joigus

Sorry if I misunderstood. If they got close to a BH, and they get captured in it, according to the HB* picture of it, they would be re-emitted in the form of thermal radiation, which means they would no longer be entangled. A BH is not a good entanglement-producing machine, as it has an entropy associated to its surface. This entropy is not entanglement entropy, it's a further scrambling of information than what entanglement entropy represents. This is all a bit dicey though. Not everybody agrees on what the HB picture of BH's is telling us. * Hawking-Beckenstein

You didn’t explain that was your intention and I still don’t understand what you mean. An illustration of entanglement should require at least two world lines, one for each particle, and each particle would need to stay within its respective light cone. Your illustration on the upper left “most” resembled entanglement but none of them made sense as representative of entanglement. In your picture on the upper left, I see one one event in the future and one in the past but no world lines for the entangled particles Entanglement violates the EPR situation in that one entangled particle can interact with its partner(s) instantly as if the they were side-by-side. Entangled particles need no physical connection to interact- not even light. It is instant action at a distance that violates the EPR. Your illustration on the upper left “most” resembled entanglement but none of them made sense to me as representative of entanglement. "In the same light cone" means that one particle, usually an electron, can interact instantly with any other similar particle within the same light cone provided that conditions between the two permit. This is possible in QM but not in classical physics so that is a major contrast between the two and I wouldn’t call it “nothing.” In the the classical situation, one particle can only interact with another either directly or through some physical interaction. QM needs no physical interaction. Again: "In the same light cone" doesn't mean anything. I've shown you two distinct cases of events; a couple of them were space-like separated; the other two were time-like separated. In both cases, you can make them be either in the same light cone, or in different light cones, at will. It's painfully obvious you didn't understand. Now rinse, and repeat. Sometimes, understanding something is a whole shampooing experience, as @iNow shrewdly suggested. Keep practicing. Your lack of understanding of basic physics is appalling. Epsilon and mu naught are not independent properties of space; the product of both is. The unit of charge can be independently chosen without any epsilon naught. In fact, in the cgs-unit system, there is no epsilon naught, and the basic unit of electric charge can be defined with dimensions of M1/2L3/2T-1. If you use such classic books as Landau-Lifshitz, you'll see they only use dimensionful electric charge units. I know the topic to be confusing to some people, that's why I once won a bet on this particular question. The bet was about how you can --if you want-- actually define the unit of electric charge in terms of mass, length, and time. Modern quantum field theory uses dimensionless electric charge. It's an option, and it all depends on definitions. But --and here's the essence of your misunderstanding of this particular question-- because in this universe magnetic fields are produced only as a consequence of changing electric fields, this activation of the magnetic field requires the propagation of something to be iniciated. The other constant thus becomes a measured value, which is essentially a speed. The workings of electric circuits critically depend on this speed. Here's a good Veritasium video that will make you understand this concept. It's highly imbued in physical intuition, and I highly recommend it: Good luck!

Under most typical scattering scenarios gravity is far too weak to be of any significance. If you try to collide particles at an energy high enough, and with an impact parameter --closeness of approaching particles-- close enough to produce a BH, I don't think ordinary QM is sufficient to deal with it. I don't know how to deal with that situation, TBH. I do know enough to guess --if not to know-- that any outgoing state would come out as a mixed state --if Hawking and Bekenstein are right--, which means, coherence would be lost. Maybe @Markus Hanke wants to take this up with more precise information. He seems to be on fire lately.

LOL. I had to read it again to get your drift. +1

It does say something beneath: Amplitudes. Are amplitudes physical? Are they just a tool?

You're right, though it's hard for me to concede that time were to be discrete without space --and momentum-- getting affected in a similar way. Yes. Predictions? Another thing I'm missing in most of these revolutionary ideas is the conservative aspect. Namely: How you keep in its place everything else we know to work. If you want to improve a building, you normally don't go about it changing the foundations. Another interesting aspect of these revolutionary ideas is that their authors are no spring chickens. New physics used to be the preserve of people in their twenties. Now it's coming from people who've been there for quite a while. I think that says something about the "crisis of theoretical physics" we're going through.

Good question. Highly depends on the nature of the interaction bringing them up together, as well as the way in which they interact with each other. If you accelerate the hell out of them, they start to emit radiation, and they finally collide and perhaps radiate some more, you can rest assured they will lose quantum coherence and no longer be entangled. Entanglement is generally produced under conditions of very ordered, very tidy, local interaction, and particles are brought to a ground state of some kind, or perhaps particles emanate from a coherent source, like in SPDC. The take-home idea is: Almost anything you do in a careless way will break quantum coherence. That's my "analysis." Let's see what other people think.

