Pilot Wave Theory & Non-Locality

[sanman]

So Heisenberg's Uncertainty says that we can't know both the position and the velocity of a particle accurately, because measuring one will disturb the particle enough that it's no longer possible to accurately measure the other as it was. So one or the other has to remain unknown to us.

This likewise applies to the famous Slit Diffraction experiment.

So there were 2 rival theoretical interpretations of the Slit Diffraction results. The Copenhagen interpretation was that the particle is able to interfere with itself because the traveling particle is in the form of a wave spanning various possible locations, including both the slits as it passes through them, to later interfere with itself.

But then there is the DeBroglie interpretation (also later re-stated by Bohm), which is that the particle is having specific location (not a wave), but its trajectory is in the form of a probabilistic wave function, and it's this indeterminacy of trajectory which is what gives the diffraction interference results.

Way back in the day when these rival theories were debated, the Copenhagen interpretation won out, because the other side couldn't justify the Slit Diffraction results when entangled photons were used.

Until now:

https://www.quantamagazine.org/pilot-wave-theory-gains-experimental-support-20160516/

So the argument is now coming forth that the entangled state cannot reliably indicate the state of the traveled partner in Slit Diffraction experiment, due to Non-Locality.

So it sounds like the Pilot Wave Theory can be just as legitimate as Copenhagen, at least as far as the Slit Diffraction experimental results are concerned.

I rather like this Pilot Wave theory, because I find it too counterintuitive to think of a particle as a wave. But seeing a particle's trajectory as indeterminate seems fair, because intuitively, that trajectory is a road not yet traveled - it's about where the particle could go.

But I want to better understand what the implications of this theory and its Non-Locality mean. Why does DeBroglie-Bohm Theory require Non-Locality? I always thought that Locality was something that applied to the macroscopic world, and wasn't applicable to the quantum world. (ie. macroscopic objects can't travel faster than C, but quantum-scale particles can instantly tunnel faster than C)

I just assumed that DeBroglie-Bohm/PilotWave Theory and its indeterminacy for trajectory merely means at any given moment, a particle has the possibility of pursuing all possible velocity vectors -- not some weird idea about traveling to all possible points in the universe.
So just as in Copenhagen you would talk about tunneling from one position to another instantaneously, then analogously under PilotWave, you would talk about a particle jumping from one velocity frame into another instantaneously. So position/location are replaced with velocity/velocityframe, and Locality/NonLocality has nothing to do with this. We'd still accept that C is the fastest possible velocity, and so "all possible velocity vectors" as mentioned in my previous paragraph, means all possible velocities below C. That's my instinctive interpretation, anyway - is it wrong for me to make such an interpretation?

Finally, how would someone set up a Bell's Inequality experiment to test Pilot Wave Theory? How do you test for Non-Local hidden variables? Do you have to use 2 different localities that are separated by appreciable light-distances? How about an experiment that's set on both the Earth and Moon, which are light-seconds apart - could a Bell's Inequality test for Pilot Wave Theory be set up that way?

 

[phinds]

So Heisenberg's Uncertainty says that we can't know both the position and the velocity of a particle accurately, because measuring one will disturb the particle enough that it's no longer possible to accurately measure the other as it was.

That is most emphatically NOT what the HUP says. The HUP is NOT a measurement problem, it is a statement of the fundamental nature of matter.

 

[sanman]

That is most emphatically NOT what the HUP says. The HUP is NOT a measurement problem, it is a statement of the fundamental nature of matter.

I apologize for my ignorance, but so let me quote Encyclopedia Britannica:

https://www.britannica.com/science/uncertainty-principle

Uncertainty principle, also called Heisenberg uncertainty principle or indeterminacy principle, statement, articulated(1927) by the German physicist Werner Heisenberg, that the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory. The very concepts of exact position and exact velocity together, in fact, have no meaning in nature.

Is that a better articulated definition?

Personally, I've always thought that Heisenberg's Uncertainty, as it pertains to the fundamental nature of matter, was just the consequence of Vacuum Fluctuations (ie. Brownian Motion). But anyway, that's a digression - I simply mentioned Heisenberg's because it imposes indeterminacy on a particle, and that indeterminacy can be interpreted as a wave function with the result being wave-like behavior, including the interference pattern seen in the Slit Diffraction experiment.

