joigus

No mercy, please! +1

Far fewer. I hate to make grammatical mistakes!

Good tip.+1. Is this homework, @Prasant36? Edit: You also need Abelian character for showing closure

OK. Give me the dynamics of the Solar System with only integrals of motion derived from continuous symmetries. You can't. And the reason is that the system is not integrable (the number of integrals of motion is insufficient, far less than the number of degrees of freedom.) This is how: You wrote down Einstein's equations in the vacuum from the Einstein-Hilbert action. I just assumed you were talking about GR. Were you not? I know (and I've told you so) that there are problems that you can solve with an energy-like integral of motion. Example: Using the Schwarzschild solution to derive the anomalous motion of Mercury. But this is not generally valid. If you think it is, give me the integral of the energy for the FRWL metric. You can't. And the reason is that the metric does not have time-translation symmetry. Need I say more? Something tells me I do.

Yeah, I don't know what you did with the quoting function there, @ruibin.niu. Be careful. I think there are some merits to your gedanken, but you got the analysis wrong. Careful application of SR formulas (Einstein's velocity transformation law) gives you that, \[\theta_{i}<\theta_{r}\] While you're assuming that Snell's law, \[\theta_{i}=\theta_{r}\] is correct. It is not for moving mirrors. You can find the derivation in Landau-Lifshitz; Classical Field Theory, Vol. II. You have a larger reflection angle than incident angle, which accounts for the relative direction of light rays in the \[v_{\parallel}\] for both observers to coincide and the whole picture to be consistent.

If you're not a supporter of GR, don't ever use a GPS navigating system; because GPS-monitoring satellites routinely use GR in order to find your location. And they seem to do a good job of it. You see, "supporting" a theory (your words) is not like supporting a football team. You need to go back to page one on the book of science and start all over again. There's something very basic you haven't understood. https://www.physicscentral.com/explore/writers/will.cfm#:~:text=GPS accounts for relativity by,functions within about 2 minutes.

Pre-Clovis artifacts have been popping up for quite a while. Very interesting topic. +1 There's even a hypothesis whose main proponent is Dennis Stanford, from Smithsonian, that puts forward the idea that some Solutreans populated parts of the Americas following the track of seals across the North Atlantic. The last thing I've read is that DNA analysis has shown that no relevant traces of proto-European DNA have been found in native Americans of non-mixed descent. But there's more information on the Wikipedia article.

Oh, you're sooo right. +1. I will rephrase the flaw in the OP's argument: Snell's law, as is, does not hold for moving mirrors. https://physics.stackexchange.com/questions/405904/deriving-the-law-of-reflection-for-a-moving-mirror-in-relativity

Very good point. +1 While it is true that you've show an intuition of something unexpected, we know how all kinds of very similar naive intuitions fail one by one when you apply the formalism. Can you provide equations, showing the velocities and the angles in both inertial frames, or are you expecting everybody else to believe it only based on intuition? Do you want somebody else to do the analysis for you? IOW: Why should anyone bother with this?

You make some very good points here. +1. You also introduce an element which must have slipped my mind, which is the one of usefulness. This element of usefulness actually had more to do with the original meaning of my question. The ethical question, important though it is, was not what I had in mind. That doesn't mean I don't welcome any other aspects that other members may have in mind. I do. Also, I'm not saying that the ethical question is out of reach for rational thinking, which I think it is. Concepts such as common sense, equanimity and the like are quite useful (again) to get to working standards for ethics. Golden rule is the best example. I agree that potential for harm should not be the criterion upon which we base what we ought to know and what we oughtn't.

And a take-home lesson about diet. Maybe bad science is science unchecked by philosophical concerns?

The technique that Markus describes is actually something I've seen done in theories of gravity when people try to discuss emergent time. But I think you're right that the sequencing aspect is lost or not entirely obvious. That's why I suggested the introduction of a proper length parameter as the most likely candidate to where, mathematically, time comes from. Suppose you have a physical system with variables (x1,x2,...,xN). If you had N-1 implicit equations or "constraints": f1(x1,...xN)=0 f2(x1,...xN)=0 ... fN-1(x1,...,xN)=0 This would amount to having a common history for all the x's. The complete deterministic solution to a particular system's evolution deployed before your eyes. Giving values to all of them except one allows you to infer the value of the remaining one. Although that value may not be unique. For example. At a certain point in your life you asked your sweetheart to marry you. That's x7=1. But there are two values for the answer that she gave you: x8=1 and x8=0. That's because at some point she said "no", you asked again a week later, and she said "yes". Assigning values to the rest of the variables of the universe, you can get "back" to the event you want to picture. This gives you a bird's eye view of the history. If you have a metric for the x's, you can do something quite impressive in principle if your metric is positive definite and based on a quadratic form. You build the infinitesimal interval along your implicit curve: ds2=gijdxidxj and define your sequencing (primitive time) as either, dt=+sqr(gijdxidxj) or dt=-sqr(gijdxidxj) I know @Markus Hanke has some exceptions/criticism for this procedure. But I think it's a mathematical language that very much fits what we know about the mathematics of the world, has many of the essential features of time in it, and leads to a quite clear-cut setting (if not solution) of the problem: Why is it that we only see the world evolve in one of the two orientations that the metric allows you to pick? The mathematics seem to confirm that: You chose one or the other, but once you're fixed on one, no valid re-parametrization can give you the other. I have an intuition that this may have to do with the Michel/Studiot argument about the cup of tea. But I must go over their arguments again, I must say. Edit: x-posted with Eise Edit 2: The metric should be defined on the f's, not the x's. So it'd be, ds2=gijdfidfj

Trying to use reason to understand the internal arguments of religion is as hopeless as trying to thread a needle through a loop.

