joigus

I've been saying this for several years on these forums (also others like @MigL or @swansont, and probably others still). My words then were "energy is only a useful concept in small patches of ST": For the benefit of OP, here's a nice video by Veritasium explaining it: Long times are also "big patches of space-time", which fits the leading example by Veritasium. Very, very, very misunderstood concept, that of energy. Sigh! Only when the system is Lagrangian and the context is time-independent does something like an energy arise. Otherwise... not.

Agreed. What's the matter? 🤭

Thank you for adding more context. May I ask you what particular problem led you to this integral?

Space pre-exists to what exactly? Matter?

In none of the standard formulations of QM is the uncertainty principle presented as a postulate. It can be proved as a theorem from the relation between observables, states, and probabilities defined in the postulates. It is also confirmed in its statistical sense from experiments. Furthermore, it has explanatory power in that particular sense in a wide range of phenomena, from Josephson junctions to polarisers, etc. It's nothing to do with a winding number, but indeed refers to statistical frequencies. If space-time coordinates are maximally determined, energy-momentum is minimally determined, how could space-time be energy? You seem to be using some kind of LLM or chatbot to generate what feels like a linguistic version of the shell game.

Among other things already pointed out to you, there are robust quantum mechanical reasons why E=ST cannot make sense. Such variables are complementary in quantum mechanics (canonically conjugate). Meaning: when one of them is precisely determined, the other becomes "infinitely fuzzy". Only that consideration should be enough to make you cease and desist on the whole thing. So..., again, no.

You're waxing esoteric now. Honestly, I can't get past your spacetime \( \equiv \) energy mathematical nonsense.

Complex logarithms are marvelous beasts, but they're sharp-toothed. They have something called "branch cuts", which come from "branch points", meaning loci where the function becomes discontinuous in a very non-trivial way, giving rise to so-called Riemann surfaces (the complex plane splitting into infinitely many copies of it, each for one prescription of the polar angle in the argument that the function accepts). Trying to perform a definite integral involving a product of logs with branch points in different places on the complex plane would be hard enough. These integrals normally involve integration paths that need to be extended to closed loops involving infinity in order to be able to use Cauchy's theorem and thus make sense of them just numerically. You need to start with things like \( \int_{-\infty}^{\infty} \) or \( \int_{0}^{\infty} \) and then analitically continue (so-said) the path to go through infinity. I shudder to think what kind of an ill-defined mess trying to propose them as functions (indefinite integrals) would lead us to. For starters, there are the best reasons to expect them to adopt infinitely many functional values. Think about it: Numerical methods are really really advanced today. If you've found a mathematical object that resists analysis by using them, it's probably because of some fundamental theoretical reason. I hope that was helpful. I'm sorry I can't help you with your Fortran.

I apologise for I did misunderstand something you said. Your circular angle is not the standard hyperbolic "angle" of relativity, or any analogue of it for that matter. Rather, it is what to me looks like a circular definition (no pun intended). Thus, you present the kinematic / gravitational-potential quantities as functions of a respective points on respective copies of a \( S^{1} \), otherwise known as circle. You declare, eg, \[ \theta_{1}=\arccos\beta \] and, \[ \theta_{2}=\arcsin\kappa \] And, what are \( \beta \) and \( \kappa \)? Just the inverse functions of those. No mystery there. The \( \kappa \) trigonometric function, BTW, does not apply on the whole of \( S^{1} \), but only on half of it (the part where the sine of \( \theta_2 \) is positive. You do need a metric to talk about angles and distances (or pseudo-distances). If you want to do away with a metric altogether, I agree with @studiot that you should try something like projective geometry or the like. But physics is about metrics, distances and angles. It just is. So you would have to come up with a way to define what you understand by measuring thing, for lack of metrical properties. Saying it sounds hard is an understatement. May I remind you, Einstein didn't base GR on tensor analysis just on a whim, but because of the principle of general covariance, that many people tend to disregard. You cannot dispose of tensors just like that. Equations of physics must be generally covariant for very robust reasons: They must transform in a way that makes all observers agree on what they measure when everything is expressed in terms of invariants, even though the particular numbers they get on their rules and clocks might differ. "Covariance" (and thereby tensors) is nothing but a fancy name for that prescription. We don't tell students they're dealing with tensors in pre-university physics, as well as many other university courses, but unbeknown to them, they're most of the time dealing with order-1 or order-2 Euclidean tensors, Galilean tensors, Minkowski tensors, or (in GR) even higher-order diffeomorphism-covariant tensors. There's kind of an unwritten rule not to tell students of physics that's what they're actually doing most of the time. The quantities you're using, on the other hand, seem to be observer-dependent, which goes against the principle of general covariance. Or it seems to be very hard to reconcile with it. (Please refresh the page for LateX display.)

