joigus

As I never claimed that, there is no way that I might still claim that. Einstein's view of realism is untenable today. However, Einstein's original argument was about space variables. But spin cannot be understood in terms of space variables. In fact, spin variables cannot even be consistently understood as coming from any internal reality based on commuting variables, or "just parameters." Period. Why don't you read what people say, draw conclusions carefully, are rigorous about what you say yourself, and stop offending? If you did, and were, it would be possible to talk about the interesting problem of why QM --when you hold a certain interpretation of it-- produces this illusion of non-locality that's not really there. There are interesting parallels, possibly, in how biological evolution --when you hold certain interpretation of it-- leads to an illusion of design that's not really there. But you don't and aren't, so this discussion is leading nowhere.

Last paragraph in response to: Realism is violated by QM in the most glaringly obvious way: QM uses states for which, x-projection of spin is up x-projection of spin is down x-projection of spin is 40% up / 60% down, 70% up / 30% down, 50% up / 50% down, etc. In fact, for those states for which x-projection of spin is definitely "up," y-projection of spin is 50%up/50% down, and so is z-projection of spin. So, if you want to make one variable determined, all incompatible variables are undetermined. It has all these tradeoffs built in. IOW, QM violates realism in a way in which it implements an inherent, irreducible, totally from-the-ground-up indeterminism. Deeply-rooted indeterminism. Indeterministic to the bone and marrow. It does it in such a way that, for Hilbert spaces of dimension 3 upwards, you can even build 3 mutually commuting observables for which attributing hidden variables to determine the 3 corresponding eigenvalues is impossible (Kochen-Specker theorem.) With space-time not playing even the remotest part in the argument. Furthermore: For entangled states with maximal entanglement entropy (Bell, GHZ, etc.) not even the individual quantum states are determined, let alone the underlying "reality" of eigenvalues. Furthermore: Identity of a particle doesn't mean anything --anything measurable, that is-- in QM.

I'm with Gauss on this one. +1 Remove all nonsense propping-up-to-mystical nuances from anything intended to clarify our understanding. Vocabulary is a good place to start. I share your taste. I'd rather multiply complex numbers than add them. Adding complex numbers is messy; multiplying them is nice. I also agree that complex numbers are an indispensible part of QM. Unfortunately QM forces us, not only to add them, but normalise the result, after having added them, which is even more awkward than just adding them. I think the problem of what mathematical representation makes our description least awkward will always be an open question. The parametrisation of the sphere is, in this respect, a cautionary note that I never forget.

Disclaimer: It wouldn't be all of 2x2 matrices. It would only be those of the form, \[ z=\left(\begin{array}{cc} x & y\\ -y & x \end{array}\right) \] Those, and not other 2x2 real matrices, are complex numbers. These rings have fascinated me for decades. You could get an approximation as close as desired to the real numbers by means of rational combinations of 1 and the square root of any integer number that's not a perfect square. The p and q would have to be rational, instead of integer. Would that be a way in which the continuum can be approximated by a discrete mapping that frees physics from singularities and other similar "diseases"? Absolutely spot on. Just a name. Nothing "spooky" in imaginary. Agree. Non-commutativity: totally peculiarly quantum, but not due to complex nature.

Well, one single ocurrence doesn't tell you anything. That's a very important point. It's easily dismissed as a coincidence. OTOH, if every single time you saw a particular cat doing that, you would have to conclude it's likely not a coincidence. If you saw that happen with the same cat every single time, maybe a natural hypothesis would be that the owner of both the cat, the TV set, and being in control of the sequences shown to that cat, has arranged things in such a way that the cat has been trained to recognise the situation and produce the desired effect. Conclusion: Coincidence is not such. There's been an antecedent common cause to give rise to observed correlations. If, OTOH, every single cat you try this with displayed same behaviour... Well, that would be a puzzle. Every time the correlation becomes more and more puzzling, because you widen the sampling, and it becomes less and less likely that it be a coincidence. You would have both to widen your statistical scope --perhaps invoke Bayesian methods--, have a theory to explain why this would happen, further test your theory by sampling more and more of the parameter space that your theory suggests, etc.

