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Could the Heisenberg Uncertainty Principle turn out to be false?

Thought Experiment

Ponder, for a moment, if I had a cube with 10cm sides which I'll name The Box. By some unexplained means (future technology, magic, the work of deities, insert whatever you want), The Box had a special property: it would determine with absolutely zero uncertainty* the momentum of every particle inside of it (and only those inside of it). You can imagine it hooked to a computer with a listing of each particle and it's momentum, or whatever you like.

Edit: I've been informed that perhaps zero uncertainty is unattainable in the momentum, so if this is the case then perhaps simply "Known with enough certainty such that the combination of the momentum uncertainty with the size of the box yields $\sigma_m \sigma_x < { ħ \over 2}$, or in other words, the pair are known with more certainty than the Heisenberg's Uncertainty Principle says can be known."

  • What would this device be likely to cause in our universe, with our physical laws? Since by the Heisenberg's Uncertainty Principle (or the wavefunction commutation) their positions cannot be known, then it would seem to follow that I can no longer know they are in The Box, or indeed anywhere in the universe. But I know they are in The Box, because they are on the screen. Even if some small amount of uncertainty about The Box's location can be shown, because I have perfect certainty of the momentum, nothing about it's position can be known (by the HUP/WC) - so knowing anything about it is a violation.

  • Would this cause all particles to leave The Box once it was activated, leaving a perfect vacuum, devoid of even virtual particles (since once they popped into existence, I could determine their momentum and that they were inside The Box)?

  • If it caused a perfect vacuum inside of it, then it would seem that such a box would indeed not break HUP/WC at all - since I would still not have any knowledge of momentum and position of any particles. Could one argue that it is compatible with our laws of physics then, provided that activating it caused the expellation of every particle inside of it?

  • What would the existence of a region of true vacuum do to the surrounding matter, if anything at all?

  • Or would nothing out of the ordinary happen whatsoever, and it just turns out that the box 'beats' the HUP / defies the wavefunction commutation? Or perhaps, "forces classical behavior inside The Box"?

  • Would the confirmed existence of such a box force the reconsideration of QED Theory? As in "Well, that checks out, so I guess Quantum Theory wasn't a complete model of our universe"? Or would we just refine it, changing the details of the HUP/WC somewhat? (Stated another way: would we still have QED if HUP was proven false)

  • Other alternatives to consider? Details that I missed in formulating the thought experiment? Helpful suggestions?

Note: if you're not interested in considering the thought experiment, then don't. Wild conjectures will be fine, and the purpose of the question is to assist my understanding of the implications of the HUP/WC. "The Box couldn't exist" or "That can't happen" isn't helpful or relevant. I'm asking that consideration of it's existence and validity is already accepted (it's accurate and not just making things up), not asking for how to build one or why we haven't made it yet.

Edit

It looks like a number of the comments are getting at this central point, but not explaining it - just asserting it. Please add an answer to provide a description of what you mean, and it would likely be the answer I'm looking for:

"if you really assume nothing else than that you have a Universe in which HUP refuses to hold, it's clearly too little information to deduce anything else. But in the very same comment, you're also asking whether QED would have to be discarded. You bet. All of modern physics would have to be discarded." - Luboš Motl

What do you mean by 'modern'? Does Gravity have to go? Relativity? Big bang cosmology? Rocket Science? The Laws of Thermodynamics? String Theory? All of QM? I want to know what specifically will be contradicted, and why.

Now, please don't strawman my experiment into HUP not holding at all, everywhere - in other words, HUP being false in all cases, places, and times - I'm not asserting that (just doubting the ultimate certainty of the truth of HUP). At a minimum, HUP does not hold inside The Box, yet it very well may hold everywhere else in the universe. Given this, it seems to me that QM would not necessarily be contradicted, and could easily be saved on a basic level into something analogous to Particles can be represented by a wavefunction everywhere that is not inside of The Box, and thus QM is not contradicted, just refined.

Given this case, is it still your position that the very existence of The Box invalidates all of 'modern physics'? Please be clear on what that means.

