Entanglement

[JonG]

The phenomenon of quantum entanglement appears to rely upon the belief that prior to measurement, a system is represented by a linear combination of eigenstates but that, when the measurement is made, its wavefunction collapses into a single state (which one isn't known beforehand) which is shared by the whole system.

 

If the system was instead in a single state before measurement, any measurement, regardless of where it was made, would give a result consistent with that state and the mystery of entanglement wouldn't arise.

 

What I am trying to do is to decide whether the above presumption is what is implied by the paper published by Pusey, Barrett and Rudolph and described here:

http://phys.org/news/2012-05-paper-controversy-nature-quantum-function.html

Edited September 1, 2015 by JonG

[swansont]

The phenomenon of quantum entanglement appears to rely upon the belief that prior to measurement, a system is represented by a linear combination of eigenstates but that, when the measurement is made, its wavefunction collapses into a single state (which one isn't known beforehand) which is shared by the whole system.

 

If the system was instead in a single state before measurement, any measurement, regardless of where it was made, would give a result consistent with that state and the mystery of entanglement wouldn't arise.

 

If the system was in a single state beforehand, then you would get different results from what we see in some experiments.

[JonG]

"If the system was in a single state beforehand, then you would get different results from what we see in some experiments."

 

I don't understand why the results would be different. If the single state were to be the same as that which the wavefunction is assumed to collapse into, why would the results of a measurement be different? I would be grateful if you could indicate which experiments can only be explained on the basis of a collapsing wavefunction.

Edited September 2, 2015 by JonG

[Strange]

Sounds like you are looking for Bell's Theorem: http://drchinese.com/David/Bell_Theorem_Easy_Math.htm

[JonG]

"Sounds like you are looking for Bell's Theorem: http://drchinese.com...m_Easy_Math.htm"

 

Bell's inequalites are clearly related to the interpretion of entanglement experiments, but I am not sure that they relate to the suggestion put forward by Pusey at al. The essential difference seems to be whether a system is in a particular quantum state prior to measurement or whether the act of measurement put it into that state.

 

I don't think that the Pusey et al suggestions involve things like "hidden variables" that are often mentioned in this context.

[Strange]

 

I don't think that the Pusey et al suggestions involve things like "hidden variables" that are often mentioned in this context.

 

This article ends with: "Their theorem does, however, depend on a controversial assumption: that quantum systems have an objective underlying physical state."

http://www.nature.com/news/a-boost-for-quantum-reality-1.10602

 

Isn't that what is described as a hidden variable in Bell's Theorem?

[JonG]

Isn't that what is described as a hidden variable in Bell's Theorem?

 

The hidden variable notion arose with Einstein who appears to have believed at some point that something was missing from quantum theory. However, the Pusey at al suggestion doesn't require anything to be missing from quantum theory - it seems to be more matter of how one interprets the idea of a wavefunction.

 

I have to admit that this area is littered with terms like "hidden variable" to the extent that one is unsure what is being referred to. Also, the precise meaning of "objective underlying physical state" is not clear.

 

(I don't know how well the Pusey et all suggestions stand up to close scrutiny in accordance with Bell's inequalities but it isn't obvious that they would be relevant.)

 

 

 

[Strange]

(I don't know how well the Pusey et all suggestions stand up to close scrutiny in accordance with Bell's inequalities but it isn't obvious that they would be relevant.)

 

Well, clearly they, and others who have looked at the work, are familiar with Bell's Theorem so one has to assume that it does not trivially invalidate this work. (It is times like this I wish I had the expertise to really understand what they are doing!)

 

Their paper is here: http://arxiv.org/abs/1111.3328

[JonG]

(It is times like this I wish I had the expertise to really understand what they are doing!)

 

I know exactly what you mean. There are times when I fee that if I were to delve into everything that I find puzzling on page 1, I would never get to page 2 !

[swansont]

"If the system was in a single state beforehand, then you would get different results from what we see in some experiments."

 

I don't understand why the results would be different. If the single state were to be the same as that which the wavefunction is assumed to collapse into, why would the results of a measurement be different? I would be grateful if you could indicate which experiments can only be explained on the basis of a collapsing wavefunction.

 

What do you mean by the system is in a single state? Because entangled particles can be thought of as being in a single state. The way you stated it I assumed you meant in a known state, but I could be wrong.

 

In a larger picture, I'm not sure the article is arguing about what you are asking. I don't see the relationship between entanglement and whether wave functions are "real" (and I don't see much in the way of clarification of what they mean by "real")

[JonG]

What do you mean by the system is in a single state? Because entangled particles can be thought of as being in a single state.

