Wondering about QM whether things are actually all deterministic?

[Pio2001]

You're right, the confusion of Alice's state with the joint state of Alice and Bob should be avoided.

That's why I prefer the second formulation : the joint state completely evolves in a time t, that is strictly inferior to x/c, where x is the distance between Alice and Bob : this is non local.

 

[Hurkyl]

the joint state completely evolves in a time t, that is strictly inferior to x/c, where x is the distance between Alice and Bob : this is non local.

The evolution of their joint state over this region of space-time depends only on what's going on in the union of the two laboratories, correct? So the evolution of this state which is spread out across the two laboratories depends on nothing that is outside the past light-cone of this region. This is consistent with locality, not a proof of non-locality!

It is true that there is one part of this region (Alice's laboratory) whose past light-cone fails to contain other parts of this region (e.g. Bob's laboratory), and the fact that the joint state depends on the entirety of the region. But you only look at the global state; you can't have a reasonable claim that states evolve non-locally if you don't look at localized portions of the state.

Now, relative states are not a MWI-specific thing; they are basic tools of the mathematics of quantum mechanics. We have them because they are useful. They make a host of issues obvious, such as why Bob cannot use their entangled particles to send a FTL signal to Alice. (Any measurement Alice can perform depends only on the relative state of her half of the entangled pair) You're free to ignore them if you wish, but I think you're hurting yourself.

 

[Pio2001]

The evolution of their joint state over this region of space-time depends only on what's going on in the union of the two laboratories, correct? So the evolution of this state which is spread out across the two laboratories depends on nothing that is outside the past light-cone of this region.

Yes, I agree.

This is consistent with locality, not a proof of non-locality!

We can't tell anything about the locality or not of this situation : imagine that Alice sends a supraluminic message to Bob. She obviously violates locality.

However, all your constatations still hold : The evolution of their joint state over this region of space-time depends only on what's going on in the union of the two laboratories, and on nothing that is outside the past light-cone of this region.
...Except that in this particular case, there is no way we can tell that "this is consistent with locality".

You're free to ignore them if you wish, but I think you're hurting yourself.

Sorry, that's not stubbornness from me, just ignorance

 

[Hurkyl]

We can't tell anything about the locality or not of this situation : imagine that Alice sends a supraluminic message to Bob. She obviously violates locality.

The result is consistent with locality, but of course does not prove it. (That's why I was careful to say "consistent with locality", not "proves locality")

But in your example, if we looked at Bob's relative state, we would see a time evolution that is not determined by the conditions in Bob's laboratory, which would disprove locality.

We only see that your example is non-local by looking at the localized bits.

 

[ueit]

Not necessarily. For example the charges in A can emit an electromagnetic wave by themselves if they are in an initial configuration that has enough potential energy.

That's true in electrostatic. In electrodynamics, those laws require that electromagnetic waves travel at a speed equal to c.

For moving charges you must integrate over their past positions taking into account the finite speed of light. This means A will be dependent on the past state of B and B on the past state of A. However, given the fact that the evolution of both A and B is deterministic it follows that A and B cannot be independent.

 

[Pio2001]

In the hypothesis "If A and B are two space-time regions separated by a space-like interval, then nothing that is done in A can have an effect in B and conversely", A and B are not place, nor objects. They are space-time regions. The "past of A" is a space-time region that is completely outside of A.

What you are saying is that A depends partly on some parts of the past light-cone of B. Right, but A itself is completely independant of B.
Once a signal emitted in B reaches "an object that took part in the A space-time event", A is over.

you can't have a reasonable claim that states evolve non-locally if you don't look at localized portions of the state.

Can't we say that writing the state with kets describing eigenstates of Alice or Bob, knowing that they were in A and B respectively, and knowing that they didn't move faster than light, is itself a way of looking at localized portions of the state ?

 

[ueit]

In the hypothesis "If A and B are two space-time regions separated by a space-like interval, then nothing that is done in A can have an effect in B and conversely", A and B are not place, nor objects. They are space-time regions. The "past of A" is a space-time region that is completely outside of A.

What you are saying is that A depends partly on some parts of the past light-cone of B. Right, but A itself is completely independant of B.
Once a signal emitted in B reaches "an object that took part in the A space-time event", A is over.

Perhaps it would be better if you could propose a way in which your assumptions could be fulfilled in practice for two systems of point charges.

 

[Pio2001]

Exactly the way you stated above : For moving charges you must integrate over their past positions taking into account the finite speed of light.

It seems to me that this is the meaning of the locality hypothesis used in Bell's theorem : the movement of a charge in A $$(x_A, y_A, z_A, t_A)$$ can't affect the movement of a charge in B $$(x_B, y_B, z_B, t_B)$$.
It can however affect the movement of a charge at $$(x_B, y_B, z_B)$$, but only at time $$t > t_B$$.

 

[ueit]

Exactly the way you stated above : For moving charges you must integrate over their past positions taking into account the finite speed of light.

It seems to me that this is the meaning of the locality hypothesis used in Bell's theorem : the movement of a charge in A $$(x_A, y_A, z_A, t_A)$$ can't affect the movement of a charge in B $$(x_B, y_B, z_B, t_B)$$.
It can however affect the movement of a charge at $$(x_B, y_B, z_B)$$, but only at time $$t > t_B$$.

I agree on that. The issue is not the locality assumption but the independence assumption. If each system depends on the past state of the other system they cannot be said to be independent. The motion of Earth at t does not depend on the position of the Sun at t but at t-8 min. However, we do not conclude that the motions of the two bodies are independent. The reason we cannot go from locality to independence is the deterministic structure of the theory. Saying that A depends on the past of B is no different than saying that A depends on B.