joigus

All correlations in quantum mechanics can be explained in terms of the Schrödinger equation, or a mixture of it and things in the way of Maxwell-Boltzmann distribution, etc. A maximally-entangled state is a trivial case of the Maxwell-Boltzmann distribution, when you think about it. No need to endow the universe with hidden higher-dimensional tunnels to explain those. They are perfectly explained. No mechanism is needed, and that's the beauty part.

Science is not about refutation. It's about picking the simplest idea that explains the facts. Quantum mechanics does derive those correlations. It doesn't assume them as a premise. You need QM plus Nature's drive towards maximum entropy. There you are. You let the system "relax" to a maximum entropy and apply the superposition principle: The state is automatically the Bell state --mod an arbitrary global phase. It's been prepared that way by just letting it be. It's your idea that seems to assume some "internal" machinery to explain the idea that in quantum mechanics is totally natural.

No. They are built-in quantum correlations. When a quantum system cools down to a maximally entangled state, the amplitudes are what quantum mechanics dictates and Von Neumann's entropy becomes maximal. Then you decide to split up the system spatially and, after however much time you let pass, the odds for different "strings" of observables of choice are exactly what they were at the beginning. It's all initial correlations. No need for extra dimensions to find a shortcut.

In so-called quantum teleportation, the measurement outputs must be sent at regular speeds (as @KJW told you). We've discussed this before on the forums. There is no teleportation of anything and no violation of locality. But, as I told you, misnomers die hard.

No. @KJW 's point is deeper than you think. QM is not a random theory. It is a deterministic theory (with a huge arbitrariness) that gives rise to all the microscopic randomness by way of this element (extraneous to the dynamical theory itself) that we call measurements. Oh, and there's nothing non-local about it. Not a bit.

I know all that, "dude". I'll wait for your doh! moment, don't worry.

Dude, we don't know anything today we didn't know back then about this particular point. And Gell-Mann explains it very eloquently indeed. Learn some physics. And read what you're told. Here, again: Nothing gets from A to B. All the weirdness started in one point in space. Why would it be telling us anything about non-local correlations? Entangled states are prepared at one and only point in space-time. The fact that people still think there's something non-local going on is a testament to the power of words. Nothing more.

No, wait. You might learn something here: Then read The Quark and the Jaguar. Then leave all your ignorance about this matter in the past. Nothing gets from A to B. All the weirdness started in one point in space. Why would it be telling us anything about non-local correlations? Zeilinger himself recognised this. But the spooky (and profoundly misleading) term "non-local" dies hard!

They won the Nobel price for reasons other than what you say, because you sorrily misunderstand what they proved.

Wrong. What's a fact is incompatibility of behaviour of quantum states with local realism. Subtle, but important difference that thousands upon thousands of people misunderstand constantly. We've had some of that here.

There is no instantaneous (non-local) "exchange" that we know of in quantum mechanics. We cannot "exchange" anything outside of the future causal cone of an event. No can do. The (local) gauge is the particular choice of the local phase of the wave function. The (global) gauge is the particular choice of the global phase of the wave function. How could an arbitrary choice give rise to a phenomenon? Gauge is beyond phenomena. It's been described as a "redundancy", or an "arbitrariness". I don't understand.

A hidden geometry is usually destructive? What are gauge phenomena? You should consider the possibility that you misunderstood the paper and the paper also misunderstood quantum mechanics. Those are by no means mutually exclusive. I'm old enough to have been known to have misunderstood a misunderstanding. Can you give us the low-down?

Do you mean "measure theory" as in mathematics? MT is concerned with metric properties of a function (generalisation of volume). Measurement in physics is completely different. quantum amplitudes (I prefer to say that over "wave function") must be measurable in a mathematical sense (the famous L2(R3) class of integrable functions, which require the Lebesgue theory of the measure (in particular in order to include distributions). That doesn't mean they can be measure in a physical sense. Sorry if I'm coming across as a something of a stickler for precision in the terms. I need precision at every step.

I don't think the whole motivation for introducing random variables boils down to solving the finer points of topology TBH. Going back to the main point, it's not clear to me that quantum probabilities represent some kind of brand new concept of probability that Laplacian probabiliy (or Kolmogorov's for that matter) could not already handle. The actual divide, IMO, is in how quantum probabilities derive from these strange things called "amplitudes" (complex quantities that force us to do the Boolean algebra of YES, NO, OR, AND, etc, on them instead of on the probabilities themselves). The question could be every bit as cogently posed as "why is it that the basic logic of the world we see is projected on these amplitudes?" What "are" these amplitudes and how do they relate to the things that seem to "be"? That's the essential difference, not a new concept of probability incompatible with the former. EDIT: I'm aware (as @swansont has pointed out) that Kolmogorov came later than QM. But his concept is very much a generalisation of the old one AFAIK.