Sorry, I meant addition. A false friend tricked me. A little bit more on this fascinating --at least to me-- topic: Suppose that, for some reason, you are repulsed by numbers which are the square root of a negative real number. You can always obtain a numeric structure that's totally equivalent to complex numbers by means of the following trick: Complex numbers "secretly" are 2x2 real matrices. Now, 2x2 real matrices can always be uniquely expanded into a symmetric part and an antisymmetric part. Here's how you do it. Introduce the special matrices that are going to be respective stand-ins for 1 and i: \[ E=\left(\begin{array}{cc} 1 & 0\\ 0 & 1 \end{array}\right) \] \[ I=\left(\begin{array}{cc} 0 & 1\\ -1 & 0 \end{array}\right) \] and define a complex number \( z \) with real part \( x \) and imaginary part \( y \) --and its conjugate-- as "secretly," \[ z=\left(\begin{array}{cc} x & -y\\ y & x \end{array}\right) \] \[ z^{*}=\left(\begin{array}{cc} x & y\\ -y & x \end{array}\right) \] Then, the absolute value (squared) of \( z \) is, \[ z^{*}z=\left(\begin{array}{cc} x & -y\\ y & x \end{array}\right)\left(\begin{array}{cc} x & y\\ -y & x \end{array}\right)=\left(\begin{array}{cc} x^{2}+y^{2} & 0\\ 0 & x^{2}+y^{2} \end{array}\right)=\left(x^{2}+y^{2}\right)E \] The product of \( z \) and \( z' \) --another complex number-- is \[ zz'=\left(xx'-yy'\right)E+\left(xy'+x'y\right)I \] etc. Now, whether complex numbers are "secretly" 2x2 real matrices, or conversely 2x2 real matrices "secretly" are complex numbers is, of course, totally immaterial from a purely mathematical POV. Errata It should be: \[ z=\left(\begin{array}{cc} x & y\\ -y & x \end{array}\right) \] \[ z^{*}=\left(\begin{array}{cc} x & -y\\ y & x \end{array}\right) \] So I guess my answer is: Yes, we do need complex numbers. We can dress them as 2x2 real matrices if we want, but we need them is some disguise or another.

As Markus says, all of physics is local. Why it is local is a mystery. Whether it is local is not.

Interesting. +1 People have been thinking about alternatives to complex formulations of QM for ages. I think Schrödinger himself initially thought that the presence of complex numbers in his equation might point to some flaw in his argument. There's always the trivial possibility of replacing the number 1 by the 2x2-dim identity matrix, the number i by a 2x2-dim antisymmetric matrix with determinant 1, and say something with philosophical undertones like "oh, the number i doesn't exist; it's just a 2x2 matrix!"

Sum of complex numbers can be implemented by 2-vectors. But product of complex numbers cannot. Product of complex numbers is equivalent to inner product (real part) and vector product (imaginary part). So their algebraic properties package more than ordinary 2-vectors. You can, of course, define special operations for 2-vectors that replicate all the properties of complex numbers. You can also do it with matrices, but in the end you would be doing the same thing.

Yes. There was something: the quantum state. It had all the correlations packed in. So it's not really saying anything about locality. Understood? Let me guess: No. Not necessary, not because of what you say, but because you don't need to explain it to me --I did a seminar on it in 1996-- or to Swansont, or to anybody else here. Physicists have been using PDC for a long time, and Bell already mentions it in his work. The key to its workings is non-linear crystals. The word spontaneous is not necessary, as it involves LASERs, and inherits the S from "spontaneous emission of radiation." The "spontaneous" part of it, certainly, doesn't add anything significant to the discussion of locality. You keep scavenging for words that seem to suggest non-locality is a fact, which is what you wish to be true. And it's not.

(My emphasis in bold) Yes. Another thing that bothers me is that sometimes it's a transaction or handshake --TIQM--; while other times it's the collapse of the quantum state --Copenhagen. One would think it's one or the other. But, as I said before, let them clean their own house.

I think it is. Besides, Heraclitus' is much less anthropocentric.

If that's your argument, it's as good as saying that the description of an angel consists in that it's defined as a single being of pure grace. This is a non-argument. You have no experimental basis for your FTL signal, nor theoretical description of it. (my emphasis in bold) Wrong. The spatial part of the state propagating to the left is a quantum superposition (up)1(down)2-(down)1(up)2, and the spatial part of the state propagating to the right is too. What do you mean spontaneous? You mean parametric down conversion of photons? It's essentially the same case we've been discussing all the time. Eise is reminding you that none of your points are new. We've visited them before. But every time you make a new comment, I find more and more ways in which it's obvious you totally misunderstand both the facts, and the formalism of quantum mechanics. There is no such a thing as "the identity of a particle" in quantum mechanics. The state is undetermined in the particle indices. There is no such thing as "spontaneous down conversion." Etc. And you haven't "described" the signal yet. You've just given it a fancy name.

