Given infinite time, is it possible to randomly draw a rational (instead of an irrational) from the interval [0, 1]? And if so, is it possible infinite times?
In this case it does. Describe any effective measure to pick a random sample from the interval and you will have cheated into choosing from the computable reals instead (of which there is a countable amount)
I don't think that's correct. You're describing a limitation of our physical computing devices (or perhaps physical reality itself) as opposed to a theoretical reality. At least as far as I can tell.
Surprising that he could have that intuition in 1935, before the Unruh effect was known of, before AQFT was invented, and really before most of QFT was formulated.
Hawking radiation and the Unruh effect both rely upon the fact that there is no absolute Hilbert space in which QFT unfolds, the Hilbert space used is observer dependent.
For example, in the Unruh effect an inertial observer sees the vacuum in their Hilbert space as having no particles. However, a uniformly accelerating observer sees that same vacuum as containing particles.
This state of affairs is addressed via algebraic quantum field theory (AQFT), which doesn't take a Hilbert space as the primary thing one starts with, but views Hilbert spaces as derived concepts.
reading about AQFT, found this: "no examples are known of AQFT-compatible interacting field theories, and in particular the standard model cannot at present be made AQFT compatible". Should I continue to read?
Not all things are possible, only potentially possible ones.
If you take all the numbers between zero and one, you will find an endless supply of distinct numbers but none of them are 3.
Experimental physics takes it one step back: it's all about setting bounds on what is potentially possible. A model of the universe might say that the numbers are between zero and one, but there's some other model that says there could be 3s.
Note that this epistemic uncertainty is not the same thing that the article is focused on. The article is mostly about one specific model, which itself has some randomness baked on.
If so, this has interesting implications for the cause of the baryon asymmetry problem.
Either the baryon number started non-zero and was conserved; or non-conservation of baryon number (protons vs antiprotons etc) have to be paired with equivalent non-conservation of lepton number (electrons vs positrons etc); or it can happen without simultaneously balancing the lepton number, and charge isn't conserved.
Unfortunately (for me) those implications are above my level. I can't usefully converse with an LLM about it, as this isn't a domain I know well enough to detect if it's making stuff up.
CPT symmetry isn't conserved, so that's not necessarily a given.
We don't know the mechanism which generates the gauge symmetry that makes charge discrete or generates conservation laws from symmetries, so it's risky to be too prescriptive about what is and isn't possible.
In the limit you can imagine a meta-technology which manipulates the mathematical structures that generate reality instead of just assuming the rules are fixed. That might or might not be possible, but the rules have to come from somewhere and there's no absolute guarantee they're hardcoded.
So, what I meant to say was that using the computational gadget from physics, none of the branches will violate conservation of charge.
However, my post sucked and I didn't get around to emphasizing that. In quantum mechanics, it's possible for some state to have zero probability, and it's those probabilities that we're talking about everything being possible.
There's also the epistemic side where we know that there's a chance our theories are wrong in any given way. Those can't go to zero based on our model since the whole point is we're not restricting to a model. BTW, I really like your example as a good, clean limiting case.
-------------
I'm sure people have come up with theories that violate conservation of charge, but they'd have to break U(1). I don't know what conservation CPT would break, if any; Noether's theorem shouldn't apply to it as a discrete symmetry.
The C in CPT is not only a change f charge but also a change of electron <---> positron, and quark <---> antiquark, and ...
The conservation or charge comes from the U(1) gauge symmetry. That is almost obvious if you ignore the mixing with the weak interaction, but after the mix you still have a U(1) gauge symmetry anyway.
Mass isn't close to being conserved. If an electron and positron annihilate, they become two massless photons, for example. You don't need to invoke an expanding universe.
In an expanding universe, energy isn't conserved. (Unless we do the trick we always do with energy and just define it to be conserved https://youtu.be/lCgKTpIzjRk?t=174 )
I don't know exactly why you think this applies to charge conservation. The U(1) symmetry is where charge conservation comes from and it isn't affected by an expanding universe.
There is "rest mass" and "relativistic mass". The GP is talking about "rest mass" that is not conserved even in simple examples.
