# I Why isn't tunnelling considered proof of hidden variables?

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1. Jan 18, 2017

### scifimath

When I hear that mass of a particle has managed to hop through a solid barrier ..it tells me that the mass was a variable and not physical at the time.

2. Jan 18, 2017

Staff Emeritus
Is there a question in there? All I see is an incorrect statement. If you have a question, please ask it. If you are trying to learn by making incorrect statements hoping they will be corrected, please don't. It's slow, inefficient and makes the experts cross.

3. Jan 18, 2017

### scifimath

oh boy, did I hit a nerve with this? If you don't want to consider the contents of my post, then just answer the title question?

4. Jan 18, 2017

### Staff: Mentor

There's only one answer to the title question: "How on earth could anyone possibly imagine that tunnelling is proof of hidden variables?" I expect that we will all agree that that is a completely unhelpful, unsatisfactory, and even insulting answer... I certainly don't think it's a good answer.

So let's back up a bit. A hidden variable theory is one that identifies quantities (the "hidden variables") that we cannot directly observe (perhaps in principle, perhaps just because we don't know how to build good enough lab equipment) that obey laws that we may or may not know (depending on the specific hidden variable theory that we're considering). The results of applying these laws to these quantities is that the physical system will end up obeying the probabilistic predictions of quantum mechanics, and therefore the hidden variable theory is the "real" reason why quantum mechanics works.

Perhaps the best example of a successful hidden variable theory is the explanation for the classical ideal gas law $PV=nRT$. Every gas obeys that law (as a really good approximation), but why? It turns out that the hidden variable theory behind that law is ordinary Newtonian mechanics: If you could know the position and velocity of every molecule of the gas (these are the hidden variables), then Newton's laws applied to these particles will lead to the ideal gas law.

It's not at all clear to me how quantum tunnelling (which does NOT say that the mass hops across a barrier, it says that if there is a non-zero probability of finding the particle on either side of the barrier, then you may find the particle on either side of the barrier) can only be explained by saying that such an analogous hidden variable theory must exist for quantum mechanics.

Last edited: Jan 18, 2017
5. Jan 18, 2017

### scifimath

Quantum tunneling does not say mass hops across a barrier, but the experiment can display this result ..so just ignore that fact? You tell me a hidden variable is one in which identified quantities can't be directly observed ..well, we can't observe the quantity of mass a particle has while in superposition. The equations are satisfied because of this hidden variable, not because mass is physically there.

6. Jan 18, 2017

### Staff: Mentor

Really? It says the particle can go from one side of the barrier to the other. The particle has mass. So if the particle hops across, so does the mass it has. What's the problem?

Why not?

It might help if you unpacked your description a little more: "in superposition" of what states? (Hint: they're not states with different masses.)

7. Jan 18, 2017

### scifimath

cool, so you believe in hidden variables?

8. Jan 18, 2017

### Staff: Mentor

I don't know what you mean by "hidden variables". That's why I'm trying to get you to give more details about the theoretical model you are using. I suspect it is not the correct one, but I can't tell without more information.

9. Jan 19, 2017

### scifimath

I'm using the one that allows hidden variables. You aren't going to like this, but I don't think anything while in any type of superposition event has physical mass. Mass is held as a hidden variable value while the particle is in the form of energy (waves).

10. Jan 19, 2017

### Staff: Mentor

Unfortunately that doesn't help. Can you give specific references--textbooks or peer-reviewed papers--that you are getting your understanding of QM from?

11. Jan 19, 2017

### Staff: Mentor

I'm not sure if it is appropriate on I-level questions, but in case you (or someone else) want(s) to take a closer look on the underlying theory, or the meaning of hidden variables, here are some online sources:

http://quantummechanics.ucsd.edu/ph130a/ - QM theory (UCSD)

A Hidden Variables Approach to Quantum Mechanics (a Dissertation): http://www.imperial.ac.uk/media/imp...sertations/2009/Robert-Dabin-Dissertation.pdf (Imperial College London)

Some thoughts on Bell's theorem: Hidden variables and hidden time in quantum theory: https://arxiv.org/ftp/quant-ph/papers/0504/0504089.pdf (Russian academy of science)

12. Jan 19, 2017

### Staff: Mentor

Everything is always in some "type of superposition", because every quantum state is a superposition in some basis. There is no difficulty at all in defining the mass of something, no matter what superpositions are needed to describe its state.

