joigus

Feynman: The chicken tried everything it could. It only looks like one chicken doing one thing because he fell down a stationary-phase path.

Time for the free falling trajectory is actually a maximum, not a minimum. Unintuitive? Perhaps, but that's the way it is.

No, it's not. Length and time contraction are some kind of foreshortening. But the angle analogue is v/c, and it's based on the geometry of a hyperbola, not of a sphere (or circle). But never mind that now. And it is an observer-dependent effect. If for some reason you are thinking that the object you're looking at doesn't have the length you seem to perceive, you may choose to change the angle and you'll see something different. But exactly the same as the foreshortened arm has a proper length (invariant), moving objects have a proper time (their co-moving time). About 'twins' trips: Exactly the same as you can go from one corner of a square 9 m² room (of 3 m-wide walls) to the contiguous one along the wall, measuring a distance of 3 meters, you may decide go to the contiguous corner the long way, by sequentially covering the other two corners, and cover 9 m (3+3+3) around the other direction. That's exactly the same that happens to the non-inertial twin that went around to the same place on a non-inertial trip. The first twin has gone along a flat wall and has noticed nothing significant. The non-inertial twin has had to cross two corners and has noticed curvature. I'm not sure I'm helping with this alternative explanation. If not, feel free to ignore me. I'm amazed by the patience displayed here by almost everybody else here, TBH. They don't give up on you. They just don't. I confess my inability as of today of concocting such careful and detailed Alice-Bob analyses as have been offered to you. I have a tendency to search for shortcuts. Edit: Rather than shortcuts, to concentrate on the formalism and learn to relax about puzzling un-intuitive notions. I do mistrust my intuitive notions.

That's a very big positive. The way I see it, academia advances in small steps. It is of course necessary, and immensely valuable. But perhaps the most significant big leaps are taken by people who are carefree, driven by an honest need to understand. They connect many more dots. They have time on their side. That's what I believe.

I agree to leave Einstein alone for a while. He more than lavishly fertilized all of modern physics. Now that you mention Chandrasekar, he apparently spent most of his last years studying implausible space-times. It seems that successful theorists spend their last years doing what they like, what they find beautiful, and lose interest in more pressing problems.

I was about to produce the letter to Max Born, but @studiot already linked to it: I have underlined the appropriate words. So he was actually correct. https://blogs.scientificamerican.com/observations/einstein-and-the-quantum/ A perhaps more open attitude, not exactly giving up on his idea, but apparently more keenly aware that he may have made a mistake, can be found in a testimony by John Wheeler: https://arxiv.org/pdf/0801.1654.pdf I honestly cannot believe that one of the founders of the field (as Studiot mentions) could be pushed out of it by the new generation, led by Bohr. It's almost irresistible to think that Einstein thought that if that was the direction physics was going to follow, he didn't want any part of it, and so he signed his own eviction notice. He'd rather, to use a metaphor, start digging a tunnel somewhere else hoping he might eventually find another way from the other side of the mountain, and meet everybody else midway through the tunnel.

OK, Daniel. I see how you can think that. First, please believe me: I do not need to be reminded of Einstein's brilliance. But during the years when the likes of Fermi, Uhlenbeck and Goudsmit, Pauli, and Dirac, were getting spectacular results one after another (electron's spin, prediction of anti-particles, spin-statistics connection, etc.) it's not just that he made a wrong guess, it's that even long after 1926, he didn't seem to be paying much attention at all to what was going on around him, in the world of physics. While it's true that he was also busy with questions about singularities, cosmology, etc. within his theory, he did seem to turn a blind eye, to some extent, to the results that the quantum theory was accruing. The results were there, he didn't deny them, but for some reason he chose not to be driven by them in his pursuing of a unified theory. He became far more motivated by his theoretical grand scheme. How could that be? Had it happened to a second-rank mind, I would be less than half as surprised. Picture a different Einstein sitting down to study the fundamentals of QM, adopting once again the attitude of a student. Saying to himself: "OK, I don't like this business of QM, but let's get inside it and see what's in it that I'm not getting." That's not what happened. Had Einstein let the formalism of QM become second nature to him, there is no doubt in my mind he would have found the deep epistemological principles that underlie it, instead of the half-digested understanding we've had that has brought so many decades of confusion. My question, really, was broader, and if the example of Einstein bothers you too much, feel free to ignore it. Please, let me rephrase it. When a scientist has been very successful, is there a risk that they become kind of smug, to the point of being a little bit unreasonable? To the point of being blinded by their previous success?

