B Special Relativity violation via Quantum Mechanics?

[thedubdude]

TL;DR Summary

Can quantum objects violate Special Relativity. A momentum measurement can cause a quantum object to appear anywhere in the universe because the position probability never goes to zero.

We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any quantum object whose momentum is known ... to some degree (but not precisely). This means the objects position could be anywhere, even for example, a billion light years from the position at which the momentum measurement was made (of course with increasingly lower probability). But if the object actually ended up, a billion light years away, wouldn’t that violate special relativity? The object would seemingly have traveled 1 billion light years away from the momentum measurement event in no time at all. How is that possible without violating the speed of light as the fastest speed anything can travel?

 

[Dale]

Summary:: Can quantum objects violate Special Relativity. A momentum measurement can cause a quantum object to appear anywhere in the universe because the position probability never goes to zero.

How is that possible without violating the speed of light as the fastest speed anything can travel?

Quantum field theory does not violate special relativity. It has special relativity built into it.

The uncertainty principle describes states, not measurements. This means that if you produce a state with completely certain momentum then the state has completely uncertain position. You can measure the position and momentum to arbitrary precision and the momentum will always be the same but the position will be all over.

 

[andresB]

Notice that the usual Uncertainty relations have to be modified if you care about relativistic physics. See the introduction in Landau and Liftshitz "quantum electrodynamics".

 

[PeroK]

Summary:: Can quantum objects violate Special Relativity. A momentum measurement can cause a quantum object to appear anywhere in the universe because the position probability never goes to zero.

See also QFT for the Gifted Amateur. Section 8.3 is entitled The Death of Single-Particle QM, and includes a calculation that the probability of finding a particle outside its future light cone is non-zero. Cue Multi-Particle Quantum Field Theory.

 

[thedubdude]

Notice that the usual Uncertainty relations have to be modified if you care about relativistic physics. See the introduction in Landau and Liftshitz "quantum electrodynamics".

I don't have access to this volume. Perhaps you could give a brief summary and explanation? Thanks.

 

[thedubdude]

See also QFT for the Gifted Amateur. Section 8.3 is entitled The Death of Single-Particle QM, and includes a calculation that the probability of finding a particle outside its future light cone is non-zero. Cue Multi-Particle Quantum Field Theory.

I don't have this book. Please be so kind as to give a brief summary of how this relates to my question. Thanks.

 

[thedubdude]

Quantum field theory does not violate special relativity. It has special relativity built into it.

The uncertainty principle describes states, not measurements. This means that if you produce a state with completely certain momentum then the state has completely uncertain position. You can measure the position and momentum to arbitrary precision and the momentum will always be the same but the position will be all over.

I don't understand how this resolves my original question? Please elaborate. Thanks.

 

[PeroK]

I don't have this book. Please be so kind as to give a brief summary of how this relates to my question. Thanks.

The answer is no, quantum objects cannot violate SR (Special Relativity).

If you naively assume basic QM then you can create violations of SR. That's what is presented in the QFT book I mentioned. That indicates that basic QM must be upgraded to a more sophisticated theory that is compatible with SR. That's where QFT (Quantum Field Theory) comes in.

 

[PeterDonis]

We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any quantum object whose momentum is known ... to some degree (but not precisely). This means the objects position could be anywhere, even for example, a billion light years from the position at which the momentum measurement was made (of course with increasingly lower probability). But if the object actually ended up, a billion light years away, wouldn’t that violate special relativity? The object would seemingly have traveled 1 billion light years away from the momentum measurement event in no time at all. How is that possible without violating the speed of light as the fastest speed anything can travel?

All of this is based on a model of "objects" that "move". But relativistic QM, i.e., quantum field theory, is not a theory of "objects". It's a theory of quantum fields. What we normally think of as "objects" are just particular states of quantum fields, and what we normally think of as "motion" is a particular kind of distribution of quantum field states in spacetime.

In other words, in order to understand relativistic QM, you have to change your fundamental model of what your theory is a theory of.

 

[PeterDonis]

the speed of light as the fastest speed anything can travel?

It's worth noting that the "causality" limitation in SR--which is normally stated as "nothing can move faster than light"--is somewhat different in QFT. In QFT, as noted in my previous post, we don't actually have "objects" that "move" in the same sense as in classical SR. The QFT "causality" condition is simply that measurements of quantum fields at spacelike separated events must commute--i.e., their results cannot depend on the order in which they are made. This makes sense because if two events are spacelike separated, their ordering is frame-dependent, and physical observables should not depend on something that is frame-dependent.

 

[andresB]

I don't have access to this volume. Perhaps you could give a brief summary and explanation? Thanks.

Luckily, you can read it for free in the preview in the amazon page https://www.amazon.com/dp/0750633719/?tag=pfamazon01-20

 

[Dale]

I don't understand how this resolves my original question? Please elaborate. Thanks.

Your analysis used the wrong version of QM. You need to use quantum field theorem. There is no possible way to get a violation of SR with QFT since SR is built into the theory from the foundation.

 

[vanhees71]

The most concise explanation of this issue can be found in

S. Weinberg, The Quantum Theory of Fields, Vol. 1, CUP (1995)

There the necessity for the microcausality condition and the related properties like the unitarity and Poincare covariance of the S-matrix elements and the cluster-decomposition principles are very clearly explained in a modern no-nonsense way.