Community
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Ehryk
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  • I guess it would just be a "classical physics" box, and would suggest a universe where physics was just that. – Pricklebush Tickletush Dec 14 '12 at 10:04
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    Consider this thought experiment; 3+2=77, pigs can fly, the moon is made of cheese and 'everything everyone has ever learned is false', then what is the price of a BigMac? – TROLLHUNTER Dec 14 '12 at 10:05
  • @Holowitz - then there's more to addition than previously discovered, our theories on flight are incomplete, the lunar colonies will have plenty to snack on, we're all wrong, and $3.59. Your comment is precisely what I took time above to distinguish as unhelpful, and you clearly aren't interested in considering it - so why bother commenting? – Ehryk Dec 14 '12 at 10:09
  • @AlecS So would you then take the existence of such a box in our universe to mean that our universe is wholly classical? Or just classical inside the box? If so, why would it appear to be Quantum Mechanical when really being classical? How about making it an answer? – Ehryk Dec 14 '12 at 10:14
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    No thats not all, the whole process of reasoning breaks down if you have a contradiction, you can conclude anything. Your question refers to 'our physical laws', what are those when everything is false? – TROLLHUNTER Dec 14 '12 at 10:16
  • Dear @Ehryk, I think that Holowitz's task is completely analogous to yours, indeed. And your solution to Holowitz's problem is just wrong, or cherry-picked, to say the least. As he correctly says, if the assumptions are contradictory, then everything goes. 3+2=77 implies 2+2=4 but it also implies 2+2=5, and everything else. Your choice of conclusions that "all dreams may come true and physicists are stupid and should be ignored" given the assumptions only shows your bias. One can also deduce that "physicists are kings and even swimming is impossible", or anything else, from the assumptions. – Luboš Motl Dec 14 '12 at 10:30
  • And just to be sure, it would already be bad if you were asking about a different world where some well-established laws of this Universe don't hold. Saying just that the world is "different" doesn't specify how it actually behaves. But your scenarios are worse than that - they're logically contradictory. For example, you want to consider QED without the uncertainty principle, and so on. But the Q in QED means "quantum" and it means that the uncertainty principle and related assumptions are assumed to hold in QED. So if you also assume that the UP fails, it's a contradictory set of assumptions – Luboš Motl Dec 14 '12 at 10:35
  • I have only made one assumption: the existence of a box within which HUP is violated. YOU have assumed HUP/QED, so you are then finding a contradiction. I have not, nor am I maintaining that QED holds - indeed I asked what it would mean for QED - would it be refined, or discarded? – Ehryk Dec 14 '12 at 10:37
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    @Ehryk: if you really assume nothing else than that you have a Universe in which HUP refuses to hold, it's clearly too little information to deduce anything else. But in the very same comment, you're also asking whether QED would have to be discarded. You bet. All of modern physics would have to be discarded. But no one can tell you what it would be replaced by – most likely, some classical theory, but no details can be determined – simply because you clearly haven't provided enough information. – Luboš Motl Dec 14 '12 at 10:40
  • This is more pointed and specific question to help illuminate implications of such a scenario. At the core they've got the same concept in mind, but a different approach. To clarify then - IF The Box existed, all modern physics is out the window? ALL of it? What's modern mean? Electricity, gravity, transistors, magnetism, string theory, big bang cosmology? What specifically would have to go, besides just QED? Why does all QED have to go? – Ehryk Dec 14 '12 at 10:45
  • Ehryk, concerning the note you added: "Note: if you're not interested in considering the thought experiment, then don't." This is a completely invalid description of our interactions. We were interested in your thought experiment and we immediately solved it and told you what it implied. What happened later was that you were apparently not interested in the answers or satisfied with them, perhaps because of some boundaries you are not willing to transgress even if it's required by pure logic. – Luboš Motl Dec 14 '12 at 11:02
  • ... what it implied given that the HUP holds, yes. It may not under all conditions, everywhere, at all times, and clearly not in the thought experiment I provided. Further, QED isn't 'based on' HUP, HUP comes from part of QED. It seems a reasonable question to ask why one could not just 'refine' QED such that the HUP is gone sometimes under certain conditions (sort of what relativity did to Newtonian motion, not discarded it). You're not fully considering it, then acting as if you are. I didn't ask 'What if P and not P'. – Ehryk Dec 14 '12 at 11:04
  • ". I'm asking that consideration of it's existence and validity is already accepted " - Aren't you asking too much here? Since HUP is a basic result in QM, if you remove QM how can you use QM to speculate about what would happen in a context where QM didn't apply? – RedGrittyBrick Dec 14 '12 at 11:24
  • Don't be too harsh on Ehryk... I think he just doesn't understand the matter which he's dabbling on too much so he posted an apparently contradictory answer. Come'on, it isn't THAT bad. Just explain the concepts to him! – resgh Dec 14 '12 at 12:16
  • @RedGrittyBrick are you saying that HUP and QM are synonymous? What do you mean by 'basic result'? One way to look at this would be "What would need to be true if the universe was really classical", but that's only provided the rejection of HUP invalidates all of QM, which if it is true I'd like to know why. (Why can't QM be refined such that HUP isn't universal under all conditions, times and places?) – Ehryk Dec 14 '12 at 16:27
  • @Ehryk: HUP "arises from the wave properties inherent in the quantum mechanical description of nature." - Can you revise your question to just ask something like "How is HUP inherent in QM"? (it might be better as a new question given the number of comments already) – RedGrittyBrick Dec 14 '12 at 16:36
  • P.S. Derivation of the Heisenberg Uncertainty Principle – RedGrittyBrick Dec 14 '12 at 16:48
  • @RedGrittyBrick that derivation operates on the assumption that particles not only can be represented as waveforms SOMETIMES, but rather they are completely represented by the wavefunction, at all times, places and conditions. What if a wavefunction did not represent the particles inside The Box? HUP would not then be an inherent property. – Ehryk Dec 14 '12 at 21:21

