joigus

Aha! So deterministic is a special case of non-deterministic... They do. QM is non-Markovian. Markovian systems don't keep memory of their previous history. Quantum mechanical systems do. Except when you measure. When you measure you do erase a big chunk of the past history of the system. So you have to be very specific and very precise about when this whole Markovian thing comes into play. It's not impossible. I didn't say it's nonsense. It's just you haven't convinced me. Others don't seem convinced either. So far, I'm afraid I can't follow your 'aspect'.

A little bit along the lines of what Phi and Swansont said, tell your friend: Try to start by being your own critic. Be objective. Try to think, 'how could this idea be wrong?' instead of so much on 'why don't people immediately see how beautiful this idea is?' The history of science sometimes focuses too much on the epiphany, the eureka moment, and glosses over the bouts of painful self-criticism the authors themselves had to apply. Also by others. The history of sience is full of simply elegant ideas that had to be hammered out into useful ones.

Ok, let's stop right here and do a sanity check. In what sense do you see evolution of the quantum state (never mind pure states evolving via Schrödinger or density matrices evolving via V. Neumann eq.) as a Markovian process? I fail to see how they are related. Schrödinger eq. allows for evolution of superpositions. V. Neumann too, if only perhaps more obscurely, because they are integrated over in the p's (the statistical weights). You must mean something like results of measurements somehow occur "internally" as Markovian processes that must be implemented in the evolution of the quantum state, completing it, quite unpredictably. For some reason to be ascertained later, they comply with Born's rule that the odds follow the square of the wave function, or bilinears of it. Otherwise, I don't know what you mean.

Sure, but you said, It is that what I argued not to make much sense. For starters, typical quantum mechanical space states are infinite-dimensional. But even in the case of relevant sub-spaces (eg, spin), the space of pure states has dimension 2S+1, while the space of density matrices has dimension (2S+1)2. So, again, what do you mean a density matrix is "much smaller"?

The key to the concept of a density matrix is that, whenever your quantum state is not maximally determined, the most natural thing to assume mathematically is that the collectivity you're handling is a statistical mixture of different so-called "pure" vectors with statistical weights p1 , p2, etc. It is a mathematical convenience to define it as a matrix: p1|1><1|+p2|2><2|+... Nothing more. Anything you can define with a matrix you could define equally well with a series of scalars (bilinears, in the case of QM). This doesn't make much sense, as a basis of the Hilbert space spans the whole set of possible states. The total is the span of the basis states... Or I'm missing your point completely. Quantum mechanics is non-Markovian. Present states depend on their past histories... Errr... more stuff... Non-linearity could be relevant at many levels. Evolution could be non-linear, observables could be non-linear functionals defined on elements of a linear vector space, etc. These things have been tried to death, of course. And sub-quantum Markovian processes have and are being tried. Cellular automata, for example. I'm almost sure of that, although I'm no expert. Look up Gerard 't Hooft interpretation of quantum mechanics...

Ok. So let's leave it alone, as long as you agree that Bell's theorem experimental violation implies there can be no local hidden variables (a local reality that underlies quantum mechanics). I agree with @studiot that you don't need Markovian probabilities to accomodate quantum mechanics. You only need a concept of probability in the terms that he defined. What's different is the existence of these "potentialities" if you will, that we call "probability amplitudes".

Again, no. There is a restriction on local realism, because there is a restriction on realism, because three perfectly sensible experimental questions, namely "Is A true?", "Is B true?", and "Is C true?" cannot have yes / no as answers simultaneously. In fact, the CHSH state was prepared in one and only one causally connected patch of space-time, so nothing non-local is going on. Many people misunderstand this. Some of them write books. What can you do... Then why bring it up, especially as an incorrect statement? QM's concept of probability differs from classical probability only in that classical probability doesn't have anything in the way of quantum amplitudes, which as we know give rise to interference phenomena. This gives way for interesting correlations that do not appear classically. Otherwise it's more or less the same concept.

