Quantum entanglement from different frames of reference and the conservation laws

Question

From my understand, if the wave function of a particle in entanglement collapses by being observed, the other particle's wave function also collapse immediately.

My questions are:

1. Is it possible to find a frame of reference where the collapse of the wave functions does not occur simultaneously.
2. If there is such frame, does it mean the conservation laws (energy, momentum, spin...) are temporarily violated (during the time different of the two collapses)?

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As the question is not clear, let me make an example.

A Higgs boson at rest in the lab frame decay into an electron and a positron. As the spin of the Higgs boson is $0$, thus the sum of the spin of the beta particles from the decay must also be $0$.

In the lab frame, a physicist measures the spin on the X direction of the electron and get the value $1/2$. Due to the measurement, the electron spin is no longer in superposition (and we say that its wave function collapse).

As spin conserves, the spin of the positron is also determined immediately, and thus its spin state is also reduce.

In the lab frame, the collapse of the wave functions, or the reduction of the states of the beta particle occur at the same time at two different places. That what Einstein called "spooky action at a distance", but we will not discuss it here.

The question arises when we change to a frame moving at a constant velocity to the lab frame. Due to the Lorentz transformation, the observer in this new frame will see the reduction of the states occur at different times. So he come to a conclusion that spin is not conserved momentarily.

Can we tell if the new observer right or wrong, or we don't have a good answer?

Answer 1

Your question cannot be answered precisely, because no one knows exactly what "collapse" is or how it works mechanically. Some interpretations of QM deny that something labeled collapse even occurs (i.e. they say collapse is not physical, as @BillAslept mentions). However, this much is known - assuming there is something called collapse:

1. Time of collapse has no bearing whatsoever. If you want to say there is collapse at one place in spacetime X that occurs before it occurs in another spacetime location Y, that's fine. But strictly speaking, there is no standard theoretical notion that something at X "causes" something to happen at Y (in the normal sense of the word "causes").

2. It is equally satisfactory to say Y's collapse causes X's earlier collapse, as strange as that sounds. In fact, particles can be entangled after they are measured. If that doesn't throw traditional notions of causality into question, I don't know what does. That process is called Delayed Choice Entanglement Swapping. See for example:

Experimental delayed-choice entanglement swapping

3. Keep in mind that no experimental test of entanglement has ever demonstrated anything relating to ordering of observation (collapse) as a factor. If there is such an element, it is completely hidden to testing. Note that the theoretical treatment of entanglement predictions does not give any preference to ordering, as only the final measurement context is a factor.

4. Consequently, in consideration of the above: It should be clear that reference frame plays absolutely no known role in the experimental predictions or outcomes. Any statement otherwise is simply an assumption with no observational or theoretical basis.

5. And finally: no conservation laws appear to be violated in entanglement tests. There are some interpretations in which that might occur, and there have been proposals to transmit energy using entanglement. However, nothing concrete is evident at this point giving any indication that conservation of anything might be violated.

I hope this helps.

Answer 2

The answer to your question depends on what is happening in reality to bring about the outcomes of quantum experiments.

One common view of quantum theory is that you should use the equations of quantum theory to make calculations but ignore any implications they might have for how the world works. Since you can't say that an experiment is set up correctly unless there is an explanation of what is happening in reality when it's set up correctly this is a non-starter.

There are alternatives to quantum theory that modify the equations of motion so that there is a physical process that selects only one outcome:

https://arxiv.org/abs/2310.14969

These theories have problems with reproducing well tested predictions of relativistic quantum theories so I won't consider them further:

https://arxiv.org/abs/2205.00568

The equations of motion of quantum theory without such modifications do not include collapse. In quantum theory a measurement is just an interaction that produces a record of some observable that can be copied. These interactions suppress interference between different values of the observables but don't eliminate the other values: this ic called decoherence. Macroscopic objects undergo such interactions on a scale of space and time that is small compared the scale of its evolution so we don't see interference in everyday life:

https://arxiv.org/abs/quant-ph/0306072

On this scale reality looks approximately like a collection of non-interacting universes as described by classical physics:

https://arxiv.org/abs/1111.2189

https://arxiv.org/abs/quant-ph/0104033

This is commonly called the many worlds interpretation but it is just an implication of unmodified quantum theory.

There are relativistic quantum field theories that are used to explain what is happening to quantum systems when the effects of relativity are significant. Those theories are Lorentz invariant and so their predictions don't depend on reference frames. Decoherence theory suppresses states in which conserved quantities aren't conserved so there is no problem with conservation laws:

https://arxiv.org/abs/0903.1802

Entanglement correlations arise as a result of locally inaccessible information in decoherent channels and the correlations only arise when the results of measurements are compared: there is no spooky action at a distance:

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

The observer would know that his relative state has changed but this can be understood as an entirely local process:

https://arxiv.org/abs/2008.02328

So the observer wouldn't see and wouldn't expect to see violations of conservation laws.