantly focused on those patterns, you will see them in everything. So you might wind up feeling like you are embarrassing yourself constantly even though external reality has no validation mechanic to prove this. Are people saying you are embarrassing? And should you care, if they do think this? That judgement is their own burden.
You can keep wondering, but to me that's the same as thinking everything is traumatic because the reality of the present is 'connected' to the memory of the past. All those links, you can keep stepping back into them until you feel like, "I am reliving this again", but, that happens frequently enough and I dunno.
Labeling things stupid just means you have less tools to work with when a stupid thing might actually be the more smart thing to work with. Doesn't mean you won't make mistakes. As far as intelligence is concerned, I'm not sure any human is intelligent enough to be it while knowing what it is.
the only thing relevant is the map and how it reacts to probing
Sounds like Postmodernism to me. If you think it's not, then let me point out that you can just substitute "text" for "map" and you're pretty much there.
There must be something underlying the maps, because so many of those maps have turned out to be wildly wrong, completely barking up the wrong tree. It's not even that they didn't answer the questions correctly -- they were so wrong, they were asking nonsense questions in the first place.
There is a nice little allegory by Raymond Smullyan, where some ancient philosophers are debating what keeps the world from "falling down." I think it's in "5000 BC," and is the story by that name.
I was responding to, "There may as well be no territory, the only thing relevant is the map and how it reacts to probing."
If there are only maps, then when map A is wrong, I can just make my own map B for which map A is a good map. In that case, no map is falsifiable, and all maps are equally valid. It's Postmodernism!
The article says that one of the attractive qualities if string theory is that it has no free parameters. But then says that the particles a forces of the standard model are determined by the number and size of extra dimensions. Those sound an awful lot like free parameters.
Can someone with more than a passing familiarity with the field explain?
One might say, given the fundamental particles, there is a unique set of number and sizes of extra dimensions. That is, there are no free parameters if it's going to fit this universe.
The same thing happened in relativity. c is not a free parameter; it has to be the speed of light in this universe. You could argue that it could have some other value and relativity would still work correctly. That might be true in some sense, but it wouldn't work as a correct description of this universe.
Note well: I do not have more than a passing familiarity with the field. What I am saying here may not be a correct description of the actual state of string theory.
Also note that I find "there are no free parameters" and "but it gives rise to this landscape, where there's nothing nailed down in terms of actual physics" to be somewhat difficult to reconcile.
Normally in a physical theory, you have some equations describing the dynamics and you go looking for solutions to these equations. The dynamical equations may have some parameters (such as the constant G in Newtonian/Einsteinian gravity), and then there are usually additional parameters required to describe the solutions (such as the mass M of the gravitational field source).
String theory has the unusual property that its dynamical equations don't have free parameters. The dynamics is apparently unique. But there are many many solutions to these equations, and so there's a huge space of parameters from that. In particular, if you go looking for ways of embedding the Standard Model in string theory, all of its dynamical parameters (like the electron mass and Newton's constant) are realized as solution parameters.
Can I make Newtonian mechanics into a dyanically 0-free-parameter theory by stating that F == gMm/r^2 , where g is a solution parameter ("the gravity of the universal landscape" ?
You can do this -- and indeed, promoting constants to fields is a common technique in the analysis of field theories. But it's cheating if you say the constant is dynamical and then don't say what the dynamics is. In field theory, you have to make additional choices here, and there are a lot of additional parameters that enter.
In string theory, you don't have to/get to make a choice at all. The dynamics is uniquely determined. It's not exactly a free lunch, but it's a very unusual feature for a physical theory.
It is bullocks and just the excuse of a declining number of scientists who have spent their life's work on String Theory and will never admit that the program has utterly failed as a "Theory of Everything"
This feels off to me. Einstein’s process did not come from the mathematics, but from an idea of what was happening. This enabled a great number of odd predictions which were verified (the Sun would bend the visible pathway of a star, there would be gravitational waves, etc...). String Theory feels like a theory which is starting at the wrong place. Not an idea of what process is happening and then seeing if the results fit, but an attempt to connect all the results into a theory. Pas bien por moi!
> String Theory feels like a theory which is starting at the wrong place. Not an idea of what process is happening and then seeing if the results fit, but an attempt to connect all the results into a theory.
Are you saying that it doesn't make any predictions (and is therefore unfalsifiable)?
There are no predictions even in principle. It has nothing to do with the predictions being at a sufficiently high enough energy level that we can't verify...
>"Are you saying that it doesn't make any predictions (and is therefore unfalsifiable)?"
As I understand, its the opposite. String theory "predicts" any and every possible observation, then they cherry pick whatever predictions are already accepted as fact to say there is evidence for the theory.
Sure, but regular quantum mechanics does the same thing. It's under-constrained and allows for too many possibilities. So you assume that the observations wrought by Newtonian physics must be valid and use that to constrain the theory down to something that can be useful.
The difference is that the string model doesn't (yet) have any observations which we could use to constrain it in an analogous manner. But in studying it, one would hope to find areas of the theory that indicate where those observations could be made.
The point being, it is not so simple to just look at string theory and say you can a priory determine it is flawed or wrongly motivated. That same kind of reasoning would likely have prevented Planck & Einstein from starting quantum theory.
I'm not sure what this means. Is it different from just making an observation? Eg, "this light in the sky is of this color at that location", or "this object drops at that speed".
It just means that we need the correspondence principle to find useful quantum mechanical models. Without that, you're just talking about algebras acting on Hilbert spaces.
> Sure, but regular quantum mechanics does the same thing. It's
> under-constrained and allows for too many possibilities.
No it doesn’t. There are a few good guiding principles that make it
possible to build models that turn out to be an accurate description
of nature. These guiding principles don’t manifest themselves in a
set of axioms of a mathematical theory nevertheless they are there.
And they are part of the theory, just not set in stone like the
underlying mathematical structure. But that doesn’t matter at all as
long as you are doing science and not math.
Take classical EM, measure the masses of the electron and atomic
nuclei, and write down a suitable Hamiltonians. Viola, you have an
explanation of almost every phenomena that’s relevant in our daily
life and way beyond. Similar principles exist in elementary particle
physics and lead to standard model.
> String Theory feels like a theory which is starting at the wrong place.
I think there's also a place for setting aside our prescriptive rulers and looking at String Theory in its own right.
As a programme it has contributed significantly to detangling the intractibilities in quantum field theory. Heck, it apparently even finds applications in such "mundane" applications as condensed matter physics by showing coorespondences between fluids and black holes. As a pure math endeavor, it's contributions to algebraic geometry are hard to miss.
Personally, I think a lot of the "problems" with String Theory only arise when circumscribing it to be a certain kind of cosmological model.
I'm reminded of this beautiful quote from Chris Fuchs, regarding his advisor, the great John Archibald Wheeler:
> [Wheeler] would say things like, “In the end, the only law is that there is no law.” There’s no ultimate law of physics. All the laws of physics are mutable and that mutability itself is a principle of physics. He’d say, there’s no law of physics that hasn't been transcended. I saw this, and I remembered my joke about how the laws of physics must be wrong, and I was immensely attracted to this idea that maybe ultimately there actually are no laws of physics. What there is in place of laws, I didn't know. But if the laws weren't 100 percent trustworthy, maybe there was a back door to the stars.