This and some of what you've said in your other threads suggests that you are still misunderstanding what a quantum particle is. You'll find plenty of non-serious sources talking about how something can be a particle or a wave, or is a particle when it is observed and a wave otherwise, but that's just not what's going on. It is ALWAYS a wave.

You aren't to make much progress until you drop some of your misunderstandings about how QM works. I've suggested Susskind in another of your threads, and @fresh_42 has suggested some excellent but more advanced sources. Giancarlo Ghirardi's "Sneaking a look at god's cards" is also quite good, although aimed at a B-level thread instead of I.

Last edited: Jan 19, 2017
13. Jan 19, 2017

### Staff: Mentor

There are interpretations of quantum mechanics without hidden variables, and they describe the observed tunneling nicely. Therefore, tunneling is not a "proof of hidden variables".
There are also interpretations with hidden variables, they can describe tunneling as well.

The different interpretations lead to the same predictions for experiments - you cannot distinguish between them.

14. Jan 19, 2017

### Demystifier

It seems that OP thinks that mass is a "hidden variable" because if hiddenly varies during the tunelling.

15. Jan 19, 2017

### scifimath

I consider pilot-wave theory as accepting hidden variables.

What? You can't observe/measure anything while in superposition.

I choose to think outside the box.

So one theory says it was magic and the other actually has something to say about it.

16. Jan 19, 2017

### ZapperZ

Staff Emeritus
This is incorrect. The existence of bonding-antibonding bonds in Chemistry is an evidence that one can detect the presence of superposition by measuring what is essentially a non-commuting observable. The presence of the coherence gap in the Delft/Stony Brook experiment is another clear example[1]. The coherence gap is there due to the superposition of two opposite directions of the supercurrent.[2]

To think outside of the box, you have to first know where the box is.

Zz.

[1] C.H. van der Wal et al., Science v.290, p.773 (2000); J.R. Friedman et al., Nature v.406, p.43 (2000).
[2] A.J. Leggett "Testing the limits of quantum mechanics: motivation, state of play, prospects", J. Phys. Condens. Matt., v.14, p.415 (2002).

17. Jan 19, 2017

### scifimath

Are those "weak" measurements? Do any of them tell you there is mass present besides satisfying an equation?

18. Jan 19, 2017

### ZapperZ

Staff Emeritus
No, those are references to counter your claim that "... You can't observe/measure anything while in superposition..." None of those employ "weak measurements" of any kind. It simply employs basic QM 101 that all undergraduates learn.

Zz,

19. Jan 19, 2017

### Staff: Mentor

Let's try another example.
We pass a beam of electrons through a vertically oriented inhomogeneous magnetic field (google for "Stern-Gerlach apparatus" - that's the device that produces such a field). Some of these electrons are deflected upwards and other are deflected downwards, so we end up with two beams of electrons coming out. One beam is composed of spin-up electrons and the other is composed of spin-down electrons, but every single electron in both beams is in a superposition of spin-left and spin-right. We can easily measure the mass of any of these electrons, even though they're in a superposition.

20. Jan 31, 2017

### Mark Harder

Scifimath, I don't understand what you mean by this. Can't a variable (position, location, time etc.) be physical?

My understanding of tunneling is that the 'mass', by which I assume you mean a particle, is actually a probability density with nonzero spread in space, even in the presence of an incompletely constraining potential. What 'tunnels' is the tail of this probability distribution. In other words, there is a nonzero probability that the particle will be observed outside the potential box. Realistic examples are tunneling of charge-carriers through a semiconductor junction and tunneling of electrons and even protons across energy barriers in the active sites of some enzymes (I imagine there might be examples from simpler heterogeneous chemical catalysts, but I can't name any right now.)