Heisenberg Uncertainty Principle Violation?

[manyworldsBob]

TL;DR Summary

Does this scenario violate the Heisenberg Uncertainty Principle?

Hello, 2 questions please about the Uncertainty Principle and the following scenario:

I shoot at each other, 2 electrons each with equal but opposite velocity such that they repel each other?

(To me, this indicates that you know the momentum of each electron and you know each position, all simultaneously.)

1. Does this scenario violate the Heisenberg Uncertainty Principle?

2. Does Quantum Mechanics require adherence to the Heisenberg Uncertainty Principle?

Sorry for the Physics 1A questions, but it's been 50 years since I took it and I'm confused. :-)
Thanks in advance.

 

[PeroK]

Summary:: Does this scenario violate the Heisenberg Uncertainty Principle?

Hello, 2 questions please about the Uncertainty Principle and the following scenario:

I shoot at each other, 2 electrons each with equal but opposite velocity such that they repel each other?

(To me, this indicates that you know the momentum of each electron and you know each position, all simultaneously.)

1. Does this scenario violate the Heisenberg Uncertainty Principle?

2. Does Quantum Mechanics require adherence to the Heisenberg Uncertainty Principle?

Sorry for the Physics 1A questions, but it's been 50 years since I took it and I'm confused. :-)
Thanks in advance.

The question is how do you know that you have shot two electrons at each other with equal but opposite velocity? And, how do you know their position at any given time?

Just writing down a scenario doesn't make it physically possible. As far as the HUP is concerned, you need a precise experiment.

 

[manyworldsBob]

Thanks. For question #2, I should have been a little more clear.

Does the Many Worlds Interpretation require adherence to the HUI?

[I don't think that is required, butI haven't seen the explicitly stated anywhere.]

 

[PeroK]

Does the Many Worlds Interpretation require adherence to the HUP?

Yes, otherwise violating the HUP would be a prediction of MWI that could be tested.

 

[manyworldsBob]

Thank you.

These questions were with regard to my trying to partially understand a version of MWI of QM in a book I've been reading.

My understanding in reading the book is that the author's version of MWI ("Everettian light") consists only of:
1. QM (the whole world aka System ) is represented by a specific Wave function
2. The System is described by the Wave function's evolution as defined by the Schrodinger Equation ===implies also===> Heisenberg Uncertainty Principle

In searching this forum I see many, including your posts on MWI and this specific book, and that there appears to still be some debate as to at least 2 things:
1. Does it solve the measurement problem in the Copenhagen Interpretation?
2. Specifics of Wave collapse, and its significance.

To me, it is an interesting theory but I'm not ready to jump aboard the MWI train just yet. In reading other posts, apparently, I'm not the only one.

Thanks again for your help.

 

[StevieTNZ]

Thank you.

These questions were with regard to my trying to partially understand a version of MWI of QM in a book I've been reading.

My understanding in reading the book is that the author's version of MWI ("Everettian light") consists only of:
1. QM (the whole world aka System ) is represented by a specific Wave function
2. The System is described by the Wave function's evolution as defined by the Schrodinger Equation ===implies also===> Heisenberg Uncertainty Principle

In searching this forum I see many, including your posts on MWI and this specific book, and that there appears to still be some debate as to at least 2 things:
1. Does it solve the measurement problem in the Copenhagen Interpretation?
2. Specifics of Wave collapse, and its significance.

To me, it is an interesting theory but I'm not ready to jump aboard the MWI train just yet. In reading other posts, apparently, I'm not the only one.

Thanks again for your help.

Which book is this? And MWI is not a theory, it is an interpretation of quantum theory.

In the Copenhagen Interpretation (CI), as far as I'm aware, there is the quantum world split with the classical macroscopic world. At macroscopic detectors, that's where measurement occurs. However, this is at odds with the quantum mechanics prediction the detector enters a superposition itself and the combined |system>+|detector> have an observable from which interference can be observed. So I'd say CI, as I understand it, is wrong.