This sounds like semantic befuddlement (though, not on Wheeler's part; he was just engaging in wordplay).
Physical laws are not 'laws' in the sense that nature is required to abide by them. They are simply features of natural behavior that have been so overwhelmingly observed that we treat them as axioms.
An example of this is the 'law' of conservation of mass. Strictly speaking, nature does not follow this law. Nuclear reactions and subatomic interactions do not conserve mass. They conserve other quantities, but not mass in and of itself.
The idea that there is no ultimate law of physics is not novel or interesting. It's obvious on its face, unless you do not properly understand what 'law' means in the context of physics.
Law of physics implies a casual relationship in nature. Saying there are no laws of physics is saying nature is acausal. B always follows A for no reason other than it just happens to do so in our universe. This is the Humean view of causation, which is constant conjunction instead of there being a reason that A results in B.
The plus side is that you don't have to deal with causality, which is a tricky concept. Hume persuasively argued that causality is neither empirical nor a result of logic. The downside is that all necessity is totally arbitrary. It just so happens ... As such, there is no reason for anything we observe. Just descriptions.
You are postulating here a priori that causality governs the movement of the universe. That is a philosophical position on how to interpret physical observation, but whereas archetypal temporal cause-and-effect phenomena is frequently observed, there are yet many physical phenomena that you and I regard as fact don't have obviously observed temporal causes. For example, we observe the Big Bang as well as the accelerating expansion of the universe, but don't have good explanations for their temporal cause. And everything in the universe is temporally caused by the Big Bang...
So what I'm trying to say here is that your claim here that causality governs the actual laws of nature is suspect, both because your comment has not been elaborate enough to specify what you mean by causality, and because one of the most popular notions of causality, i.e. temporal causality, seems, to a first approximation, not be a good model of the observable physics: it postulates a temporal cause for the big bang, but no time prior to the big bang is observable.
A law _implies_ a causal relationship because a law is thought to model a universal relationship (B always occurs when A). How you interpret the causality depends on your metaphysics. It can be descriptive based on constant conjunction, if you're so persuaded.
Scientists will state that B happens BECAUSE of A, when A is thought to be a necessary condition for B. That's the causal implication.
What, then, causes the phenomenon that fields interact with particles?
Historically, there has been a multitude of ideas and phenomena that have been labeled as causation. Aristotle, back then, identified four notions of causation, and the modern reader immediately will feel that some of these notions themselves are still too general. When you make a claim like "nature obeys causality", you need to be more precise in what you refer to by nature and causality, else your claim is far too ill-defined to mean much of anyting.
It's not obvious on its face, as it must be "properly understood" as you say. It takes years of education before people realize that the known laws of physics are just approximations or historically refined by discovering new details.
"conservation of mass" is either utterly trivial ("Nothing comes from nothing... except stuff that does") or has grown its asterisks over time.
> It takes years of education before people realize that the known laws of physics are just approximations or historically refined by discovering new details.
It's in high school chemistry textbooks. Typically in the first chapter or two. I'm assuming the audience of this site has taken at least one chemistry class in their life. Whether or not they paid attention is their own problem.
For those like me who are not too happy with this kind of "science" (for one, the title is worded in a way that makes this highly controversial view of reality sound like state of art in physics), "Not Even Wrong" [1] by Peter Woit is a great read for multiverse skepticism (mostly centered on "string multiverse", not quantum "many worlds").
What does "baked into reality" mean? We can never know more about reality than what we observe, and furthermore conservation laws are axiomatic -- conservation simply means that we are able to account for (almost) everything we observe, in a consistent way.
You said it right there. "Almost." We keep on prying and doing experiments, and we can't find any exception. If we've tried hard enough for long enough, we can start to conclude that we're probably getting close to reality. If we pry and we find it's "almost" then we know it's not baked into reality.
When conservation is broken, we name a new form of energy, and (so far), we find that it can by accounted in a consistent, predictable way. (Dark matter is an unsolved problem.
[Citation Needed] Yes, we still don't know what Dark Matter is, but do you understand that dark energy is not dark matter, and the current model for dark energy involves space expanding and more dark energy appearing due to the space expanding? Citing dark energy is tantamount to admitting that conservation of energy isn't universal.
When it comes to fundamental science, a consistent map is the territory.
Arrgh. You're getting your pointers mixed up here. A context where science is the territory would be the study of Science, as in the philosophy of science. When it comes to fundamental reality, Science is the map and fundamental reality is the territory.
That which gives rise to experimental results and perception. If you don't think there's a real world responsible for those, then how do you explain what we sense and the results from experiments? What makes the technology work? God?
I surely don't know. That's metaphysics, not science.
But you can clearly do science on the technology. People do this with high degrees of success, developing theoretical models with high predictive ability. It's called "reverse engineering." If you're going to retreat into metaphysical mumbo-jumbo, that's up to you. The doing and the results will speak for themselves, and no one will pay attention to the metaphysical mumbo-jumbo obscurantists.
I mean that if reality (nature, the world) isn't responsible for our experiences of a world, including scientific experiments, then what is? Does the empirical just a appear for no reason with nothing behind it?
kudos to stcredzero for a humorous and tactful exit... I'll be the killjoy and explain his joke, which I think was a last-ditch attempt illustrate the point he's been trying (and failing) to get across all thread, which is that
> When it comes to fundamental science, a consistent map is the territory
isn't the case.
Science/empiricism merely produce predictive models; over the last few hundred years, these models have improved dramatically, but they are nonetheless only maps of a territory ("reality"), and it's still fundamentally uncertain that the underlying assumptions (that laws of nature exist/that reality is mappable) are reliable.
> "Map is not the territory" applies to simplifications that omit detail.
Even if we had a perfect model, which we don't (and it's not clear that such a model is obtainable) that could predict everything, it would still be separate from the territory. You might think this is a pedantic distinction, and in your ideal world where we have a unified field theory, it certainly would be, but like I said above, it's not clear that such a thing is obtainable, so it's important to hold onto the distinction lest we forget the fact that we're still sitting on an incredibly young and uncertain foundation.
Off-topic question that seems to trivial to take to Stack Exchange but I am struggling to find an answer to, maybe a physicist comes by and can provide an answer or relevant reference.
Let's take a spin 1/2 in the superposition state |0> + |1> ignoring normalization and then add the rest of the universe including a measuring device, an observer, and all the other bits and pieces of the environment. This state then undergoes unitary time evolution past the point where we measured the spin and the observer had a look at the measuring device.
It now seems to me that if the final state is a definite |0> or a definite |1>, then this measurement outcome must already have been present in the initial state, not necessarily as hidden variables of the spin but somewhere, for example in the micro states of the measuring device. If the final state could indeed be either |0> or |1> independent of the initial state, time evolution would not be unitary, it would not even be a function of the initial state.
The only other option seems to be that the final state is still a superposition and we have to reach for something like the multiverse interpretation to reconcile the fact that we indeed observe a definite final state. So what is the correct or at least common way to think about this? Time evolution is only approximately or sometimes unitary? The measurement outcome is, similar to decoherence, determined by the environment? The final state is still a superposition? Non of those seems to be a particularly attractive choice. Or did I somewhere make a stupid mistake?
