joigus

No, no. You go. What is non-locality to you? So far, I'm the only one of us that's shown you the calculations and basic principles (conservation laws, observables, quantum evolution, maximally entangled systems) at play, in a way that seems to be to, at least to a certain extent, to the satisfaction/agreement of everybody else but you. You've shown nothing but your unconditional adhesion to a well-known silly and incorrect interpretation that's been running around for decades to the desperation of many renowned physicists. Then I give you a simple problem in classical physics to illustrate how if you try to solve a "paradox" by using words instead of writing down the maths, you can be easily mislead. You don't even understand that simple problem (the cyclists are not pedalling downhill; rather, they're falling downhill, etc.) You misinterpret every single thing I say. That was designed as a test for your attention span. And the key to why you misinterpret the physics is in your own words: (My emphasis.) It takes a lot more than a quick view of the literature to understand physics. So now I think it's your turn. What is non-locality? Be careful, because physicists use this term in loosely overlapping senses sometimes, and it's necessary to tread carefully. This is not something that you will be able to sort out by googling it up in a couple of minutes.

OK. No problem. Trying to be cautious here, I wouldn't say it's necessarily just an artifac. But it's not telling you anything that's not already implied by the theory you're working with. Could it be giving you a clue about something? Perhaps. I don't think that's the case, and the reason is quantum mechanics. And quantum mechanics tells us it's rather an area that's important. In its most elaborate version this has come to be known as the holographic principle. The two fundamental universal constants in GR are G and c. You solve the equations for a particularly simple case, and it tells you that at r=2GM/c2 something peculiar happens. You call this radius associated with a BH of mass M its Schwarzschild radius. Now you consider different M's and divide them by their corresponding RSchwarzschild. It gives you always the same ratio, which is a universal constant. What else could it give you? The Schwarschild radius of any M is proportional to that M, and the constant of proportionality is a universal constant. There's a similar situation with quantum field theory. There, what you have is \( \hbar \) and c. For any object of mass m it gives you a characteristic length, called the Compton wavelength, which is, \[ \frac{\hbar}{mc} \] It does play a special role in the theory. But the fact that the product of an object's mass times its Compton length gives you always the same value, does not necessarily tell you anything that's not already implied by the theory. When you try to put together quantum field theory and GR, at least on dimensional grounds, you do obtain a clue that the really deep quantity is not a length, but an area. I suppose what I'm trying to say is: The problem with dimensional analysis is that there is no unique way to interpret one of these "coincidences." I'm a bit tired now. I need some sleep.

This reminds me of an old debate I had with someone who asked me if/why a cyclist who is more massive than another has an advantage when going downhill. I said he does. "Is it not true that the acceleration of the cyclist does not depend on how massive he is? So both the massive, and the less massive cyclists would experience the same acceleration." "Yes", I said. "For cyclists falling downhill on a frictionless slope, that's true. But you're forgetting friction." "But is it not true that the friction coefficient does not depend on the cyclist's mass either? "Errr... sure." I said. If you listen to the argument like that, in words, it sounds like he was right. But, Because he couln't be bothered with writing a simple equation, he was incapable of understanding why I was right. In the first case, the acceleration is the same because the force is proportional to the mass. In the second case --with friction-- the force of gravity is still proportional to the mass --necessary for acceleration to be the same in the 1st case--, while the force of friction is not. That's why the acceleration is different. The things that are independent of mass are different things. The problem is, if you just follow the words, you're incapable of understanding the reasoning. Words in physics, by themselves, are very deceptive. If the probability amplitude, with its correlations born in it, can be written with the spatial terms factored out, it's precisely because it doesn't matter where they are as long as we don't measure spin. The spin structure of the state was the same when the particles were together. It's like the person in my story. He was puzzled. We're saying the same thing! Yes, but you're interpreting incorrectly, and drawing wrong conclusions! Is that any better?

I don't have glitter, but I'll try my best: Now that I've learned the magic words?: I'm out.

I was. I said "probably," plus I didn't say Einstein was misquoted this time. I just said he's often misquoted. Probably more than anybody else. I'm making room for the possibility that Solomon communicated telepathically with Einstein, or knew him personally.

Here. Let me be helpful. You need to explain, not only your idea but, based on your idea, why all previous experiments to detect an aether have failed. Lorentz invariance is tightly packed with CPT invariance in quantum field theory, as Markus told you. You can't have one without the other. Are you proposing to give up CPT? So no, it's not "for no reason." And I woudn't dare applying an adjective to you. Is that clear enough?

From, https://www.scienceforums.net/guidelines/

If you mean call you to task for ignoring the rules of the forum, yes.

Maybe that's what's in order. Or maybe a diagram will be necessary to explain this to the author.

OK. I see the first try didn't hit the target. Could you answer to any of @Markus Hanke's objections to your idea? Or will you just ignore them and keep freely and anabashedly playing with words and pictures?