 

Yes, they would be in the single state - the one on which measurements were made. But the usual contention is that, before measurement, the state of the particles is represented by a linear superposition of eigenstates which collapses into a single state when a measurement is made.

 

In a larger picture, I'm not sure the article is arguing about what you are asking. I don't see the relationship between entanglement and whether wave functions are "real" (and I don't see much in the way of clarification of what they mean by "real")

 

The article (I refer to their published paper) is not specifically about entanglement but it does make the statement: "If a quantum state is a physical property of a system then quantum collapse must correspond to a - problematic and poorly defined - physical process."

 

In the article, they advocate that the quantum state is a physical property of the system and this implies that the process of "collapse" is as they put it, problematic and poorly defined. However, collapse into a single state appears to be the "process" usually invoked to explain why measurements on entangled particles correspond to each other. (As far as I am aware, nothing is known about this collapsing process - it is simply postulated). So I think that their views have some relevance to the usual accounts of entanglement.

 

Relevant quotes referring to what is written above:

 

"Many others have suggested that the quantum state is something less than real. In particular, it is often argued that the quantum state does not correspond directly to reality, but represents an experimenter's knowledge or information about some aspect of reality. This view is motivated by, amongst other things, the collapse of the quantum state on measurement."

 

Their distinction between real and unreal amounts to whether or not the regions of phase space corresponding to the descriptions of the system in different states overlap or don't overlap. However, it's necessary to read through the article to see that - they are not using term "real" in some casual way. Briefly, they give examples along the lines of: - If a system with a property which has the value P occupies a region of phase space, and this region overlaps with one corresponding to the property having the different value P', then this property can't be real because in the region of overlap it would have two different values.

[swansont]

What do you mean by the system is in a single state? Because entangled particles can be thought of as being in a single state.

 

Yes, they would be in the single state - the one on which measurements were made. But the usual contention is that, before measurement, the state of the particles is represented by a linear superposition of eigenstates which collapses into a single state when a measurement is made.

 

 

The problem is that if the particle was in a particular state before the measurement, the experiments would give a different result than what we see.

 

Example: let's say you have entangled photon polarizations. One is perpendicular to the other. If you measure one as being vertical, the other one will always be horizontal. You might assume that they were always in those states.

 

But what if we measure identical systems with the polarizer at 45º? If they are "really" H and V, respectively, then there is a 50% probability of each being +45º and -45º. That is, you will get both being +45º a quarter of the time, and both being -45º a quarter of the time. But with entangled particles we get one at +45º and the other at -45º. Always. So the particles are not in a known state before the measurement, they are in a superposition.

[JonG]

[i} So the particles are not in a known state before the measurement, they are in a superposition.[/i]

 

This is not what is being suggested. Whichever view is taken, the state of the system would be unknown before measurement. In fact, it's hard to see how these different ways of looking at the experiments could differ in their predicted outcomes. According to one view, the act of measurement causes a wavefunction to collapse into a single state and what is observed corresponds to that state. According to the other, the system is in that entangled state before the measurement was made and wavefunction collapse doesn't occur. In both cases, the states would be entangled but there is no way of predicting what the state is going to be before the measurement is made. Whichever way one looks at it, the state of the system when a measurement is made would be of the same degree of uncertainty - it's a question of how did it get into that state rather than what the state is.

 

My interest in this really is to do with the idea of collapse of a wavefunction. As suggested by the authors referred to earlier, this postulated collapse is a process about which we know almost nothing and, in the case of entanglement, it leads to the conclusion that information about the state of the system is transmitted between spatially separated points instantly. This latter problem would not arise if the system was assumed to be in the state it was found to be in before the measurement was made.

 

Oddly, some entanglement experiments actually cast doubt on the collapsing wavefunction explanation. I believe that Alain Aspects experiment using photons established that there could be no causal link between the measurements on different photons, and yet the wavefunction collapse explanation suggests that one measurement initiates the collapse of the wavefunction which then determines the outcome of the other experiment!

[swansont]

According to the other, the system is in that entangled state before the measurement was made and wavefunction collapse doesn't occur.

 

So what's the wave function for such a state?

 

My interest in this really is to do with the idea of collapse of a wavefunction. As suggested by the authors referred to earlier, this postulated collapse is a process about which we know almost nothing and, in the case of entanglement, it leads to the conclusion that information about the state of the system is transmitted between spatially separated points instantly. This latter problem would not arise if the system was assumed to be in the state it was found to be in before the measurement was made.

 

But we know from experiment (as I described) that the system is not in this state before the measurement was made, so that's moot.