joigus

I can't stress enough how much I agree with this. Give it a couple of years and that letter will come through.

I do. Believe me. Just yesterday a video appeared with the effects of bombing on a Palestinian kid that couldn't be older than 7 or 8 and I couldn't bear to watch it. What worries me most is that this kid (assuming he gets over PTSD, and such) will not join the forces of jihad some day, and a better future than that is in store for him. That, and an immediate stop of rampant antisemitism. And also the future of so-called progressive thinking, with re-examination of basic premises and careful separation of problems. And...

No problem with me. Thank you. Good answers. Some of them anyway. So this scalar field is a part of every other quantum field and comes from the K geometry? I still don't understand why you equate the energy of a point charge to the energy of a photon? What energy of a photon? A photon can have just about any energy.

The EM fine-structure constant is about 1? (!?!?!?) What does a EW-mixing angle --or any other standard-model mixing angle for that matter-- have to do with a coupling constant? If they are related, there should be a pretty convincing argument for it happening. What makes you think electrostatics is relevant when dealing with particles' self-energies? Why does a photon have a self-energy? Why should it equal the self-energy[?] of a point charge?

No, that's no example of either one of them, because: (from oxfordlearnersdictionary.com) At what point did I cross into 'hyperbolic' or 'metaphoric'? I think I was quite literal. Flooding the sentence with adjectives does not constitute by itself any kind of exaggeration or dishonest comparison. Each and every one of those adjectives totally apply to Hamas' way of launching their "liberation war". The part "lest we finally understand somehow what we're really dealing with here" was intended as sarcasm. Demagogues rarely use sarcasm. But I am guilty of sarcasm, that's all. Well, things going on in alleged concentration camp and what kind of reactions, comings and goings --or lack thereof-- take place, have some bearing on judging whether said place is a concentration camp or not. But never mind. I do recognise that as possibly the weakest part of my argument. I'm glad that wasn't intended for me: Unless it's actually me and you think I'm lying and really I don't care about that 99%? I wonder where you got that number from. Of course Gazans are the first victims of most of what's going on there. Never mind that 3/4 of them seem to have applauded the mayhem of 10-7. What do they know? Regular Abdullah or Fatimah in the street is no political analyst. Not to mention the poor kids. And, Never mind it's quite impossible to tell which one is a civilian and which one is not. UNRWA also plays a big role in decreeing that no Palestinian will be relocated, that never mind that Hamas has been documented as stealing supplies, and that the condition of refugee (only for Palestinians) lasts forever and is inherited from parents to children, to grandchildren, to grand grandchildren, and so on for all of eternity, so that they can never ever go to a safe place. Never mind that the UNRWA (a refugee-problem managing organisation that's exclusively for the Palestinian problem) has been found to publish twits incriminating Hamas, only to delete them minutes later. Here's a sequence of "innocent civilians" manhandling a woman that's been identified as Re'im music-festival attendant, Art student Inbar Haiman, after an Israeli air strike, These poor people are in a multi-pronged stranglehold by their own religious creed, some neighbour countries not really giving a f**k about them, Netanyahu making deals with the devil and hard-pressed for expediency, and other neighbour countries pushing their particular agendas. A horrible tragedy for all involved that will go on and on, be in no doubt about it. As it's only too obvious seeing how the roots of the problem are not even being addressed. Two-state solution. Yeah, righ! See you in 10 years to check how that's gone down.