Anyway, in addition to the questions I asked before, I'd also like to ask if Pilot Waves can apply to non-quantum macroscopic objects, like a baseball or a marble. DeBroglie is the originator of Pilot Wave Theory, and we know that DeBroglie wavelength can apply for macroscopic objects, even if it's so small as to not be apparent.

 

[phinds]

https://www.britannica.com/science/uncertainty-principle

In that article they do in fact make exactly the statement that you made.

Any attempt to measure precisely the velocity of a subatomic particle, such as an electron, will knock it about in an unpredictable way, so that a simultaneous measurement of its position has no validity.

. They clearly don't understand the HUP. The statement is incorrect. The HUP is not about single events, it is about the fact that nature does not allow identical outcomes at the quantum level given identical setups. The classical world insists on that which is why the HUP is such a big deal.

 

[sanman]

In that article they do in fact make exactly the statement that you made. . They clearly don't understand the HUP. The statement is incorrect. The HUP is not about single events, it is about the fact that nature does not allow identical outcomes at the quantum level given identical setups. The classical world insists on that which is why the HUP is such a big deal.

To me, that implies Quantum Objects are experiencing something like Brownian Motion.

 

[phinds]

To me, that implies Quantum Objects are experiencing something like Brownian Motion.

I can't see why, since the two have nothing to do with each other.

 

[sanman]

I can't see why, since the two have nothing to do with each other.

To me, it seems like the uniqueness and non-reproduceability of the outcomes on various quantum objects is due to influences imparted onto them by something like Brownian Motion. And furthermore, Brownian Motion would explain various things, like DeBroglie Wavelength, Vacuum fluctuations for stable equilibrium against Blackbody radiation, etc. Instead of having multiple irreduceable phenomena, just reduce them all by attributing them to a single cause (Occam's Razor).

 

[sanman]

Anyway, regarding the whole Non-Locality thing, why is Non-Locality necessary for the PWT to work? Why wouldn't the indeterminacy be related to velocity vector instead of location? The way I interpret it, is that the quantum particle can have determinate position and an indeterminate velocity vector which can potentially be of any value allowed in the universe (ie. having any direction, but with magnitude less than C)

What's wrong with that interpretation for DeBroglie-Bohm / Pilot Wave Theory?

 

[sanman]

Hmm, so I see another thread on this forum mentioned DeBroglie-Bohm theory, talking about Non-Local Hidden Variables and mentioning that DeBroglie-Bohm would require those in order to achieve a determinate universe. And Non-Local Hidden Variables were mentioned as being variables/influences that would be outside of the past lightcone. But so a lightcone can exist symmetrically into the future, can't it? And quantum particles are said to be Time-symmetric, right? So why isn't it possible that the Non-Local Hidden Variables would be from the Future Lightcone too, and not just the Past Lightcone?

 

[PeterDonis]

@sanman, there are a few confusions that need to be cleared up:

First, the Copenhagen interpretation and the DeBroglie-Bohm interpretation are, as the terms I have just used indicate, not different theories. They are different interpretations of the same theory, non-relativistic quantum mechanics. Both interpretations make the same predictions for all experimental results, so there is no way to test which one is correct by experiment. They just tell different stories about what is supposedly happening "behind the scenes" in order to produce the results.

Second, the Quanta magazine article you linked to is misdescribing the state of things. All interpretations of QM agree on the predicted results ot the experiments referred to in the article; they just, as I said, tell different stories about how those results are produced. So the experiments do not support one interpretation over another, though they do provide further confirmation of the highly counterintuitive predictions of QM.

Third, non-locality is not an aspect of a particular interpretation; it is an established fact, since violations of the Bell inequalities have been experimentally confirmed in a variety of settings.

 

[PeterDonis]

What's wrong with that interpretation for DeBroglie-Bohm / Pilot Wave Theory?

Nothing, since it's what the Pilot Wave model (which is really an interpretation, as I said in my previous post) says. Particles always have determinate positions in this model. But those determinate positions are not directly observable; any attempt to measure the position of a particle will be subject to the uncertainty principle.

However, this does not get rid of the non-locality, because the particle's position is affected by the quantum potential in this model, and the quantum potential is non-local; it explicitly depends on the wave function over the entire universe.