It's been a long time since my QM course, but, assuming by unitary you mean deterministic, then the answer is that time evolution of a particle's state is NOT deterministic. It is probabilistic. For large collections of particles, the probabilities come to overwhelmingly favor a single average state, but the state of any single particle remains non-deterministic.
This is in contrast to, for example, classical statistical mechanics where individual particles are considered to behave deterministically, but we simply lack the ability to measure their behavior. In (the Copenhagen interpretation of) QM there is no underlying determinism at all.
You might not like this idea (it's certainly non-intuitive), but decades of experiments have shown that the alternatives are all, most likely, wrong.
You are not too far off, as a first approximation you can say unitary means deterministic. But you are wrong with the time evolution not being deterministic, time evolution in quantum mechanics is deterministic. What seems not to be deterministic in the general case are measurement outcomes, that is where we take the Born rule, square the probability amplitudes, and get the probabilities for the different measurement outcomes.
But here lies the incompatibility I am asking about, time evolution is unitary and is in a sense incompatible with the Born rule stating that different measurement outcomes are possible. You can not have unitary time evolution and different possible measurement outcomes starting from the same initial state, at least not in a really obvious way.
The Bell Theorem shows that any local hidden variable theory wouldn't match the experimental data we already have.
There's other options for getting around the weirdness of the Copenhagen interpretation that aren't ruled out by the data we have, but most of them are even weirder.
The many-worlds interpretation is arguably simpler than the Copenhagen interpretation because it gets rid of the collapse postulate. And depending on how literally you take the Copenhagen interpretation, it may not even be self-consistent. At best it provides no explanation how the apparent collapse of the wave function happens, at worst it suggests that the world evolves according to two fundamentally incompatible laws, unitary time evolution and probabilistic projection onto eigenstates during measurement.
I don't want to argue for the many-worlds interpretation, I don't really like - and I am aware that this is a somewhat stupid thing to say about a physical theory. But I also have to admit that it makes sense from a point of simplicity and consistency and compares favorable to other interpretations.
> The only other option seems to be that the final state is still a superposition and we have to reach for something like the multiverse interpretation to reconcile the fact that we indeed observe a definite final state.
I think what you're describing is the infamous Measurement Problem:
1. Hamiltonian evolution is linear
2. Measurements produce nonlinear projections onto eigenvectors in accordance with the Born rule
Note that this projection is a function of the initial state - but a probabilistic function, so therefore not reversible.
There isn't really a satisfying answer to this question yet. Decoherence explains how the system evolves to a mixture of eigenstates but not the collapse into a single one, nor the Born rule.
Note that this projection is a function of the initial state - but a probabilistic function, so therefore not reversible.
I understand what you want to say, but I think it is not correct to call it a function. The term »probabilistic function« does appear in Google results but it seems not to be a common one. I also spent a few minutes looking for a mathematical formalization of a random number generator as a function with no inputs returning a random number adhering to a given probability distribution but could not find anything. Mathematicians seem to be pretty good at avoiding problematic definitions and according to Wikipedia some do this deliberately. The best formalization I could find would be a function from the initial state to a random variable but I was unable to figure out in a couple of minutes how I would mathematically formalize the step from a random variable to a concrete result of a single trail.
Decoherence explains how the system evolves to a mixture of eigenstates but not the collapse into a single one [...]
I never managed to really wrap my head around decoherence, I always only had a quite fuzzy picture of it. But now it is starting to click, it's about the transition from superposition states to probabilistic mixtures, the transition from uncertainty due to superposition to uncertainty due to ignorance.
I just finished teaching a Jr/Sr undergrad Quantum Mechanics course last semester, so I'll take a stab at answering this.
There are two approaches to answering this question. One of them invokes the concept of "the collapse of the wavefunction" at the moment of measurement: when an observer actually measures the outcome of such an experiment, the universe probabilistically selects one of the possible outcomes as "true" and proceeds from there. This "collapse" process is explicitly non-unitary. You may ask, "What entities qualify as 'observers' to trigger collapse?", and the answer is basically "It's not well-defined." As you might gather from that, it's not clear to me that you can include an "observer" in this sense as part of the overall wavefunction of the universe at all, though perhaps people who have studied the foundations of quantum mechanics in more detail could give a better answer.
The other option is pretty much exactly what you've described in your final paragraph: you don't invoke "collapse of the wavefunction" at all, and the final quantum state of the universe after measurement is indeed a superposition of "|0> and observer who saw '0'" and "|1> and observer who saw '1'". Because anything we'd call an "observer" will be a large, complex system, there will very rapidly be a vast number of tiny, "pseudo-random" differences between the two branches of the wavefunction, ensuring that there won't be opportunities for the two branches to experience significant constructive or destructive interference in the future: they'll evolve pretty much completely independently from then on. (This concept is called "decoherence", which you've made reference to, and I'm definitely not an expert on it, but I'm told it's become quite important in research on quantum computing.) There's still a probabilistic question of which branch of the wavefunction a given observer might experience (and understanding why that happens is an enormously subtle question; I've seen some work by Sean Carroll among others trying to make progress on it), but once a given observer has measured a particular outcome to the experiment, the math of quantum mechanics guarantees that they'll continue to measure consistent results after that. This is more or less the Everett "many worlds" interpretation of quantum mechanics.
As you might gather, I'm partial to the latter interpretation, in part because it's where the math seems to most naturally lead (the first time I felt like I really understood quantum mechanics was after a very math-heavy graduate course taught by Robert Geroch), and in part because I've never been able to make sense of what wavefunction collapse might mean (and never been happy about its violation of unitarity).
There's a third option, which historically arose out of the issues you describe with your first approach. This is to deny that quantum theory is a description of an objective, observer-independent reality. Rather it is a kind of "personal rule book" which informs an agent's beliefs about future interactions with the world.
As you might gather from that, it's not clear to me that you can include an "observer" in this sense as part of the overall wavefunction of the universe at all, though perhaps people who have studied the foundations of quantum mechanics in more detail could give a better answer.
I did some more reading and it seems that at least some try to do what I also considered, try to attribute the randomness in the outcome to the randomness and uncertainty in the initial state of the measuring device, observer, and environment. This then raises the question why all kinds of measuring devices produce the same distribution of measurement results if the concrete outcome essentially only depends on the initial state of the measuring device. And this also has the smell of a hidden variable theory where the hidden variables are in the measurement device, would this be compatible with EPR?
I also took away some things to follow up on from your comments on Everett but unlike you I don't really like multiverses and so this will have to wait for some time. I however agree that Everett makes the most sense with regard to completeness and consistency.
There's a quote, in I believe one of Greg Egans books, about the idea that the probable end state of physics will be just a bunch of isomorphic theories, which I wish I could find right now.
For understanding why that might be, I find this to be an elegant little example: take a pattern of black and white stripes; is it white with black stripes, or is it black with white stripes? The two formulations are identical in consequence of what they describe, even though they frame things inversely. (Of course this is just a metaphor to hint toward something in the nature of language, and is not really a deep scenario if you dig into it.)