I was going to drop out of this discussion, but I can't leave it at this: Well, you can compare it if you want. If it is, it's a very peculiar concentration camp, where the "inmates" apparently spend billions of dollars in weapons to make their life more... bearable? One of the borders is also sealed (by Egypt) but for some magical reason that border does not contribute to making it a concentration camp? And when Egypt occupied the land in the past, that was no occupation. No, no, no. But when Israeli settlers build irrigation systems, that's an occupation. And even after they pack their bags and go, they were still occupying the land!!! (According to this Albanese person from the UN.) With their minds, I suppose. In other words, it's simply a metaphor, and a very bad one at that. Metaphors, comparisons, and hyperbole are the favourite rhetorical tricks of demagogues. And they use them to great effect. You just remove the word "like" and it works its magic. "That thing" becomes "the other thing". It's not that reminds you of the other thing, which seems to invite lots of questions. It just is the other thing. And critical thinking just shuts down. And sure, let's not mention that big, scary, monstrous, barbaric, medieval, inhumane, irrational, unmentionable thing that we don't want to mention, lest we finally understand somehow what we're really dealing with here. I'm sorry that you feel that way. From where I stand, it looks like a thankless task to study for years and years and years, without getting anywhere, and thinking all that study time could have been spent in something more productive, more constructive, more beautiful. It feels like Sysyphus.

I think we're losing the patient.

"Differentiation" is frequently used as synonymous of "taking the derivative". Interpreted in that sense, it is an operation which, given a function of the right class (differentiable functions) produces its derivative, which is another function. Example: \[ x^{3}\overset{\frac{d}{dx}}{\mapsto}3x^{2} \] We say that we have "differentiated" \( x^{3} \) to obtain \( 3x^{2} \), its "derivative". 3xerivative". Mathematicians sometimes talk about a function being "differentiable" when you can express little increments of it as a linear function of the increment in its variable. This linear function of the increment is what they (the mathematicians) call "the differential". With our previous example, the difference between the values of \( x^{3} \) evaluated at \( x+h \) and the same function evaluated at \( x \) is, \[ x^{3}+3x^{2}h+3xh^{2}+h^{3}-x^{3}=\left(3x^{2}\right)h+\left(3x+h\right)h^{2} \] Now, the idea is that, when \( h \), the increment in the independent variable, is very small, the increment in the dependent function is a linear function plus something "very small". And indeed, \[ \left(x+h\right)^{3}-x^{3}=\left(3x^{2}\right)h+o\left(h^{2}\right) \] where, \( o\left(h^{2}\right)=\left(3x+h\right)h^{2} \) really is "something very small" when \( h \) itself is small. This is what physicists write as, That's why physicists like to write, \[ y=x^{3} \] \[ dy=\frac{dy}{dx}dx=3x^{2}dx \] when rigorous mathematicians would rather have us write something like, \[ \triangle y=3x^{2}\triangle x+o\left(\left(\triangle x\right)^{2}\right) \] Now, a function has a derivative at \( x \) if and only if there increments of it can be expressed as a linear function of the increment plus a little correction that goes to zero as the increment goes to zero. Did that help at all? If not, please just ignore it.

That was very interesting, thank you.

No, I said "Copernican revolution" meaning "humans are not at the centre". You always take scientific discussions to an anthropocentric frame. And people naturally call you out on that. In this particular thread I think it was @Sensei who first pointed out, it's a matter of perspective. The first Copernican revolutionary was arguably that unknown genius from prehistory who invented the grammatical mode "3rd person plural"

Two words: Copernican revolution.

I think what Seth means is QM allows for the final state in a complex multi-step reaction being "there" as a potentiality, so to speak, in the form of a quantum amplitude driving the process. Classical thinking, OTOH, seems to require first one step, then another, then another. Something like that?

I really don't want to butt in on the very interesting discussion you were having with Seth. But here's an interesting point: It is precisely because microscopic variables are so extremely sensitive to initial conditions, these systems (called ergodic) become highly indifferent to initial conditions (reach thermal equilibrium quite efficiently) macroscopically. How about that for pointing out that nothing is as simple as it might seem in physics?

x-posted with @Genady

Outcome of what? Thermodynamics of system can be predicted under certain circumstances. Where molecule X is going to be, no. Absolute certainty doesn't exist.

Not necessarily. Thermal equilibrium isn't.

Linearity is applied to sets of variables and how they depend on each other. So it's not like a presence, "linearity is here" or "it smells of non-linearity".

