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I'm curious if any matter/antimatter or electron/positron entanglement is possible in theory or has been attempted?
So can/do they test for correlation and violation of Bell's Inequality? Or is it just assumed they are entangled...Yes. B0 and anti-Bo mesons produced at CESR, PEP-II or KEK-B (only the last is still running) are entangled.
Violations of Bell's inequality don't show the presence or absence of entanglement; finding such violations is a sufficient but not a necessary condition for entanglement.So can/do they test for correlation and violation of Bell's Inequality? Or is it just assumed they are entangled...
That is exactly what I was trying to get at. If matter/matter entanglement were shown to violate Bell's inequality but matter/antimatter were shown never to violate it could it be concluded that entanglement is a chiral property?Because some entangled systems do violate the inequality, we conclude that entanglement cannot be explained by such a theory.
Does this mean "static hidden variables"? As in pilot wave theory (which is non-local) it works as a static wavefunction encompassing entangled pairs? Sorry if what I'm asking about is obscure or unclear.What Bell's theorem does show is that no local hidden variable theory can violate the inequality. Because some entangled systems do violate the inequality, we conclude that entanglement cannot be explained by such a theory.
I have no idea what you mean by "static hidden variables", but you are correct that pilot wave theory is non-local and therefore is not precluded by Bell's theorem.Does this mean "static hidden variables"? As in pilot wave theory (which is non-local) it works as a static wavefunction encompassing entangled pairs? Sorry if what I'm asking about is obscure or unclear.
The wavefunction calculated by the Schrödinger equation is static is what I mean, it does not change over time, correct? But are there any papers on dynamic local variables which I assume would be deterministic but I can't find anything by searching...pilot wave theory is non-local and therefore is not precluded by Bell's theorem.
Ah, yes, I overlooked that point. Trying to simplify concepts in my head I tend to miss things now and then. Thanks everyone for your help.they have a changing phase for states with nonzero total energies.
What do you mean by "chiral property" here? I don't think "chiral" means what you think it means.it could it be concluded that entanglement is a chiral property?
I meant (for example) that the spin of atoms might have an asymmetrical component as in clockwise or anticlockwise rotation but I see the flaw in that line of thought.What do you mean by "chiral property" here? I don't think "chiral" means what you think it means.
Why not?I did not think a bound state with an attractive potential and non-identical particles could be entangled.
A bound state is one in which the potential can be chosen to go to zero at infinity and the total energy will be negative.Does this forum have consensus definitions of bound and entangled states?
The wave function doesn't change as the position changes. The wave function is a single function of position--actually, for positronium it's a function of two positions, the position of the electron and the position of the positron. Or you can reformulate it as a function of the center of mass position of the system and the distance between the electron and the positron; the latter is nicer because all of the interesting stuff, like the potential energy between the electron and the positron, depends only on the distance between them, not on the center of mass position.What is Bothering me is that at infinity I end up with two separate wave functions that don't overlap
Positronium in the singlet state decays into 2 gammas (each of spin=1, polarized so that spin is conserved) and in the triplet state into 3 gammas. I believe it is the gammas that are entangled NOT the electron and positron in the bound state of positronium. Of course angular momentum is conserved in these decays.I think that if you manage to create an electron-positron pair by any means, the particles will be entangled to some extent just because momentum has to be conserved in pair production.
That's correct, they are, because their total spin is fixed by conservation of angular momentum.I believe it is the gammas that are entangled
That's not correct. See my previous post.NOT the electron and positron in the bound state of positronium
The good thing with science is that you have to make the definitions really clear. To say "I have an entangled state" is not accurate enough. It doesn't tell you what's entangled. So we have to say what is entangled!Thank you PeterDonis And Nugatory. Clearly, what I need is a DEFINITION of an entangled state and it looks like Nugatory has given this forum a definition. Let me think on this for a bit. I learn best by examples...Are you saying that Positronium is an entangled state? What is Bothering me is that at infinity I end up with two separate wave functions that don't overlap...so I no longer have an entangled state.