Markus Hanke

If that’s the case, then… …is necessarily wrong. There can’t be global energy-momentum conservation in the presence of curvature.

That’s interesting, I didn’t know that. I find it a bit surprising actually, since there are some definite advantages to divorcing writing from phonetics.

I would argue that whichever framework provides the best fit with all (!) available observational and experimental data is always the preferable one. But for this you need a proper mathematical framework, or else you can’t compare the model to real-world data. However, you haven’t provided any framework or model, just a loose collection of thoughts and claims in verbal form, most of which don’t make much sense from a physics perspective. For example, assuming global conservation of the energy-momentum tensor necessarily implies a vanishing Riemann tensor. Thus you need to show mathematically that whatever scaling mechanism you propose is able to fully reproduce all degrees of freedom of gravity without recourse to curvature. You haven’t done this; just verbally claiming that this is so isn’t enough.

It would be a superposition of ordinary passwords, of course :)

It was never intended to replace characters, it was just meant as a means to transcribe their phonetic value where and when this is needed (language learning, typing, foreign publications etc). That being said, I’m sure it would be possible to come up with a system that could capture both phonetic value and distinctions in meaning, ie provides a 1-1 map between character and transcription. But such a system would likely be rather cryptic and require just as much effort to learn than the characters themselves, so I don’t see an advantage. On the contrary, it would make communication between peoples of different ethnicities and/or regional dialects more difficult; in China, that’s an important consideration too. Funny that no one talks about the opposite - replacing the alphabets in European languages with a logographic writing system, supplemented by some kind of syllabary to capture morphological elements such as endings etc, like is done in Japanese.

The trouble is that, in general, one pīnyīn syllable - including tone markers - will correspond to several, sometimes even a substantial number of, characters. For example, if you were to look up the pīnyīn syllable jì in a standard dictionary, you will find listed 39 characters that have this reading and tone, each with a different meaning. Of course, when given within a whole sentence, the meaning is often clear from context, but not always; ambiguities would be too frequent to make this really viable.

I’m re-learning my Chinese at the moment (having lived in China 25+ years ago, and having forgotten most of it through lack of practice), and I can attest to this being a real issue. Visually recognising a character is much easier than writing it down from memory, and if one does not regularly practice writing, one often finds oneself unable to do it, even with relatively frequent and well-known characters. In the case of Chinese at least that would be pretty much impossible, due to the large number of homophones. Also, Chinese people are very proud of their writing system (and rightly so), they would never accept its abolishing in favour of romanisation.

Gravitational effects on those scales are trivial only under ordinary energies, ie isolated atoms, or as parts of ordinary matter at ordinary pressures and temperatures. However, if you increase energy levels sufficiently - eg by forcing a very large amount of matter into a very small volume under extreme pressure and temperature - there comes a point where gravity and its hypothetical quantum properties can no longer be ignored even at small scales.

I don’t really get this either. Not all EM fields oscillate, and neither do mass distributions (usually). So the frequency of what are you referring to, exactly?

So we are in fact rescaling atoms, which, as pointed out already, does not work.

Gravity does physically work at quantum scales also; at least we don’t have a reason to believe otherwise, though actually measuring it is very difficult, due to how weak it is at those scales. The question is only how does it work, and that’s what we don’t know. A quantum system can be put into a superposition of states, but if you try to formulate a corresponding superposition of geometries in the context of GR, then things just don’t work out nicely. So the problem is that our usual tools that work so well for the other three fundamental interactions, give us only gibberish when applied to gravity.

You see, the problem here is that these AI’s are LLMs, ie large language models. Simply put, given a string of words, they essentially calculate a probability for what the next word in the string should be, thereby building up text (and same for equations). These probabilities are based on previously learned input, which is mostly very large volumes of pre-existing text. In other words, the LLM-AI can only generate things based on what already exists; it cannot truly invent or derive something entirely knew, nor does it “understand” either your question or its own output. It’s simply a probability-based algorithm. That’s why sometimes the answers you get are wrong or misleading. What your AI has generated here is simply the Lagrangian formulation for a generic vector field, where you have given this vector field the physical meaning of local displacement. There isn’t anything mathematically wrong with this (as far as I could spot), but neither is this anything new or revolutionary - it’s basically just a generic formulation as you’d find it in any textbook on Lagrangian field theory and/or continuum mechanics. As being an LLM, it can’t give you anything different. What the AI has failed to tell you though is that no vector field theory - irrespective of its precise details - can capture the correct degrees of freedom for gravity. For example, if you try and model gravitational radiation with your vector field, you’ll end up with two possible polarisation modes at a 90° angle; in reality though, the polarisation modes of gravitational radiation are inclined by 45°. To correctly model gravity, you need at least a rank-2 tensor field, and there are very stringent constraints on how the Langrangian for such a model might look. But these are things you need to be able to understand; an AI can help, but it can’t do that work for you. My advice would be to step back from this for a while, and use some time to learn already established physics and maths first. Then you can come back to this with a much better understanding, and a much better equipped toolbox.

I’m wondering, do you yourself understand what the AI has generated there? The crucial ingredient in here would be the potential energy function \(V_{eff}\), without which one can’t write out the full Lagrangian. Do you have an explicit expression for this, or at least a way to find that expression for a given physical scenario?