 

[PeterDonis]

so a lightcone can exist symmetrically into the future, can't it? And quantum particles are said to be Time-symmetric, right? So why isn't it possible that the Non-Local Hidden Variables would be from the Future Lightcone too, and not just the Past Lightcone?

What you are describing is yet another interpretation of QM, called the Transactional Interpretation, originated (AFAIK) by John Cramer. It still makes all the same predictions for all experimental results--it just, as I've said, tells a different story from the other interpretations about how those results are produced.

 

[sanman]

Thanks so very much for your enlightening answers.
But so then there's no way to design an experiment which will exploit/highlight the difference in interpretation between Copenhagen and DeBroglie-Bohm/PWT?
Surely if there are conceptual differences, there must be some way to expose them to experimental scrutiny.

For instance, Copenhagen supports positional indeterminacy and Quantum Tunneling (a proven phenomenon), because it allows the quantum particle to instantaneously shift from one position to another.

https://phys.org/news/2015-05-physicists-quantum-tunneling-mystery.html

Meanwhile, DeBroglie-Bohm/PWT supports velocity indeterminacy, which to me implies instantaneous acceleration - ie. instantaneous change from one velocity frame to another.

Regarding position vs velocity, it's not a case of "six of one, half a dozen of the other" - position and velocity are 2 different things, and it seems like the indeterminacy of each should impose some difference in consequences (isn't that why they're called non-commuting observables?)

 

[PeterDonis]

so then there's no way to design an experiment which will exploit/highlight the difference in interpretation between Copenhagen and DeBroglie-Bohm/PWT?

That's right. All QM interpretations use the same math (or rather equivalent math as far as experimental predictions are concerned), so they will all agree on what the results of any experiment will be. They will just, as I said, tell a different story about how those results are produced. But we can't test those stories experimentally; we can only test the results.

Surely if there are conceptual differences, there must be some way to expose them to experimental scrutiny.

Only if those conceptual differences can somehow be turned into actual differences in predictions. If that happens, then we don't have different interpretations any more, we have different theories, and we can test them against each other just like any other theories. But that has not happened with QM.

Copenhagen supports positional indeterminacy and Quantum Tunneling (a proven phenomenon), because it allows the quantum particle to instantaneously shift from one position to another.

This description is an interpretation, not an experimental result. The experimental result is the probability of observing an electron outside the potential barrier that is being "tunneled" through, as a function of time since the start of the experiment. Nobody ever measures an "instantaneous shift from one position to another".

As an aside, phys.org is not a reliable source if you actually want to learn science. It sensationalizes results by misdescribing them to make them seem much more radical than they actually are.

DeBroglie-Bohm/PWT supports velocity indeterminacy, which to me implies instantaneous acceleration - ie. instantaneous change from one velocity frame to another.

Same comment as above.

Regarding position vs velocity, it's not a case of "six of one, half a dozen of the other" - position and velocity are 2 different things, and it seems like the indeterminacy of each should impose some difference in consequences (isn't that why they're called non-commuting observables?)

No. They are non-commuting observables precisely because their indeterminacy is fundamentally connected--if you know the indeterminacy in one, you automatically know the indeterminacy in the other. (Btw, the actual observables in this case are position and momentum, not position and velocity. Velocity is often mentioned, but if you look you will see that that's only in cases where a single particle type is being considered, like an electron, so that the mass can be assumed to be constant and we can convert at will between velocity and momentum.)

 

[sanman]

Alright, so can we at least say that the DeBroglie-Bohm/PWT interpretation is currently no less valid than the Copenhagen interpretation?
(At least in regards to describing experimental results)

Is there any other area or experiment where DeBroglie-Bohm/PWT comes up short, as compared to Copenhagen interpretation?

So if someone puts forth a paper which is premised upon referencing DeBroglie-Bohm/PWT, that isn't in and of itself a reason to discredit or doubt it?

 

[PeterDonis]

can we at least say that the DeBroglie-Bohm/PWT interpretation is currently no less valid than the Copenhagen interpretation?

Viewing an interpretation as more or less "valid" is misleading. Interpretations can't be "valid" or "invalid", except in so far as the theories they are interpreting make correct predictions or not. If you have a theory that makes correct predictions about experimental results, you can tell whatever story you want about how those results are produced, and it won't matter, since the story you tell is not what you use to actually make the predictions--you use the math of the underlying theory.