"More than lack of food" implies lack of food and other factors, which I don't think is what you mean. I think you mean something other than lack of food. Because it seems obvious to me that lack of food there was not, at least for the general population before the situation got to the dramatic point it has. And I didn't. But I admit was somewhat lazy with my criterion. So here's some analysis taking your definition as the starting point. This doesn't seem to be the case for Gaza/Israel. Unless you're willing to accept several million people of the same ethnic and/or religious minority have met a very different fate for absolutely no identifiable reason. Some of those people of exactly the same ethnic and religious group seem to have made their way to the Supreme Court, the Knesset or the IDF. They are Israeli citizens: These data are from Israel only, not Gaza or the West Bank. More: https://en.wikipedia.org/wiki/List_of_Arab_members_of_the_Knesset For 20 years Gaza has been under the rule of Hamas. I'm not sure that Palestinians have been forcibly retained in Gaza for all that time. But I do get from testimonies that leaving is considerably difficult, and it must go through special permission, and ridiculously elaborate security measures, including digital cards and such. Nevertheless, here's a screenshot from the World Bank data webpage corresponding to Gaza+West Bank Which seems to imply that some people seem to have managed to trickle out, in spite of all those guards watching them from the turrets. Let's see about life expectancy Similar to Albania, considerably higher than Rwanda, about the same as Tunicia. All of those well-known concentration camps? https://data.worldbank.org/country/west-bank-and-gaza Population growth of only Gaza: Population of Gaza in 2005: 1,299,000 people. Population of Gaza in 2023: 2,300,000 people. Although I can imagine that it must not have been easy for many of them to leave due to the economic conditions --and that in spite of the large amounts of money thrown at them that could have been invested otherwise, as @MigL has observed before. Moreover, it is apparent that no Arab countries are willing to take regugees from Gaza, or no Arabs from Gaza are willing to go to other Arab countries, or both. They seem to like to go to NY or London, for some reason. Prisoners in their territory? Quite a number of them enjoyed work permits and crossed the border on a daily basis to work in the kibbutzim with their socialist benefactors. An opportunity to collect intelligence for the attacks that Hamas couldn't and didn't miss. So no, Gazans were not under guard when the attacks of October 7th happened. Frankly I find it impossible to recognize any condition from the definition you presented that applies here. What about the bit "those deemed political enemies" in your definition? Well, the logistics of the map of the West Bank doesn't look to me as the places where part of the population is divided according to what they think. It looks more like the logistics of urban guerrilla: Isolating places where the chances of getting shot from a window are more than so-and-so percent. And that's what they are. So there's nothing political about it. But of course the main issue is not political, in spite of many people trying to make it political. It's mostly that thing that shall not be named. It's that thing that shall not be named what gives it the character of an unsolvable problem. If you misdiagnose an illness you guarantee that it will never get better. If tomorrow all the Muslims of Palestine converted at once to, say, the Ahmadi Muslim faith --which are now a tiny, tiny minority there, the problem would be solved in a matter of months. Unfortunately, they are mostly Sunni followed by a minor amount of Shia, and the rest of the Muslims consider the Ahmadi heretics. So no, it won't work. And it never will. It takes a religious component for a problem to become so vicious, so stagnant, so irredeemably impossible as this one. It will never get better. Not for as long as the religious component of it survives. I grew up seeing the buildings of Beirut smashed to smitherines on the TV, and I'm pretty sure I'll leave this world with a similar scenery from the Middle East. Only this time on YT. Etc, etc. The situation is a tragedy for everyone involved, and it breaks my heart seeing Palestinian kids used as cannon fodder by Hamas, but pretending that the State of Israel is some kind of Khmer Rouge of the Middle East is just ridiculous. And no, it's not going to solve the problem either. It's going to make it worse and worse. This kind of hiperbolic discourse (like those morons saying "apartheid", "genocide", etc in the campuses) only weakens the arguments coming from any kind of progressive thinking. And if you ask me, they only make the Trumps and the Wilders and the far-right extremists more likely to seize power, not less. They're biding their time, make no mistake about it. Sorry for the lengthy diatribe. I will probably shut up pretty soon. It's a pain to participate in these debates, because the fog of propaganda makes the main arguments almost invisible.

