joigus

Try with different definitions of existence and see if you can make some progress in your understanding. Maybe everything is fleeting, under the proper time perspective. You didn't mention what your definition is, BTW.

You're probably right. We got lost in geometry. I suspect there's something about time that's not entirely geometric. To me, it has the unmistakable flavour of abstract algebra. Suggestions from QFT are clear. Deeply involved in microcausality, operator-ordering questions, and the CPT theorem.

I don't know either.

Why not? Minkowski is R4 with signature (-+++), while R4 with signature (++++) is 4-dimensional Euclidean space. S1xR3 with signature (-+++) would be a Minkowskian cilinder, while with signature (++++) would be Euclidean. Metric signature and topology are quite independent.

What about a 4=1+3 cilinder? A cilinder is flat, it's S1xR3, but it's not R4.

Do you mean provide another example of tautology, which we would only escape by proposing further relations in the initial tautology? My example was classical mechanics, which would lead us too far from OP's goal at almost any amount of detail. But I think it's plausible that, if we were to make any progress in the problem of time, new concepts would have to appear, being circular in their initial formulation not constituting a difficulty impossible to overcome. If I were to try, I would take inspiration from similarly groundbreaking advances. In the case of Newton, F=ma seems to be both a definition of both mass and force, which at first sight doesn't look as much of a step towards progress, does it?... Until you formulate a law of force F(x,v), the concept of inertial frame as somewhere far removed from sources of interaction where systems satisfy the 1st law, etc. The problem with time is it's so difficult to conceive of intuitions that would lead the way as, in the case of Newton, isolated systems, force, and mass.

IMO, we shouldn't be too afraid of tautologies, as long as we have an external hypothesis to get us out of it. In fact, if we're ever gonna find a way to understand time, I think it's very likely that we have to do it by formulating some kind of tautology, and then ponder what the external assumption must be if we're to make it into a predicting machine. An outstanding example is Newtonian mechanics. The bare formulation is as tautological as can be. What is force? Mass times acceleration. But hang on. What is mass? Oh, that's easy: It's the ratio between force and acceleration in any direction. We wouldn't get anywhere from just that. But there's a hidden assumption: Whatever we want mass to be, it must be the same in every direction. And then there's the amazingly consequencial assumption that, under different simple circumstances, force depends on position in some particularly simple way. Then we're in business, because we can predict. Something that, with the sheer tautology, was impossible.

It is a scalar field that's needed in inflationary models of cosmology to provide a mechanism for the vacuum to go through different phases of expansion. A scalar field is a field represented by a number at every point of space and every instant of time, so that it doesn't change at all under rotations. In a way, it's very much like the Higgs field. It affords you to "imprint" needed properties on the other fields and space-time itself to account for observed properties that don't quite fit the model without it. It's considered by some to be somewhat ad hoc --convenient, but not very well understood or logically compelling.

Exactly. It's always a why from a how, or a how from a further how. And an initial how --what to assume-- is always susceptible of a further why. That's why there's always a how in the last analysis. How about that?

Interesting...

Yes, I don't know what all of this has to do with interpretations of QM, but composition of collinear boosts is not linear in velocities, although it is in rapidities[?*] (which are essentially hyperbolic-angle arguments.) That's probably what @Markus Hanke meant. The part where I get lost, as I say, is what any of this has to do with QM and its interpretations. I do not wish to keep talking about this, as it has no bearing on the particular aspects I'm more interested in, but suffice it to say that linear or non-linear depends on the arguments on which the object is considered to be acting. Eg, and totally analogous to collinear boosts, rotations about the same axis are linear in the angle, but not in the trig functions the rotation depends on. * Is that the word?

Thank you, Markus. +1. As usual, you helped to take the discussion back on its track. And that's right. They are linear. Thank you for your attentive reading. +1 I must confess I must go back to @Genady and @Lorentz Jr's parallel discussion and understand the point. The argument has spilt over into different aspects of physics, and it's hard to keep up.

