Markus Hanke

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.

Ok, so you’re working on a flat manifold. But what do you mean by “loop Lie bracket”? What are you taking a Lie bracket of, exactly? I don’t know what “uniformity of information” means. If the manifold is flat, as you stated above, then the vectors will coincide after parallel transport; but of course that means you don’t have any gravity in this situation.

But this is not what we are doing. And what you’ll find is that they don’t coincide, just as the maths say. There’s no such thing as “hidden curvature”. If the manifold is curved, the vectors can’t coincide - that’s all there is to it. I don’t know where you are getting this from, but if makes no sense. Given the Levi-Civita connection on a manifold with curvature, the Lie bracket of two vector fields measures the extent to which differential operators associated with these fields fail to commute; specifically in this case, it’s related to the commutator of covariant derivatives, which on a Riemann manifold is not zero, unless the manifold is perfectly flat. In other words, parallel transport is path-dependent in a curved spacetime. I’m afraid this doesn’t make any sense.

No it won’t. On a curved manifold the initial and final vectors can’t coincide. This result is easily shown, and entirely independent of any physics models such as GR. You need to remember that differential (Riemann) geometry was already well established long before Einstein - GR simply uses this discipline of mathematics to formulate its framework. There is no notion of “duration” associated with this; you simply compare the effects of the connection on your manifold to the original vector. Another, perhaps simpler, way to state the same thing is that on curved manifolds, covariant derivatives do not commute, which is likewise easily shown. GR is by design a purely classical model, it describes no quantum effects. The symmetry group associated with GR (cosmological constant or not) is non-compact and infinite-dimensional; any spin-2 quantum field theory based on such a symmetry group will be non-renormalisable.

That’s exactly the problem. You’re assuming that these fundamental interactions don’t change, but at the same time you’re saying that atoms “shrink” over time relative to some absolute background. This doesn’t work, since the interactions don’t scale - if you try to shrink atoms, you break the physics in the process.

Yes. Or else you can also calculate it directly from the metric. This is one way to define the Riemann tensor, though it doesn’t have to be a parallelogram…any closed curved will do. Firstly, the space the parallel transport is performed on is already 4-dimensional spacetime, so in general you’re transporting in space and time. Secondly, the crucial point is whether the transported vector, once it returns to its starting point, coincides with its original version before parallel transport, or not. In a curved spacetime, it generally won’t, so the Riemann tensor will allow you to find the difference between the two (ie a new vector that points from the tip of the first vector before parallel transport to the tip of that same vector after parallel transport). All of these vectors are 4-vectors in spacetime. In GR, the connection on the manifold is given, being the Levi-Civita connection. Since this connection is torsion free, the only dynamics can come from curvature, so the Riemann tensor captures the entire geometry on your spacetime. Note though that the Einstein equations in GR do not by themselves completely fix the Riemann tensor (or even the metric). You always need to supply extra boundary conditions to uniquely determine the geometry.

That doesn’t work, since neither the weak nor the strong interaction (ie their respective Lagrangian) are invariant under rescaling, irrespective of how you fudge any constants.

All atomic clocks tick at exactly “one second per second”, and all ideal rulers measure exactly “one meter per meter”, in their own local frames. What changes is only the relationship between local frames across spacetime. This is what time dilation and length contraction are - they are relationships between frames, not something that physically “happens” to the clocks and rulers themselves in their own frames. The consequences of such relationships between frames are just as real and physical, but it’s nonetheless crucially important to understand the difference.

The job of physics is exclusively to develop descriptive models of aspects of how the universe works on a fundamental level - it is simply about knowledge and understanding. What people do with this knowledge is a whole different question, which lies outside the domain of physics itself. For example, quantum physics has given us the MRI machine at your local hospital, but also the nuclear bomb. As for the specific model on this thread, it’s too early to ask about potential implications, because no final fully renormalised version exists yet. Only once the mathematical groundwork has been done, can we judge whether this is worth investigating further, and what the model actually tells us about the world, if anything.

I think it’s an interesting approach, that may very well turn out to be quite viable. The huge advantage here is of course that this model directly integrates into the Standard Model, since it’s build on the same paradigm from the ground up. The basic idea here is that you start with flat Minkowski spacetime, and then define a suitable gauge field on it that has the same degrees of freedom as ordinary GR, so that the observables cleanly map into each other. It turns out that this works if you use a collection of spinors as the fundamental mathematical object. You can then simply apply all the well established techniques of quantisation and renormalisation, since we’re just working with a field on ordinary Minkowski space. The authors have shown that the resulting model is renormalisable to first order, which is a great start. Much of the technical details are kind of over my head too, but I get the main ideas, and I think it’s very promising. I don’t see any obvious reason why the renormalisation shouldn’t work to higher orders too, but we’ll have to see. It’s also interesting to note that this model contains no new free parameters, it works entirely with already known fundamental constants.

So then you need to impose extra boundary conditions to establish a unique relationship between your scalar field and the metric (or the Riemann tensor). Fundamentally the issue is that a rank-0 scalar field does not contain the same amount of physical information as a rank-2 tensor field.

But as @KJW has already pointed out, gravity is not just time dilation. You cannot in general reduce the degrees of freedom of gravity to a single scalar field; you need at least a rank-2 tensor for this.

I’ve just tried it in the sandbox, but it doesn’t seem to work for me, at least not using the “\ [“ syntax. What is the correct way to use it now? \[R_{\mu \nu}-\frac{1}{2} g_{\mu \nu}R=\kappa T_{{}\mu \nu}\] PS. Never mind, it seems to be working now.

\[math]R_{\mu \nu}-\frac{1}{2} g_{\mu \nu}R=\kappa T_{{}\mu \nu}\[math]