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- Thread starter Superposed_Cat
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Nugatory

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If a pair of particles had their spins determined at birth, then knowing all pieces of information about the histories of both particles would explain any correlation we see,

Because of this, we can get mathematical consequences of such statements.

These mathematical consequences are known as Bell inequalities.

Remarkably, scientists have done very careful experiments which show that real measurement outcomes do not obey Bell inequalities.

Because of this, we can conclude that their spins are not somehow already determined at birth.

What this ultimately means, is still being resolved to this day.

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Thank you all

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It's my understanding that this proof is not exactly about violations of Bell's inequalities. They are violated either way. However, if we can argue that the polarization was established at the creation of the EPR pairs, then local causality (with nothing travelling faster than c) can be used as an explanation of the observed correlations in polarization. This is one of the "loopholes" often discussed when dealing with these issues.

The mathematics is the superpositioned |ψ〉 vector and it's associated basis states defined by how it might be measured. (We can think of the rotation angle of a polarization filter that we might use for measurement as defining our basis states.)

The question is whether or not there is superposition at the point of measurement (or whether the polarization angle was determined at the point the EPR pair was created).

I'll outline an experimental configuration that I believe can sort it out, but I'll leave it to others to actually work out the proof.

Let's assume we have an EPR pair creator, and also a station A and station B, both at some distance (in opposite directions) from our EPR pair creator. Now, let's assume that both station A and station B have equipment to measure the polarization angle of their respective EPR entangled photons. This is a simple polarization filter with a back-plate to see if the photon got through. Let's further assume that station B has the ability to rotate their polarization filter at incredibly fast speeds (so fast that they can rotate it and also measure their photon faster than light could travel from station A to station B). I believe that this setup, along with the correlation that emerges when measuring several EPR pairs is enough to show that polarization is not determined at EPR pair creation (and that superposition is maintained until measurement).

I look forward to comments from others.

Regards,

Elroy

p.s. All of my thinking was in terms of

- #6

Nugatory

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I'll outline an experimental configuration that I believe can sort it out

It's been done already: http://arxiv.org/abs/quant-ph/9810080

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After some contemplation, I've decided to ask a related question in this thread. I hope it's not viewed as hijacking the thread. Here's the question:

__What is superposition__ (of, let's say, the polarization of a photon)?

In a certain sense, this is exactly the same question that Superposed_Cat asked. But let's think few a couple of relevant points.

* We often "measure" a photon (with measurement defined as sending it through a polarizer and then seeing if it got through). And, after measurement, we often say that it has "collapsed" into a certain state. However, any state, from an alternative perspective can be viewed as continued superposition. For instance, if we send a photon through a vertical polarizer (and it gets through), then, if we send it through a polarizer at 45°, it will appear superposed (with half getting through and half not getting through). Therefore, we can't say that**all** the photons (that got through) "collapsed" into the exact same state.

* To reiterate the above, any "known" state (basis state) of a photon can be viewed differently and then appear superposed.

* We can also bring elliptical and circular polarization into this. For instance, let's say our polarization filter has the ability to not only filter linearly, but it has the ability to polarize elliptically and circularly as well. We often "imagine" linear polarizers as a "slit" in a screen. And we rotate this slit to measure linear polarizations at different angles. However, we might imagine that this "slit" can be "stretched open" making an ellipse. When it's "fully stretched open", it makes a circle. If we stretch it open even more, it just closes on the orthogonal axis (Y vs X, or X vs Y, with Z being the direction of photon progression). So, with an ellipse, we still have a major axis.

When we talk of elliptical or circular polarization, we can also talk about whether the photon wave is rotating clockwise or counter-clockwise (depending on how the phase is offset in the Z direction). This brings up an interesting point. It can be argued that, when a photon is sent through a vertical linear polarizer (and it gets through), that it is in a state of circular superposition. We don't know if it's undulating down first and then up, or if it's undulating up first and then down. We would have to send it through a circular polarizer to determine that, which would "collapse" (destroy, superpose) it's linear polarization. Therefore, without even changing our angle, we can view linear polarization as a continuing superposition. In a similar vein, we can argue that circular polarization is a superposition of vertical and horizontal linear polarizations.

---

The concept of a Bloch sphere attempts to visually represent all possible polarization states, with the X,Z plane representing all linear polarizations (including their superpositions), whereas any non-zero value on the Y axis (regardless of X or Z values) represents elliptical and/or circular polarizations. (Values of Y=1 or Y=-1 would be circular, with values of Y closer to zero indicating elliptical polarization.)

Even with this visual concept of the Bloch sphere, we still have the unit Bloch vector pointing in some specific direction (defined by the polar coordinates theta and phi, where theta is 2 times the linear polarization and phi is the phase offset representing elliptical and circular polarization). To say again, we still have the unit Bloch vector. Therefore, from some specific perspective, the photon is**NOT** in superposition, whereas, from all other perspectives it **IS** in superposition. Sure, we move the Bloch vector every time we take a measurement, but this argument still holds.