From what I know quantum computers would be feasible for tasks such as factoring numbers, cryptography, and the like. Not very suitable for emulating categorical thinking. But all of this could change in a matter of years. Who knows.

When and where you said wave functions are random variables. Random variables in QM are the observables. Wave functions have a status of their own.

That's the rho for the scatterers!! Form factors measure the spatial shape of scatterers. OMG. Please don't ask artificial intelligence again. It's almost indistinguishable form natural stupidity. Can you set me free now? Yeah, let's keep this short, please, oh please. where ρ(r) is the spatial density of the scatterer about its center of mass (r=0), and Q is the momentum transfer. (quote from https://en.wikipedia.org/wiki/Atomic_form_factor). If you've done some physics it takes you about half a second to figure out that's what they mean. Even if you don't remember the whole context. For Pete's sake.

Yes, you have mixed them up. Scattering theory is about an incoming state that comes from \( t=-\infty \) and evolves towards an outgoing state that evolves towards \( t=+\infty \) . Quite different from \[ \left|\psi\right|^{2} \]. Born's rule is about one and the same state. Scattering is about an incoming and outgoing states, both close to plane waves, and infinitely distant in time. Do you really know about quantum mechanics? Doesn't sound like you do. Oh, come on, drop the attitude, will you? I know quite a bunch of details about quantum mechanics, and I don't need prosthetics for my intelligence. AI has failed to answer some of my deepest questions. Miserably so. No wonder, really. AI works on the logical span of what humans have already thought. It's clueless about what's next. If you could paraphrase what it's trying to do (sometimes to astonishing perfection, I'll give you that), it is: How could I convince myself this is what human interlocutors would want to hear?

I think you're conflating here Born's rule with the first Born approximation (scattering theory). Very different things, even if both bear the name "Born". Born's rule is the general assumption that probabilities are bilinears of amplitudes. Born's approximation, OTOH, is the simplification that scatterers can be considered as given, and unaffected by the scattered. Further, the Fourier transform of any x-dependent quantum distribution is yet another thing. Namely, the momentum representation of said local distribution. So you're conflating three different things here. Two of them bear the name 'Born". The other one was born at about the same time. None of them is born out by what I know about quantum mechanics.

What I mean --hopefully-- more precisely is that, as you imply, wave functions are determinations from a range of physical conditions (examples: hydrogen atom's ground state, free particles, etc) whose only undetermined co-factor are global or even local (in cases where the dynamical theory is a gauge theory) phases that can be chosen locally at will (not measured or indeed measurable at all). Summarising: Wave funcions have, 1) A factor that is completely determined 2) Another co-factor that is a huge arbitrary Mind you, "huge" here is, if anything, an understatement. It is futile to keep discussing here if there isn't a least common denominator of what is known to be the case for quanta. Having said that, I sympathise with attempts to "better understand" what possible sub-reality[?] quantum mechanics is telling us about. But variables half of which merit the qualifier of "completely determinable" and the other half "completely arbitrary", to me at least, cannot qualify as random, as @Killtech seems to purport. Sorry for my tardiness in answering, but life-changing events are taking place for me lately. [?] Less-stringent reality than what our intuitive criterion would have it?

Random variables have probability distributions. As such, they must be observable. Otherwise what does it even mean for a hidden variable to have a certain probability to adopt a particular value, if that value cannot be observed? AFAIK, in HMM, probabilities are assigned to the Y's (the measured variables), not to the X's (the hidden states). The X's are there to provide conditional probabilities P(Y|X). Someone might have called these X's "random". If that's the case, I think it's a misnomer. Anyway, the wave function is not a random variable, except for mixture states, in which it is. But its status as such is a little bit flaky (there is a huge arbitrariness in the choice of wave function).

Not really. The wave function is not considered to be a random variable, for good reasons. It's a representative of infinitely many valid wave functions that all embody the totality of statistical properties of the system. All these wave functions differ from each other in a constant phase factor. You said yourself the wave function cannot be observed. Random variables can be measured. Otherwise it doesn't make much sense to call them random variables, does it?

No. The momentum operator is an endomorphism (a function from square-integrable functions to square-integrable functions). It is no random function. It's the measured values are random.

I didn't know whom it was addressed to.

Please learn to use the quote function. We don't know what particular argument you're answering to. Yes. Can you give us an outline of what it is?