 

[PeroK]

In searching this forum I see many, including your posts on MWI and this specific book, and that there appears to still be some debate as to at least 2 things:
1. Does it solve the measurement problem in the Copenhagen Interpretation?
2. Specifics of Wave collapse, and its significance.

To me, it is an interesting theory but I'm not ready to jump aboard the MWI train just yet. In reading other posts, apparently, I'm not the only one.

Advocates of MWI claim it solves the measurement problem, but others claim this is only at the expense of introducing an equivalent problem in terms of explaining the Born rule.

It certainly removes the need for wavefunction collapse, but again explaining the probabilities is problematic.

 

[manyworldsBob]

Which book is this?

Something Deeply Hidden by Sean Carroll.; checked out from my public library.

 

[manyworldsBob]

So, my understanding of Sean Carroll's version of MWI presented in his book Something Deeply Hidden is that it is very dependent upon entanglement, and then branching of the wave function. [Please correct me if I misunderstand.]

He seems to imply, in my opinion and from my recollection, that entanglement occurs quite frequently and readily.

I'm thinking that the recent claim of tardigrade entanglement with a qubit in https://arxiv.org/pdf/2112.07978.pdf and then today's peer refutation (https://phys.org/news/2021-12-peers-dispute-tardigrades-entangled-qubits.html) of the tardigrade entanglement is not good for the MWI proponents.

But, maybe I oversimplify and/or am wrong?

 

[StevieTNZ]

I'm thinking that the recent claim of tardigrade entanglement with a qubit in https://arxiv.org/pdf/2112.07978.pdf and then today's peer refutation (https://phys.org/news/2021-12-peers-dispute-tardigrades-entangled-qubits.html) of the tardigrade entanglement is not good for the MWI proponents.

But, maybe I oversimplify and/or am wrong?

If there was entanglement, there was entanglement. If there wasn't, there wasn't. It doesn't render any interpretation that reproduces the predictions of quantum theory incorrect.

 

[Nugatory]

He seems to imply, in my opinion and from my recollection, that entanglement occurs quite frequently and readily.

It does. Entanglement refers to the fact that when two previously independent (each one is described by its own wave function) quantum systems interact, the result is a single composite system with one wave function that describes the post-interaction properties of both. Thus pretty much any interaction involves some degree of entanglement when described using quantum mechanics.

None of this has any bearing on your original question about the uncertainty principle. It is mathematically impossible to construct a wave function in which both the position and momentum (or any other pair of incompatible observables) are determined more tightly than allowed by the HUP.

 

[manyworldsBob]

(1) It does. Entanglement refers to the fact that when two previously independent (each one is described by its own wave function) quantum systems interact, the result is a single composite system with one wave function that describes the post-interaction properties of both. Thus pretty much any interaction involves some degree of entanglement when described using quantum mechanics.

(2) None of this has any bearing on your original question about the uncertainty principle. It is mathematically impossible to construct a wave function in which both the position and momentum (or any other pair of incompatible observables) are determined more tightly than allowed by the HUP.

Thank you for your thoughtful reply.

(1) An example of entanglement of large objects given in Sean Carroll's book was one in which a person runs into a brick wall, with subsequent entanglement, and branching of the wave describing the system into one of the many branches, one of which the human bores through the wall.

Given the [alleged] difficulty in showing entanglement of a microscopic tardigrade, and my understanding that it is harder to show entanglement of large objects, I stated my opinion (in words, not equations) that I personally have a problem with a theory that creates an infinite number of entangled worlds with copies of people.

I could change my opinion as soon as a human, or even a tardigrade is successfully entangled in the lab, and presented in a peer reviewed paper.

(2) I asked the original question because, immediately after discussing the HUP in chapter 4 of Sean Carroll's book, the author's first experiment in chapter 5 is one in which two electrons both with known position and momentum was discussed. Subsequent experiments discussed electron spin. That confused me. I just wanted to make sure I understood the HUP.

At the time of the original question, I intended to keep the book and its author out of the discussion; until I was directly asked the question.

Thanks again.

 

[PeroK]

(1) An example of entanglement of large objects given in Sean Carroll's book was one in which a person runs into a brick wall, with subsequent entanglement, and branching of the wave describing the system into one of the many branches, one of which the human bores through the wall.