Hey, for me as well. We should keep an open mind... and filter out ideas too out there. Another very interesting revolutionary more in a direction that resonates with me is Julian Barbour. I don't know if you've heard of him. His core idea is that the relevant quantities to describe the Cosmos should be interrelationships expressed in the form of ratios, rather than coordinates. I gather that he and his collaborators are having a hard time relating this --at first glance-- very interesting idea to the nuts and bolts of the physics we already know and love. Maybe I will start a thread about Barbour, if I can.

Interesting, but I'm skeptic. Revolutions in physics normally stem from a well-balanced mixture of conservatism (a lot of it) and at most one very bold new statement. Sounds too revolutionary for the likes of me. If professor Gisin gave me a good account of something playing the role of, QP−PQ=iℏ with something other than continuous mathematics, I would pay a lot of attention, if not be immediately won over. It's not that some aspect is better addressed with the new idea. It's the not-so-easy order that everything else stays more or less where it was.

Again, no answer. The light cone of what? Didn't you understand that my pictures were meant to explain that two events being in the same light cone doesn't mean anything? Didn't you understand that? In my picture on the upper left, both events are in the past cone of an unspecified future event that plays no role in an EPR situation. So "in the same light cone" specifies nothing. Except that it is obviously a speed from dimensional grounds. Not only that; if you assume no sources (or being far away from sources) the meaning as a speed becomes even more obvious (can something be "more" obvious...?). The reason is that Maxwell's equations become wave equations for either E, B (or the scalar and vector potentials) and 1/sqrt(mu_naughtxepsilon_naught) being the phase velocity of the waves in the vacuum. The problem is non-locality is much, much harder to accomodate to everything else we know than non-realism. The projection postulate is non-local, but it is in a way not to produce any measurable non-local consequences whatsoever. The "founding fathers" of QM were not stupid. The problem is: What makes quantum superpositions not to live forever, and anything like "classical data" become necessary to describe the evolution of the state? IOW: What in the quantum state carries along these "classical data" (the outcomes of measurements)? In still other words: How do we accomodate in the quantum formalism the fact that one or many of the evolving components of the quantum state suddenly become irrelevant? We should do this in a way that preserves unitarity, linearity, and locality. Seems like an impossible task. Linearity is probably the most suspect of all...

+1. +1. Interesting...

Meaning "from behaviour of visible matter around them."

Reverse-image search produced this: https://www.cam.ac.uk/research/news/black-hole-powered-jets-fuel-star-formation It seems to be the result of a super-massive BH swallowing a region of star formation and producing as a result a pair of powerful jets of ejected material. The central bright region is probably the accretion disk of said BH. Not every spot of light is the BH. Black holes can't be seen directly. You can infer their position from gravitational lensing or from behaviour of matter around them.

https://en.wikipedia.org/wiki/Measure_(mathematics) https://en.wikipedia.org/wiki/Fractal Hausdorff measure (fractals): https://en.wikipedia.org/wiki/Hausdorff_measure I hope that helps.

(Emphasis mine.) What do you mean??? Here's a visual aid: Same particles, same events for time-like separated particles. And, Same particles, same events for space-like separated particles. What light cone are you talking about? Same light cone of what exactly? Will you make a smidgen of sense at some point in this simulation of a discussion? I'm ignoring the rest of your nonsense. Let's start with the basics. Otherwise, you're gonna turn everyone crazy here. "Especially electrons..." Yeah, that makes sense too!

Same reason why the colour of my sclera, and the colour of yours are the same: Some event in the past determined both. In the example I'm offering you, the evolution of a family of primates. Unless one of us is a possum who's learned to type. Let that be me. Oh, by the way, I've just received a message from next Christmas: Our future selves tell me we are still discussing this.

I think Markus meant "measure" in general. There are many cute puzzles like this that are similar and involve other kinds of measures, like Hilbert's curve covering a patch of plane. On the other hand, mathematics based on natural numbers is known to be incomplete, and no theory of this kind can prove its own consistency, so I would relax about the whole thing. Besides, there is no unified set of axioms for all of mathematics, as far as I know. You can relate chunks of it, but not all. I would relax even more. I may be wrong, but I think in this post-Bourbaki era mathematicians tend to be more freely constructive and more deeply involved in guesswork. This has proved to be very fruitful for both physics and mathematics.

What particular physical aspect of the round house kick do you want to understand by means of the moment of inertia? If you want to totally understand the theory of the moment of inertia, you need some integral calculus (although you can do without much) and some vector algebra (perhaps a bit more than calculus.) But qualitative discussion of some simple cases can be done without big mathematical hurdles.

