# Causality and quantum entanglement

• acegikmoqsuwy

#### acegikmoqsuwy

I have a quick question about what is going on with the following scenario:

There are three planets: A, B, and C. They are arranged in the following manner: A is 4 light years away from B and 2 light years from C; the distance between B and C is 3 light years. Now suppose that there are two electrons, κ and λ, known to have opposite spins, but they have not yet been measured (and as a result, their spins are undecided). κ is sent to B and λ is sent to C. There exists a machine on B that reads the spin of the electron, and sends a certain colored laser at A depending on the spin measured. There exists a machine on C that determines the exact location of the electron, and sends a distinct colored laser at A depending on the position measured. If the machine is unable to determine the exact location, a blue laser is sent to A. Now suppose that κ enters the machine on B, and a green colored laser is sent toward A. λ enters C moments after the laser on B was fired at A. The spin of λ is now determined because of the measurement on κ. Thus the position of λ cannot be determined and a blue laser is sent to A. There is an observatory on A waiting looking for signals from B and C (suppose they all worked together in performing this experiment). A first sees the signal from C as a blue light (as expected), and then sees the green light from B two years later.

The conclusion of the experiment is that A sees the event on C occur first, and then the event on B occur. If the event on B caused the event on C, then how or why does this happen? (Or is there some sort of flaw in the experiment?)

Quantum mechanics predicts nonlocal correlations that violate the Bell inequalities at spacelike separation.

This means that there is no explanation of the correlations that respects relativistic causal structure, eg. http://arxiv.org/abs/0707.0401

However, quantum mechanics is consistent with relativity because
(1) there is no faster than light signalling of classical information, eg. http://arxiv.org/abs/0911.2504
(2) the probabilities of the events are frame-invariant, eg. http://arxiv.org/abs/1007.3977

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1. I must accept the evidence of such things happening, but I struggle to believe the possibility that nothing is happening until we observe it. I believe that we must accept that it is happening whether we are there to observe it or not. But that is not the point of your question. By the way, these electrons would have to be traveling at the speed of light for that to happen (but let's just assume that our experimenters have somehow found a way to do so), but actions would not play out as you had predicted. If the electrons were fired at the same time and were immediately sent back once they had reached their destination, it would be completely opposite. Because C is closer, electron λ would reach it's destination first (in 2 years), and would have it's location measured and the laser from C would be sent back to Earth. Because it only takes 2 years to reach C and another 2 years for the laser to return, electron λ would have returned to Earth at the same time that electron κ would be reaching it's destination. So because of this, the spin would be unable to be measured because the location has already been measured. So 4 years after electron λ's laser has returned, electron κ's laser would return, and would have been unable to measure κ's spin. I hope this helps :)

There exists a machine on C that determines the exact location of the electron, and sends a distinct colored laser at A depending on the position measured. If the machine is unable to determine the exact location

If the machine on C tries to measure the position of the electron, it will succeed every time. The uncertainty principle just tells us that when we do the experiment many times, we will find a statistical spread in the distribution of the position measurements even though we started with the same initial conditions.

By the way, these electrons would have to be traveling at the speed of light for that to happen
We can easily avoid that issue... just say that they are traveling at speed ##c-\epsilon## where ##\epsilon## is some very small number. The important thing is the edge of the light cone, and that is defined by ##v=c##.

So because of this, the spin would be unable to be measured because the location has already been measured. So 4 years after electron λ's laser has returned, electron κ's laser would return, and would have been unable to measure κ's spin. I hope this helps :)
No such thing would happen, because there's no problem at all with measuring the position of electron κ: Put a suitable scintillation counter in its path, watch for the flash, you have its position.

We can easily avoid that issue... just say that they are traveling at speed ##c-\epsilon## where ##\epsilon## is some very small number. The important thing is the edge of the light cone, and that is defined by ##v=c##.

No such thing would happen, because there's no problem at all with measuring the position of electron κ: Put a suitable scintillation counter in its path, watch for the flash, you have its position.
So does that mean that we could have both measurements? I briefly thought that there was the possibility of being able to know both because you can't really have an opposite location in this scenario.

So does that mean that we could have both measurements?

Yes. The uncertainty principle doesn't prevent you from making arbitrarily precise measurements of two properties of a quantum system, it prevents you from preparing a quantum system in such a way that you know ahead of time what both of those measurements will be.

In the most frequently cited case, if you prepare a large number of systems ("ensemble" is the standard term) in the same way and with a particular value of position you can still measure the momentum as accurately as you wish but you will get different values for different members of the ensemble. Conversely, if you prepare a large number of systems in the same way and with a particular value of momentum, you will find that you get different values of the position for different members of the ensemble.

nitsuj and acegikmoqsuwy
I know that it is possible to observe two events happening in the opposite order that they occur in.

