joigus

Thanks a lot, @Dord. The Andromeda looks sooo 3D... Here's some beetles of the genus Chrysolina: https://en.wikipedia.org/wiki/Chrysolina They eat leaves. Some species have been used for weed control. Why do they look so metallic?

Studiot: You may be interested in this: https://www.amazon.com/Chicken-Book-Page-Smith/dp/082032213X Got it. LOL

Swansont: Did the chicken cross the road? Any references?

Geodesics are obtained by minimizing the action. The action in relativity is proportional to proper time. Geodesics correspond to inertial observers. Proper time is maximum instead of minimum. Action in physics is stationary, rather than minimum really, so the positive-negative character is not so clear. AAMOF, action across different physical theories typically is a saddle point. In relativity it's a maximum instead of a minimum because of hyperbolic geometry (I think it's all in the hyperbolic geometry of space time). Action must always be stationary, but not necessarily positive definite. And in relativity it's not. It's rather a two-sided debate. Basically @michel123456 vs everyone else. Among the rest, the only debate I see is how to find the argument that clinches the case and doesn't end up in Michel spending another 20 years doubting relativity. You don't strike me as someone who agrees too quickly on anything. Whenever you agree, I brace myself.

As usual, Ed Witten drew far-reaching conclusions, but missed the chicken completely.

I nod in awe, because that's awesome.

I've just found this and then noticed @CPG had already linked to it. No wonder. Very interesting. +1 https://www.brainfacts.org/ Main sections: Thinking, Sensing and Behaving Diseases & Disorders Brain Anatomy and Function Neuroscience in Society In the Lab ------------------- It also features a 3D brain to play with: https://www.brainfacts.org/3d-brain#intro=true

It's rather that localised sources (matter) give rise to spread around gravitational fields (the little g's, the acceleration 3-fields, althought they're not invariant or covariant objects). Because they spread, they change from place to place. As Markus says, the misunderstanding is common. I also have made the same mistake. Even after one learns it, sometimes one forgets. ----------------------------- Ignorable ramblings: Something very peculiar happens with GR. In most other field theories, you have sources; and field divergences are identified with sources by means of field equations, so that the fields kind of "pour out" from the source. Schematically: divergence(field) = (C)x(source) C=coupling In GR, both gravitational field and sources are divergence-less. And one is identified with the other. I've no idea of what the Einstein tensor represents from a purely geometrical POV. The particular combination of second derivatives of the metric that the Einstein tensor represents is built in such a way that it does not "pour out" from anywhere. Neither does energy-momentum. GR is a completely different scheme of things: field = (C)x(source) and divergence(field) = 0 divergence(source) = 0 Where the field is G, the Einstein tensor (not the little g's), this very peculiar combination that does not represent all the degrees of freedom coded in the curvature, but only certain sums of it.

The point is subtle. The equivalence principle tells you that locally, gravity is indistinguishable from acceleration. But gravity (curvature) goes the next step. Curvature gives you a criterion to judge whether your "field" comes from real presence of energy-momentum (its source, what generates it) or is just an effect of your coordinate system (equivalent to "state of motion", but not just that, but also scale factors, ie., prescriptions for measuring lengths and times, etc.). In your uniformly accelerated room no tidal forces would appear, because there is no curvature. Picture, if you will, a "naively curved" surface, like a cylinder. A cylinder looks curved to you only because you're looking at it from an embedding 3-dimensional space. But the cylinder is really flat, so geodesics (whether null or not) would be comparable to straight lines that only the 3-d observer would see as curves. In reality, inner observers would never see any trajectories separate. Nor would the observers inside the accelerated room appreciate any separation between photon trajectories. There is Doppler effect, yes, but that's not curvature. Curvature (deviation of geodesics) is equivalent to tidal forces, not just accelerations.

Just re-phrasing Markus: Any acceleration field you can remove globally by changing the coordinate system does not betray curvature. Acceleration fields can be compensated locally, but curvature persists. Y-a-t'il de la curvature? Cherchez la T mu nu! Except for point-like sources, which are just a fantasy.

I've just had a déjà vu!

Everett: Which chicken and which road are you talking about, guys? Brilliant!

Sounds like you just had an epiphany about science but at the same time are trying to find your intellectual way through it and are experiencing a bit of an indigestion. Start with big but simple numbers. E.g., how many molecules are in 4 grams of hydrogen?: Chemistry tells us it's close to 10²⁴. That means 10⁶ times 10⁶ times 10⁶ times 10⁶. That is 1 million million million million little clusters of matter bouncing around. Physics tells us there are fields interweaving these granules of matter. So nothing is simple there, really. Now consider: How many neurons are in my brain?: about 10¹¹. That means one hundred thousand million little fat/protein packed bodies (your neurons) firing in changing patterns and interacting with their neighbours. Polarity of your neurons gives you the basic (0,1) alphabet that control systems require. How many atoms arranged in sequential patterns inside each and every neuron? Depends. Some neurons are short, others are close to 1 meter. But you can assume the average number of atoms in each neuron to be somewhere around 10²³ again. But those 10²³ in every 10¹¹ are now arranged in patterns. Like tiny machines that have been built for doing specific things, instead of the chaos of gas molecules bouncing over and over. How amazingly complex can the behaviour of 10²³ times 10¹¹ ordered-in-patterns little things be? That number is 10³⁴, which means ten thousand million million million million million little things playing a role in the machine. I wouldn't say that's you, but that what makes you. Science is not easy, because it requires your imagination to stretch, to go places it's never been before in your world of going up or down the stairs or throwing a ball, or frying an egg. Edit: x-posted with bufofrog

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?