It seems likely that the descriptions we formulate in physical theories work because they create a pattern which is isomorphic to patterns we extract in physical measurements—but there's something in the nature of the universe and/or language so that there tends to be many ways to create some linguistic thing which produces exactly the same pattern.
That's actually one of the main ideas of positivism: that if two theories lead to the same physical predictions, they are the same theory. When positivism is presented as "every true thing is empirically knowable" it sounds kind of shaky, but if you instead go for, "you can't tell the difference between two internally-consistent claims unless you compare them with the world," then it sounds a lot more likely to be true.
> "you can't tell the difference between two internally-consistent claims unless you compare them with the world," then it sounds a lot more likely to be true.
But only if it's the case that we end up with more than one theory which explains the phenomena equally well. That doesn't seem to be what ends up happening. We don't have an equivalent to GR, QM, Evolution, or any other well established, large scale theory.
Positivism sounds closer to math than it does science. And that's because nature is a certain way, which means you probably can't have equivalent theories at sufficiently granular levels.
My understanding is that there are multiple precisely equivalent formulations of classical mechanics (Newtonian mechanics being one of them, but then there's e.g. Lagrangian mechanics[0] and other more exotic things).
Perhaps that doesn't cross your threshold for 'sufficient granularity'—but it took quite a bit of time to find the alternate formulations in classical mechanics (after Newton I mean), so just because we don't yet have them for certain more modern theories doesn't mean they aren't forthcoming.
Also, I'm pretty sure there are at least very nearly equivalent formulations of QM, e.g. the de broglie pilot wave stuff (often termed as an alternate 'interpretation', but my understanding is that the differences extend even to the level of mathematical formulation, and are not just some detached reflections on the 'meaning' of the theory or whatever.
I think the strongest argument for positivism is that you can generate arbitrarily many trivial "different but the predictions are the same" theories from any parent theory just by doing algebra. You can also generate arbitrarily many "the predictions are slightly different but our present experiments can't resolve it" theories from a parent theory by littering it with new, small constants and tiny interactions. Occam's razor will lead you astray about that, too: most of modern physics was at one time a small constant or a tiny interaction.
What else could be? The universe is outside our language(s) to describe it, so there's no reason to have only one isomorphic theory. The only alternative is to have two (or more) incomplete theories, but then combining them makes one "unified" theory.
Even in pure math, outside of physics, the same applies.
The only other possible alternative would be , what, one tiny theory that is essentially simple and minimal in every possible way, yet somehow models everything, in the spirit of ANKOS?
Is it just me, or does string theory seem like epicycles all over again: if you throw enough center-intersecting circles into the engine, it can emulate just about any observed movement of objects in the sky; a sort of "circular regression" in the same way that piling up polynomials gives us Polynomial Regression. String theory is like "dimensional regression". Regression is a powerful tool, but is NOT designed to directly "explain" phenomena, only emulate them.
Newton et. al. came along and gave us a much simpler model of gravity and the solar system such that we could toss out the messy nested circle models. (We still can't say that Newton's model is fully "right", but it's certainly simpler.)
Well, string theory is kind of the anti-epicycle. The epicycles in Ptolemaic astronomy were added to make the math conform to reality, but people didn't believe that the planets actually moved in epicyclic motion. Superstring theory started from the opposite standpoint: the Standard Model is math that works out, but the theory is messy, so superstring theory sought to make an "elegant" theory that checked out with the math... and ended up with a theory that is so general it can't really be disproven.
The end result is the same, but the paths to get there are completely different.
String theory was originally exciting because it had a graviton that worked, and to my knowledge it is really the only theory that contains both the standard model and gravity. LQG is not yet at the point of reproducing 3+1 space as far as I know. So, here's my proposal: saying that the earth orbits the sun in a universe where QED also is true isn't proof of string theory, but it does falsify the standard model and so far to my knowledge most of string competition.
> but it does falsify the standard model and so far to my knowledge most of string competition.
Not really. The Standard Model makes no prediction about gravity; it makes no claim to. Gravity is so weak that it can be ignored almost everywhere where the other forces come into play: the contribution of gravity compared to electrostatic attraction on the atomic order is smaller than 0.01ZWD is to world GDP... for all of human history. The places where you have to worry about gravity and the other forces at the same time are places where we have precisely no ability to make observations that could distinguish between theories.
> When it comes to fundamental science, a consistent map is the territory. "Map is not the territory" applies to simplifications that omit detail.
But physics does leave out detail. It's an abstraction over many particular instances. Nature isn't a physics equation. An equation doesn't generate a field of force, nor does it have any causal powers.
> We can never know more about reality than what we observe
If that were true, then theoretical physics wouldn't exist. Much of scientific theory involves unobservables, or processes way too long for us to observe. Most of evolutionary history is unobservable. We have to fill in the gaps with a theory explaining the fossil record, genetics, and the organisms around us.
We don't have time machines, nor billion year old cameras.
Multiverse theories like string landscape, eternal inflation, or many-worlds generally have this property: Almost anything that possibly could happen will happen in some universe. But, it is said, that some universes are more frequent than others. From local observations we infer the global laws of physics, which tell us the relative distribution of different types of universes. But, surely there will be some "deceptive" universes, in which (purely by chance) observers are always mislead as to what the actual laws of physics are. Experimental error always goes in the same direction, such that the true laws of physics are never known, and those observers rationally believe in false laws of physics instead. Now, an observer in such a universe will rationally infer a given probability distribution of universes based on their local observations, but the distribution they infer will be completely wrong. My question is: how do we know we are not in such a universe? To say such universes must be exceedingly rare (even though existent) is sort of circular, because our conclusion they are rare is based on our idea of the global probability distribution, but in order to validly make the inference from local observation to global distribution we have to assume we are not in such a universe. But, if we can't know we are not in such a universe, then we can't know that some universes are "more likely" than others, which is a central claim of these theories, and what distinguishes them from David Lewis' modal realism. This is why I think all such "multiverse" theories should be rejected.
This is the one major reason I lost most of my desire to continue grad school (I was studying astrophysics). I chose physics specifically because I wanted to understand the universe. The way I thought of it was that I wanted to lift the hood of reality and see how things "really" worked. As a kid, I'd read a number of books on science and had heard of a quest for a Theory of Everything. I'd decided this was a quest I wanted to go on. I thought of it as the most worthy singular hidden treasure and I was willing to devote my life to digging for it.
But over the course of my undergrad, and hours debating with friends, and reading even more, I started to get an uneasy feeling. I decided to go to grad school, partly, because I still held on to the belief that there really was treasure at the end of that rainbow, and that we really could, if we were clever enough, "figure out" how things "really" worked. But, in grad school, it just continued to dawn on me how impossible it was for there to be only One True Theory. One way I thought about it was to regard physics as a program. Even if there were separate theories for different scales, or domains, it didn't matter, you could still regard the whole knowledge base as a single program and the scale and domain, along with physical observables, as inputs to the Physics Program. The output would be predictions for the state of the universe (or some subset, it didn't matter) at some later time, i.e., it would predict later observables' values.
The thing was, I had a hard time finding any logical justification for why there had to be only one program that could take in the known inputs and produce the known outputs. That is, there was no way to logically prove that there could not be multiple equivalent programs that could produce the same output given the same input. I.e., there was no way to logically justify the notion that there could only be One True Physics. That is, the treasure I believed I'd be digging for, didn't not exist, it was just that there was more than one treasure, and anyone could find their own.