Most modern books try to eliminate "relativistic mass" because it's misleading, for example is good to calculate acceleration perpendicular to the movements (for example in a cyclotron) but it's not good to calculate acceleration in the direction of the movement.
So most modern books they call the same idea just "energy" and use that "energy" to calculate gravitation. "Energy" is conserved in special relativity and almost conserved in general relativity.
But the "relativistic mass" is useful in some problems and is widespread in popular culture and don't ask about the weird parts of the mass of the proton, so it's difficult to kill the idea.
I just read the article and can not make any sense of your comment. It does not relate to anything of the actual article content (but only superficially to the title itself).
I think there is a possible future where "I" am a talking cucumber, though?
Ignoring that you have to give up a sense of personal identity at this point, there is nothing in the laws of physics that says the matter that makes up what we're presently calling me can't morph into a talking cucumber with a brain with my memories in it. It's just absurd number of extremely specific things that have to happen out of an ever more absurd number of possible things to happen.
Indeed such a strange configuration of matter would arguably no longer be "you", but I think an even more immediate point of philosophical incoherence is that it would certainly not be a cucumber. [Cucumber != cucumber] => false, QED.
If talking cucumber was too pedestrian for you, we could add stipulations until your intuition collapses. Perhaps, starting next week, the Earth begins to spontaneously turn into raspberry custard on Tuesdays. Perhaps the entire universe turns to custard! Just think of it - billions of lightyears of custard in every direction. Whoops, did I say billions? Too grounded! Let's make it a googolplex. And a single lone piece of rhubarb, floating somewhere in the middle of it all...
...sorry, couldn't resist. Joking aside, while we can quibble about the boundaries of the possible, the fact remains that there are boundaries - at least, if we're still talking about known physics. No evolution of the universal wave function will lead to a world where pi suddenly equals 3.
Yes! But at some level, doesn’t it kind of get blurred?
That is, we are trying to come up with rules describing the underlying rules, right? The world isn’t made of stuff, it’s made of rules, right? Or math? Just not the same notation, at least.
Help! I feel like I’m falling off a metaphysical cliff!
You’ve probably been reading a lot of physicists that believe in the Many Worlds view. Nature did a poll of physicists last year[1] and it’s still only the third most popular interpretation, behind the Copenhagen Interpretation and information-based interpretations like QBism.
Yeah, this is also why I said many and not most :)
But I think if you ask experts (philosophers of nature, people into foundational quantum mechanics) most of them would be many worlds proponents.
I finished my masters in a quantum computing lab. The reality is that most physicists just don't care about foundational QM, and stick to the Copenhagen interpretation. To me the Copenhagen Interpretation does not even count as a complete theory. It just stays very fuzzy on when wave function collapse happens, which makes it impossible to falsify.
There are issues with how that question was worded
>Questions: 'Which of the following, in your opinion, provides the best interpretation of quantum phenomena and interactions?'
in what do they mean by 'best'. For calculating and doing practical physics then sure Copenhagen Interpretation. But for what is the underlying reality of the universe you might get a different answer.
Copenhagen has an observer - your particle goes all ways through both slits deterministically following Schrodinger type stuff until 'the observation' when a dice is effectively rolled to choose one. But how to the laws of physics know the bunch of atoms far away is in the form of an observer having a look? It would be cleaner laws of physics wise for them to ignore that, resulting in multiple observers seeing different outcome. But for calculating, rolling a die is easier.
That’s a misunderstanding of what an observer is. An observer is better thought of as an interaction which distinguishes between states; there need not be a conscious observer. For example, long wavelength light interacting with the electrons in the double slit experiment does not affect the interference pattern because long wavelength light interacts with both states of the superposition in the same way. Short wavelength light has different physical characteristics than long wavelength light and interacts with one state of the superposition differently than the other, resulting in decoherence and the wave function “collapsing”.
There are other problems with the Copenhagen Interpretation, but this isn’t one of them
I know, there's some tricky business with energy conservation (I'm not pretending I understand it all though). It is for me an easy analogy though. Even Hilbert space has to stick to some rules!