Yes. The uncertainty principle doesn't prevent you from making arbitrarily precise measurements of two properties of a quantum system, it prevents you from preparing a quantum system in such a way that you know ahead of time what both of those measurements will be.

Does this mean that it is impossible to theoretically create an experiment in which events appear to occur in a different order than they actually do AND in which the events are dependent on each other?

I know that it is possible to observe two events happening in the opposite order that they occur in.

Does this mean that it is impossible to theoretically create an experiment in which events appear to occur in a different order than they actually do AND in which the events are dependent on each other?
The only such experiment I have heard of that seem to make events appear in a different order would involve different frames of references and observers in separate locations.. But apart from that I'm not completely sure...

I
Does this mean that it is impossible to theoretically create an experiment in which events appear to occur in a different order than they actually do AND in which the events are dependent on each other?

It is impossible. This isn't a quantum mechanics thing, it's a special relativity thing.

If two events are spacelike-separated, meaning that a light signal cannot travel from one to the other (for example, the two events are separated by one light-year in space and less than one year in time according to some observer) then:
1) They will be spacelike-separated for all observers usng all reference frames.
2) Different observers in different frames will come to different conclusions about which happened first (or whether they happened at the same time).
3) It is not possible for the events to be dependent on one another, which eliminates all the awkward problems with effects happening before their causes.

Conversely, if the two event are timelike-separated, meaning that it is possible for a light signal to travel from one to the other, then:
1) They will be timelike-separated for all observers using all reference frames.
2) All observers will agree about the relative ordering of the two events; one of them happened before the other.
3) It is possible but not required that the first event is the cause of the second.

Does this mean that it is impossible to theoretically create an experiment in which events appear to occur in a different order than they actually do AND in which the events are dependent on each other?
Yes. In QFT this is ensured by the fact that spacelike operators (faster than light) commute (the order of measurement doesn't matter).

Yes. The uncertainty principle doesn't prevent you from making arbitrarily precise measurements of two properties of a quantum system, it prevents you from preparing a quantum system in such a way that you know ahead of time what both of those measurements will be.

In the most frequently cited case, if you prepare a large number of systems ("ensemble" is the standard term) in the same way and with a particular value of position you can still measure the momentum as accurately as you wish but you will get different values for different members of the ensemble. Conversely, if you prepare a large number of systems in the same way and with a particular value of momentum, you will find that you get different values of the position for different members of the ensemble.
Your explanation seems to be at odds with wikipedia;

" In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously. For instance, in 1927, Werner Heisenberg stated that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa."

Can you resolve this apparent difference?

If two events are spacelike-separated, meaning that a light signal cannot travel from one to the other (for example, the two events are separated by one light-year in space and less than one year in time according to some observer) then:...
I don't think that's a very good description of spacelike-separated events. In the first place, if a light signal cannot travel from one event to the other, that is true for both spacelike-separated and timelike-separated events. And secondly, I think a better way to state it is if the two events are separated by some distance but at the same time according to some observer then they are spacelike-separated and an inertial ruler at rest with that observer would measure the spacelike spacetime interval between them.

Conversely, if the two event are timelike-separated, meaning that it is possible for a light signal to travel from one to the other, then:...
No, a light signal cannot travel between two timelike-separated events, that would be true for lightlike-separated events. For timelike-separated events, a massive object can travel from one event to the other. Specifically, an inertial clock would measure the timelike spacetime interval between them.

At least that's how I understood these separations. Correct me if I'm wrong.

Your explanation seems to be at odds with wikipedia;

" In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously. For instance, in 1927, Werner Heisenberg stated that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa."

Can you resolve this apparent difference?

The first sentence of that wikipedia article is consistent with what I said, or at least it would be if it were a bit more rigorous about stating exactly what is meant by "could be known". But note that it says "could be known", not "will be measured" - being able to predict the statistical distribution of measurement results across the members of an ensemble is rigorously what is meant by "could know".

The second sentence is confused. Heisenberg did say in 1927 that measuring the position of a particle necessarily changes the momentum and vice versa, but that's not the uncertainty principle as it is now understood.

There are many discussions over in the QM forum.

nitsuj
At least that's how I understood these separations. Correct me if I'm wrong.

You're right. I was being sloppy in trying to capture the intuitive notion of "can't get there from here without faster than light travel".

The second sentence is confused. Heisenberg did say in 1927 that measuring the position of a particle necessarily changes the momentum and vice versa, but that's not the uncertainty principle as it is now understood.

This is why I liked your explanation. It kinda turns wiki's explanation on it's head, instead referring to the prediction...not the actual measurement. i.e. the prediction being the "meat" of the uncertainty principle.