My Particularly Troublesome Version of the EPR Paradox

[Simultaneity]

In quantum physics, a wave function instantaneously collapses once an observable is measured. For instance, if an electron's angular momentum in the z direction is measured, then the angular momenta in the x and y direction immediately become indeterminate due to the Heisenberg Uncertainty Principle. If two particles are entangled and described by a single wave function, such as two particles that are products of a previous particle that decayed and whose combined spin is known due to conservation of angular momentum, and an observable is measured on one of them, the wave function instantanously collapses on the other, no matter how far apart the particles are. Experiments can and have been done to show instantaneous transmission of information (such as which direction the measurement took place along). But special relativity says that there is no such thing as a universal "instant" for all observers in all frames of reference. So, suppose Observer A is watching a space ship pass by at a very fast constant velocity. Observer B is in the middle of the ship. Two light beams are emitted, one from the front of the ship (the edge of the ship farthest along the direction of motion according to Observer A), such that Observer B observes they have been simultaneously emitted at the same instant. Observer A sees that the light beam from the back of the ship takes longer to reach the middle than the light beam from the front, because it must catch up with the ship, while the ship is racing to meet the light beam emitted from the front. Both observers agree on the speed of light, which is universal. But if the light beams reach Observer B at the same time according to Observer B, Observer A must also see this: If Observer B sets up a machine that kills a cat if both beams reach him at the same time, Observer A would obviously agree that the cat is dead (physics thought experiments are a dangerous place for cats). So Observer A must see the beam of light being emitted from the back of the spaceship before the beam of light is emitted from the front of the spaceship in order for the beams to meet in the middle. If a series of clocks is placed along the length of the ship that Observer B sees as synchronized, Observer A will see the clocks that are further forward in the direction of motion as reading fractions of a second less, depending on how far forward they are. So, now we take our two particles that are entangled, and we put one at the front of the ship and one at the back of the ship. Two machines are set up that measure each particle's spins, and the machines each take a measurement along a different direction. Observer B sees the particle at the front of the ship being measured slightly before the particle at the back of the ship, while Observer A sees the opposite, because the back of the ship is further along in time for Observer A than it is for Observer B. So what happens to the wave function? Which axis does it collapse along? It seems natural that Observer B might be fundamentally correct, since he isn't moving with respect to the particles, but suppose we have four particles that are entangled, and the other two are in corresponding positions on the ship that Observer A is on. Observer B sees himself as being still and Observer A as moving, so neither observer is still with respect to the particles. This is not an extremely technical paradox: The mathematics only require an undergraduate level of physics education, but to my knowledge no one has ever resolved this paradox.

[Cap'n Refsmmat]

Experiments can and have been done to show instantaneous transmission of information (such as which direction the measurement took place along).

Whoa whoa. What experiments are these?

[imatfaal]

Simultaneity - do you have a link for any experiment demonstrating instantaneous / ftl transmission of information? I didn't think it was possible and would love to read up on it

Edited August 2, 2012 by imatfaal
x-posted with Capt in duplicate thread

[D H]

In quantum physics ... paradox.

Whoa, dude. There's a name for what you wrote: Wall O' Text. There are these nifty devices in English called paragraphs. Please use them, and please separate those paragraphs with blank lines. Otherwise many of us will just see an unreadable wall of text.

 

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Whoa whoa. What experiments are these?

Aspect's experiment, to name but one. There have been a slew of tests of Bell's theorem (which is what the OP is alluding to) since Aspect. None have contradicted Bell's theorem. These experiments have closed off the various loopholes in Bell's theorem, leaving but one conclusion: Bell's theorem is correct and does apply to our universe. Bell's theorem is a rather disturbing part of quantum mechanics. Basically, you can't have both locality (quantum mechanics is restricted by the speed of light) and scientific realism (The Moon is still there when you don't look at it). You have to discard one or the other, or both. Pick your poison.

 

However, Bell's theorem does not say that FTL communication is possible. It just says that spooky action at a distance is one way to look at quantum mechanics. There are a number of no-communication theorems that do preclude FTL communication and that are compatible with Bell's theorem.

[immortal]

 

 

Aspect's experiment, to name but one. There have been a slew of tests of Bell's theorem (which is what the OP is alluding to) since Aspect. None have contradicted Bell's theorem. These experiments have closed off the various loopholes in Bell's theorem, leaving but one conclusion: Bell's theorem is correct and does apply to our universe. Bell's theorem is a rather disturbing part of quantum mechanics. Basically, you can't have both locality (quantum mechanics is restricted by the speed of light) and scientific realism (The Moon is still there when you don't look at it). You have to discard one or the other, or both. Pick your poison.

 

 

 

I don't think you can have an either-or option. As Norsen argues we need to discard both. Isn't it?

 

http://arxiv.org/pdf/quant-ph/0601205.pdf

[IM Egdall]

Bell's theorem is a rather disturbing part of quantum mechanics. Basically, you can't have both locality (quantum mechanics is restricted by the speed of light) and scientific realism (The Moon is still there when you don't look at it). You have to discard one or the other, or both. Pick your poison.