Another WAG. Could you answer to any of @Markus Hanke's objections to your idea? Or will you just ignore them and keep freely and anabashedly playing with words and pictures?

No, they're not based on EPR. EPR published their paper hoping it would settle the question. They thought quantum mechanics is incomplete. Murray Gell-Mann thought otherwise. It's not discredited. EPR was conceived to coin a concept that would be able to discern if quantum mechanics was right or he --and other critics-- were right. Non-locality is not a long-established reality. It's sometimes actually used --wrongly, because many people do not understand what it means-- to discredit new ideas on the grounds that they would be non-local. Then you certainly don't understand the question. \( \frac{1}{\sqrt{2}}\left(\left|\uparrow\downarrow\right\rangle -\left|\downarrow\uparrow\right\rangle \right) \) independently of the space-time factor of the state. In fact, the space-time factor of the state is completely omitted. Don't you find that peculiar? OK. Let me stop you right there, because it is plainly obvious you don't understand quantum mechanics here. Quantum particles have no identity. They are indistinguishable, and they are in a way much more profound than macroscopic objects can be made extremely difficult to tell apart. Not even Nature "knows" which electron is which. There is no "which electron." They're just instantiations of a quantum field. It's actually more profound than instances of a computer program, for example, which have a process tag and a time stamp. Electrons have no tags. GHZ in its original form is about three particles, and the GHZ state is \( \frac{1}{\sqrt{2}}\left(\left|\uparrow\uparrow\uparrow\right\rangle -\left|\downarrow\downarrow\downarrow\right\rangle \right) \). The observable to measure here is \( \sigma_{x}\left(1\right)\sigma_{x}\left(2\right)\sigma_{x}\left(3\right) \). You can extend that to more than three particles, and I'm sure people have been busying themselves doing that. But again, there is no mystery but the mystery of quantum mechanical correlations. It all comes from a local conservation law, which is conservation of angular momentum. In this case, spin angular momentum. The GHZ observable is a diagonal (eigenvale-to-eigenvalue) function of total x-component of angular momentum, which is locally conserved. A lot of people are still confused about this? Sure.

Good job! Poor old late Einstein is falsely quoted more than anobody else in science, probably.

Then Don Lincoln would be well advised to read my comment: And do QM calculations for ten years as a punishment for making the widespread foolishness that Gell-Mann talked about, even more widespread. The gloves example serves the purpose of showing that initial correlations don't require spooky action at a distance. Nothing more. They differ --very importantly-- in that left or right-handedness, colour, material, etc., are well-defined at all times. Contrary to quantum mechanical systems, for which the mere assumption that these properties have a definite value would lead you to untenable assumptions like non-locality or existence of negative probabilities, or both. Because we think quantum mechanics is correct, we don't need to assume such foolish things. Do you see my point?

No, it's no hidden gem. It's already implied by the maths of a simple exact solution of the theory. Let me try an analogy. A physicists who's given the solution for the quantum harmonic oscillator tries multiplying the energy of the ground state by the period for different harmonic oscillators. It always gives the same value!!! Yes, it does because it's h-bar (Planck's constant), as (h-bar)x(omega)xT = h. That "same value" is nothing other than Planck's constant. It was there from the very beginning. You feed G and c into your theory. You calculate solutions. They depend on G and c, of course. You get back a certain combination of G and c. No mystery, is it? Be careful, because physics has a way of tricking you into thinking you're getting something new when you're actually going in circles.

I did. And this is the reason: Fabricate: to invent false information in order to trick people Then, you didn't address any of my concerns. I do yours though: What do I mean by "fixed"? The same as "number 3 is fixed." Or do you think number 3 expands too? Eigenstates do not expand. So far, you haven't made a smidgen of sense. No, we can't start there, because you don't understand even the first thing about quantum mechanics. All the elements of a Hilbert space that have physical meaning have a measure of 1, because they are interpreted as probability amplitudes, not points in a topological space. You don't understand anything, can't be bothered to ask, and don't answer to any objection. I'm out too.

No, the inner dot product in the Hilbert space is not a fixed reference. It can change with time. It's the eigenstate that doesn't change. "Eigenstate" means "proper state" or "characteristic state" in German. It is a fundamental ingredient of quantum mechanics. Eigenvalues ("proper values" or "characteristic values") don't change either. Let alone "expand." The Higgs field has nothing to do with curvature. It's a quantum field defined on a flat space-time introduced to explain mass (rest energy) in the standard model of elementary particles. A field is more like an arrow rotating in an abstract space, and sitting on a geometric space. A quantum field is a similar thing, but jumps up and down between different levels that tell you the number of quanta. Einstein never knew anything about the Higgs field. Neither did Newton, of course, because both were dead when it was introduced. Field variables don't have curvature. They're not even "numeric" things. They're non-commuting things. Eigenstates don't fluctuate, though they are defined up to a global phase (a fixed complex number of length 1.) Eigenvalues are not conserved quantities in general. E (eigenvalue of the energy operator) corresponds to a conserved quantity in some contexts. X (eigenvalue of the x-position operator in quantum mechanics) never --repeat, never-- does. I'm sorry, but you're not making any sense in the context of standard physics.

