Relativity & Uncertainty: Exploring the Impossible

[Thanshin]

There's something I don't manage to understand in the union between the relativity of simultaneity and the uncertainty of a quantum system's state.

Observer A is in a lab on Earth.
Observer B is approaching Earth at half the speed of light.

On Earth, we build an experiment that gives a result between two possibilities, based on the measured state of a particle. That experiment sends a light beam to observer B, containing information about the measured state.

Because of the relative speed of Observer B, the time on Earth in which the signal is sent, is in the future of Observer A.

By the time Observer B receives the signal, the experiment has already taken place on Earth. However, not soon enough as to have sent the signal to Observer B.

I'm under the impression that from Observer A's frame of reference one of these possibilities happened:

• The information about the measured state traveled faster than light to ObserverB.
• The measured state was an inevitability. In Observer A's future, the state was already decided before the measurement.

None of those options seem possible.

 

[Dale]

There are two events of note here. One is A performs the experiment and sends the signal, the other is B receives the signal. The events are lightlike separated, so the order of these two is the same in all reference frames.

 

[Thanshin]

the order of these two is the same in all reference frames.

It's not the order that bothers me, but A's point of view. From A's frame of reference, the moment in which the experiment is made, is in B's past.

That does't imply any problem, except that it implies that in B's past the result of A's experiment was already decided. The fact that the order of events is maintained, and that the signal can't go to B faster than light, requires the result of the experiment to already be decided in A's future.

So, for A, everything works as long as the result of his experiment is deterministic, which I understand shouldn't be.

 

[Dale]

It's not the order that bothers me, but A's point of view. From A's frame of reference, the moment in which the experiment is made, is in B's past.

What does this mean? The experiment is in the past of which event?

The term "in B's past" doesn't have a well defined meaning. It always needs to be specified which event is being considered.

 

[Thanshin]

I'm not sure I can describe it without a diagram, but I'll try.

At a time t (from A's point of view):

• From A's point of view, The experiment is Y seconds in the future.
• From A's point of view, B is X light seconds away.
• From A's point of view, the experiment hasn't taken place and it's result is undetermined.

However, still from A's point of view, A can calculate from B's speed, that in B's frame of reference, B's present is Z seconds in A's future.

There is a certain time t' at which Y and Z are equal. At that time, always from A's frame of reference, the experiment is still Y seconds in the future, but A knows that from B's frame of reference the beam of light is already on its way towards B.

When the beam reaches B, they both agree about the chain of events from both frames of reference. However, from B's point of view, at time t, even from A's frame of reference, the result of the experiment was already determined.I have a feeling that the problem is that from B's frame of reference what A calls time t isn't the same moment B identifies as "the moment in which the present on Earth was in A's future".

Now I feel that if I had a tool to draw a minkowski diagram to explain myself, instead of better explaining the question, I'd find the answer/mistake in my reasoning.

 

[Nugatory]

That does't imply any problem, except that it implies that in B's past the result of A's experiment was already decided. The fact that the order of events is maintained, and that the signal can't go to B faster than light, requires the result of the experiment to already be decided in A's future.
...
I'm under the impression that from Observer A's frame of reference one of these possibilities happened:

• The information about the measured state traveled faster than light to ObserverB.
• The measured state was an inevitability. In Observer A's future, the state was already decided before the measurement.

None of those options seem possible.

There are some threads over in the QM forum discussing this problem. Try searching there for discussions of FTL entanglement and causality.

The key here is that there is no way of experimentally distinguishing between A's measurement going first so that we know the result of B's measurement when and if he makes it, and B's measurement going first so that we know the result of A's measurement when and if he makes it. Either way we have two measurements, and if we get together after the fact to compare them we find that they are related in the way that quantum mechanics predicts. But as far as experiment and the theory of quantum mechanics is concerned there is no meaningful way of saying that (and no reason to care whether ) one measurement "really" happened before the other.

You might also want to google for "no-signalling theorem quantum mechanics" - because no information is transmitted in this manner, the possibility that information is being transmitted faster than light need not even arise.

However, you should also check out http://www.drchinese.com/Bells_Theorem.htm (maintained by our own Dr Chinese) to understand the experimental difficulties with assuming that the both results were predetermined.

Followups in a new thread in the QM forum please...

 

[Dale]

B's present is Z seconds in A's future.

I am not aware of any such calculation. You can calculate if B considers two specific events to be simultaneous, but there is no specific event which corresponds to "B's present".

There are only two identified events in this scenario: the experiment/transmission event, and the reception event. All frames agree that the experiment/transmission occurs before the reception. There is no event called "the present" or "the past". If you pick any third event then you can calculate how it is timed relative to the other events, but you have to define some specific event.