Is there any other area or experiment where DeBroglie-Bohm/PWT comes up short, as compared to Copenhagen interpretation?

How can there be? As I've already said, both of them are interpretations of the same theory, and make the same predictions for all experimental results.

if someone puts forth a paper which is premised upon referencing DeBroglie-Bohm/PWT, that isn't in and of itself a reason to discredit or doubt it?

Papers which confuse theory (the machinery that actually makes predictions) with interpretation (the story that the authors want to tell about how things work "behind the scenes") are always questionable. Papers which talk about an interpretation but make clear the distinction between interpretation and the theory itself are fine.

 

[cosmik debris]

There are various Theories of Explanation, they are ways of determining a good story from a bad story. This is probably philosophy but you can start here: http://www.iep.utm.edu/explanat/

Cheers

 

[sanman]

So here's something I found

http://discovermagazine.com/2017/may-2017/the-war-over-reality

Valentini has devoted his career to almost single-handedly resurrecting the pilot wave idea. Now his years of work actually have a chance — a small one, he admits — of being vindicated. Of the many interpretations of quantum theory, pilot wave theory is unique in that Valentini has found a way in which it might be experimentally tested. No other interpretation of quantum mechanics can make that claim. Many Worlds, Bohr’s interpretation and others are all experimentally indistinguishable — they reproduce the results of standard quantum theory. But if Valentini is right, certain effects predicted in pilot wave theory may have left an imprint on the cosmic microwave background, the primordial radiation left over from the Big Bang that still pervades all of space.

The temperature of that radiation is almost a perfectly uniform 2.725 degrees Celsius above absolute zero. Detailed observations, however, have found slight variations in the radiation. Standard quantum theory can explain nearly all of these variations, but in 2015, new data released by the European Space Agency’s Planck spacecraft revealed evidence of small anomalies in the background radiation. And that is just the kind of thing Valentini has been looking for. While conventional quantum theory predicts that random quantum fluctuations in the early universe have left celestial imprints, pilot wave theory predicts fluctuations that are less random, leaving slightly different wrinkles in the cosmic microwave background radiation.

“It’s tantalizing,” Valentini says. “We’re carrying out the analysis partly to understand things better and partly to see what the data can tell us about the predictions that we have.” Another two years of data and analysis should settle the question.

So it seems there are differences in actual predictions between DeBroglie-Bohm and Copenhagen interpretations. And to me, that's the way it should be - if the ideas are different in some ways, then that must result in some physical difference that can be exposed. Hopefully at some point, some physical evidence will be uncovered which allows one idea to prevail over the other, yielding progress in our understanding of the universe.

 

[Demystifier]

So it sounds like the Pilot Wave Theory can be just as legitimate as Copenhagen, at least as far as the Slit Diffraction experimental results are concerned.

Of course that it is as legitimate as Copenhagen, but it was so even before the recent experiment mentioned above.

Nevertheless, it is good to know that now they are able to perform weak measurements even with entangled particles.

 

[Demystifier]

So it seems there are differences in actual predictions between DeBroglie-Bohm and Copenhagen interpretations.

This is analogous to the claim that there are differences in actual predictions between statistical mechanics and thermodynamics. In thermal equilibrium, there are no differences. Outside of thermal equilibrium, there are.

Similarly, there are differences in actual predictions between dBB and Copenhagen only outside of the so-called quantum equilibrium. But it is not clear whether it is possible to find a state in Nature outside of quantum equilibrium. Valentini assumed that it might be possible, but he did not present a strong argument for that assumption.

 

[vanhees71]

Let me put the answers to the HUP issue just a bit differently. The problem is that Heisenberg got his own discovery wrong. He was immediately corrected by Bohr, but it was to late: Heisenberg has published his first paper on the subject before discussing with Heisenberg.