Well, you're right. You must assume quantum mechanics, of course. It's not just plain non-commutativity. You must assume in particular the correspondence between observables-operators and eigenvalues-spectrum of measurement. That's why I didn't say Bell's theorem can be described in terms of non-commuting observables. I said they are the essence, but QM must be in the back of your mind. Bell's theorem is about whatever variables that can take on definite values at the same time. As the theoretical structure of QM forbids non-commuting operators to take on a definite value at the same time, there's the connection. But you do need the apparatus of QM, sure.

Oh, man. If something is it. That is it. A logic that sometimes doesn't allow you to say this and that. That's the essence of Bell''s theorem without a doubt.

(My emphasis.) Ok. I promised myself I wouldn't participate in this thread. Its centre of gravity is soooooo far removed from the real root of the problem that I just don't think there's any chance of setting it in the right direction. But, Modern-day concentration camp? Really? Prisoners in Gaza (image from today 12-8): Prisoners in actual concentration camp (Dachau): The first photo doesn't look like people in misery to me, tbh. Concentration camp? An impressive concentration of beer bellies more like it. Some of these men should give up on compulsive eating and start watching their glucose/LDL cholesterol levels. Seriously. They should stop hogging all that food down in the tunnels, or their heart disease will catch up with them long before Israel's bombs do. Having said that, peace to all.

Oh, absolutely.

I'm just an old geezer with an inclination for the philosophically spicy aspects of science, but thank you. I disagree. The relativistic version is: https://en.wikipedia.org/wiki/Dirac_equation which is linear. It's the one that's used in the standard model, for example. Klein Gordon is also linear: https://en.wikipedia.org/wiki/Klein–Gordon_equation You can also play with it and introduce a non-linear self-interaction term. You also have sine-Gordon, which was extensively studied by Sidney Coleman, for example: https://en.wikipedia.org/wiki/Sine-Gordon_equation which has beautiful, beautiful solutions called "breathers"... There is a non-linear model of the Schrödinger non-relativistic equation which is cubic in the quantum amplitude: https://en.wikipedia.org/wiki/Nonlinear_Schrödinger_equation Etc. The subject is extraordinarily rich and full of forks in the way. Non-linearisation of evolution has been tried. One example is this modified non-relativistic Schrödinger equation with a self-interacting term \( \psi \left| \psi \right|^{2} \). Another one is the NL Dirac equation, which is relativistic, but non-linear in evolution. Another more drastic attempt to refurbish the whole thing is non-linear quantum mechanics, in which the whole suite of postulates is re-defined in terms of non-linear functionals instead of linear operators. If anyone is interested and has an alternative life to study it, I think here's a "reports" kind of article (that I haven't read): https://arxiv.org/pdf/1901.05088.pdf And so on, and so on.

They are linear in at least two different senses I know of: 1) Evolution is linear [quantum state](at time t'>t) = [Linear operator][quantum state](at time t) and, 2) probabilities of observing property Q with particular value q: amplitude(Q=q, at time t) = [linear operator on q][quantum state](t) The probability being the square of the absolute value of this probability. So linearity plays a big role in QM to say the least. So, mathematically, what it's telling you is "dynamical states are vectors" and "observable attributes are special matrices acting on those vectors".

Yes. I must say I don't know a lot about the transactional interpretation. Now that I think of it, I wouldn't call the transactional interpretation a flight of fancy. It's taking known physics and putting it to good use, which is what I think is likely to be the answer to the questions most people would like to see answered. Yes. From what I remember in the Wheeler-Feynman theory of radiation, they devised a perfect absorber at spatial infinity that guaranteed that no causality-violating effect would take place. One of the big misteries about quantum mechanics has been this one precisely. I'd phrase it like, where does non-linearity come into play in quantum mechanics? Non-linearity is ubiquitous in Nature. How come linearity seems to be a sine qua non of QM? It's very strange. Exactly. You'd expect microscopicity to be the realm of non-linearity. Instead of that, the operational rules (the prescriptions to relate the maths to the measurables of the experiments) become considerably weird and unintuitive --but linear!!--, while the evolution law of the state becomes... linear too??!!