MarcoBarbieri

1 minute ago, Genady said:

"Same time" in which reference frame?

Suppose you are in the same initial frame as the other observer. You with "your" electron and he with his (hers). Keep the electrons isolated (but entangled). Set your and his clock. He moves away in a well defined way. So you can account for time "delay". If he is at rest again wrt you, then you do your measurement of z, and he of x. At a before agreed time. Aren't z and x determined then at the same time?

Just now, Genady said:

When you measure any of them, they are not entangled anymore. So, any measurement of one electron doesn't measure anything about the other. Each has the normal uncertainty.

But what if you measure them at the same time?

On 8/3/2021 at 9:43 AM, joigus said:

Just to correct myself. There are cases in which you can say an electron changes its spin, of course. But not for spin-entangled states. For example, you put an ion in an ion trap and subject it to a magnetic field. The ion will flip its spin. The devilish property of a maximally-entangled state is that you cannot say its spin has any particular value whatsoever.

Yes, it's very much like that; they're initial correlations. The tricky part is that correlations are quantum. All hell breaks loose when correlations are quantum and you want to think about the gloves as actually possessing all these properties at a given time.

Quantum mechanics embeds a different (non-classical) kind of logic when you express it in terms of properties you can measure. 'Quantum gloves' need to be able to occupy states that are neither right-handed, nor left-handed (superpositions); neither black nor white, etc.

And we need to be able to measure several properties of the gloves. If we want to have properly quantum gloves and display all the 'trickery' of quantum entanglement, we would need:

1) Several measurable properties. Take three observables, say: handedness (H), colour (C), and material (M).

2) Measurements of any one of these properties (observables) completely mess up measurements of the other; and you can't measure (H,C), or (C,M), (H,M), at the same time. (Incompatible observables.)

3) (For simplicity) the observables have a discrete dichotomic spectrum (possible values when measured):

• H {left-handed, right-handed}
• C {black, white}
• M {natural, synthetic}

4) When the gloves are in a definite state of handedness, the H-incompatible properties C and M are maximally scrambled, or 'blurry': Equally likely to be black or white; equally likely to be natural or synthetic. The gloves simply don't have those C, M properties when H is well defined!

If they had, it's not difficult to prove that, for many series of repeated experiments on a given glove:

Probability(left-handed & white)+P(black & synthetic) greater or equal than Probability(left-handed & synthetic)

This is called Bell's inequality, and it's just a consequence of the properties H, C, and M actually having a value. Quantum probabilities violate this inequality for certain choices of observables.

But wait a minute. Didn't we say that properties H (handedness) and C (colour) are incompatible? How can I even make sense of Probability(left-handed & white)? I'm not supposed to be able to measure handedness and colour at the same time! (for the same glove).

Yes, but the whole basis of this combined-probability setup is based on the assumption that when I measure, eg, H for one glove and the result is 'left-handed', I know with certainty that, were an experiment to be performed at the other glove's location, it would produce the result 'right-handed' with total certainty. And sure enough, it does, when I do so. So I'm counting 'left-handed' outputs for the other glove as 'right-handed' outputs for this glove. This is very important to keep in mind.

So the gloves would have to be kinda schizoid.

But the whole thing is local. In order to see that, let's go back to a pair of electrons. We take electrons from separate parts of the world, completely uncorrelated. We bring them together and have them interact. They reach a maximally entangled state called the singlet. This only happens because they've been proximal and interacting (local!!!). Now (and not before) they display perfect anti-correlation. If I perform my experiment on them when they're still next to each other, they display all the craziness that I've just described.

Now the state decays (splits apart). I perform the same sequence of measurements. The perfect anti-correlation is still there. It hasn't changed. So it didn't come from me doing anything on one of the electrons and the other 'sensing' what I did. It came from the initial interaction that produced the anti-correlations.

Murray Gell-Mann was very frustrated that people, decades after Bell, Clauser, Shimony, and all that saga, still called this 'non-locality'.

Just as an indirect evidence of how much confusion this term 'non-local' has caused in physics, here's a quotation:

(taken from a scientific forum.)

Ooooooo-kay.

Ha! That's ("oooooo-kay") is what my wife says regularly. Only for that an upvote already! Why I react, is because hidden variables "interpretation" (I'm not sure it's an interpretation) says particles have always well defined positions (and thus momenta). I can remember reading that a future experiment could decide between hidden variables and pure chance. Wouldn't present quantum theory had looked different if at Copenhagen it was decided the pilot wave is real? Bye bye many worlds. ..

Anyhow. Suppose I measure the spin up direction on one electron and the x component of spin on the other. Wouldn't that mean you know both the spin and its projection, which are normally obeying the uncertainty relation? 

On 1/20/2022 at 9:48 PM, MigL said:

And if we consider the Mexican hat  potential, then even periods of accelerated expansion could be exlained in terms of oscillations about the real zero level.

How can a field, the Higgs field, have a central maximum (the top of the hat) in energy when the field is zero? Aren't we, by this artificially constructed image, led to the conclusion that the Higgs mechanism is an imaginary mechanism only? With no real existence?

Negative mass/energy solutions are part of the virtual disconnect Feynman diagrams involving one particle "bubbles" in the vacuum. It were exactly these solutions that created the negative curvature of the 4-dimensional substrate on which two 3-dimensional universes banged into existence. The two massless basic quantum fields of nature and the seven gauge fields mediating between them, accelerated away from each other on both sides of the 4-dimensional Planck-sized "throat", or wormhole, connecting two infinite regions of 4-dimensional space. The negative energy of the virtual particle states caused the negative curvature of the initial singularity. Like the curvature on the inside of a torus i.e, around the the mouth of the torus. The two massless basic fields combined to massive quarks and leptons on one side of the open 4-dimensional torus, while on the other side  the anti versions banged into being. Dark energy solved. Mass production solved. Matter-antimatter solved (no asymmetry at all). Consequence: Higgs mechanism is a modern-day variant of phlogiston. Extra: anomalous muon g2 no mystery.