As has been emphasized by @phinds and others, the Heisenberg uncertainty relation is about a restriction due to state preparation and not a restriction of what can in principle be measured accurately. It's a mathematical theorem, which is not very difficult to prove. It says for any state $\hat{\rho}$ of a quantum system the standard deviations of observables $A$ and $B$, represented by the self-adjoint operators $\hat{A}$ and $\hat{B}$ obey the uncertainty relation
$$\Delta A \Delta B \geq \frac{1}{2} |\langle \mathrm{i} [\hat{A},\hat{B}] \rangle|,$$
where the averaging is taken by the usual rule
$$\langle A \rangle=\mathrm{Tr}(\hat{A} \hat{\rho}).$$
Set e.g., $A=x$ and $B=p_x$, then you get the usual position-momentum uncertainty relation,
$$\Delta x \Delta p \geq \frac{\hbar}{2}.$$
It's saying that a particle's position and momentum have, no matter how you prepare the state of the particle, standard deviations obeying this uncertainty relation.

You can measure standard deviations by preparing a lot of particles in a given state ("ensemble") very often and then measure as accurately as you can position or momentum. You'll find a distribution of these quantities around some mean value and standard deviations. The measurement of either observable must be much more accurate to resolve the standard deviations due to the quantum uncertainties, and you need sufficient statistics, i.e., sufficiently large ensembles of equally prepared particles to make sure to measure the standard deviations due to the quantum-state preparation rather than statistical uncertainties of the measurement.

The issue about how a measurement disturbs the quantum state, is much more difficult to resolve. It's also subject of current research. There's a book on the subject by one of the main participants in this research community

http://www.springer.com/de/book/9783662141045

 

[star apple]

That's right. All QM interpretations use the same math (or rather equivalent math as far as experimental predictions are concerned), so they will all agree on what the results of any experiment will be. They will just, as I said, tell a different story about how those results are produced. But we can't test those stories experimentally; we can only test the results.
Only if those conceptual differences can somehow be turned into actual differences in predictions. If that happens, then we don't have different interpretations any more, we have different theories, and we can test them against each other just like any other theories. But that has not happened with QM.

If we have a new quantum theory (not just interpretation), this means either pilot wave were detected as in BM or Many Worlds proven.. should the new theory and new experimental prediction by principle or theoretically should affect high energy physics (electroweak or slightly below Planck scale) too? Because Schrodinger quantum mechanics is just approximation to Quantum Field theory.. and QFT can be applied even to strings. So if there was a new quantum theory.. would it only affect low energy sector processes (like below the electroweak scale) or should it theoretically even affect (or be relevant) as high as the GUT or near Planck scale? Because I can't imagine an Objective Collapse only affecting molecules and the Schrodinger Equation only and not the high energy QFT processes.

This description is an interpretation, not an experimental result. The experimental result is the probability of observing an electron outside the potential barrier that is being "tunneled" through, as a function of time since the start of the experiment. Nobody ever measures an "instantaneous shift from one position to another".

As an aside, phys.org is not a reliable source if you actually want to learn science. It sensationalizes results by misdescribing them to make them seem much more radical than they actually are.
Same comment as above.
No. They are non-commuting observables precisely because their indeterminacy is fundamentally connected--if you know the indeterminacy in one, you automatically know the indeterminacy in the other. (Btw, the actual observables in this case are position and momentum, not position and velocity. Velocity is often mentioned, but if you look you will see that that's only in cases where a single particle type is being considered, like an electron, so that the mass can be assumed to be constant and we can convert at will between velocity and momentum.)

 

[PeterDonis]

if there was a new quantum theory.. would it only affect low energy sector processes (like below the electroweak scale) or should it theoretically even affect (or be relevant) as high as the GUT or near Planck scale?

The only way to answer this question is to come up with a new theory that makes different experimental predictions and has those predictions confirmed.

 

[star apple]

The only way to answer this question is to come up with a new theory that makes different experimental predictions and has those predictions confirmed.

Can someone here give me an updated list or candidates of popular new quantum theory (in the class of Lee Smolin, Barbour, Rovelli or other consensus accepted formalism.. and not the crackpots) versus just interpretation where the latter has same math as the orthodox.. is lattice quantum field theory supposed to be a new quantum theory or just updated calculational tool...?

I can imagine Bohmian Mechanics needing to modify the high energy sector (for example requiring more fundamental particles (vs quasi particles) in condense matter like analogy as briefly described by Demystifier. Hence in this version of BM, it is really a new quantum theory. Does anyone know of others where the higher energy needs to be modified too?