joigus

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".

True. There's also the problem of T(r), because that's not a constant with r. I suggest to let @Martoonsky speak.

Sorry, we almost x-posted. You didn't see my edit. The only thing that makes sense to me for the red line is the g(r) field strength. Edit: The only thing that doesn't check with me is the sign. It should be negative (inward pointing).

\[V_{\textrm{int}}\left(r\right)=G\frac{M_{\oplus}}{2R_{\oplus}}\left[\left(\frac{r}{R_{\oplus}}\right)^{2}-3\right]\] \[V_{\textrm{ext}}\left(r\right)=-G\frac{M_{\oplus}}{r}\] Edit: It's the line going down with distance linearly. Edit 2: Sorry, that's g. The line going down linearly with distance is the gradient, that is, g.

Red is V; blue is rho times g. g is zero at the centre.

Nah, that's LSZ: https://en.wikipedia.org/wiki/LSZ_reduction_formula That comes later. It's Wick's theorem I was talking about. Thank you, @Markus Hanke. +1

I agree. "Out of equilibrium" I didn't mean as a serious objection. It was meant for completeness.

I see no way in which this could be wrong! +1 Edit: Sorry; I can only see one: The system is not in equilibrium.

Mmmm. Suggestion: Let it grow a little bit more and take another picture.

Thanks. And you're dead right. +1. I stepped back on this particular topic because Swansont and you were more focused and had this more under control and I wasn't helping. I was "waxing theoretical". I think that's the idea.

It definitely looks like some kind of marasmius. Only Marasmius oreades is edible, and fleshier, of those I know. Most of them generally look very much like the one you got there. A good representative is Marasmius capillaris: https://www.google.com/search?tbm=isch&sxsrf=ALeKk03N8VOMmcPUcPsa5XQgDzLvbwg5Ag%3A1595675562082&source=hp&biw=1280&bih=856&ei=qhMcX_7LAsW6aZH9qNAL&q=marasmius+capillaris&oq=marasmius+capillaris&gs_lcp=CgNpbWcQAzICCAA6BAgjECc6BQgAELEDOgQIABAeOgYIABAIEB5QmAFYvSpgkyxoAXAAeAGAAbMCiAH_EpIBCDE0LjQuMi4xmAEAoAEBqgELZ3dzLXdpei1pbWc&sclient=img&ved=0ahUKEwj-yLXYoujqAhVFXRoKHZE-CroQ4dUDCAY&uact=5 Most of them also grow on dead leaves. I'd forgotten most of what I used to know about fungi. I had to look it up and bring back memories. Thank you for bringing this up. +1

Apparently you see some need for calming down. I'm personally at my calmest. It would be nice if you quoted me with some actual content.

Yes! It's only that there were several lemmas. Wick's theorem was the re-ordering trick; and then you sandwiched the operators with the vacuum and got the ready-to-use result, which maybe had another name, an acronym like FDW or something... But Wick is one of the central names in the bunch of results. I'll go back to your other arguments later. You make very good points. We have similar line of thinking about one particular central question (space-time as shaped by conscience rather than fundamental). But you see an obstacle that I don't, so I'm interested. If you see an obstacle (or maybe a leap of faith or gap) it's definitely worth considering. Another post led me into thinking about the nature of space itself, so there's food for thought there too. I posted a comment that was very naive. I had to correct myself. Measuring space is not as straightforward as I thought when I applied SR's definition based on light rays going back and forth. What about very distant objects? You must appeal to indirect methods to guess the age of stars. So, nothing simple or straightforward about that from a practical POV... Anyway. Later.

Very similar arguments (the fact that you can add an arbitrary 4-momentum to a physical 4-momentum without changing its on-shell character) appears in theorems in QFT like, Soft boson theorems (soft pion theorems first historical argument) Ward-Takahashi identities Definition of Feynman's propagator: integral extended to all momenta, including off-shell: https://en.wikipedia.org/wiki/Propagator#Scalar_propagator Take a look at this scalar propagator. It's an integral to the whole momentum space. Edit: More info for you, @studiot. Off-shell amplitudes in the propagator have to do with internal legs in Feynman diagrams. The amplitude for a particle to be created at one point and annihilated at another. The soft-boson idea is to do with low-energy (virtual) bosons that escape to infinity (external legs in Feynman diagrams). Another bundle of key words for it is "infrared divergences". When you calculate the cross section in, e.g., QED, even after you renormalise charge, mass, etc., it still has infinities due to arbitrarily low-energy ("soft") photons going off in all directions. You must do a cut off to remove those photons you will never detect on account of your detectors having an effective energy threshold (they can't detect arbitrarily "soft" photons escaping to infinity).

Wrong method?