Which is nonsense. The problem with this is that a person transforming into a giant fish is just as likely as boring through a wall. Along with everything else you can think of that, however remotely, is physically possible.

You're a gazillion times more likely, for example, to get stuck half-way through the wall.

There's no experimental evidence that these unlikely events happen to macroscopic objects; and, the context in which they can be said to happen (if they can never be observed) is problematic.

 

[Nugatory]

that I personally have a problem with a theory that creates an infinite number of entangled worlds with copies of people.

There is something not to like about every interpretation of quantum mechanics, and you have identified what's not to like about MWI.

We adopt interpretations to help us think about what the math is telling us. MWI is really amazingly unhelpful for thinking about people running into walls - so your best bet is to use a different interpretation when thinking about that problem.

 

[PeterDonis]

I personally have a problem with a theory that creates an infinite number of entangled worlds with copies of people.

The MWI does not create any worlds or copy anything; in the MWI the wave function always evolves unitarily, and unitary evolution can't create or destroy anything.

The "worlds" in the MWI are decoherent branches of the entangled wave function, but entanglement does not and cannot create or copy anything; it just entangles already existing degrees of freedom. Strictly speaking, the individual branches are not "copies", because no individual branch has a definite state; this is a general property of entangled states. (This fact is actually one of the main sticking points of the MWI.)

 

[manyworldsBob]

MWI is really amazingly unhelpful for thinking about people running into walls - so your best bet is to use a different interpretation when thinking about that problem.

In that regard, I have returned Sean Carroll's book to the library, and I have checked out and currently reading, Einstein's Unfinished Revolution The Search for What Lies Beyond the Quantum by Lee Smolin. His preface to the book seems more in line with what I am looking for; whether it actually delivers is TBD.

I am also watching lectures given by Professor Susskind http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter .

 

[StevieTNZ]

Thank you for your thoughtful reply.

(1) An example of entanglement of large objects given in Sean Carroll's book was one in which a person runs into a brick wall, with subsequent entanglement, and branching of the wave describing the system into one of the many branches, one of which the human bores through the wall.

Given the [alleged] difficulty in showing entanglement of a microscopic tardigrade, and my understanding that it is harder to show entanglement of large objects, I stated my opinion (in words, not equations) that I personally have a problem with a theory that creates an infinite number of entangled worlds with copies of people.

(1) is an example of quantum tunnelling. Roland Omnes, in his book https://en.wikipedia.org/wiki/Quantum_Philosophy describes the probability of macroscopic objects 'quantum tunnelling' as very low but not zero. The entanglement would exist between the human and the brick wall.

I would say it is unfair to compare a potentially unsuccessful entanglement of a tardigrade with a qubit with the ability to show entanglement between larger systems. For example, about 10 years ago this paper was published -- https://www.science.org/doi/10.1126/science.1211914

 

[manyworldsBob]

Quantum tunneling, entanglement, quantum entanglement; whatever you want to call it, I need to see it myself, or read a reputable, peer reviewed paper detailing it's occurrence to believe it.

I would say it was "unfair" that while taking an undergrad level Quantum Physics class while obtaining my BS in Chemistry from UC Berkeley, I was only presented with one theory of Quantum Physics. It was some 45 years later that I heard of Bohm's exile in Brazil partly due to his temerity in challenging Bohr and von Neumann with the Pilot Wave theory, and partly due to McCarthyism. Very unfair.

It was either in Adam Becker's fine book, What is Real? or Sean Carroll's book that I first heard about the Pilot Wave Theory. It sounds much more believable to me.

In any event, I am greatly enjoying Lee Smolin's book, and as he states in his book, current Quantum Theory orthodoxy is incomplete, imo.

What is also exceptionally unfair is that my golf drives have a greater probability of branching into a world in which my ball entangles with a shrub out of bounds, than a branch in which it entangles with the flag stick on the green.

Merry Christmas.

 

[PeroK]

Quantum tunneling, entanglement, quantum entanglement; whatever you want to call it, I need to see it myself, or read a reputable, peer reviewed paper detailing it's occurrence to believe it.