This thought diminished some of the romance, so to speak, of the Quest for Truth, so I lost interest, for a time. Enough to stop taking grad school classes and just start working (coding). Maybe one day I'll create a program of my own.
Your comment stayed in my mind, about the (maybe futile) quest for the "one true theory". Today I was reading an article [1], and a passage reminded me of what you were talking about:
Schrödinger’s theory proved easier to use than Heisenberg’s, in part because it is more intuitive. Furthermore, first Schrödinger and then Paul Dirac proved that the two theories are equivalent. In physics any two theories that make precisely the same observable predictions are observably equivalent. And one of the predominant philosophical views of the age — logical positivism — held that any two observably equivalent theories are really one and the same theory.
...
Einstein demanded a clear and comprehensible account of what is going on in the physical world — at all scales — in space and time. Bohr thought that the key to quantum mechanics was the realization that no such thing could be had.
Physical theories imply physical laws and consistent variables which require consistent math and hard scientific research; There is no escaping that. To say that physics is like a "landscape" is like comparing scribble of a stick man to a Picasso. There is a lot we don't know about the universe, I think its time for writers and physicists to get on board with that and analyze the shit out of their vague and opaque understandings before hitting the enter key.
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[ 15.0 ms ] story [ 2235 ms ] threadhttps://wiki.lesswrong.com/wiki/The_map_is_not_the_territory
Another piece of widespread ignorance I've seen here on HN, is the treatment of conservation laws as if they're baked into the fabric of reality. This results in programmers making philosophical/cosmological arguments in ignorance. As far as we know, conservation laws are not baked into reality. Instead, they are very useful analysis tools which can take advantage of symmetries. (Or near-symmetries.) Any given conservation law can disappear if a given symmetry doesn't apply, but Noether's Theorem still remains.
https://www.youtube.com/watch?v=04ERSb06dOg
If you want to see an example of how social media "bubbles" can impede the dissemination of knowledge, note that I've actually been flagged on HN for trying to explain this, apparently because someone misread this as advocacy for perpetual motion machines. It is not! (Also, because I used <facepalm> -- but when you're wrong, you're wrong, and when you're wrong and you think it's clever, it feels worse.)
(That title, "The Map is Not the Territory" acts as a pointer to a series of literary references. https://en.wikipedia.org/wiki/The_Map_and_the_Territory )
https://en.wikipedia.org/wiki/Time_translation_symmetry https://en.wikipedia.org/wiki/Time_crystal
Edit: Also: https://www.reddit.com/r/askscience/comments/52has4/what_is_...
https://arxiv.org/pdf/1603.08001v4.pdf
Periodic, discrete symmetry holds, continuous is toast. Interesting.. Maybe there should be a rule of thumb (XKCD?) that says for any intuition one may hold, some researcher somewhere is, at ``this'' moment (in some measuring system) constructing a contrived situation that will break it via some contrivance that is strange in inverse proportion to the homeliness of the intuition? ....And some talky-site-poster (me in this case) is preparing to make it yak about it?
These are merely systems such that the system itself lacks such a symmetry. This will indeed allow a change in the "effective" laws of physics (like electrons having different effective mass in metals or semiconductors than in free space, and quantized momenta), and give something interacting with the system the illusion that energy or momentum is not conserved. But this is only an illusion: momentum and energy of something interacting with the system are exchanged with the system.
This shouldn't be mysterious though -- a time changing potential already didn't preserve the energy of what it's interacting with, and a crystal can absorb momentum as a whole without any local disturbances that could be seen by a particle in it (e.g. Mossbauer effect). But the upshot is that what counts as a symmetry depends on what's fixed under your analysis vs what's part of the state space.
https://www.youtube.com/watch?v=yArprk0q9eE
We already know that conservation of energy isn't absolute. It is, however, a very powerful analysis tool, just as Euclidian geometry is a very powerful powerful analysis tool. It's very accurate on certain scales, however, that's not how the universe works if you look closely enough.
I think that's going too far. As far as we know, the symmetries could be baked into reality. And, via Noether's Theorem, so therefore are the conservation laws.
Are you aware that the symmetries have been falling and that physicists been retreating? First, parity symmetry fell in 1956, resulting in a retreat to CP symmetry, which also fell. Now we're to CPT symmetry, which implies that there is no time symmetry, which in turn has been verified by physicists.
https://www.youtube.com/watch?v=yArprk0q9eE
It's not a game. You ironically committed the Map/Territory error, in a Map/Terriotry discussion. A condition of underlying reality where a given symmetry exists, or only appears to exist, can't fall. It either is or isn't. But the mental model -- the Map -- using symmetry can indeed be shown to be false and fall.
And if you're going to try to manipulate what I said to make it fit the axe you're trying to grind, then I'm done talking to you.
I did no such manipulation. I bet you can't substantiate that with reasoning and quotes. In any case, I am well satisfied to let 3rd parties read and decide for themselves.
(Ironic in the Alanis Morrisette sense, not the hipster sense.)
And furthermore, it's not simply that any given random kind of particle is either "Yes or "No" on each of the 3 corners, while constrained to be "Yes" on the combination. There is a strong bias toward Yes in all three points -- which is even more asymmetry than was previously thought possible. (A fact that samples at 100% true or 50% true is far more symmetric than sampling at 98% true -- the bias needs a deeper explanation, or more fundamental parameters of the universe)
You can believe things about how people think and this can affect how people think. Sometimes precisely, such as in the case of a mental illness diagnosis a person may have been indoctrinated into believing is their identity, sometimes generally, chaotically, without direct transmission perfectly.
I'd compare Machiavellian motivations here, belief about belief with the intent to control comes from the desire to control and rule through thinking, but the domination of thought/behavior of individuals through one's thoughts alone... people eventually become aware of intents, if there's always that imbalance. The problem often stems from assuming one has earned the right to dominate and another must do X,Y,Z to earn respect. Quite frankly, humans from birth to death and every point in between are equivalently autonomous and worthy of being able to think the way they want to, without having to do anything to have earned such a right. Thinking otherwise is a good example of being wrong and clever in a way that can be quite haunting.
I think these kinds of validations get conflated with hard data. Often, it is a lot easier to just listen to people and let them believe what they want to. Gotta trust people to come to their own conclusions independently.
In the age of machine learning, behavior shaping, I think a lot of this is quite topical.
Let's say I build a theme park in the form of a giant map of the world. I could then print a map to my theme park.
Quite frankly, humans from birth to death and every point in between are equivalently autonomous and worthy of being able to think the way they want to, without having to do anything to have earned such a right.
You can think any way you want to, and I will respect your right to think that way. I can respect that you think, but that doesn't mean I have to respect what you think.
That's totally fine, just in my personal experience, stuff like that has a funny way of coming back in thought.
I find that no matter what words come out in reality, transmission through language, it never really tells you very much about how a person actually thinks. Kind of hard to know how another person thinks, because, that kind of seems like believing in telepathy.
Let's say that the mere act of me saying what I 'think' causes my thinking to change, instantly, perfectly flipping to a perfectly opposite perspective. What's there to respect at that point?
