Is Entanglement Finite or Timeless in Varying Spacetime Curvature?

[EskWIRED]

The concept of entanglement has gotten me thinking.

I am wondering what would happen if two entangled particles were to be prepared, with one of them being held in the lab on the Earth, while the other is placed into a spaceship and accelerated at a great rate for a long time, akin to the Einstein twin paradox.

If a measurement were to be taken of the accelerated particle, I take it that the particle on Earth would be affected, in the same manner that any pair of entangled particles would behave.

But WHEN would this take place for the particle on earth?

The measurement would occur, from the frame of the Earth-bound particle, far into the future. Would the Earth-bound particle be affected by the "future" event after some delay? Or would the affect occur such that it is "simultaneous" (in some frame) with the measurement?

Or am I adding some sort of misunderstanding into the mix and complicating things unnecessarily? I can't quite wrap my mind around this well enough to even think I might be able to propose a correct answer.

Can anybody point me to a discussion or explication of entanglement which takes into account different and varying curvature of spacetime for the entangled particles?

 

[Nugatory]

If a measurement were to be taken of the accelerated particle, I take it that the particle on Earth would be affected, in the same manner that any pair of entangled particles would behave.

That's not the right way of thinking about it. When we take a measurement on the accelerated particle, we get a result so know what the result of a measurement on the earth-bound particle would be - but for all we know, that measurement on the earth-bound particle has already been taken, so our measurement isn't "affecting" anything.

It is somewhere between unknowable and meaningless to ask which measurement went first and therefore "caused" the result of the other measurement. All we can say is that the two measurements will always be properly correlated, regardless of the order in which various observers say the measurements were taken.

 

[EskWIRED]

That's not the right way of thinking about it. When we take a measurement on the accelerated particle, we get a result so know what the result of a measurement on the earth-bound particle would be - but for all we know, that measurement on the earth-bound particle has already been taken, so our measurement isn't "affecting" anything.

So then why is it said that entanglement implies FTL transfer of information? My understanding is that the measurement of one collapses the wave function of the other, and that "previous" superposition of the other is "then" changed into a definite state.

Are you saying that both particles are "always" in the same state? I thought that "prior" to the measurement, both were in states of superposition?

And I thought that the measurement of one "instantly" changed the state of the other from superposition to a definite state.

Is this the root of my misunderstanding?


(BTW, my use of quotation marks is meant to preserve the notion that the two particles are in regions of vastly differing space-time curvature at the "time" of the measurement.)

 

[Nugatory]

So then why is it said that entanglement implies FTL transfer of information? My understanding is that the measurement of one collapses the wave function of the other, and that "previous" superposition of the other is "then" changed into a definite state.

That's one interpretation. However, the mathematical formalism of quantum mechanics will neither confirm nor deny that that's what happens; it just makes statements about the results of measurements.

And I thought that the measurement of one "instantly" changed the state of the other from superposition to a definite state.

That's also an interpretation. It doesn't work very well under relativistic conditions where the word "instantly" is problematic.

(BTW, my use of quotation marks is meant to preserve the notion that the two particles are in regions of vastly differing space-time curvature at the "time" of the measurement.)

That's fair, but be aware that space-time curvature is something of a red herring here. The difficulties are there even in flat space-time.

 

[DrChinese]

So then why is it said that entanglement implies FTL transfer of information? My understanding is that the measurement of one collapses the wave function of the other, and that "previous" superposition of the other is "then" changed into a definite state.

No one usually says that any "information" is transferred FTL. As far as anyone knows, there isn't any such. You might say that the one particle acts "as if" its property (say spin) value is sent to the other. You could also call it redundant information.

There is no basis under which there is any demonstrably different outcome when the order of measurements is reversed. So it is pretty much a point of philosophical interpretation as to how you view some of these things. There is no known accepted physical mechanism which used to describe this.

 

[lyncsta]

WOW!.. I never thought of it like this. My understanding(which may be wrong) is that the both tethered electrons are affected immediately despite speed or location. Not too long ago I was watching a video on some physicist trying to see a effect on an electron before they alter its tethered partner. In other words, trying to see an effect of a cause they are yet to create, backwards time travel!. That may be relevant to your question.