Not really. What QM and CHSH experimental results display is incompatibility with a somewhat involved hypothesis called "local realism". If I had an alternative life to repeat this discussion again, I think I would be able to convince you that the downfall of local realism is due to the "realism" part of it, not to the "local" part of it. The Schrödinger equation is perfectly local. Field theory is perfectly local. This should be enough of a clue that nothing non-local is going on in QM. What is formally non-local is the projection postulate (far-away and long-gone subamplitudes of the wave function must "die" immediately). But it has no discernible consequences that would allow to --eg-- send signals, transport energy, etc. Which only reinforces the idea that nothing non-local is actually going on.

That would probably be considered hijacking. Maybe @AbstractDreamer could expand on their statement in a thread of their own, I suppose. Not for me to decide anyway.

I'd put it even more simply: GR was valid 5 minutes ago, but not 5 minutes from now? Quantum mechanics will be valid only after I finish my ice cream? There is no such thing in physics as "the present" (the all-pervading separator between past and future as far as human experience is concerned). What is the present, according to physics? If you have an answer, any answer, let me know. Thereby my McEnroe point.

I've had a John McEnroe moment: You cannot be serious!

I'd say it's homeopathic in the blend. Rigour of physics being the substance to be dilute to zero, and wildness of intuition being the diluent. And no mathematics...

This I remember from previous readings referred-to as "discontinuity of the fossil record", and if I remember correctly, Darwin already was very much aware of it.

It's long been known that the Dirac algebra is isomorphic to quaternions. Unfortunately, it's also been known for a long time that quaternions are insufficient to represent the properties of elementary particles. Models based on octonions have been tried with more success than those based on quaternions (Hestenes et al.). See, eg, https://pirsa.org/c21001 And ripples in space? Space is not a substance. It's more like a format.

I am. I wish I were.

There is a fine line between a numerator and a denominator. Only a fraction can make sense of this.

Let me put it this way: It's trivial. GR trivially violates QM, therefore, HUP. Is that any better? Trivial it is. You can bet your life's savings on that.

Classical GR (or any other non-quantised theory) obviously violates HUP, as coordinates and their canonical momenta commute. You need coordinates, a Lagrangian, and canonically-conjugate momenta that do not commute with the former, for the HUP to be satisfied. There is no Planck's constant, nor non-commuting operators in GR.

Hardly, as there is no such thing as a fixed metric background in general relativity. There is only an equivalence class of metrics, of which all the topological invariants are preserved, because the valid group of transformations is that of diffeomorphisms. How am I presupposing something I know to be irrelevant? I don't think you understand either standard cosmology or the principles of general relativity, as one of the departure points is that you can shuffle and reshuffle the metric at will. It's the interval that gives you the physics.

Maybe it was a really elongated object on a hypothetical orbit, rather than a hypothetical object in an elongated orbit.

I don't think the left is more scientifically-learning. I think the implication arrow would go the other way: Scientifically-learned people tend to lean left.

Actually this is a good analogy of what AI should do for us. Unfortunately many people use it as prosthetics for intelligence.

How is someone who is asking for a framing assuming any particular framing?

Thank you all for your responses. Yes, much better. Interesting... Seems like AI often has problems with what I'd call "connecting the dots". And by that I mean what @Ghideon mentions later: context. Like "probably this guy is refering to general relativity" and "probably this guy understands the question in terms of quantum field theory". After all, that's where such question is most relevant. The question whether a theory is scale-independent or not refers to the coupling constant. So yes, I meant in QFT. This could probably be understood as another instance of missing the context, but on a different level.

Has there ever been an instance when AI has given you an answer that leaves a lot to be desired? It would be an interesting exercise to ask a non-trivial question in your discipline of choice to a reputed AI engine, and see how the answer improves with time, as the case may be. In this case I've used Google's AI module, which might not be the best. Here's my question, the answer, and what I think is wrong with it (O, for "objection"): Q: Is gravity's strength scale-dependent? A: No, the strength of gravity is not scale-dependent in the way that a small object experiences significantly different gravity than a large object. Newton's law of universal gravitation states that gravity's strength depends on mass and distance, not the size or scale of the object itself. While there are theoretical considerations about scale-dependent gravity in certain contexts, the everyday experience of gravity is not significantly affected by scale. O: Ever heard of GR? Mass does not source gravity. Energy does. When I say "gravity", I expect AI to understand GR, if only as a possibility. So gravity is very strongly scale-dependent. In fact, it is the only unredeemably scale-dependent interaction as far as I know.