29 years, to be more precise. I could hardly agree more.

I didn't mean to say that Einstein was arrogant, and AAMOF I didn't. I said "entitled to be arrogant", implying a moment of self-indulgence in exaggeration, rather than a trait of the great scientist that he was. "Be" as in "don't be silly", not implying that the other person is silly, but that they're acting silly. You're never "entitled to be" something you actually are: "You're not entitled to be French, Jean Jacques; so don't be!" Come on. Another reason for misunderstanding may be that "arrogance" in its Latin roots (French arrogance, Spanish arrogancia, Latin arrogare= "claim") has, I've just found out, worse resonances in English than in Latin. For us Spaniards it just means "smugness". On the online Oxford Dictionary, eg., it's even worse than in your source: Anyway, Einstein did say that, had the laws of physics been proven to disobey his theory, instead of what turned out, he would have thought that the "I would feel sorry for the dear Lord". In other words, "if God had disagreed with me, he would have been wrong." And yes, I understand that "God" was just a figure of speech for Einstein. While I see some element of hyperbole or exaggeration there about his own abilities, it's a well-deserved one. Thereby my use of the words "entitled to be." But maybe you're right and he was just communicating dispassionately and without any bit of smugness the cold reality of facts. Somehow, it doesn't sound like that to me. OTOH, Einstein did spend more than 30 years just refusing to study quantum mechanics in any length, resisting to accept it, and working on a theory of the unified field that proved to be hopeless. The very fact that someone of the immense scientific stature of Einstein could engage in an episode like that, to me, proves that my point is in order.

That's not a test; it's a working hypothesis. Only stupids never assume they are (being one.) I know for sure I'm going to be stupid at least a couple of minutes a day. My main effort is to try and keep it within that minimum. 99% really? Com'on.

I must say you're right in that there is a time effect. Although some scientists too seem to go on a personal voyage to nowhere, after the "exclusion" is reached, and once they have acquired a level of reputation. Paid-their-dues stubborn effect, so to speak. Mmmm... There may be an age/experience side to it too. Einstein is a very good example AAMOF. He spent quite a long time from his late years trying to falsify quantum mechanics. If that's not steadfast, I don't know what is.

This topic has come up before in different threads, for reasons not hard to understand: https://www.scienceforums.net/search/?q=Dunning-Kruger&quick=1 And there's at least one thread dealing with it: Just a quick definition: https://en.wikipedia.org/wiki/Dunning–Kruger_effect A visual aid: My idea is that the topography of this curve is more complicated than it looks in the qualitative graph above. My question: Are there more bumps along the curve? How can we be sure we're past the danger zone? Is there any reliable self-test? How can you be sure you're not being "arrogant" like any run-of-the-mill crackpot, or in a milder form, like Heisenberg (“Only technical details are missing)”: https://www.bbvaopenmind.com/en/science/leading-figures/heisenberg-the-quantum-philosopher/ Or perhaps, entitled to be arrogant, like Einstein?: https://en.wikipedia.org/wiki/Eddington_experiment#Immediate_impact Or, in other words, are experts also susceptible to, say, a second-order Dunning-Kruger effect?

Slow neutron experiments are not high-energy experiments. Google for fission and slow neutrons. Many other experiments aren't.