Should we abandon the use of the word "collapsed" and, instead, use the words "reoriented as per measurement"? When we "peek into" the Bloch sphere at some point on the surface, if the Bloch vector isn't pointing straight at us, we then know that it's pointing directly away from us.

Does superposition truly make sense in terms of a single photon? Might we do better to say "random polarization among a group of photons"? And then, this goes back to Superposed_Cat's question. If we can argue that a single photon is NOT superposed from "some" perspective (even if that perspective is unknown), then why can't we say that that unknown perspective was determined at the emission of the photon from our EPR pair creator (and not at the time of measurement), thereby reclaiming Einstein's local causality?

Just some things I'm thinking about.

Again, I look forward to comments, even if they show flaws in my thinking.

In a certain sense, this is exactly the same question that Superposed_Cat asked. But let's think few a couple of relevant points.

* We often "measure" a photon (with measurement defined as sending it through a polarizer and then seeing if it got through). And, after measurement, we often say that it has "collapsed" into a certain state. However, any state, from an alternative perspective can be viewed as continued superposition. For instance, if we send a photon through a vertical polarizer (and it gets through), then, if we send it through a polarizer at 45°, it will appear superposed (with half getting through and half not getting through). Therefore, we can't say that

* To reiterate the above, any "known" state (basis state) of a photon can be viewed differently and then appear superposed.

* We can also bring elliptical and circular polarization into this. For instance, let's say our polarization filter has the ability to not only filter linearly, but it has the ability to polarize elliptically and circularly as well. We often "imagine" linear polarizers as a "slit" in a screen. And we rotate this slit to measure linear polarizations at different angles. However, we might imagine that this "slit" can be "stretched open" making an ellipse. When it's "fully stretched open", it makes a circle. If we stretch it open even more, it just closes on the orthogonal axis (Y vs X, or X vs Y, with Z being the direction of photon progression). So, with an ellipse, we still have a major axis.

When we talk of elliptical or circular polarization, we can also talk about whether the photon wave is rotating clockwise or counter-clockwise (depending on how the phase is offset in the Z direction). This brings up an interesting point. It can be argued that, when a photon is sent through a vertical linear polarizer (and it gets through), that it is in a state of circular superposition. We don't know if it's undulating down first and then up, or if it's undulating up first and then down. We would have to send it through a circular polarizer to determine that, which would "collapse" (destroy, superpose) it's linear polarization. Therefore, without even changing our angle, we can view linear polarization as a continuing superposition. In a similar vein, we can argue that circular polarization is a superposition of vertical and horizontal linear polarizations.

---

The concept of a Bloch sphere attempts to visually represent all possible polarization states, with the X,Z plane representing all linear polarizations (including their superpositions), whereas any non-zero value on the Y axis (regardless of X or Z values) represents elliptical and/or circular polarizations. (Values of Y=1 or Y=-1 would be circular, with values of Y closer to zero indicating elliptical polarization.)

Even with this visual concept of the Bloch sphere, we still have the unit Bloch vector pointing in some specific direction (defined by the polar coordinates theta and phi, where theta is 2 times the linear polarization and phi is the phase offset representing elliptical and circular polarization). To say again, we still have the unit Bloch vector. Therefore, from some specific perspective, the photon is

Should we abandon the use of the word "collapsed" and, instead, use the words "reoriented as per measurement"? When we "peek into" the Bloch sphere at some point on the surface, if the Bloch vector isn't pointing straight at us, we then know that it's pointing directly away from us.

Does superposition truly make sense in terms of a single photon? Might we do better to say "random polarization among a group of photons"? And then, this goes back to Superposed_Cat's question. If we can argue that a single photon is NOT superposed from "some" perspective (even if that perspective is unknown), then why can't we say that that unknown perspective was determined at the emission of the photon from our EPR pair creator (and not at the time of measurement), thereby reclaiming Einstein's local causality?

Just some things I'm thinking about.

Again, I look forward to comments, even if they show flaws in my thinking.

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DEvens

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Given quantum mechanics you can show an inequality. This inequality will be obeyed if the world is quantum mechanical. To get the world to be both causal and deterministic (i.e., not quantum mechanical) this inequality must be violated.

So, in order to build a theory that retains both causality (only events inside the backward light cone can influence an event) and determinism (the outcome of an experiment is determined uniquely by the inputs) you must violate Bell's inequality.

However, you can keep causality if you give up determinism. And this is the usual situation in quantum mechanics. The "spooky action at a distance" only arises if you insist on viewing every event as determined exactly. If events are only probabilistic then the seeming violation of causality entirely goes away.

Example: Suppose you had two arms of an experiment that measured spin "here" and "there" from a central source. You might think that spin up here determines spin down there, and that this amounts to sending a signal faster than light. You might think that you could sit on one side of the system and have the other be arbitrarily far away. Then you could agree that spin up here meant "1" and there spin down meant "1". You might think you could use this to send a signal. If the locations were light years apart (as one such experiment has been done using signals from pulsars that went through gravity lenses and split in two) you might think you could send a signal many light years in zero time.

But you cannot determine in advance that you will see spin up here. So you cannot use this to send a signal. The event is not deterministic, so the causal problem goes away.