Yes, and in a more general way Noether thm applies in QM/QFT as well (energy conservation is just a special case). Symmetries become operators acting on the Hilbert/Fock space (ie representation).
With the caveats:
- anomalies-> symmetries/conservation broken by quantum noise (has to be cancelled in valid theories)
- Heisenberg’s incertitude
Sure, that could be a reason why it isn't conserved. My point wasn't that we know ways it isn't conserved, only that theoretical understanding isn't universal or necessarily true.
"Hilbert space is the space of all possibilities." -- Wolfgang Ketterle
He gave this pithy summary of his answer to a memorable discussion in a Nobel Laureate panel about what it actually means to explore Hilbert space, from a more practical perspective. That discussion from may be a good complement to the title article of this thread.
Others in this thread already correctly noted that just because something --- 'thing' more precisely defined as some action that results in an observable outcome --- exists in Hilbert space doesn't mean it's possible. But what Ketterle and others were getting at is that, as we make new theories and experiments, we can explore more of Nature and what's possible within, guided by the structure that Hilbert space could give to our questions' outcomes.
That being said, Ketterle explains it much better than I do.
69 comments
[ 2.2 ms ] story [ 36.9 ms ] threadDisclaimer: total armchair philosophy.
But then again, he was John von Neumann.
For example, in the Unruh effect an inertial observer sees the vacuum in their Hilbert space as having no particles. However, a uniformly accelerating observer sees that same vacuum as containing particles.
This state of affairs is addressed via algebraic quantum field theory (AQFT), which doesn't take a Hilbert space as the primary thing one starts with, but views Hilbert spaces as derived concepts.
-- David Hilbert.
Experimental physics takes it one step back: it's all about setting bounds on what is potentially possible. A model of the universe might say that the numbers are between zero and one, but there's some other model that says there could be 3s.
Note that this epistemic uncertainty is not the same thing that the article is focused on. The article is mostly about one specific model, which itself has some randomness baked on.
Either the baryon number started non-zero and was conserved; or non-conservation of baryon number (protons vs antiprotons etc) have to be paired with equivalent non-conservation of lepton number (electrons vs positrons etc); or it can happen without simultaneously balancing the lepton number, and charge isn't conserved.
Unfortunately (for me) those implications are above my level. I can't usefully converse with an LLM about it, as this isn't a domain I know well enough to detect if it's making stuff up.
We don't know the mechanism which generates the gauge symmetry that makes charge discrete or generates conservation laws from symmetries, so it's risky to be too prescriptive about what is and isn't possible.
In the limit you can imagine a meta-technology which manipulates the mathematical structures that generate reality instead of just assuming the rules are fixed. That might or might not be possible, but the rules have to come from somewhere and there's no absolute guarantee they're hardcoded.
However, my post sucked and I didn't get around to emphasizing that. In quantum mechanics, it's possible for some state to have zero probability, and it's those probabilities that we're talking about everything being possible.
There's also the epistemic side where we know that there's a chance our theories are wrong in any given way. Those can't go to zero based on our model since the whole point is we're not restricting to a model. BTW, I really like your example as a good, clean limiting case.
-------------
I'm sure people have come up with theories that violate conservation of charge, but they'd have to break U(1). I don't know what conservation CPT would break, if any; Noether's theorem shouldn't apply to it as a discrete symmetry.
The C in CPT is not only a change f charge but also a change of electron <---> positron, and quark <---> antiquark, and ...
The conservation or charge comes from the U(1) gauge symmetry. That is almost obvious if you ignore the mixing with the weak interaction, but after the mix you still have a U(1) gauge symmetry anyway.
In an expanding universe, energy isn't conserved. (Unless we do the trick we always do with energy and just define it to be conserved https://youtu.be/lCgKTpIzjRk?t=174 )
I don't know exactly why you think this applies to charge conservation. The U(1) symmetry is where charge conservation comes from and it isn't affected by an expanding universe.
There is "rest mass" and "relativistic mass". The GP is talking about "rest mass" that is not conserved even in simple examples.