Not even the froggiest idea, mate. But I will quote @TheVat:

Eigenstates are fixed references in the Hilbert space. They'd better not change... at all. I think you mean something else.

I can't make heads or tails of your diagram really. What's eigenstate expansion to you?

No. The singlet state is totally trivial under rotations. Rotations act on it trivially: they don't change it at all. That's why it looks like (up)x(down)-(down)(up) in any representation you choose. It does not code any orientation in it. The matrix that rotates it is the identity matrix. It is blind to rotations. I can try to rephrase this over and over... That's all I can do, I'm afraid.

Kind of... What Bohr argued was that the very nature of the measurement process somehow produces the results themselves, in such a way that the statistical constrictions on the outcomes and the measurement process itself were inseparable. Analysis of measurement in later decades clarified that even if you have filtering measurements, preparations... (no intervention with an interacting piece of equipment) quantum correlations are there. So they're not due to intervention during the measurement. The question of hidden variables really started with David Bohm (pro) and John Von Neumann (against). It was David Bohm who, to the best of my knowledge, started to work on "hidden variables", and Von Neumann who started thinking deeply about this problem, and formulated a first version of a theorem of impossibility. Then came Gleason with a theorem about the impossibility of assigning a binary function (true/false) which was continuous on the Bloch sphere, and from there, the last --more powerful for some-- version of that is the Kochen-Specker theorem. Bell's inequalities are a further refinement of an argument by Clauser, Horne, Shimony and Holt. There is another argument of impossibility by Greenberger, Horne and Zeilinger, that Mermin simplified, with just one observable. There is another argument by Conway and Kochen... To this day, there's so much literature about the subject that it's possible to spend a lifetime's worth of study learning it. As Swansont said: If you know some Pauli-matrix and angular momentum algebra, it's an interesting exercise to write down the singlet state and rotate it. People normally write it as |up, down> - |down, up> with a normalisation factor, and referred to the z direction. As if the z-direction played some kind of role in it. I doesn't. The states really are indeterminate. You can use any axis you want and it has the same form: |upx, downx> - |upx, downx> = |upy, downy>- |downy, upy> = |upn, downn>- |downn, upn> = etc. It's all a whole quantum state with like "no parts in it", "no internal arrows", so to speak. That's entanglement for you. Try it, it's very illuminating. The only thing that's physical is the whole vector. Then you obtain the expected value of spin along any direction you want and it always gives you zero for the sum. Then you do some further quantum mechanical calculations and consider the evolution operator from, say, t=0 (when the singlet is prepared and the particles are next to each other) and a time T when the particles have come apart, and you will see that no expected value depends on the fact that the spatial factor of the states has taken them apart. It's all in the maths of QM. As I said: The correlations are there when the singlet is prepared, they're there a minute later, they're there until you perform another measurement. And no experiment that I know of contradicts this. So yes, it's like the gloves in the sense that the correlations are initial. No superluminal action at a distance. Period.

No problem. Part of the reason why this is all very confusing is because so much nonsense has been spread for so long that we think these theorems, as well as the experiments, say what they actually don't. The abstract nature of quantum mechanics makes it quite difficult --if not impossible-- to get any intuitive picture of the part of it that's really bizarre. So we forget that another part of it is just propagation of waves.

If the EP breaks down, then we no longer have GR. If so, why bother with Schwarzschild solution? It would be misguiding us all along. Sound, as well as strong forces, do not exist in that region of space, because it's a vacuum solution. And yes, tidal forces are important, they're coded in the connection coefficients, and they become the more relevant the farther away you get from the point you choose to expand your metric. The Doppler effect is like the "time-component" of these tidal forces, so to speak. It's coded in the \( \Gamma^{0}_{00} \) of the connection. You can obtain this from the geodesic equation. And sure enough, the observer would notice something funny going on with all kinds of optical effects. What he wouldn't notice is any ficticious forces due to acceleration --provided the horizon is big enough in comparison with his own size. Generally, the 0-component terms are far more noticeable because of the large value of the speed of light. It's quite an exercise of imagination to picture how an observer might experience such a voyage, but certainly I would expect all kinds of strange optical phenomena. Mirrors not reflecting properly probably being one of them.

You do sound like a bot, but thanks for the clarification. How can two incompatible notions of space be both correct? What appearance? What does a Hilbert space look like? And a Higgs field? Space-time is a background, while the Hilbert space of a particle is the space of all possible states of that particle that take values on that background. How could they be indistinguishable? They're very different things. No. A Hilbert space does not expand. It had better not, as you get probabilities from it. Neither does the Higgs field. It had better not, for good reasons too. Why do you say these things (and more) that don't make any sense? I'm sorry for trying to test your human nature, but you made very loose connections, and sounded to me like a bot. Also, personal opinions don't play any role in mainstream science.