 

[DrChinese]

WOW!.. I never thought of it like this. My understanding(which may be wrong) is that the both tethered electrons are affected immediately despite speed or location. Not too long ago I was watching a video on some physicist trying to see a effect on an electron before they alter its tethered partner. In other words, trying to see an effect of a cause they are yet to create, backwards time travel!. That may be relevant to your question.

Again, some of this is a matter of interpretation of what you are viewing. That said...

There have been experiments in which BOTH photons were detected BEFORE they were entangled. The decision to entangle was made later.

Also, there have been experiments in which photons were entangled that NEVER co-existed. One was created and absorbed before the other was even created. This from independent laser sources.

So some causal elements clearly violate traditional classical rules, none of which affect the predictions or applications of QM.

 

[dm4b]

Hasn't it been shown that entanglement in space is mathematcally equivalent to entanglement in time? I thought I saw a paper on that once before, but can't find it now.

 

[EskWIRED]

There is no basis under which there is any demonstrably different outcome when the order of measurements is reversed. So it is pretty much a point of philosophical interpretation as to how you view some of these things. There is no known accepted physical mechanism which used to describe this.

So is entanglement simple and mundane? Is it anything more than two bodies in the same state (excluding location, of course), such that if you examine one, you gain information about both?

If one were to rip a white sheet of paper in half, dislocate the halves, and then examine the close half, one would then know that the dislocated half is also white.

Is entanglement no more profound an effect than that?

 

[Nugatory]

Is entanglement no more profound an effect than that?

It is much more complex and bizarre than that. What you're describing is roughly what we would call a "local realistic hidden variable theory" and it works fine for the simpler cases of entanglement. For example, a pair of particles are emitted with opposite spins; I measure one of them and get spin up, I measure the other and get spin down, it seems perfectly reasonable that they were just born with opposite spins and that's all there is to it. A common example, similar to your torn sheet, is a pair of gloves: Put one glove in each box, send one box far away, open the near box, and if I see a left-handed glove then I immediately know that the other glove is right-handed. And as you say, there is no great magic there - we just assume that the gloves were left-handed or right-handed and different when they went into the boxes.

However, let's try a more complex case. We have a whole bunch of married heterosexual couples. It so happens that in this population, if one spouse is blue-eyed the other one is brown-eyed, and if one is brunette the other is blond-haired. Thus, by looking at one member of the couple, we immediately know the eye color, hair color, and sex of the other member; it's just like the gloves or your sheet except with three variables instead of one.

But let us further suppose that we only get to make one measurement on each member of the couple: we can observe the sex, or the hair color, or the eye color, but not all three. Meanwhile, our remote lab partner is observing the other member of the couple, and is independently choosing what he will measure; we'll compare notes later. He assumes that every time he sees a brown-eyed person, I'll be seeing a blue-eyed one - although I will not know this if I've chosen to observe the sex or the hair color instead.

Now, suppose when we compare notes we discover that the number of brown-eyed women passing through my lab was greater than the number of blond women plus the number of brown-eyed brunettes of either sex? That is totally impossible if the hair color, eye color, and gender are all three preexisting attributes of each individual.

Yet that is exactly how quantum-mechanical entanglement between pairs of particles works when we work with three independent variables instead of just one. That's the theoretical prediction (google for "Bell's theorem") and the experimentally confirmed result.

 

[lugita15]

So is entanglement simple and mundane? Is it anything more than two bodies in the same state (excluding location, of course), such that if you examine one, you gain information about both?

If one were to rip a white sheet of paper in half, dislocate the halves, and then examine the close half, one would then know that the dislocated half is also white.

This is what people intuitively assume when they first hear about entanglement, but it's stranger than that. See this link for a good explanation.

 

[DrChinese]

So is entanglement simple and mundane? Is it anything more than two bodies in the same state (excluding location, of course), such that if you examine one, you gain information about both?

If one were to rip a white sheet of paper in half, dislocate the halves, and then examine the close half, one would then know that the dislocated half is also white.

As already mentioned by Nugatory and lugita15, it is much more than that. That was the EPR position, 1935. The issue is that Bell discovered that the measurement outcomes are dependent on the settings in a manner that is inconsistent with your view. If you try putting down values for outcomes a la the piece of paper you will see why. You can't get the statistics to match experiment.