You realize, of course, that Bohmian Mechanics doesn't make these things go away. It only explains them in an even more bizarre and elaborate way that orthodox QM. It restores determinism (which is important to some people) but at the expense of introducing an unobservable layer of substructure that is not strictly necessary.

The other issue is that QM didn't end in the 1930s. The quark model of particle physics and QFT (Quantum Field Theory) have been developed since then.

Physics is not a religion, where physicists decide on a theory and stick with it through dogmatic adherence. They stick with it because it gives them the best chance of further developments. And, it's harder to make progress starting from Bohmian mechanics than from orthodox QM - directly because of the additional complexity.

This is not a question of sheer politics, but of practical decisions on how best to move physics forward.

One reason you can prefer BM is that you are under no obligation to produce research results. It's a bit like me suggesting that if I were a professional golfer I would play with three clubs in the bag. I can say that because I don't have to go out and win golf tournaments!

 

[manyworldsBob]

You realize, of course, that Bohmian Mechanics doesn't make these things go away. ...

Physics is not a religion, where physicists decide on a theory and stick with it through dogmatic adherence. They stick with it because it gives them the best chance of further developments. And, it's harder to make progress starting from Bohmian mechanics than from orthodox QM - directly because of the additional complexity.

I do realize that, which is why I agree that current QM is incomplete and I prefer to say, "I don't know". But I am not responsible for further developments in physics.

While I agree Physics is not a religion, some of my conversations about physics feel like some of my conversations I've had with people of faith.

Thanks for your reply.

 

[PeterDonis]

Quantum tunneling, entanglement, quantum entanglement; whatever you want to call it, I need to see it myself, or read a reputable, peer reviewed paper detailing it's occurrence to believe it.

The literature is full of reputable, peer-reviewed papers detailing the occurrence of these things.

I was only presented with one theory of Quantum Physics.

That's because there is only one theory of Quantum Physics. The pilot wave interpretation is not a different theory; it's just a different interpretation of the same theory. As are Copenhagen, Many Worlds, and plenty of others. None of these interpretations are different theories because they all use the same (or equivalent) math to make predictions, so they all agree on the predicted results of all experiments, which means you can't use experiments to distinguish between them.

 

[PeroK]

While I agree Physics is not a religion, some of my conversations about physics feel like some of my conversations I've had with people of faith.

The fundamental difference is that the ideas that underpin QM were forced on physicists by experimental evidence. The difficulty with science generally that many people have is that it is not democratic. To take something hopefully uncontentious: we don't all have a vote on whether Andrew Wiles proof of Fermat's Last Theorem is valid or not. Only a handful of experts in the relevant fields of pure mathematics are able to verify his proof. The debate is not open to the general public.

In truth, that requires trust that those experts are being honest. That they haven't all got together and conspired to pass an invalid proof as genuine. But, trust and confidence in the integrity of a group of people is very different from faith.

 

[manyworldsBob]

That's because there is only one theory of Quantum Physics. The pilot wave interpretation is not a different theory; it's just a different interpretation of the same theory. As are Copenhagen, Many Worlds, and plenty of others. None of these interpretations are different theories because they all use the same (or equivalent) math to make predictions, so they all agree on the predicted results of all experiments, which means you can't use experiments to distinguish between them.

Maybe multiple interpretations that cannot be distinguished by experimentation, while convenient for some in some cases, might indicate the need for a different and/or more complete theory.

But like your article, Fundamental Differences in Interpretations of Quantum Mechanics, in which you write, "... and realize that the argument [discussion] has no “right” or “wrong” outcome and that the best we can do at this point is to accept that reasonable people can disagree on quantum mechanics interpretations [and the theory itself] and leave it at that."

Thanks for your replies.

 

[PeterDonis]

Maybe multiple interpretations that cannot be distinguished by experimentation, while convenient for some in some cases, might indicate the need for a different and/or more complete theory.

That is in fact one of the key things that drives people to publish different interpretations. But so far no more complete theory that works has emerged from any QM interpretation.