joigus

An unpublished article by Erwin Schrödinger has been discovered, containing some surprises about the great Austrian physicist's thoughts regarding the interpretation of quantum mechanics. I will look at it more closely, but if anybody can take a look, please post have any comments you might have. Nowadays, the only viable way out for those who defend the possibility of hidden variables seems to be superdeterminism (not only were the measurement results determined since the beginning of time, but also the observables that the experimenters were going to measure—or, put another way, what things are going to be visible and what things are not). An extreme position, but logically consistent. I don't know how Schrödinger's article will read in light of these considerations. ScienceAlertA Lost Schrödinger Manuscript Reveals a Surprising Twist...For more than 80 years, a manuscript penned by one of the founders of quantum physics has been gathering dust in an Austrian library.https://arxiv.org/pdf/2610.20752

Yes, this checks with my link, and could very well be what was going on. The 'rolex' could be symbols of divinity, according to, From, https://www.metmuseum.org/art/collection/search/322486 I'm not surprised that the images seem to be templates to a certain extent, as well as to the fact that they seem to sacrifice realism to symbolism. All these practices were imbued with a practical nature, somewhere between conveying information and art for its own sake. This is just conjecture on my part, of course.

Yes, that might well be the answer. It's very likely a botanical, IMO. Either a cone from a coniferous tree or a male date palm. Here are demonstrably realistic AI-generated depictions of 1) A cedar's cone, 2) A Middle-Eastern pine cone, and 3) the spathe of a male date palm: 1) 2) 3)

This looks Assyrian to me... Assyrian is Mesopotamian, so @TheVat was right, I think. I'm just trying to zero in closer if possible. And it seems the apkallu (old sages from the past) was the right interpretation too. The 'purse' is actually a bucket, and the pine-cone thing is of unclear nature: https://www.metmuseum.org/art/collection/search/322486 Cedars from Lebanon play a prominent role in Mesopotamian culture since time immemorial, so... Maybe the grenade-looking thing is a cedar's pine cone? I don't know.

You can express velocity in terms of average potential energy or in terms of the period of a cyclic motion. There's no 'ontology' to any of those. Newton did a similar trick to show planetary motions require an inverse-square force law from Kepler's laws. There's also a trick involving average potential energy and average kinetic energy by using the virial theorem. There are many, many such tricks. Newton himself implied that he couldn't care less about the underlying 'ontology' (hypotheses non fingo = "I frame no hypotheses"). It's just algebraic manipulations. You're making it very hard for me to believe you understand elementary physics. Ha, ha, ha!

Computer science people would probably consider a differential equation solved if existence and uniqueness is satisfied, as they can always solve it by feeding it to the software. There's always the question of when experts consider a problem to be of sufficient entity. Yes, sorry. You did.

Not every algebraic manipulation deserves an brand-new ontological coinage. @exchemist is a pretty good early-warning system for this kind of thing. He's clued us all in a while ago.

It's essentially the modulus of velocity. I'm a stickler for precise language, sometimes to unreasonable lengths. Because kinetic energy depends on (modulus of velocity)², I figured that was the proper term relevant there. I imagine v² having an enormous value would have presumably many physically relevant consequences (dissipation, temperature, and what not) that could make the standard NS mathematical model really not that terribly important in terms of the physics. I'm not anywhere close to being an expert on all this though.

Oh, I wasn't complaining. It's an excellent opportunity for me to remind myself of that beautiful part of the theory. Thank you.

Agreed. Although there isn't such a thing as a general solution. In the mathematical theory of ODEs, eg, not even linear equations have known solutions for any inhomogeneous term (analogous to applied external force). They can be systematically found for a catalogue of simple known functions. Let alone non-linear systems of eqs. with arbitrary applied force. I've spent years wondering myself 'why is this problem so crucial?'

Oh man, oh man. When you said Heine-Borel and "finite coverings" it brought up the flavour of things I've studied so long ago. It's good motivation to review this stuff, so thank you for that. You're right. I'm not saying it's not fun. The philosophy of it I find much, much less fun.

If space and time are not continuous, Zeno's paradox cannot even be set up, as it wouldn't make any sense to subdivide space and time intervals in thinner and thinner slices. There goes your paradox --or Zeno's, to be more precise. On the other hand, if they are continuous, Zeno's paradox is trivially solved by adding up a convergent numerical series, as @studiot pointed out. So... Do we really need to keep overthinking this?

Ontology of time? You're gonna have a problem defending that with more than one scientifically-well-trained customer here. The posing of the problem itself rests entirely on the assumption that time and space are infinitely-divisible continua. Otherwise, there is no paradox. That's, I think, very much what @MigL is trying to tell you.

I'm not asking for that. But don't forget the Navier-Stokes equations are diff. eqs. for a velocity field. And the conundrum was "are there singular solutions?" Meaning: "do they blow up in finite time?" So how could the velocity components becoming infinite have any fundamental significance? I say this knowing full well that some people around here, good people, do not like the word "fundamental". I'm glad we're back. No kidding, there are theoretical frameworks for highly relativistic fluids in astrophysics. When the model doesn't work anymore, one is forced to rethink the model. It's a completely different outlook to that of mathematicians. For them the model is the thing.

I quite agree with what you said here. There's also the matter of whether the external force can be seen as realistic at all for the case giving rise to singularities (something I have not considered in any detail). Furthermore, as it is an equation for a velocity field and we know celerities greater than the speed of light are forbidden, Navier-Stokes cannot be a fundamental equation of physics the way other microscopic equations are suspected to be. I think it's more mathematicians, or mathematical physicists, that consider the NS problem a holy grail of science.