 

 

So do you mean by this to say that per Bell's theorem experiments either:

 

1) Local but no scientific realism - the universe is local but a particle's variable attributes are not there until you "look at them", or

 

2) Non-local but there is scientific realism - the universe is non-local but a particle's variable attributes are there before you "look at them"?

 

I thought Bell's theorem experiments show the universe is non-local, period. And the interpretation using standard qm says there is no scientific realism -- a particle's variable attributes are not there until you look at them. However other interpretations like Bohm's qm are non-local but do maintain scientific realism.

 

Do I have this right?

Edited August 2, 2012 by IM Egdall

[D H]

I don't think you can have an either-or option. As Norsen argues we need to discard both. Isn't it?

If he is, he's wrong. That shoots down the local but non-realistic many worlds interpretation as well as the non-local but realistic Bohmian mechanics, basically leaving only the Copenhagen interpretation. AFAIK, MWI, Bohmian mechanics, and the Copenhagen interpretation all have survived the onslaught of Bell's Theorem. Norsen's critique, along with Zeilinger's experiments do not apply to Bohmian mechanics (which Zeilinger acknowledges), mainly because the hidden variables in Bohmian mechanics are weird, just like the rest of that interpretation.

 

Aside: I used the term "scientific realism" when it would have been better to use "counterfactual definiteness". The latter term is the correct one, but nobody outside physics knows what it means. The former term is not quite correct (unless one reinterprets scientific realism to mean counterfactual definiteness, that is).

[immortal]

If he is, he's wrong. That shoots down the local but non-realistic many worlds interpretation as well as the non-local but realistic Bohmian mechanics, basically leaving only the Copenhagen interpretation. AFAIK, MWI, Bohmian mechanics, and the Copenhagen interpretation all have survived the onslaught of Bell's Theorem. Norsen's critique, along with Zeilinger's experiments do not apply to Bohmian mechanics (which Zeilinger acknowledges), mainly because the hidden variables in Bohmian mechanics are weird, just like the rest of that interpretation.

 

Many physicists acknowledge Norsen's work and argue that it is indeed that counterfactual definiteness is logically derived from locality and hence both should be discarded.

 

http://arxiv.org/pdf/1102.2855.pdf

 

 

One interpretation of the sentence quoted above is that there is a choice between locality and counterfactual definiteness, and that, in operational interpretations in particular, we can have a satisfactory resolution to the problem of Bell’s theorem if we drop counterfactual definiteness. This interpretation is mistaken, however. Norsen (quoting other earlier treatments) convincingly argues that counterfactual definiteness is not a separate assumption, but in fact follows from local causality (and the results of quantum mechanics which specify that perfect correlations between some outcome events can be achieved in the EPRB set-up) [33]. Indeed, it is clear in Bell’s last published account of his result [3] that the argument begins with causality and leads to counterfactual definiteness. Thus, whether or not we start with a bias on the subject of hidden variables, if we accept Bell’s local causality as a good formalisation of the idea of a relativistic causal principle, then we are forced to accept conterfactual definiteness. In other words, when standard logic is assumed, rejecting counterfactual definiteness amounts to rejecting local causality (and Einstein Locality).

 

This is what I had read and so I asked you. Rejecting one means rejecting the other.

 

Aside: I used the term "scientific realism" when it would have been better to use "counterfactual definiteness". The latter term is the correct one, but nobody outside physics knows what it means. The former term is not quite correct (unless one reinterprets scientific realism to mean counterfactual definiteness, that is).

 

Yes, counterfactual definiteness is the correct term indeed. QM doesn't rule out an objective world but it says it is definitely not in any way we think it is (no element of physical reality corresponding to a physical quantity). Non-separability and non-locality are the main features of our Nature.

[Simultaneity]

Simultaneity - do you have a link for any experiment demonstrating instantaneous / ftl transmission of information? I didn't think it was possible and would love to read up on it

 

There's a list of the main published findings here.

http://en.wikipedia.org/wiki/Bell_test_experiments

[juanrga]

In quantum physics, a wave function instantaneously collapses once an observable is measured.

 

The collapse is not instantaneous. Moreover you are assuming that the system was not prepared in an eigenstate of the observable, in whose case there is not collapse.

 

For instance, if an electron's angular momentum in the z direction is measured, then the angular momenta in the x and y direction immediately become indeterminate due to the Heisenberg Uncertainty Principle. If two particles are entangled and described by a single wave function, such as two particles that are products of a previous particle that decayed and whose combined spin is known due to conservation of angular momentum, and an observable is measured on one of them, the wave function instantanously collapses on the other, no matter how far apart the particles are. Experiments can and have been done to show instantaneous transmission of information (such as which direction the measurement took place along).

 

No experiment exists where information is instantaneously transmitted.

 

When quantum mechanics was being developed about 100 years ago, there was a belief that collapse violated relativity, but this is false. The topic of relativistic collapse of wavefunctions is, today, a mature topic in quantum physics.

