When Did Einstein First Encounter Quantum Entanglement?

[vanesch]

I think the lecturer must have meant "cannot be entangled with another particle if we are to use this analysis," rather than "it is impossible for further entanglements to exist." In principle, particles are vastly mutually entangled, including the fact that many are indistinguishable in the first place (like all electrons, etc.). But physics is not about what is, it is about how we can treat what is and get the right answers, to within some desired precision. In practice, we can find situations where entanglements are vastly unimportant, or we can find situations where simple entanglements matter but more complicated ones don't. Physics is very much about building up to the complex from the simple, and that it works at all says something about what a tiny fraction of the information the universe encodes is actually "active" in determining the outcomes of our experiments.

Indeed. I think we said this already before in this thread: massive entanglement gives in most cases exactly the same observable result as no entanglement. This is why there are families of interpretations of quantum mechanics which go for the "no entanglement" view (all projection-based interpretations), and those that go for the "massive entanglement" view (all MWI-like interpretations). The link between both is decoherence.

When you look at quantum dynamics, when two subsystems interact, most of the time this results in an entangled state between both, even if initially, we had "pure product states", that is to say, each system had its own independent quantum state, and the overall state was just the juxtaposition of these two sub-system states. As it is very difficult to deny a system to interact with its environment (scatter a thermal photon, hit a molecule of air, interact with a phonon in a solid - a vibration - ...), usually a system quickly gets entangled with its environment (if you follow quantum dynamics). Turns out that you can ONLY distinguish entangled states from statistical mixtures of pure product states if you do a correlation measurement on ALL entangled components in a ROTATED measurement basis. If you omit one, the remaining correlation will show up as identical to that of a statistical mixture.
So if your system hit a remaining air molecule, scattered a thermal photon, and created a phonon in a crystal of the metal of your vacuum tube, then in order to see this entanglement, you'd have to measure simultaneously your system, that air molecule, that photon, and that phonon, in an incompatible basis with the original one. FAPP, that's impossible. So FAPP, your system is now in a statistical mixture of pure product states, EVEN if it contained entangled components (that is to say, your system was 2 or more subsystems on purpose).

So you can now say that the "measurement" has "projected out" the states of the system (and you have a statistical mixture of measurement outcomes) - that's Copenhagen and Co ; or you can say that your system got hopelessly entangled with its environment (including you): that's MWI and Co. The last approach has the advantage that it follows from quantum dynamics directly and is why personally, I like it. But the results are the same: no weird correlations are seen from the moment there is interaction with the environment.

This is why entanglement experiments are hard and never done with cats.

 

[Ken G]

So you can now say that the "measurement" has "projected out" the states of the system (and you have a statistical mixture of measurement outcomes) - that's Copenhagen and Co ; or you can say that your system got hopelessly entangled with its environment (including you): that's MWI and Co. The last approach has the advantage that it follows from quantum dynamics directly and is why personally, I like it. But the results are the same: no weird correlations are seen from the moment there is interaction with the environment.

This is why entanglement experiments are hard and never done with cats.

Exactly, and indeed I am making a similar point in the current cat paradox thread (no doubt it has been made many times before in that context). I would just add to your extremely insightful description of the role of entanglement in MWI and Copenhagen the comment that personally I'm not too crazy about MWI and the "hopelessly entangled approach" for two reasons:
1) it seems to ignore the role of the observer, just when relativity and other areas of physics (consciousness studies?) are starting to force us to come to terms with our own role in our own science (and at some point in the future I imagine that physics will have to start being framed as how we interact with and process our environment, more so that how our environment acts independently of how we process it), and
2) it seems to assume that the universe as a whole is not already in a mixed state. In other words, MWI proceeds from the idea that a closed system must always evolve from a pure state to a pure state, so as more and more systems come into contact, the entanglements cascade upward into more and more complex "closed" systems, but none of that cascade actually means anything if one cannot assume that the initial states are pure. When we look at how pure states get created in our laboratories for testing, we see that they always appear by coupling to a macro system that essentially "soaks off" all the entanglements of the pure state (or as you put it, so hopelessly decoheres them that they may as well be gone). So it's not that macro systems cascade pure states up a hierarchy, it's the opposite-- the pure state cascades down the hierarchy. Open systems are not the enemy of pure states, they are the cause of pure states. If the universe as a whole, as well as any semi-closed subsystem of it, starts out already in a mixed state, we'll never get larger systems to be in pure states-- only smaller ones.

Taking that second point from a quantum statistical mechanics perspective, we can say that the entropy of a pure state is zero. So if the whole universe is in a pure state, then its entropy is zero, and the idea that entropy can increase is just a kind of illusion of our corner of the "many worlds." But if we say that the universe as a whole is a mixed state, then it can evolve into mixed states of even higher entropy, as we might normally imagine happens with entropy. So Copenhagen gives us a kind of "WYSIWYG" approach to quantum mechanics, which I find to be true to the way we try not to add too much to the science that nature isn't forcing us to add. Though I admit someone else might actually like the finality of a zero-entropy universe. I suppose it's a point that will be debated for a very long time, and just when one approach seems to have won hands down, that pendulum of scientific discovery will swing again.

 

[vanesch]

Exactly, and indeed I am making a similar point in the current cat paradox thread (no doubt it has been made many times before in that context). I would just add to your extremely insightful description of the role of entanglement in MWI and Copenhagen the comment that personally I'm not too crazy about MWI and the "hopelessly entangled approach" for two reasons:

Ok, long ago and far away, I have been a strong defender of MWI here, but I decided to stop that (after having gone through all the arguments 20 times) simply because at the end of the day, it occurred to me that in fact it doesn't matter. Also I don't want this thread to be highjacked by a pro/con MWI discussion. But...

