Markus Hanke

So if there aren’t any electrons, for example if I have a sample consisting only of protons and neutrons (ie ionized hydrogen) in a stationary state, then this sample will exhibit no gravity? Also, you are forgetting that gravity is generated by things other than massive particles - for example electromagnetic fields have a gravitational influence, as do pressure, stress, strain etc. Don’t be ridiculous - if you propose an alternative theory of gravity, you need to be able to quantify its predictions. We are doing physics here. Verbal claims aren’t enough, and as an engineer you should understand this. You can’t even know yourself if your proposal is consistent with reality, if you can’t quantify things. For example, if I’d ask you to tell me the trajectory of some test particle (eg a probe) given initial and boundary conditions, how would you do it? You have no mathematical framework, nothing at all, other than verbal claims. It’s useless.

It is a constant only within the same medium, but it is always invariant. I’ve already provided a link to show that the experimental and observational data available to us is inconsistent with the notion of a spatially varying speed of light. You can’t just ignore that and claim the opposite. Let’s think about this for a moment (it’s not like no one has ever considered this before). Ordinary cosmological redshift is due to the expansion of spacetime between the emitter and the observer; it is not a local effect. Therefore, all spectral emission lines of distant sources are shifted by the exact same amount, preserving the overall spectral pattern. This is what we observe. The same is not true for a c that varies with location, because also the fine structure constant directly depends on c, so it would change as well - and as it so happens, the relative energy level splittings in atoms scale with \(\alpha^2\). This means that a varying speed of light would lead to different spectral lines getting shifted by different amounts, so the overall pattern is not preserved - in direct contradiction to what we actually observe. So no, these two effects do not produce the same results, and observation tells us clearly which one actually applies.

These are scenarios where quantum effects become important, so just GR alone isn’t going to be enough here. Also, the Big Crunch is hypothetical.

I think these would look just like ordinary retarded waves to LIGO - what is measured there are essentially just tidal effects. But crucially, causality would be violated - we’d see the wave front arriving here before the source event actually happens in its own rest frame (ie all other signals would arrive much later). Needless to say this has not been observed.

Evidence? This claim is not consistent with any of the data available to us, which shows that speed of light in vacuum is an invariant. See here for example. The speed of light isn’t constant, it’s invariant. That’s not the same thing.

I’m sorry, but this makes even less sense. We evidently are a part of this universe, so there’s no “our” vs “the universe’s” speed of light. There’s only one c, which is the same everywhere (AFAWCT).

Great, thanks. I’ll consider it.

I see, thanks for the replies. In that case, do we have some official procedure whereby one could request a display name change from whoever is able to actually make that change? I’ve been considering changing mine (for personal reasons)…but it isn’t a big deal, if it causes too much hassle.

Is there any way to change one’s display name on this forum? Maybe I’m blind, but I wasn’t able to find such a setting anywhere.

How do you define a “speed of time”? This seems like a fairly meaningless concept to me. Can you give an unambiguous mathematical definition for this? I should note here that in non-flat space times, energy-momentum is conserved everywhere locally, but there is no global law of conservation.

Another problem that occurred to me: as far as we can tell, all electrons are exactly alike; specifically their masses are the same, and those masses remain constant. Black holes don’t tend to behave that way, even if one completely discounts any thermodynamics.

He had a chance to do his measurement precisely because light has the properties we know it does. But that’s precisely what he did not do. He measured the relative differences in Io’s timings at different points of the Earth’s orbit, and thus inferred a finite speed starting from differences in distance to Jupiter. Changes in position are the whole point of this setup.

Yes, I concede that. The argument I gave implicitly relies on Hawking’s assumptions in deriving his results, and also on those assumptions still holding on small/quantum scales. So there is indeed a question mark here. BTW, how would one reconcile quantum mechanical spin (along with their respective spin statistics) with black holes?

But that isn’t the same as saying that there are “infinitesimal black holes at the centre of elementary particles”, as you did above. Also, my initial objection still stands - if elementary particles were black holes, none of them would be stable. For example, assuming an outgoing Vaidya black hole with mass equivalent to one electron, this would evaporate after something on the order of \(10^{-107}s\). Of course, this assumes a classical spacetime, which isn’t that plausible on those scales. But still. Also, as KJW has pointed out, some particles are massless, such as the photon and the gluon, which is not compatible with them being black holes at all.

The immediate problem I see with this idea is that black holes small enough to fit “into” (what does this actually mean?) a subatomic particle would evaporate almost instantaneously, and emit large amounts of radiation in the process. We don’t see this happening; many elementary particles are demonstrably stable.