 

QM doesn't rule out an objective world but it says it is definitely not in any way we think it is (no element of physical reality corresponding to a physical quantity).

 

The work of theoretical physicists is to think how the world is. And the work of experimental scientists is to test if theoreticians ideas agree with the physical reality via measurements of physical quantities corresponding to some amount of physical reality.

[Simultaneity]

"No experiment exists where information is instantaneously transmitted."

 

Every experimental confirmation of Bell's Theorem shows the transmission of information at a speed faster than light. If a particle that is not in an eigenstate along a particular axis is measured along that axis, this automatically collapses the wavefunction for any particle that is entangled with it. For instance, an electron positron pair can be in a superposition of two states, one where the electron has positive z spin and the positron has negative z spin, and one where the electron has negative z spin and the positron has positive z spin. There is nothing special about the z axis: The same wave function can be expressed similarly with regards to the x axis. As soon as a measurement is taken along one axis, a measurement along that axis by another observer must show the same result. A measurement taken along another axis will show random results because of the Heisenberg Uncertainty Principle.

 

Here is a good place to start your study of the matter, though there are a slew of other experiments which I linked earlier in the post: http://www.nature.com/news/2008/080813/full/news.2008.1038.html

 

Note: The experimental apparatus I described in the original post is off by a bit, I realized, the measurements need to be taken in a bit more complex manner, using 45 degree angles and such. I linked a list to the experiments done to show the instantenous collapse of the wave function earlier in the thread, you can read about the methods researchers have used in those. But all point to the fact that a measurement can collapse a wave function simultaneously in two far away locations, and this does not jive with special relativity's disproof of the concept of simultaneity.

 

OK, I think I have a more accurate version of the paradox that doesn't require fancy 45 degree measurements. So, a set of electrons and a corresponding set of entangled positrons are each put on opposing ends of the spaceship. These are in spin eigenstates along the x axis such that the electrons will read a positive spin and the positrons will read a negative spin. One machine measures the spin of its set along the x axis, and the other machine on the other side of the spaceship measures the spin of its set along the y axis. According to some observers, the y spin will be measured first, but according to other observers, the x spin will be measured first. Will the x spin read the definite measurements that were known "before" the y spin was measured, or will it read random measurements? It seems like this points to preferred frames of reference. But even preferred frames of reference can't be a solution, since a ship going in the other direction could be making corresponding measurements, with some paired electrons and positrons on different ships and some on the same ship.

 

Immortal and IM, it seems to me like, whether either counterfactual definiteness, localism, counterfactual definiteness/localism, or superdeterminism is true, it can't explain why one of the measurements arbitrarily takes precedent over the other. I guess the paradox leads me toward a belief in superdeterminism, but this still doesn't explain the specifics of why the system acts as if it was measured by one of the observers first in a seemingly arbitrary fashion. I guess it might be some sort of inherent randomness of the Heisenber variety. Of course, to be technical, Heisenberg was only half right according to superdeterminism. Heisenberg said that the future outcome of a system can be such that it is not determined yet, and the measurement will be completely random. Superdeterminism says that the future outcome of a system cannot be such that it is not determined yet, but the measurement cannot be predicted.

 

If the correctness of either observer's point of view is arbitrarily determined, it seems like Heisenberg's Uncertainty Principle and the more modern version, Ozawa's Inequality (see here: http://www.scientificamerican.com/article.cfm?id=heisenbergs-uncertainty-principle-is-not-dead), are both proven wrong by this paradox. Say both sets of particles are in spin eigenstates along the x axis. One observer then sees one of the sets being measured along the x axis and displaying its eigenstate. He then sees the other set of particles being measured along the y axis and showing random measurements. But another observer sees the measurement along the y axis taking place before the measurement along the x axis: This violates Ozawa's Inequality (and Heisenberg's Uncertainty Principle).

[juanrga]

Every experimental confirmation of Bell's Theorem shows the transmission of information at a speed faster than light.

 

False. And as stated in my previous message the relativistic theory of collapse has been developed. I did not mention then that the relativistic theory of collapse is in complete agreement with the relativistic speed limit, but I assumed that this fact would be obvious.

 

Here is a good place to start your study of the matter, though there are a slew of other experiments which I linked earlier in the post: http://www.nature.co....2008.1038.html

 

This is a news written by a writer who does not know the physics. Below in the comments, you can find the two first comment by Uncle Al explaining that no information was sent faster than light.

 

If the correctness of either observer's point of view is arbitrarily determined, it seems like Heisenberg's Uncertainty Principle and the more modern version, Ozawa's Inequality (see here: http://www.scientifi...ple-is-not-dead), are both proven wrong by this paradox.

 

Nonsense. The uncertainty principle has already been proven right in hundred of experiments. Therefore you cannot prove it "wrong". In fact the above experiment (nature link) is in complete agreement with quantum mechanics.

Edited August 3, 2012 by juanrga