@Lorentz Jr, you'd be well advised to refrain from your usual hissy fits, stop using neg-reps as some kind of covering fire for your arguments, and stick to the topic. If I didn't understand your point, say it nicely and we can all get back to business. I can assure you I, and many others, think you make a valuable contribution to the forums. Lorentz transformations don't act on the v's, they're parametrised by them. That's whay I got confused. I'm sorry for having ruffled your feathers. Jeez! I've just reverted my red point.

Why do you act so childishly? Saying they are non-linear is not the standard way of referring to them, and certainly not the appropriate way. It's at best confusing. If you wish to say they are non-linear in velocities, you should specify that. That's not the way we refer to them, among other things because once you are in the domain of SR, 3-velocity is not a vector quantity on which to define linear / non-linear transformations. It's just a set of 3 parameters.

They are linear.

Absolutely no rush. This thing about topological Lagrangians giving rise to systems (quantum or not) entailing some kind of rigidity has kept me wondering for years. For trajectories of point particles, it's clear that you get the system frozen to a point. But for field theories it's not so clear. If you allow for non-commutativity (quantum) the question is even more involved. To me, it both is interesting and makes sense. But for some reason people who study topological field theories haven't put it on the front burner, for years and years. You only see it mentioned as some kind of quirk. Yeah, OK. I must confess I have to think about this harder, and read more stuff with as much attention as possible. Some of these conditions coming from constraints do look a lot like continuity equations. It's peculiar to me that conditions like the Lorentz gauge-fixing condition are formally identical to local conservation laws for a Noether charge, although they're just constraints. And in the case of gauge fixing, they seem quite arbitrary. In the case of these topological theories, they seem to appear more "naturally." At least the way I saw Lee Smolin handle them in those lectures. That's all I can say for now in the way of a reflection. It's just peculiar to me.

Yes, I think we are, to the extent that I can follow all the arguments. It's a recurring theme in Nature, I think. Simple principles, very complicated consequences.

You may be interested to know that Lee Smolin changed his mind about this question relatively recently. If you do a search of "time as fundamental" you're likely to find as many entries as for "time as emergent," which goes to prove that the question is far from settled. If you propose time as fundamental, your first order of business should be answering why it is that it appears to be a dimension, and has infinitely many versions corresponding to infinitely many observers. I'm not sure that Smolin and collaborators have got around to this question as yet. It would be nice to know if they have. I don't.

I do not expect it to be different.

That's what I like to dream. But one look at the standard model is enough to realise that the dream seems to vanish in one fell swoop. It's like the basic idea is extremely simple, but Nature uses it to make crossroads and turnarounds in any possible way: Arbitrary mixings, symmetry "offsets," apparently idle copies of the same thing with arbitrary displacements. It's as if a master engineer had made a thing of beauty, and a naughty kid had been playing with it. I agree, but I would like to add a note of optimism to it. Gravitational waves are something no ordinary primate would have dreamt of "seeing." We have this capacity to build an extraordinary prosthetics to extend the reach of our senses by cleverly arranging pieces of material.

Something we should never overlook as a possibility. We might have blind spots that are impossible to overcome. Why should the rules of the universe be written in a language that primates can understand?

To me it's not. I also think for @TheVat it isn't either --from a previous post. But QM goes further than probability. It speaks of amplitudes, which seem to be on a sub-level with respect to probabilities. What is this sub-level about? Why do we need a choice of global and local phase, but the gauge principle makes it completely irrelevant? Those are questions that keep me awake. I'm wary of interpretations that summon the brain into the big picture. I don't think it's a matter of brains. I also abhor of interpretations based on gravity, but I find a bit more difficult to explain why. I think it's more a question of classical mechanics appearing as a fully-fledged assymptotic approximation from within quantum mechanics, rather than by analogy or correspondence, plus a series of artificial assumptions.

This seems to suggest that the very process of observation involves some kind of "translation"... But the original "language" is not available to us. Pardon my quotation marks.

Razor-sharp.

How do you know?