Unfortunately, no. I did Latin and French. But as soon as I went to university, I started spending every waking hour learning English. Later I tried to learn some German and Japanese, but I was too old by then to make them stick. In English I'm quite fluent when writing and speaking, and have no accent, which sometimes I miss, as accents are often regarded as "delightfully peculiar." My English is some kind of mix between American and British. Yes, Heraclitus' "everything flows and nothing stands still" is a nice summary of it all. Isn't it? You take a bunch of phrases from the Greeks --the best ones, the scientists, the skeptics--, and all else looks like just adding details to the picture: Everything is made of atoms. Everything changes...

Subtle language barrier there. I'm not a native English speaker, and I obviously missed the nuance. Sorry.

Mathematical illiteracy is one of the best chances big oligopolies have to make bundles of money with no substance behind their claims. It's not beyond belief that some big companies will try to have you think they're giving money away. Or... maybe it was just a typo.

It's entirely possible that it was I who misunderstood you. Quantum tunneling is, in a manner of speaking, a way for something to disappear at some place and reappear somewhere else, in a totally continuous way, through its wave function. You wouldn't need any cuts or stitches, or surgical trusses. Then politics came up and I tip-toed away. Wasn't something like that what you meant?

Or quantum tunneling...

Correlation is an effect, or a coincidence. Depends. Most of the times it's an effect of something happening before, or even independently of time. Yeah, sure. It's an effect. An effect of what? Correlation (positive) between A and B. Possibilities: 1) A causes B 2) B causes A 3) Both, A and B, are caused by the same: C 4) A is caused by B plus other factors (not perfect correlation: B makes A more likely) 5) B is caused by A plus other factors (not perfect correlation: A makes B more likely) 6) Both A and B are caused by common cause plus other factors (both are more likely together because antecedent cause C makes both more likely) 7) Coincidence... If you can expand the sample space you can in principle rule this out. I think you're confused beyond recovery here. Also, you constantly cherry-pick what you want to answer. On top of that, you don't distinguish anything relevant here with any care. "Correlation is an effect." Yeah, sure. And a thing is a thing. And what's more, an effect is a something. And something is some thing. Thank you for your illuminating arguments --I'm being sarcastic.

Of what? Of number of people drowning by falling into a pool and Nicholas Cage appearing in a film?

Whois output now gives: Updated Date: 2022-10-20T01:25:16Z Registrar Registration Expiration Date: 2023-10-16T12:23:19Z Previous expiration date was October the 17, if I remember correctly. So brace yourselves in one year's time.

Dear @bangstrom. I think it's very much possible that at the bottom of your misunderstanding of this question is your confusion of causation with correlation. I've just commented on a related topic: The theme "correlation is not causation" could be where you're having difficulties. I do suggest you to do a look-up for that theme on SFN. It's come up before in many different contexts. I've seen statistics in the past going something like "people who take the bus are more prone to getting cancer." A hurried interpretation of this could be true, not because taking the bus is giving you cancer, but because, if you're more likely to take the bus, you're also more likely to be exposed to carcinogens, on the grounds that your lifestyle is more likely to be whithin that particular statistical cohort.ç Anyway, correlation is not causation.

Any conserved quantities are just conserved quantities. After you find out they're conserved, you can look upon these quantities as defined by local densities for them: local density of energy, angular momentum, and so on. But once you mathematically integrate over all values of space, they're just what we call a quantum number. The quantum number is neither here, nor there, but an overall property of the state. Same goes for non-conserved quantities that are nevertheless defined by local densities. Example: expected value of position. Only, we don't call them quantum numbers.

You're confusing correlation with causation. That's not what I'm saying. The experimenter's minds are determined by a common cause, either in the past --exactly as in the singlet state-- or not. Only state of affairs is more complicate in the case of the singlet. Confusing of correlation with causation can be very, very misleading. Sometimes, not even causal connection in the past can be significantly attributed. For causation to be attributed, you must have a theory for the common cause.

That was my best guess after doing a whois search from Linux command line. +1