joigus

The vocal cords are vibrating when you pronounce "rather" while they're not when you pronounce "with" resulting in two very different sounds. Try it, and you'll see. So, in answer to your question: Since the moment you pronounce them. Exactly as in "them" and "bath" (different). I don't care what funny words any linguist uses to describe them. I've done an experiment, and in my book that is sacred.

You could in principle make mass from non-mass. Charge doesn't work that way. For the reasons Swansont is telling you about. You need a divergence. IOW, source field lines to source out of a point. Also, models based on ribbons with kinks and antikinks, and breathers, and many other topological properties have been done to death. I don't see why it's deterministic (Planck's constant is zero?) Probabilities are kicked out of the picture? I don't see how Lorentz's dilation equation could be made more precise either. More precise in what parameter? What does it mean to do an autopsy on an elementary particle? I cannot make sense of anything you say.

Normalisation should come first. What is so suspicious about the motivation that you need an "actual motivation"? Isn't the fact that physical parameters should be expected to depend on the length/energy scale at which you observe them enough motivation?

No. It's based on amplitudes. Probability comes from amplitudes. Amplitudes cannot be explained in terms of probabilities.

I hope you also notice that English doesn't identify a particular sequence of letters with a sound. Eg, (my emphasis) the "th" sound in "rather" is very different from "th" sound in "with."

Sorry, because I was guilty of it. https://en.wikipedia.org/wiki/Scale_invariance https://en.wikipedia.org/wiki/Universality_(dynamical_systems) Universality is frequently mentioned in association to scale invariance, not because it always happens, but because it seems to always happen in connection to critical phenomena.

It rings a bell, yes: https://www.scienceforums.net/search/?q=Alcubierre&quick=1&type=forums_topic&nodes=29 Neither am I. Perhaps translation invariance @grayson? Agreed.

It's a mathematical pattern rather than a process. I'm sure something like that is the reason behind @exchemist's excellent question. Take. eg, principles of extremal time, action, length, etc. They appear everywhere in physics. It's more about a recurring mathematical theme than actually a particular process.

Keywords to look up: Scale invariance and critical phenomena Universality https://en.wikipedia.org/wiki/Scale_invariance It seems to be the case that when changes in structure formation are about to happen, a transitory stage characterised by scale invariance happens. An example is a gas about to make the transition to a liquid. But, as noted, you could have some cases of self-similarity (synonym of scale invariance) when or where no phase transition is involved. Examples: biological tissue patterns, the shape of the coastline, etc. Another kind of self-similarity seems to be in evolution itself, but not like a spatial pattern. Rather, as a pattern of embedded behaviour: A thing trying to pass on as good as possible a copy of its identity, with little things inside trying to pass on as good as possible copies of their identity,... up to a final level (chuncks of nucleic acid) of little things trying to pass on as good as possible a partial copy of their identity. And so on, which seem to be relevant words here.

You are probably correct. Amen. (Sorry for using Hebrew.) And +1 to both.

Being a little fast and loose with your logic allows you to detect people who aren't. Welcome to the forums, if I didn't say it before.

This sound more like the dynamical law is invariant under time inversions, which is quite different from saying that the direction of time doesn't apply. Not even that is true, since electroweak interactions violate CP (charge conjugation + parity conjugation). Parity conjugation being the corresponding generalisation to quantum mechanics of mirror reflection. As we have very good reason to believe the world is CPT-invariant (the combination of the 3 relevant inversions in QFT), it follows that T must be violated. As Genady said, Physicists sometimes like to play with metaphors, and conceptual hell breaks loose. When the metaphor constitutes the argument, you can rest assured the argument cannot be trusted.

Can you provide a quote?

In 4D, if special relativity is correct, yes. What @Schindelbeck is talking about though is a bit different. Every particle would be moving in 5D and --for photons in particular-- only the 4D projections of their 5D trajectories would appear to go at speed c. That, of course, if I understood correctly and pending me getting back to it and seeing if I can make sense of any of it any further, which is by no means a certainty.

Thank you. Yes, that's right. I was trying to recall ways in which the different pieces of the Einstein tensor might have some kind of meaning easy to visualise.

The Ricci scalar is also of special interest because its integral to the whole manifold gives you the genus of your manifold (number of holes). So yes, physical information is coded in it. What not so clear to me is how to visualise the tensor itself. For some reason, people keep talking about "seeing" tensors.

You mean a scalar multiple of it? "Essentially". I forgot to say "essentially". It's essentially the only tensor... You can introduce a scalar that can be gauged away in virtually every theory we have. So...

It is the only rank-2 tensor that has identically zero covariant derivative. Einstein wanted something as analogous as is possible to get to Maxwell's equations. I know of piecewise ways to understand its different pieces, but not the thing itself. IOW, if you had a conversation with a pure differential-geometry person and you asked them: "What is this G = Ricci-(1/2)R(metric) tensor to you?" They would probably go, "well, it's the way to obtain a 2-rank tensor from the Riemann tensor that is covariantly constant, if you want to, for some reason." You, "But does it codify anything about the manifold, holes, winding numbers, other topological features? Can I see it coming from something more basic" They, "Well, the R that you mention codifies the genus (number of holes), but not the G. Not that I know of, why you ask?" You, "You don't happen to know of any way to quantise it, do you?" Them, "Our time is up."

Absolutely. Both, of course, are mathematical limits. They indicate, AFAIK, that the interpretation cannot be brought to those limits experimentally and something has to give. Exactly as @MigL says. That's my understanding, anyway.

It can't happen. If a particle is at rest for just the shortest of times, the uncertainty in position becomes zero for just that time, so the uncertainty in momentum goes to infinity in every direction, and the particle immediately flies away. This is kind of a "pictorial" way of talking, of course. One must do the regular Hilbert-space operator procedure. Particles "at rest" like, eg, in an ion trap, are not really at rest. They're twirling around in some kind of stationary-state confined micro-dance.

Of course they are. Sorry, my mind is somewhere else lately. I'll be back soon.

One question then. If all of this is consistent with a more-or-less established field of research in 5D-GR, why not send your work to a peer-reviewed publication so you could get a more specific criticism to your ideas? Maybe by some experts in the field? Ok, so everything are photons in 5D. Only some of them look like photons in 4D, while others look like massive particles due to certain constraints in the loopy dimension? What is an EFE?

Depends very much on the potential energy. Free Schrödinger equation: plane waves, (harmonic)x(plane waves), etc. Schrödinger equation in potential wells, barriers etc: Plane waves with discrete harmonics, reflected and transmitted waves, etc. Schrödinger equation with inverse-square-distance potential: Hydrogen eigenfunctions Schrödinger equation with linear potential: Airy functions Schrödinger equation with harmonic-oscillator potential: Hermite polynomials, etc. So when people talk about "the" Schrödinger equation, they actually mean "the infinitely many" Schrödinger equations associated to infinitely many possible potential energy where the electron can be captured.

Photons have no rest-frame energy because photons have no rest frame.

Before you hit us with those 20+ pages, let's do some preliminary discussion if you will... You seem to posit that the energy of a particle is a static expression (derived from a scalar field) integral of phi(r)xelectrostatic_potential. Are you aware that energies must be frame-dependent and 0-component covariant? Where is the time dependence?