Most modern books try to eliminate "relativistic mass" because it's misleading, for example is good to calculate acceleration perpendicular to the movements (for example in a cyclotron) but it's not good to calculate acceleration in the direction of the movement.
So most modern books they call the same idea just "energy" and use that "energy" to calculate gravitation. "Energy" is conserved in special relativity and almost conserved in general relativity.
But the "relativistic mass" is useful in some problems and is widespread in popular culture and don't ask about the weird parts of the mass of the proton, so it's difficult to kill the idea.
Ignoring that you have to give up a sense of personal identity at this point, there is nothing in the laws of physics that says the matter that makes up what we're presently calling me can't morph into a talking cucumber with a brain with my memories in it. It's just absurd number of extremely specific things that have to happen out of an ever more absurd number of possible things to happen.
If talking cucumber was too pedestrian for you, we could add stipulations until your intuition collapses. Perhaps, starting next week, the Earth begins to spontaneously turn into raspberry custard on Tuesdays. Perhaps the entire universe turns to custard! Just think of it - billions of lightyears of custard in every direction. Whoops, did I say billions? Too grounded! Let's make it a googolplex. And a single lone piece of rhubarb, floating somewhere in the middle of it all...
...sorry, couldn't resist. Joking aside, while we can quibble about the boundaries of the possible, the fact remains that there are boundaries - at least, if we're still talking about known physics. No evolution of the universal wave function will lead to a world where pi suddenly equals 3.
It reminds me of that scene where the guy is upset about the ratio of ingredients in his wife's dessert:
https://www.youtube.com/watch?v=mRp-763aMy8
(Note that the author many times is not the person that choose the title.)
That is, we are trying to come up with rules describing the underlying rules, right? The world isn’t made of stuff, it’s made of rules, right? Or math? Just not the same notation, at least.
Help! I feel like I’m falling off a metaphysical cliff!
[1] https://gizmodo.com/app/uploads/2025/07/favored-explanations...
But I think if you ask experts (philosophers of nature, people into foundational quantum mechanics) most of them would be many worlds proponents.
I finished my masters in a quantum computing lab. The reality is that most physicists just don't care about foundational QM, and stick to the Copenhagen interpretation. To me the Copenhagen Interpretation does not even count as a complete theory. It just stays very fuzzy on when wave function collapse happens, which makes it impossible to falsify.
>Questions: 'Which of the following, in your opinion, provides the best interpretation of quantum phenomena and interactions?'
in what do they mean by 'best'. For calculating and doing practical physics then sure Copenhagen Interpretation. But for what is the underlying reality of the universe you might get a different answer.
Copenhagen has an observer - your particle goes all ways through both slits deterministically following Schrodinger type stuff until 'the observation' when a dice is effectively rolled to choose one. But how to the laws of physics know the bunch of atoms far away is in the form of an observer having a look? It would be cleaner laws of physics wise for them to ignore that, resulting in multiple observers seeing different outcome. But for calculating, rolling a die is easier.
There are other problems with the Copenhagen Interpretation, but this isn’t one of them
Subtle difference, but energy conservation for example has to be adhered to.
It just somehow always balances out in the end.
With the caveats: - anomalies-> symmetries/conservation broken by quantum noise (has to be cancelled in valid theories) - Heisenberg’s incertitude
I'm not sure we can extrapolate that out and say that can never be violated, only that we've never seen it happen.
I particularly like the one with David Wallace.
He gave this pithy summary of his answer to a memorable discussion in a Nobel Laureate panel about what it actually means to explore Hilbert space, from a more practical perspective. That discussion from may be a good complement to the title article of this thread.
Others in this thread already correctly noted that just because something --- 'thing' more precisely defined as some action that results in an observable outcome --- exists in Hilbert space doesn't mean it's possible. But what Ketterle and others were getting at is that, as we make new theories and experiments, we can explore more of Nature and what's possible within, guided by the structure that Hilbert space could give to our questions' outcomes.
That being said, Ketterle explains it much better than I do.
Ketterle's answer in context: https://youtu.be/DNhmYkTW_jI?t=4220