1) it seems to ignore the role of the observer, just when relativity and other areas of physics (consciousness studies?) are starting to force us to come to terms with our own role in our own science (and at some point in the future I imagine that physics will have to start being framed as how we interact with and process our environment, more so that how our environment acts independently of how we process it), and

It's a funny statement because I would say that if there's one thing that different MWI flavors DO think a lot about, is exactly what it means to be "an observer". My personal stance on this is that it has to do with the question "what is conscious experience" but I won't elaborate.

2) it seems to assume that the universe as a whole is not already in a mixed state. In other words, MWI proceeds from the idea that a closed system must always evolve from a pure state to a pure state, so as more and more systems come into contact, the entanglements cascade upward into more and more complex "closed" systems, but none of that cascade actually means anything if one cannot assume that the initial states are pure. When we look at how pure states get created in our laboratories for testing, we see that they always appear by coupling to a macro system that essentially "soaks off" all the entanglements of the pure state (or as you put it, so hopelessly decoheres them that they may as well be gone). So it's not that macro systems cascade pure states up a hierarchy, it's the opposite-- the pure state cascades down the hierarchy. Open systems are not the enemy of pure states, they are the cause of pure states. If the universe as a whole, as well as any semi-closed subsystem of it, starts out already in a mixed state, we'll never get larger systems to be in pure states-- only smaller ones.

Indeed, if you consider "the wavefunction of the universe" (which is needed in any MWI setting), then in fact, entropy comes about, not from the wavefunction of the universe itself, but from the amount of different "worlds" you could be in. In other words, the entropy resides in the "choice" that makes you experience THIS world, and not all those other possible worlds, and that choice is increasing.

Taking that second point from a quantum statistical mechanics perspective, we can say that the entropy of a pure state is zero. So if the whole universe is in a pure state, then its entropy is zero, and the idea that entropy can increase is just a kind of illusion of our corner of the "many worlds." But if we say that the universe as a whole is a mixed state, then it can evolve into mixed states of even higher entropy, as we might normally imagine happens with entropy.

Or you could say "as we might normally imagine happens with OBSERVED entropy".

So Copenhagen gives us a kind of "WYSIWYG" approach to quantum mechanics, which I find to be true to the way we try not to add too much to the science that nature isn't forcing us to add. Though I admit someone else might actually like the finality of a zero-entropy universe. I suppose it's a point that will be debated for a very long time, and just when one approach seems to have won hands down, that pendulum of scientific discovery will swing again.

This is why I stopped discussing it :-)

 

[zonde]

So in total you get:

25% (pass, pass), 25% (no pass, pass), 25% (pass, no pass) and 25% (no pass, no pass).


The quantum superposition approach gives you:

50% chance to have (pass pass), and 50% chance to have (no pass, no pass).

So the statistical ensemble approach 50% (H,H) and 50% (V,V) is not explaining the QM result.

I think it will be more meaningful to respond to this post one more time.

Yes that's correct that 50% (H,H) and 50% (V,V) gives 25% (pass, pass), 25% (no pass, pass), 25% (pass, no pass) and 25% (no pass, no pass) after polarization measurement.

And I am saying that this is what you actually get.
And now correlations for +45/-45 measurement you actually get only after phase measurement (interference).
So the second measurement gives high coincidence rate after +45/+45 polarization measurement (if we have (H,H) and (V,V) pairs) and low coincidence rate after +45/-45 polarization measurement.

Speaking about QM result - there is no such thing. There are experimental results and there are QM predictions.
Experimental results are interpreted using fair sampling assumption and so my reasoning is consistent with them when we discard (obviously because of second measurement) fair sampling assumption.

 

[Ken G]

It's a funny statement because I would say that if there's one thing that different MWI flavors DO think a lot about, is exactly what it means to be "an observer". My personal stance on this is that it has to do with the question "what is conscious experience" but I won't elaborate.

I don't want to hijack the thread either, and I believe I understand what you mean here-- consciousness is an emergent property of each decohered corner of the many worlds, which would neatly explain why we only perceive one such corner. There's no doubt that MWI is the king of the neat explanation-- I just feel that the mind is the source of the neat explanation, not the other way around. Like you say, there's no real difference-- perhaps the reason we cannot find which one is correct is because there's no such thing as the correct interpretation, any more than there is a correct interpretation of a great piece of music.

Indeed, if you consider "the wavefunction of the universe" (which is needed in any MWI setting), then in fact, entropy comes about, not from the wavefunction of the universe itself, but from the amount of different "worlds" you could be in. In other words, the entropy resides in the "choice" that makes you experience THIS world, and not all those other possible worlds, and that choice is increasing.

Yes, entropy still works in MWI, the issue is whether the reality is something that precedes the choice, or if the reality is the choice. It's realism or idealism, and in my opinion, when one projects both those philosophical stances onto the scientific method, the projections are identical. Much like how observations in two different frames project onto the same invariants-- if science cannot find a difference, then the message might be there isn't one.

Edit to add: In fact, it may even hold that, just as all physics theories are expected to preserve the relativity of the observer, we might require that all physical theories preserve the indistinguishability of MWI and Copenhagen. That might be an interesting angle to look at quantum gravity theories.