You were thinking. I respect that. Hell, if you were sincerely trying to think, then had a total brain-fart, I'd still respect the attempt.
What do you think? Let's compare notes.
I think your experience of thought is worth a lot more than anything I could tell you about it. (Yes, I planned that out.)
Doing differently, every single time, every new way of working through 'thought', what's the original point?
Is it fun? If it's not fun, then don't do that. Also, as far as a "point" goes, that is up to you. Let me testify to you, as an atheist, that you can find meaning in life by living it "meaningfully." Do that enough, and you will find it. Physical and aesthetic activities with others help a lot. Sharing food and experiences with true friends is key.
What do you think? Let's compare notes.
See the thread above.
I sort of find doing stuff with words fun, sometimes. It's a creative endeavor, but also fairly rigorous.
Otherwise, stare off into space, and wonder if the terrible things I don't want to happen have happened yet.
Food, experiences, aesthetics, pleasure, hedonism. I study Zen quite a bit. I don't find it fun. It's just a way to reveal truths to others because,they can't be revealed directly and accepted at face value, for some.
Words are memes. Ideas are baked in. Connections dance in patterns. Math and logic form the foundation. Mind tests for correctness. Self, universe, theory. Universe is infinite, self knowledge - finite (or is it?). Theory unites with self, universe serves as reality check. Theory united with self, is this equivalent to the universe?
What is mind? The experience of everything you've ever experienced, collapsing in on itself.
https://youtu.be/1PT90dAA49Q
What happens after that? That, I find interesting. Post modernism, maybe. Where are the new words, new theories, new patterns? Dance on top of all that exists.
I usually experience paroxysms of guilt from the embarrassment of everything stupid I've ever done.
https://proxy.duckduckgo.com/iur/?f=1&image_host=http%3A%2F%...
What happens after that? That, I find interesting. Post modernism, maybe.
Well, if there is a new wave of reason, then a backlash of unreason is not unexpected.
https://www.youtube.com/watch?v=qwZ651i5vls
You can keep wondering, but to me that's the same as thinking everything is traumatic because the reality of the present is 'connected' to the memory of the past. All those links, you can keep stepping back into them until you feel like, "I am reliving this again", but, that happens frequently enough and I dunno.
Labeling things stupid just means you have less tools to work with when a stupid thing might actually be the more smart thing to work with. Doesn't mean you won't make mistakes. As far as intelligence is concerned, I'm not sure any human is intelligent enough to be it while knowing what it is.
Sounds like Postmodernism to me. If you think it's not, then let me point out that you can just substitute "text" for "map" and you're pretty much there.
There must be something underlying the maps, because so many of those maps have turned out to be wildly wrong, completely barking up the wrong tree. It's not even that they didn't answer the questions correctly -- they were so wrong, they were asking nonsense questions in the first place.
There is a nice little allegory by Raymond Smullyan, where some ancient philosophers are debating what keeps the world from "falling down." I think it's in "5000 BC," and is the story by that name.
https://www.amazon.ca/5000-B-C-Other-Philosophical-Fantasies...
If there are only maps, then when map A is wrong, I can just make my own map B for which map A is a good map. In that case, no map is falsifiable, and all maps are equally valid. It's Postmodernism!
Can someone with more than a passing familiarity with the field explain?
The same thing happened in relativity. c is not a free parameter; it has to be the speed of light in this universe. You could argue that it could have some other value and relativity would still work correctly. That might be true in some sense, but it wouldn't work as a correct description of this universe.
Note well: I do not have more than a passing familiarity with the field. What I am saying here may not be a correct description of the actual state of string theory.
Also note that I find "there are no free parameters" and "but it gives rise to this landscape, where there's nothing nailed down in terms of actual physics" to be somewhat difficult to reconcile.
String theory has the unusual property that its dynamical equations don't have free parameters. The dynamics is apparently unique. But there are many many solutions to these equations, and so there's a huge space of parameters from that. In particular, if you go looking for ways of embedding the Standard Model in string theory, all of its dynamical parameters (like the electron mass and Newton's constant) are realized as solution parameters.
In string theory, you don't have to/get to make a choice at all. The dynamics is uniquely determined. It's not exactly a free lunch, but it's a very unusual feature for a physical theory.
Are you saying that it doesn't make any predictions (and is therefore unfalsifiable)?
[1] However measured (cubic meter of paper, maybe?)
As I understand, its the opposite. String theory "predicts" any and every possible observation, then they cherry pick whatever predictions are already accepted as fact to say there is evidence for the theory.
The difference is that the string model doesn't (yet) have any observations which we could use to constrain it in an analogous manner. But in studying it, one would hope to find areas of the theory that indicate where those observations could be made.
The point being, it is not so simple to just look at string theory and say you can a priory determine it is flawed or wrongly motivated. That same kind of reasoning would likely have prevented Planck & Einstein from starting quantum theory.
I'm not sure what this means. Is it different from just making an observation? Eg, "this light in the sky is of this color at that location", or "this object drops at that speed".
No it doesn’t. There are a few good guiding principles that make it possible to build models that turn out to be an accurate description of nature. These guiding principles don’t manifest themselves in a set of axioms of a mathematical theory nevertheless they are there. And they are part of the theory, just not set in stone like the underlying mathematical structure. But that doesn’t matter at all as long as you are doing science and not math.
Take classical EM, measure the masses of the electron and atomic nuclei, and write down a suitable Hamiltonians. Viola, you have an explanation of almost every phenomena that’s relevant in our daily life and way beyond. Similar principles exist in elementary particle physics and lead to standard model.
I think there's also a place for setting aside our prescriptive rulers and looking at String Theory in its own right.
As a programme it has contributed significantly to detangling the intractibilities in quantum field theory. Heck, it apparently even finds applications in such "mundane" applications as condensed matter physics by showing coorespondences between fluids and black holes. As a pure math endeavor, it's contributions to algebraic geometry are hard to miss.
Personally, I think a lot of the "problems" with String Theory only arise when circumscribing it to be a certain kind of cosmological model.
> [Wheeler] would say things like, “In the end, the only law is that there is no law.” There’s no ultimate law of physics. All the laws of physics are mutable and that mutability itself is a principle of physics. He’d say, there’s no law of physics that hasn't been transcended. I saw this, and I remembered my joke about how the laws of physics must be wrong, and I was immensely attracted to this idea that maybe ultimately there actually are no laws of physics. What there is in place of laws, I didn't know. But if the laws weren't 100 percent trustworthy, maybe there was a back door to the stars.
Physical laws are not 'laws' in the sense that nature is required to abide by them. They are simply features of natural behavior that have been so overwhelmingly observed that we treat them as axioms.
An example of this is the 'law' of conservation of mass. Strictly speaking, nature does not follow this law. Nuclear reactions and subatomic interactions do not conserve mass. They conserve other quantities, but not mass in and of itself.
The idea that there is no ultimate law of physics is not novel or interesting. It's obvious on its face, unless you do not properly understand what 'law' means in the context of physics.
The plus side is that you don't have to deal with causality, which is a tricky concept. Hume persuasively argued that causality is neither empirical nor a result of logic. The downside is that all necessity is totally arbitrary. It just so happens ... As such, there is no reason for anything we observe. Just descriptions.