Good point. +1 Why did god do it? Many scientists in the past, feeling very uncomfortable about making statements that denied god, chose to phrase the question as, Why did god choose to make the world like this? One answer for every question "God did it" is clearly not good enough.

Believe me, I share much of what you say here. And you've explained it very eloquently. +1. I'm struggling with many of these issues right now. It doesn't help that the subject is vast, also. I have this intuitive feeling that the situation will be enormously clarified once we understand better the role that the scalar field is playing in the whole business. Right now, the scalar field is not fundamentally understood in QFT. It's used as a device to parametrize certain constraints. The scalar field comes up in just about any model-building way that people have invented to implement known facts that we don't quite understand.

Energy is not a primitive concept. You can actually re-formulate classical mechanics pretty much without it with the Jacobi variational principle. Take a look at Barbour-Bertotti mechanics, e.g., who re-discovered the Jacobi action principle. The action would be, \[S_{BB}=\int dt\sqrt{T}\sqrt{-V}\] The theory would be diffeomorphism invariant with one constraint equivalent to E=0. You can solve classical mechanics one energy at a time. But energy as we know it looses its "primitive" meaning. No version of mechanics, GR or other dynamical theory of physics is built from the concept of energy. As always happens with physics, the more general your framework is, the more abstract the primitive quantities become. The primitive entity is the Lagrangian, but the meaning is much much less clear. Oh, and in GR energy is not conserved in general. Some metrics have a time-like Killing vector and then you can derive a particular "version" of energy. Energy in GR is not a very useful in general, very fundamental concept. I could say more, but this is starting to be a pain in the neck.

Do you want to re-activate the thread? Are you still having problems with the concept of enthalpy? The question is the same.

All of them, AAMOF: \[f\left(\alpha\right)=\tan\alpha\] \[\alpha=\frac{\pi}{2}\left(2k+1\right),\:k=0,\pm1,\pm2,\cdots\]

Complicated women are the best.

Thank you. Some gibberish you invented must be zero. Only non-trivial stuff comes from a book. No more questions, your honour.

It is simply wrong statement. Do you disagree with derivation of action variation in my article? If the derivation of action variation is correct, it means I derived equations of GR too. You do. And I quote: Then you narrow it down to a simpler form. And then you pull the rabbit out of the hat about here: And what is [5, p. 355]? Nothing other than: You're copy-pasting, as I said, from excellent physics books. How could I disagree with Landau and Lifshitz, Field Theory, Vol. II? What I'm saying is that none of this appears to follow from your ideas. Not as far as I can see. Here's a try to guess at what you've done: 1) Define an arbitrary map (not even well defined mathematically) from t, x, y, z and claim that you've shown space and time as "emergent" from your singular variables. 2) Copy and paste standard equations from physics books. 3) Puff it all up with lots of words. Throw in "conscience" and "observer" and "hypersurface". Big words. Only thing I can say is I'm sorry I can see right through it. We must be connected through a hypersurface. Exactly. Not invertible at infinitely many points. What's that multi-branching? Conscious projections? Observers?

Sorry, you do introduce it later. But I don't see how this emerges from any new assumptions of your own. 𝑣=𝑣𝑡tg(𝛼)To find the components 𝑣⃗, one can divide the rotation into relative to the axes rotations: 𝑣𝑥=𝑣𝑡tg(𝛼𝑥) 𝑣𝑦=𝑣𝑡tg(𝛼𝑦) 𝑣𝑧=𝑣𝑡tg(𝛼𝑧)

Your time and space have infinitely many singularities. And there's no inverse mapping from the alphas. It doesn't look like your v's map to the world we know and love. And no offence, but the rest of it looks like you're just copy-pasting common physics and puffing it up with lots of words, TBH. Example: Because there are hypersurfaces, there must be curvature, and thereby, there must be a geodesic equation. So you write down the geodesic equation. Nice. Why? What particles are moving along them? Where are these particles? You also copy-paste the Lagrangian of GR as if it were derived from your idea. It's not. You've just attached it to your idea. You also talk about conscience giving rise to the world. Whose conscience? Mine? Donald Trump's? How many are there? How do they give rise to the world? You also talk about energy long before you talk about Lagrangian formalism or anything that logically amounts to it. And energy is a consequence of it. Energy is not a primitive concept. I have also serious doubts that you can construct pseudo-vectors like angular momentum, helicity, etc. Need I say more? Maybe I do.

When it's being a particle, it's not being a wave; when it's being a wave, it's not being a particle. It's like a writer who plays golf. When she's playing golf, she's not writing; when she's writing, she's not playing golf. Unlike businessmen, who can play golf and do business at the same time. Edit: If you're puzzled by QM, you're in very good company. +1

You keep using that word, "theory".