2 Answers2

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(Classical) momentum can be any real number, and most real numbers dont have a finite description. So already there is a (non-relevant) problem of how you can know the momentum with infinite precision. So lets say we try to measure with arbitrary precision the momentum of particle 1, then we know $a-e<p_1<a+e$, for some value e, as we perform our measurements we can decrease e, however if you do so you you need more and more energy to probe your particle and lower e, and since any kind of box is finite, eventually you'll reach an energy where you cant know for certain that your particle is inside the box.

TROLLHUNTER
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  • I suppose what I meant rather than 'with infinite precision' was really 'precise enought that in combination with the size of the box, $\sigma_x \sigma_p < \frac{ħ}{2}$, in clear violation of HUP. In other words - precise enough that HUP is no longer true. – Ehryk Dec 14 '12 at 10:25
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    Yea, well you have to start measuring with some e that satisfyes HUP, then when you increase the energy to try to violate HUP, your bound to push the particle out. – TROLLHUNTER Dec 14 '12 at 10:27
  • Where did energy get brought into the mix? Why does it require energy or probing to 'be knowledgable' of a numerical value? Perhaps the box is so sensitive to bouncing that the momentum inside of it can be determined by reading the information from the bounces, not throwing energy at the particles. – Ehryk Dec 14 '12 at 10:33
  • @Holowitz: it is a wrong answer to your strange question because you can't make these logical steps just from the assumption that HUP is violated. In a Universe without HUP, it could very well be possible to reduce the error margin arbitrarily even with finite energy. After all, that's how it worked in classical physics where arbitrarily accurate devices could have been a priori arbitrarily light and low-energy. As Ehryk says, minimal energies needed for a precision etc. only entered physics with quantum mechanics, with the HUP. They didn't exist before that. – Luboš Motl Dec 14 '12 at 10:43
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    Right I am assuming HUP holds, just rying to tell him what would happend if you 'tried to violate it' by more and more precise measurements. – TROLLHUNTER Dec 14 '12 at 10:45
  • We have already told you that you are assuming both that HUP holds and HUP fails which is an inconsistent set of assumptions, and one may deduce any statement out of an inconsistent axiomatic system. Otherwise the momentum of a particle confined to a potential well of size $L$ (inside an otherwise empty space, not a periodic one) is uncertain up to $\hbar/L$. You can't measure the momentum more accurately because indeed, states with more well-defined values of the momentum are inevitably outside the box with a nonzero probability. – Luboš Motl Dec 14 '12 at 10:46
  • At the center of this, I'm challenging the nearly universal assumption of the validity of HUP, everywhere, under all circumstances, at all times and conditions. I had hoped that asking this in the form of a Proof by Contradiction, that somehow by accepting the invalidity of HUP there is something more contradictory that MUST be accepted (other than HUP itself). – Ehryk Dec 14 '12 at 10:47
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    Dear Ehryk, HUP isn't a nearly universally valid assumption. This would be a huge understatement. It is a universally valid assumption, everywhere in modern physics, at all times and conditions. It's a pillar of what we know about Nature. – Luboš Motl Dec 14 '12 at 10:49
  • We haven't investigated everywhere, all times, or all conditions - indeed a scarce quantity of each. That's why it seems like an assumption from my perspective, especially with the 'unknowable' assertion it contains. – Ehryk Dec 14 '12 at 10:51