That’s precisely why I asked you to show how your model handles the situation involving a signal delay near a massive body, because this is something that happens in the real physical world, and becomes practically relevant eg when communicating with spacecraft/probes in the solar system. You did not offer a response to this request. In your first post here you mentioned that in all those years no one seems to have taken notice of your work, nor shown interest. That’s because you don’t have a model, in the sense this term is used in physics. What you have is a loose collection of personal ideas about how you think the universe should work, written in verbal form; that’s not the same thing at all. One cannot, given a real-world scenario such as the one I offered, extract any kind of quantitative prediction from your ideas, and thus there is no meaningful way to relate it to any set of observational data. You can’t even know whether your own conclusions actually follow from the underlying premises, because you don’t have any way to check. You’re just speculating. To put this short and to the point - people aren’t interested, because you don’t have anything to be interested in; there’s nothing here that’s of value to physics, which has a very specific job to do. I’m sorry to be blunt, given that you have spent much time on it and are correspondingly emotionally invested; but truth is that this won’t ever go anywhere, at least not in the form it is now. Also, you seem to have a tendency to perceive all comments to be about your person, when they really aren’t; that isn’t helpful. It’s just that when you post your thoughts onto a science forum, they will be scrutinised and challenged, because that’s essentially how the scientific methods works. My advice - if you want people to take notice, you need to give it predictive powers by having a proper (!) mathematical framework so that one can extract actual quantitative predictions for specific scenarios. That’s what’s required, regardless of how you feel about maths in general. If you can’t or don’t want to do that, then it would be better to just let it go. As it stands now this is of no use to anyone - least of all yourself. Harsh perhaps, but nonetheless true.

Scale of what, exactly? Again - scaling function of what, exactly?

Ok then. Suppose you send a radar signal between two points in the solar system that are equidistant to the sun, eg 1 AU, such that the signal just grazes the sun, eg with impact parameter = 1 solar radius. How much does your model predict the signal delay due to the sun’s gravity to be? Of course you could just ask an AI, but I’d like to specifically see how you find the answer using only your model. Please show your work, step by step.

So then we are back to matter physically shrinking relative to a fixed cosmic background, which doesn’t work, as I mentioned.

A point is just a point; taken in isolation it carries no further information, so the above is trivially true. But in GR we don’t work with isolated points, we work with semi-Riemannian manifolds endowed with a connection and a metric. There’s a lot of additional structure here, which carries the geometric information that eventually makes up gravity. I can’t make any heads or tails of this, I’m afraid. If by “uncertainty” you mean non-commutation of certain geometric quantities, then this has already been attempted: https://en.m.wikipedia.org/wiki/Noncommutative_geometry I’m not up to date on where this is at right now, but I don’t think it got us any closer to quantum gravity. You won’t get very far then, since this whole area is inherently mathematical in nature.

Sounds like ordinary metric expansion to me, then.

I don’t know what this is supposed to show, to be honest. One wire is infinite, the other one is not (it returns to the same starting point). In both cases they look locally flat. But globally these situations differ. In GR, any small enough patch of spacetime can locally be considered Minkowski; but this doesn’t at all imply that the entire spacetime is globally without curvature, or that curvature is somehow “hidden”, it just means that curvature effects are small enough to become negligible, but they are still there. For example, longitudinal lines on Earth still converge at the poles, even if locally on a small enough scale they appear to be parallel. This is where the connection (and thus the Riemann tensor) come in, because it tells is how these local patches are globally related to one another.

This is not what you said earlier - you explicitly stated that matter shrinks relative to some fixed absolute background. That is a rescaling of atoms.

The question then is why we only detect that one signal from the civilisation in question, and not all the other radio signals that would have emanated (largely unintentionally) from the same location before. If a civilisation possesses radio technology, it’s unlikely they’d only employ it one single time.

Sure it will, because eventually the ant will end up again at the same point where it started, and thus realise that it wasn’t on a flat surface. While its trajectory was everywhere locally flat, the global geodesic it followed was a circle. Sure you can use these to prove the Bianchi identity, but you don’t have to. As KJW has pointed out already, you must remember that the Christoffel symbols aren’t tensors, so you can always make coordinate choices such that they locally vanish. However, Riemann is a tensor, so an a curved surface it can never be made to vanish. It measures the commutativity of the covariant derivative. On curved surfaces, covariant derivatives do not commute, and the extent to which they fail to do so is measured by the Riemann tensor.

No, here’s where the issue is - specifically the strong and weak interactions do operate on an absolute size scale. For example, the upper limit for binding between quarks is at around 0.8 femtometers, and the residual strong force between nucleons operates within ~3 femtometers. These are very much absolute values at ordinary energies. This is why the rescaling of atoms does not work.

Yes, so long as the manifold is flat. No they don’t, unless the manifold is flat. All tensors are purely local objects, and the metric tensor in particular allows you to define the notion of inner product at a point. However, the numerical values of the components of the tensor depend on where they are evaluated (thus the Christoffel symbols don’t automatically vanish), unless the manifold is flat. And then the metric tensor becomes the Minkowski metric, since we are working in GR. The Riemann tensor is defined at a point, like all tensors, but it is made up of derivatives of the metric, which don’t vanish on a curved manifold. All these tensors - the metric, Riemann etc - are in fact tensor fields, ie they are not isolated objects, but defined at all points of the manifold. So there’s no such thing as “hidden curvature” - a manifold is either curved, so that Riemann doesn’t vanish, or it isn’t, in which case Riemann is zero. There are no other options here. Note that all of this is very precisely defined using calculus on manifolds, and well understood.