I think a good way to think about this is to consider length contraction and time dilation (which always go together) as a relationship between frames, not as something that “happens” to clocks and rulers. You can specify how frames are related by stating their relative speed, or you can state the gamma factor (ie time dilation/length contraction) - these are entirely equivalent. So there is no physical force that squeezes rulers, any more than there would be if you observed your house from a distance and noted that it has gotten smaller; all that changes is how observer and observed relate to one another. In SR, that relationship is one in spacetime. Just be careful to not confuse length contraction with a mere optical illusion though - the flattened nucleus in the particle accelerator really does physically behave like a flattened disk in the lab frame, it doesn’t just “look” flattened.

In Kerr spacetime you have \[T^{\mu \nu}=0\] everywhere, so nothing there arises from the stress-energy tensor. Equivalently, one can say that the dynamics of the Kerr spacetime arise entirely from the requirement that all curvature be purely of the Weyl type: \[R^{\mu \nu}=0\] as well as appropriate boundary conditions.

In my post I responded to your comments on the energy-momentum tensor, your model wasn’t mentioned. The point was that it isn’t an ad-hoc invention, but arises from Noether’s theorem. No, that’s not my intention, I’m aware that what you’re trying to do is different. You do have to remember though that GR is a very thoroughly tested model of gravity, so whatever model you propose should match its predictions, at the very least those that have been verified. If you choose to ignore all source terms other than energy density, you’re off to a bad start. Did he? I seem to remember that he pointed out to you that the particular example at hand worked out only because it implicitly exploited a particular symmetry of the Schwarzschild metric; and also that he was of the opinion that the model was too simplistic to work for more complex scenarios.

You are deflecting from the actual point of my post, which was the energy-momentum tensor.

The energy-momentum tensor is the conserved quantity associated with spacetime translation-invariance under Noether’s theorem; it isn’t just an ad-hoc invention. But these nine components all themselves form sources of gravity, and are not derivable from just energy-density. If you ignore them, your model cannot recover all the dynamics of GR, which you claimed it is able to do.

This is true. However, I would question whether the initial/boundary conditions required to arrive at these solutions are actually physically realisable - the standard Alcubierre metric would require exotic matter, and the Kerr metric - while being a very useful textbook case - requires asymptotic flatness amongst other things, and is unstable under perturbations, so arguably it wouldn’t arise in the real world, except as an approximation in its exterior region. I would argue that perhaps ensuring that initial/boundary conditions being as physical as possible would avoid most, if not all, such artefacts. That’s a very good point, I never looked at it that way before.

I’m trying to show you that your formalism requires some of the very things you reject. Orthogonality requires some notion of inner product. Gradients require derivatives and a metric, as do lengths. And so on. These are things you can easily research yourself, I don’t think it is always necessary to typeset LaTeX for stuff I would consider basic and easily found with a simple search, after one has been made aware of them. If you presume to be simplifying GR, you are operating at a level where you can be reasonably presumed to be able to do this. The problem is that you are so sure that your idea must be right, that you are no longer receptive to feedback. BTW, there already exists an almost purely algebraic formulation of GR - check out the papers by Geroch and Heller on Einstein algebra. Note though this still requires the concept of smoothness as an additional ingredient.

It seems to me that this is precisely what GR does - it tells you mathematically how the lightcones at each event in these circumstances are related to one another. That’s causal structure. The philosophical question is rather why not all such situations seem to be realised in nature, even though they are valid solutions to the relevant equations.

The whole thing starts with two fundamental observations about the world we live in: Events in the real world are separated - they can be spatially separated (things don’t all happen at the same place), temporally separated (not everything happens simultaneously), or both. Not all events are capable of influencing all other events - only events separated in particular ways are causally connected. In other words, the world is endowed with a causal structure (at least classically). The job of physics is to make models of aspects of the world we live in. Einstein, using pre-existing work by Minkowski, Riemann and others, realised that, if one uses a semi-Riemannian manifold endowed with a metric and a connection, and allows the metric to vary while holding the connection fixed (the Levi-Civita connection), one obtains a mathematical model wherein the points on the manifold are related in the same way as events in the real world are observed to be causally related. In small enough local patches this gives you SR with its light cones, whereas globally it gives you GR and hence gravity. In either case it boils down to causal structure. So the assumption that GR makes is that one can use a semi-Riemannian manifold endowed with the Levi-Civita connection and a varying metric as a good model for the causal structure of the world we live in. I highlighted “can” because no claim is made that this is the only possible way to model these dynamics. Many other models of gravity are known nowadays, not all of which are metric models either; but GR seems to be the simplest, and the one that works best AFAWCT. BTW, the Einstein equations don’t a priori assume any specific dimensionality. One advantage of tensor equations other than general covariance is that their form remains the same in any number of dimensions. The real world looks 4D, but GR works just fine in other situations too. Seems to me that it’s rather the other way around - despite multiple posters having patiently attempted to explain to you why, in your proposal, you are implicitly using some of the concepts you initially rejected, you’re still not getting it. I strongly suspect that’s because you don’t want to get it. To be honest, I think we’re done here.

Exactly 👍 That’s what I tried to point out before.