  • We don't need to investigate "everywhere and at all times" to be sure that a principle holds. It's simply not how science works. If we look at 1,000,000 random places in the Universe and they obey a principle P, all of them, then we can conclude, at a high confidence level, that the probability that the fraction of the places where P is violated is extremely small, smaller than something... At any rate, the evidence shows that the principle always holds and your frantic efforts to deny it only mean that you're denying the evidence, you're really lacking the required scientific integrity. – Luboš Motl Dec 14 '12 at 10:56
  • At no point does one determine that 1,000 is the requisite number of places to look, and decide that is enough and the search is over. It seems to me that unwillingness to CONSIDER THE POSSIBILITY that the 1,001st place does NOT hold lacks scientific integrity. – Ehryk Dec 14 '12 at 10:59
  • Holowitz: I understood your intent and removed the downvote. ;-) – Luboš Motl Dec 14 '12 at 11:04
  • ... nor am I denying HUP, or claiming to experimentally be able to disprove it. I'm just 'accepting with a high level of certainty', and then asking about the other possibility. Accepting it to a high level of certainty is MUCH different than accepting it as TRUE in all cases, everywhere, at all times. So what if it's not? Why isn't it even worth considering? – Ehryk Dec 14 '12 at 11:18
  • Dear @Ehryk, nope, your question actually requires the readers to assume that the HUP fails and the world is still a consistent place. You haven't asked whether the HUP may fail. The answer would really be No and there would be explanations – there can't really be any HUP-violating framework of physics compatible with the known facts, aside from supernaturally fine-tuned "conspiracy theories" (like we are in the Matrix). But you were not interested in them and you are still not interested in them. You only want to hear confirmations of your invalid assumption that the HUP may be wrong. – Luboš Motl Dec 14 '12 at 11:23
  • @LubošMotl I ask the considerations of a consistent, HUP-less world in search of an argument by contradiction that is more fundamental that must be the case - like "Then gravity doesn't exist, so the HUP MUST be true". You have said that all modern physics would be invalidated, could you add an answer where you clearly define what 'modern physics' includes and does not, and summarize what would have to be jettisoned and why (gravity? big bang cosmology?)? I'm still unconvinced that HUP==QM, and that QM can't be refined in a way that HUP is not ALWAYS true (not necessarily always false). – Ehryk Dec 14 '12 at 16:37
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In Quantum Physics, momentum is not a number. Instead, it is an OPERATOR acting on the 'state' of the system. If an object is to have a completely definite momentum, it must be in something known as a momentum eigenstate. But such states have a special property: their probability of being at anywhere is not one. Thus these states are unphysical and simply forbidden by Quantum Physics, presumably a stronger prohibition than you previously thought.

resgh
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  • Then what does it mean to 'determine momentum' in QM? What is $\sigma_m$ in $\sigma_m \sigma_x = {ħ \over 2}$? How does one 'know' an operator? I don't understand what knowing an operator would look like - so to relate it to this metaphor, what would the computer hooked to The Box display for the (values? vectors?) of $\sigma_m$? – Ehryk Dec 14 '12 at 21:23
  • It should be an inequality... Anyways it means a measure of the standard deviation of momentum. The other one is the standard deviation of position. In quantum mechanics the idea is that say the state of the system is $\psi$. We have a momentum operator $P$ such that if a particle 'has momentum' $p$ then the relation $P\psi = p\psi$ hols. The states for which this holds, as mentioned, are unphysical. The computer could give you many things, depending on what the Box detects, the implementation... But they are all unphysical. – resgh Dec 14 '12 at 23:14