"a+b=7" implies that "a=3 implies b=4", and "b=4 implies a=3", without regard to what causes the other, or what caused the law to be true.
So what I'm trying to say here is that your claim here that causality governs the actual laws of nature is suspect, both because your comment has not been elaborate enough to specify what you mean by causality, and because one of the most popular notions of causality, i.e. temporal causality, seems, to a first approximation, not be a good model of the observable physics: it postulates a temporal cause for the big bang, but no time prior to the big bang is observable.
This is simply wrong. That is not what the term 'law' means in physics.
Scientists will state that B happens BECAUSE of A, when A is thought to be a necessary condition for B. That's the causal implication.
Historically, there has been a multitude of ideas and phenomena that have been labeled as causation. Aristotle, back then, identified four notions of causation, and the modern reader immediately will feel that some of these notions themselves are still too general. When you make a claim like "nature obeys causality", you need to be more precise in what you refer to by nature and causality, else your claim is far too ill-defined to mean much of anyting.
"conservation of mass" is either utterly trivial ("Nothing comes from nothing... except stuff that does") or has grown its asterisks over time.
https://en.wikipedia.org/wiki/Conservation_of_mass#History
It's in high school chemistry textbooks. Typically in the first chapter or two. I'm assuming the audience of this site has taken at least one chemistry class in their life. Whether or not they paid attention is their own problem.
[1] https://www.math.columbia.edu/~woit/wordpress/
And some are not useful except as a mental exercise. Maybe they will become useful at some point, maybe not.
You said it right there. "Almost." We keep on prying and doing experiments, and we can't find any exception. If we've tried hard enough for long enough, we can start to conclude that we're probably getting close to reality. If we pry and we find it's "almost" then we know it's not baked into reality.
When conservation is broken, we name a new form of energy, and (so far), we find that it can by accounted in a consistent, predictable way. (Dark matter is an unsolved problem.
[Citation Needed] Yes, we still don't know what Dark Matter is, but do you understand that dark energy is not dark matter, and the current model for dark energy involves space expanding and more dark energy appearing due to the space expanding? Citing dark energy is tantamount to admitting that conservation of energy isn't universal.
When it comes to fundamental science, a consistent map is the territory.
Arrgh. You're getting your pointers mixed up here. A context where science is the territory would be the study of Science, as in the philosophy of science. When it comes to fundamental reality, Science is the map and fundamental reality is the territory.
In what sense does "fundamental reality" exist?
But you can clearly do science on the technology. People do this with high degrees of success, developing theoretical models with high predictive ability. It's called "reverse engineering." If you're going to retreat into metaphysical mumbo-jumbo, that's up to you. The doing and the results will speak for themselves, and no one will pay attention to the metaphysical mumbo-jumbo obscurantists.
What do you mean by this?
> When it comes to fundamental science, a consistent map is the territory
isn't the case.
Science/empiricism merely produce predictive models; over the last few hundred years, these models have improved dramatically, but they are nonetheless only maps of a territory ("reality"), and it's still fundamentally uncertain that the underlying assumptions (that laws of nature exist/that reality is mappable) are reliable.
> "Map is not the territory" applies to simplifications that omit detail.
Even if we had a perfect model, which we don't (and it's not clear that such a model is obtainable) that could predict everything, it would still be separate from the territory. You might think this is a pedantic distinction, and in your ideal world where we have a unified field theory, it certainly would be, but like I said above, it's not clear that such a thing is obtainable, so it's important to hold onto the distinction lest we forget the fact that we're still sitting on an incredibly young and uncertain foundation.
"Nothing happens in contradiction to nature, only in contradiction to what we know of it. And that's a place to start. That's where the hope is."
Let's take a spin 1/2 in the superposition state |0> + |1> ignoring normalization and then add the rest of the universe including a measuring device, an observer, and all the other bits and pieces of the environment. This state then undergoes unitary time evolution past the point where we measured the spin and the observer had a look at the measuring device.
It now seems to me that if the final state is a definite |0> or a definite |1>, then this measurement outcome must already have been present in the initial state, not necessarily as hidden variables of the spin but somewhere, for example in the micro states of the measuring device. If the final state could indeed be either |0> or |1> independent of the initial state, time evolution would not be unitary, it would not even be a function of the initial state.
The only other option seems to be that the final state is still a superposition and we have to reach for something like the multiverse interpretation to reconcile the fact that we indeed observe a definite final state. So what is the correct or at least common way to think about this? Time evolution is only approximately or sometimes unitary? The measurement outcome is, similar to decoherence, determined by the environment? The final state is still a superposition? Non of those seems to be a particularly attractive choice. Or did I somewhere make a stupid mistake?
This is in contrast to, for example, classical statistical mechanics where individual particles are considered to behave deterministically, but we simply lack the ability to measure their behavior. In (the Copenhagen interpretation of) QM there is no underlying determinism at all.
You might not like this idea (it's certainly non-intuitive), but decades of experiments have shown that the alternatives are all, most likely, wrong.
But here lies the incompatibility I am asking about, time evolution is unitary and is in a sense incompatible with the Born rule stating that different measurement outcomes are possible. You can not have unitary time evolution and different possible measurement outcomes starting from the same initial state, at least not in a really obvious way.
How?
There's other options for getting around the weirdness of the Copenhagen interpretation that aren't ruled out by the data we have, but most of them are even weirder.
I don't want to argue for the many-worlds interpretation, I don't really like - and I am aware that this is a somewhat stupid thing to say about a physical theory. But I also have to admit that it makes sense from a point of simplicity and consistency and compares favorable to other interpretations.
What's wrong with that?
1. Hamiltonian evolution is linear
2. Measurements produce nonlinear projections onto eigenvectors in accordance with the Born rule
Note that this projection is a function of the initial state - but a probabilistic function, so therefore not reversible.
There isn't really a satisfying answer to this question yet. Decoherence explains how the system evolves to a mixture of eigenstates but not the collapse into a single one, nor the Born rule.
I understand what you want to say, but I think it is not correct to call it a function. The term »probabilistic function« does appear in Google results but it seems not to be a common one. I also spent a few minutes looking for a mathematical formalization of a random number generator as a function with no inputs returning a random number adhering to a given probability distribution but could not find anything. Mathematicians seem to be pretty good at avoiding problematic definitions and according to Wikipedia some do this deliberately. The best formalization I could find would be a function from the initial state to a random variable but I was unable to figure out in a couple of minutes how I would mathematically formalize the step from a random variable to a concrete result of a single trail.
Decoherence explains how the system evolves to a mixture of eigenstates but not the collapse into a single one [...]
I never managed to really wrap my head around decoherence, I always only had a quite fuzzy picture of it. But now it is starting to click, it's about the transition from superposition states to probabilistic mixtures, the transition from uncertainty due to superposition to uncertainty due to ignorance.
There are two approaches to answering this question. One of them invokes the concept of "the collapse of the wavefunction" at the moment of measurement: when an observer actually measures the outcome of such an experiment, the universe probabilistically selects one of the possible outcomes as "true" and proceeds from there. This "collapse" process is explicitly non-unitary. You may ask, "What entities qualify as 'observers' to trigger collapse?", and the answer is basically "It's not well-defined." As you might gather from that, it's not clear to me that you can include an "observer" in this sense as part of the overall wavefunction of the universe at all, though perhaps people who have studied the foundations of quantum mechanics in more detail could give a better answer.