It absolutely is not a non-local Lagrangian. Let me rephrase without the double negative, which might be confusing: The Lagrangian is totally local. Once the particles start flying apart, you can use free propagation to describe how the fly apart, and the initial entangled state as the initial condition of a so-called Cauchy problem. The Hamiltonian is separable, and contains only 2nd-order spatial derivatives, so local densities, fields, etc are only sensitive to nearby points. It is a 2nd-order polynomial in the spatial derivatives. Local as can be: Exactly the same sensitivity to spatial inhomogeneities as the equation for propagation of heat. And the state keeps entangled all the way. What the classical theory of heat doesn't have, that makes quantum mechanics so peculiar, is, 1) Superposition of several different "heat-radiating states" 2) A multi-system phase space It is the initial condition that cannot be separated, which has consequences on the probabilities that are encapsulated in the state. As Markus said --with my emphasis, Which is exactly what I was trying to say here, This, by the way, you found either very surprising, or implying the opposite of what @Markus Hanke --and I too, many pages before-- is implying: As the probability distributions do not depend on spatial factors while the state is evolving, as it only depends on how the state is interwoven in its spin "tags," how could it encode anything having to do with local (space) properties? Or at least, that is, provided I've understood Markus correctly.

The discussion was actually about FTL signals. More in particular, it assumed that FTL signals are actually implied by quantum entanglement. From that as a premise, it proposed the possibility that this "entangled information," whatever that means, can be somehow amplified, or "crowded." It was I who first challenged the premise that FTL signals are possible from the mere basis of QM. @uncool then proposed whether it could be the breaking of quantum coherence --or, if you will, the collapse of the wave function-- that could be used as a signal. Here: That was a very interesting point. I think I basically answered this with a clear resounding "no." But at this point the debate was getting, IMO, very interesting. Then you intervened by entering into a dynamics of a dog chasing his own tail, by repeatedly denying matters of principle and experimental evidence that nobody else here has any significant doubt about. As long as you do not agree on these matters of principle, it will be impossible to further understand why this illusion of non-locality --that's implied, eg, in the last paragraph you quoted-- occurs when one thinks of QM in the terms of Copenhagen's interpretation of the theory. I did try to steer the debate in that direction, because I think it explains the confusion as close as effortlessly as it's possible to do. You stubbornly repeated asking me for a criterion of non-locality after, many posts before, I had already given you one: That you either didn't understand or didn't bother to read. For a theory to actually be non-local, it would have to be a system that, once cast in a Lagrangian form, would have an infinite sensitivity to spatial inhomogeneities. This would reflect in the Lagrangian as having arbitrarily-high order of spatial derivatives. That's why I know quantum mechanics cannot be non-local in any fundamental way, and the whole illusion must come from some kind of basic misunderstanding of the concepts. So it is you who's stalling any progress by repeating over and over some kind of half-diggested undestanding that is not correct and leads anyone who reads it --and believes what you say-- in the wrong direction. Your attitude, from a purely scientific POV, is obnoxious. At one point, it even reached that level from a civil POV, when you indulged in calling people names, when pressed for arguments you were unable to find.

Yep. A big +1 to Hanke, as it was a very transparent account of the whole thing. Unfortunately, it's possible that this will not be the last word we hear from Bangstrom, and we get past Xmas still talking about it, to iNow's boredom and despair. We've got now 2 local experts, plus a bunch of other members, plus a panel of distinguished and reputable physicists, who've made their case against a standalone opinion. Can we call it a day?

Sorry: I meant "The free non-relativistic Schrödiger equation," of course.

The receiver instantly knows if it is “0” or “1” but they can’t know what it means because even the sender can't know what they sent. In other words. You're saying that somehow, what you say is true, just because you say so, but nobody can ascertain experimentally, or even in principle, that it's true. Your simulation of an explanation is more or less the same in all your posts: You somehow know you're right, but you can't quite put your finger on why it's right, or even what exactly it is that you're right about. At this point I'm only just curious about your convictions from a purely psychological point of view. There's certainly no science to be learnt from anything you say here. And again, quantum particles have no identity: https://en.wikipedia.org/wiki/Identical_particles#:~:text=In quantum mechanics%2C identical particles,one another%2C even in principle.

The non-relativistic Schrödinger equation in thre dimensions is exactly solvable. It's not deceptive at all what happens in one direction, as it's completely separable. The propagator can be obtained exactly and shows equal dispersion --in empty space-- in every direction, as couldn't be otherwise, because it's completely symmetric under rotations. Because the Schrödinger equation is linear, it has no soliton solutions. You are right though in that other very different things are very different things than the thing I was talking about.

I meant "coherence has been lost." Sorry! I do this again and again.