This is the "describe a simple instance" that I like to use from time to time. You started taking it personal. Here: You implied that all the answers were mere "posturing" (and not "genuine") and so that legitimised your theory. If the bundle of nonsense you are proposing were correct, energies and momenta would be periodic quantities of their arguments (circular topology), instead of being hyperbolically fashioned, so to speak. I'm sorry if I wasn't clear. You still haven't answered this. And there is little doubt in my mind you never will. Unless you correct your blunder at some point.

Well, yes. I copied it and pasted it, but it lacked gravitation. I'm still getting up to speed with most of the arguments here, BTW.

Good. As your work --it seems-- has reached a point of maturity, now it's time you take it to a professional publication and see how it fares. Don't waste another minute with people of our ilk. The Nobel Prize could be just around the corner. BTW, your geometry is still circular, not hyperbolic, as you have not made any precisions concerning the complex plane, which would turn your trigonometric relations into hyperbolic ones, as they should. Good luck!

The author must have taken that from some book on relativistic physics with choice c=1 among preliminary conventions, without realising. That's my guess, anyway. In any case, it's bound to go badly wrong when it assumes circular geometry, while relativistic kinematics is known to comply with hyperbolic geometry rather --as said by yours truly. PS: Sorry, I thought I had answered, but my answer had been cached by my browser all this time without me actually publishing it.

Chrome issue?

Please, stop using technology to dress up your vision. No good new physics can come out of it. "spacetime = energy" makes as much sense as "I am my bank account". And I also suggest to stop being so substantival. During the first stages of an idea it's far more useful to be "adjectival". Foundational principles are not derived for obvious reasons: They would be neither foundational nor principles, would they? Unless you want to build a logical loop. Then it doesn't matter where you start. You're also conflating the compact topology of a circle (trigonometric functions, angles) with the well-known non-compact hyperbolic topology of relativity of motion (hyperbolic functions, rapidities). Again a terrible start.

Infographics doesn't really help this kind of thing. Einstein's field equations do not say "spacetime = energy". "Spacetime = energy" is a meaningless statement. AAMOF, energy is not conserved in GR. Energy is only a useful concept in small patches of ST.

I've got humble powers of observation based on network commands. Now everyone's personal Nostradamus seems to be ChatGPT. :)

This is not actually a request of mine, but one of the rules of these forums. You don't seem to be familiar with them: You have LateX "wrappers" to display any formulas you might need. We can help you with that.

Some questions: What has quantum gravity to do with quantum computing? What is a Shor anomaly? How can graph theory be relevant for local continuous groups, as are those in the SM? How can the non-linear sigma model be relevant in quantum gravity? And what is "noisy" about it in your implementation? Can you present a summary of these completely bizarre-sounding connections w/o people having to click on your link? Please do report on the results as soon as they're ready, falsified or not. And last but not least, are you aware of how much LLM-generated-garbage this sounds?

Waves are oscillations that propagate, either in a medium or in a vacuum. You would be well advised to follow up on suggestions from wise members to pursue basic treatments and then perhaps use the community to answer questions on particular points you find difficult.

No, because it's energy that sources gravity, not mass. This is a common misunderstanding.

Most likely not, as you're asking sensible questions. Hello. OK. But be careful. The battlefield of physics is littered with the corpses of ontologists. Well. It does say that you can always trade mass for energy if you can find a viable way to do it. Example: Annihilate electrons with positrons and you have converted all of their mass into massless energy. Yes, all matter particles are examples of quantum fields, which are a special kind of waves. Energy is an attribute of waves, rather than the waves themselves. If matter were made out of point particles, they would also have energy. I hope that helped.

Not really. The Schwarzschild coordinates are simply a useful parametrisation to solve Einstein's field equations. Nothing more. But the Schwarzschild coordinates are contaminated by a spurious singularity at radial distance = Schwarzschild radius. A more physical set of coordinates is the Kruskal-Szekeres one. And an even more physical quantity is the interval (the metric coefficients multiplied by differences in the coordinates), which is invariant, while the metric tensor is not. What really codes the physics is the Riemann curvature tensor.

You beat me to the puch. I was actually in the process of writing this: Observation Induction --> Synthesis (generalisation) Hypothesis formulation (imagination) Deduction --> Analysis (prediction) Observation (prediction confirmation, high-precision tests, etc) (Something like that.) This which I would call the "wheel of science" must go full circle from observation to observation, as @exchemist emphasises. BTW, I totally agree about the synthetic processes being more difficult: extracting the general rule from the myriad of particular cases. Which Kant so masterfully put at the centre of scientific endeavour, with his a priori synthetic judgments. The epitome of these to me is Newton with his observation that the Moon is similar to a very big apple starting its motion with a particularly off-centre trajectory. An example kids should be taught over, and over, and over.