The other option is pretty much exactly what you've described in your final paragraph: you don't invoke "collapse of the wavefunction" at all, and the final quantum state of the universe after measurement is indeed a superposition of "|0> and observer who saw '0'" and "|1> and observer who saw '1'". Because anything we'd call an "observer" will be a large, complex system, there will very rapidly be a vast number of tiny, "pseudo-random" differences between the two branches of the wavefunction, ensuring that there won't be opportunities for the two branches to experience significant constructive or destructive interference in the future: they'll evolve pretty much completely independently from then on. (This concept is called "decoherence", which you've made reference to, and I'm definitely not an expert on it, but I'm told it's become quite important in research on quantum computing.) There's still a probabilistic question of which branch of the wavefunction a given observer might experience (and understanding why that happens is an enormously subtle question; I've seen some work by Sean Carroll among others trying to make progress on it), but once a given observer has measured a particular outcome to the experiment, the math of quantum mechanics guarantees that they'll continue to measure consistent results after that. This is more or less the Everett "many worlds" interpretation of quantum mechanics.
As you might gather, I'm partial to the latter interpretation, in part because it's where the math seems to most naturally lead (the first time I felt like I really understood quantum mechanics was after a very math-heavy graduate course taught by Robert Geroch), and in part because I've never been able to make sense of what wavefunction collapse might mean (and never been happy about its violation of unitarity).
https://en.wikipedia.org/wiki/Quantum_Bayesianism
https://arxiv.org/pdf/1003.5209.pdf
I did some more reading and it seems that at least some try to do what I also considered, try to attribute the randomness in the outcome to the randomness and uncertainty in the initial state of the measuring device, observer, and environment. This then raises the question why all kinds of measuring devices produce the same distribution of measurement results if the concrete outcome essentially only depends on the initial state of the measuring device. And this also has the smell of a hidden variable theory where the hidden variables are in the measurement device, would this be compatible with EPR?
I also took away some things to follow up on from your comments on Everett but unlike you I don't really like multiverses and so this will have to wait for some time. I however agree that Everett makes the most sense with regard to completeness and consistency.
It seems likely that the descriptions we formulate in physical theories work because they create a pattern which is isomorphic to patterns we extract in physical measurements—but there's something in the nature of the universe and/or language so that there tends to be many ways to create some linguistic thing which produces exactly the same pattern.
But only if it's the case that we end up with more than one theory which explains the phenomena equally well. That doesn't seem to be what ends up happening. We don't have an equivalent to GR, QM, Evolution, or any other well established, large scale theory.
Positivism sounds closer to math than it does science. And that's because nature is a certain way, which means you probably can't have equivalent theories at sufficiently granular levels.
Perhaps that doesn't cross your threshold for 'sufficient granularity'—but it took quite a bit of time to find the alternate formulations in classical mechanics (after Newton I mean), so just because we don't yet have them for certain more modern theories doesn't mean they aren't forthcoming.
Also, I'm pretty sure there are at least very nearly equivalent formulations of QM, e.g. the de broglie pilot wave stuff (often termed as an alternate 'interpretation', but my understanding is that the differences extend even to the level of mathematical formulation, and are not just some detached reflections on the 'meaning' of the theory or whatever.
[0] https://en.wikipedia.org/wiki/Lagrangian_mechanics
I think the strongest argument for positivism is that you can generate arbitrarily many trivial "different but the predictions are the same" theories from any parent theory just by doing algebra. You can also generate arbitrarily many "the predictions are slightly different but our present experiments can't resolve it" theories from a parent theory by littering it with new, small constants and tiny interactions. Occam's razor will lead you astray about that, too: most of modern physics was at one time a small constant or a tiny interaction.
This is M-theory basically, and Stephen Hawking, among others, has mentioned it as a possible "theory of everything".
The only other possible alternative would be , what, one tiny theory that is essentially simple and minimal in every possible way, yet somehow models everything, in the spirit of ANKOS?
Newton et. al. came along and gave us a much simpler model of gravity and the solar system such that we could toss out the messy nested circle models. (We still can't say that Newton's model is fully "right", but it's certainly simpler.)
The end result is the same, but the paths to get there are completely different.
Not really. The Standard Model makes no prediction about gravity; it makes no claim to. Gravity is so weak that it can be ignored almost everywhere where the other forces come into play: the contribution of gravity compared to electrostatic attraction on the atomic order is smaller than 0.01ZWD is to world GDP... for all of human history. The places where you have to worry about gravity and the other forces at the same time are places where we have precisely no ability to make observations that could distinguish between theories.
But physics does leave out detail. It's an abstraction over many particular instances. Nature isn't a physics equation. An equation doesn't generate a field of force, nor does it have any causal powers.
> We can never know more about reality than what we observe
If that were true, then theoretical physics wouldn't exist. Much of scientific theory involves unobservables, or processes way too long for us to observe. Most of evolutionary history is unobservable. We have to fill in the gaps with a theory explaining the fossil record, genetics, and the organisms around us.
We don't have time machines, nor billion year old cameras.
But over the course of my undergrad, and hours debating with friends, and reading even more, I started to get an uneasy feeling. I decided to go to grad school, partly, because I still held on to the belief that there really was treasure at the end of that rainbow, and that we really could, if we were clever enough, "figure out" how things "really" worked. But, in grad school, it just continued to dawn on me how impossible it was for there to be only One True Theory. One way I thought about it was to regard physics as a program. Even if there were separate theories for different scales, or domains, it didn't matter, you could still regard the whole knowledge base as a single program and the scale and domain, along with physical observables, as inputs to the Physics Program. The output would be predictions for the state of the universe (or some subset, it didn't matter) at some later time, i.e., it would predict later observables' values.
The thing was, I had a hard time finding any logical justification for why there had to be only one program that could take in the known inputs and produce the known outputs. That is, there was no way to logically prove that there could not be multiple equivalent programs that could produce the same output given the same input. I.e., there was no way to logically justify the notion that there could only be One True Physics. That is, the treasure I believed I'd be digging for, didn't not exist, it was just that there was more than one treasure, and anyone could find their own.
This thought diminished some of the romance, so to speak, of the Quest for Truth, so I lost interest, for a time. Enough to stop taking grad school classes and just start working (coding). Maybe one day I'll create a program of my own.
Schrödinger’s theory proved easier to use than Heisenberg’s, in part because it is more intuitive. Furthermore, first Schrödinger and then Paul Dirac proved that the two theories are equivalent. In physics any two theories that make precisely the same observable predictions are observably equivalent. And one of the predominant philosophical views of the age — logical positivism — held that any two observably equivalent theories are really one and the same theory.
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Einstein demanded a clear and comprehensible account of what is going on in the physical world — at all scales — in space and time. Bohr thought that the key to quantum mechanics was the realization that no such thing could be had.
[1] http://bostonreview.net/science-nature-philosophy-religion/t...
http://bostonreview.net/science-nature-philosophy-religion/t...