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However, as I understand it, you have the interpretation of Bell's inequality exactly backwards.

Given quantum mechanics you can show an inequality. This inequality will be obeyed if the world is quantum mechanical. To get the world to be both causal and deterministic (i.e., not quantum mechanical) this inequality must be violated.

There is a good thread where we've been discussing these very issues:

https://www.physicsforums.com/threads/bells-inequality.791592/

Please take a look at this thread. Several of us have done a fair job of precisely outlining this point.

Regards,

Elroy

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* We often "measure" a photon (with measurement defined as sending it through a polarizer and then seeing if it got through). And, after measurement, we often say that it has "collapsed" into a certain state. However, any state, from an alternative perspective can be viewed as continued superposition. For instance, if we send a photon through a vertical polarizer (and it gets through), then, if we send it through a polarizer at 45°, it will appear superposed (with half getting through and half not getting through). Therefore, we can't say thatallthe photons (that got through) "collapsed" into the exact same state.

* To reiterate the above, any "known" state (basis state) of a photon can be viewed differently and then appear superposed.

You're right, that for a single photon, the superposition of two polarization states is just a third polarization state. So there is no unique notion of the photon being in a superposition.

However, what the EPR experiment is about is entanglement. That occurs when you have a pair of particles that are in a correlated superposition of states. With one type of entangled photons, you produce two photons that have the same polarization, but which polarization that is, is nondetermined. You can represent this as

[itex]\sqrt{2} (|H\rangle |H\rangle + |V\rangle |V\rangle)[/itex]

where [itex]|H\rangle |H\rangle[/itex] means that both photons are horizontally polarized, and [itex]V\rangle |V\rangle[/itex] means that both photons are vertically polarized. It's not just that the photons are in a superposition of horizontally and vertically polarized states, but they are in correlated states. It's a superposition of (1) both are vertically polarized, and (2) both are horizontally polarized. That is not equivalent to any other nonentangled state.

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Also, just so you know, I will be working hard to clear this up in my own head, in the interim.

However, here's what I'm still confused about. One of the three "loopholes" (as I understand it, there are three) in the EPR paradox is that the photon pairs were correlated at the point of emission/creation, therefore obviating any need for faster than speed of light explanations. Maybe our EPR pair creator device is incapable of creating anything other than "randomly polarized" pairs, but still pairs that are both polarized in the same (or exactly opposite) ways upon creation.

Stated differently, you've claimed that the EPR pairs are in the following state:

|ψ⟩ = √2 |H⟩|H⟩ + √2 |V⟩|V⟩

And what I'm claiming is that maybe they were in either

|ψ⟩ = 1 |H⟩|H⟩ + 0 |V⟩|V⟩

or

|ψ⟩ = 0 |H⟩|H⟩ + 1 |V⟩|V⟩

upon initial creation, although we don't know which until we measure them. Furthermore, even though which state is unknown, it's not "unknowable" (i.e., for a specific EPR pair, it's not probabilistic).

I think I may have outlined the answer to my own question in post #5 above, but I'll admit that I've yet to get complete clarity on this point. Also, it's pretty much the point of the thread.

Regards,

Elroy

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Yes, I think I "get" the concept (and the mathematics) of, say, putting a qubit through a Hadamard gate and then putting it and another qubit through a CNOT gate, which is effectively what you mathematically outlined. I further understand, if Alice and Bob measure in the same way, that a perfect ("spooky") correlation will emerge.

Also, just so you know, I will be working hard to clear this up in my own head, in the interim.

However, here's what I'm still confused about. One of the three "loopholes" (as I understand it, there are three) in the EPR paradox is that the photon pairs were correlated at the point of emission/creation, therefore obviating any need for faster than speed of light explanations. Maybe our EPR pair creator device is incapable of creating anything other than "randomly polarized" pairs, but still pairs that are both polarized in the same (or exactly opposite) ways upon creation.

Stated differently, you've claimed that the EPR pairs are in the following state:

|ψ⟩ = √2 |H⟩|H⟩ + √2 |V⟩|V⟩

And what I'm claiming is that maybe they were in either

|ψ⟩ = 1 |H⟩|H⟩ + 0 |V⟩|V⟩

or

|ψ⟩ = 0 |H⟩|H⟩ + 1 |V⟩|V⟩

upon initial creation, although we don't know which until we measure them. Furthermore, even though which state is unknown, it's not "unknowable" (i.e., for a specific EPR pair, it's not probabilistic).

That's what Bell's Theorem proves is NOT the case. Your theory would explain the result if someone measured the spin in the [itex]H[/itex] direction or the [itex]V[/itex] direction, but it wouldn't explain what happens if someone uses a filter that is, say, oriented at [itex]45^o[/itex] relative to the horizontal. If the photons were really in the state [itex]|V\rangle |V\rangle[/itex], and the two experimenters both set their filters at [itex]45^o[/itex] relative to horizontal, then the results would be:

- 25% of the time, both photons would pass the filters.

- 50% of the time, only one of the two photons would pass.
- 25% of the time, neither would pass.

- 50% of the time, both photons pass.
- 50% of the time, neither pass.

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