Exactly. Let me mention some lower-level authors for you: Dirac, Pauli, Einstein, Fermi, Bohr, Schrödinger, Feynman, Schwinger, Yukawa, Yang, Parisi, Altarelli, Aspect, Zeilinger... Every major physicist of the 20th/21st century except Prigogine, maybe. There are no unanswered questions about special relativity. None. When you start learning about relativity it's well worth spending some hours thinking about Alice and Bob experiments. All of the A/B thought-experiment paradoxes in SR have been solved. But if you know anything else about physics, you start seeing many paradoxes and peculiarities get resolved and you get motivated to learn it and think in relativistic terms simply because it makes huge progress everywhere in physics. Not least because it predicts antiparticles, getting energy from mass, it gives you the right properties of helicity and chirality of elementary particles, it explains the observed speed-dependent lifetimes for elementary particles. It is also an inescapable consequence of Maxwell's equations. It gives you a consistent picture of elementary processes (congruences of events, instead of the same thing (eg. a collision) happening at two different coordinate times). If you saw a particle-antiparticle annihilation coming at you at different speeds, you would perceive charge not to be conserved, because one would disappear before the other did. My suggestion: Try to learn some electromagnetism and you'll see how special relativity is necessary. The right expression for the energy of the electromagnetic field ~E2+B2 is a direct consequence of relativistic formulation, and it has the transformations properties of an energy under Lorentz transformations. The right expression for the Lagrangian of the EM field ~E²-B² is a Lorentz-relativistic invariant, not a Galilean invariant. Galilean invariance leaves magnetism unexplained. It also explains why charge is a relativistic invariant and the conservation of charge being agreed upon by all inertial observers, as I said. It's not difficult to come up with tens more examples. It is watertight. It contradicts your intuitions, it contradicts direct human intuitions, I know, most of us here know. But then, these intuitions are wrong. Many people have tried to bring to your attention the Alice/Bob approach; others have tried a more formalism-related approach; others, experiments with muons, etc... Your arguments remind me a lot of "arguments" against evolution on the grounds that we don't see anything intermediate between a whale and a dog, dismissing the wealth of evidence as if it were irrelevant.

Are you implying that the contents of all your thoughts are this seven liner? Please tell me that's not true. As someone self-declared to belong to the military, do the words "slow neutrons" ring a bell to you?

You mean (gamma)-1x' and (gamma)-1t'. I may have swapped left and right. Equations are insensitive to swapping left and right. A=B is the same equation as B=A. All the operations I told you already: Couldn't you reproduce the partial steps up to, \[x=\frac{\sqrt{1-v^{2}/c^{2}}}{1-v^{2}/c^{2}}\left(vt'+x'\right)\] ?

What question? Oh, I see. Bob would be the primed system. Alice would be the un-primed system. So to see how Alice sees Bob, you must substitute x'=0 in the un-primed coordinates as a function of the primed ones. x_A, t_A correspond to x, t x_B, t_B correspond to x', t' You have your notations mixed. So you express x, t (x_A, t_A) as a function of x', t' (x_B, t_B) and substitute x=0 (x_B = 0) with v/c = 0.4 Does that help?

Arbitrary.

Always break down problems into easy steps. Try a numerical example with say 3, -2, 7,... Get the idea. And then do it with a, b, c,... Then go for powerful and general methods. Once you get a solution, don't just be satisfied. Think: Does it make sense? If I make v=c, what do I get? What if I make v=0? How does the equation of a light ray x=ct or x=-ct transform? Check.

Bagpipe players in the subway have always bothered me. But bagpipe players in the subway doing a headstand are even worse.

OK. Let me know if you can follow the steps up to here: \[v\left(t-vx/c^{2}\right)+x-vt=v\sqrt{1-v^{2}/c^{2}}t'+\sqrt{1-v^{2}/c^{2}}x'\] \[\left(1-v^{2}/c^{2}\right)x=\sqrt{1-v^{2}/c^{2}}\left(vt'+x'\right)\] \[x=\frac{\sqrt{1-v^{2}/c^{2}}}{1-v^{2}/c^{2}}\left(vt'+x'\right)\] OK? If you have any difficulty with that, tell me. There's one minor step left. And then the other equation. But if you understand this one, it's almost done. You can PM me, if you want.

I think we can call it a day. Everybody get ready for drumbo's next thread: "Fat people should not be allowed in public transport."

Pascal must have been under a lot of pressure when he said that. I see no way in which this could be false.

Good point. That's called the curse of knowledge. It doesn't happen only to scientists, though. There's also the curse of expertise.

Inferring correlations when you see guys in the subway is no robust way to make serious statistics. It is well known that humans tend to apply filters and bias the results when they read too much into their everyday observations. For example, when people notice some guy who's dressing in a way they already disapprove, they tend to pay more attention when he's also acting in a way they disapprove. So you must be careful with such observations.