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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.

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marked as duplicate by John Rennie, Luboš Motl, Manishearth Dec 14 '12 at 22:47

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I guess it would just be a "classical physics" box, and would suggest a universe where physics was just that. –  santa claus 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? –  user1708 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
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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? –  user1708 Dec 14 '12 at 10:16
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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
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2 Answers 2

(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.

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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. –  user1708 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
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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. –  user1708 Dec 14 '12 at 10:45
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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
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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.

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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. –  namehere Dec 14 '12 at 23:14
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