Markus Hanke

Looks like the air might be getting a bit thin for MOND: https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stad3393/7342478?login=false

Because it is directly correlated to the distance of the source object in question, and that relationship is the exact same no matter in which direction we look, and no matter what else is/is not between here and there. Also, objects don’t just recede from us, but also from each other. One must also remember that redshift is only one of several consequences of metric expansion; it’s by no means the only data point.

Current AI’s are language models, they possess no real understanding of the subject, and as such their answers are quite often wrong or misleading. That is why they are not valid sources of scientific information. So is Newtonian gravity - we measure forces because there is gravity, and there’s gravity because a force is exerted. So what? The model still works well within its specific domain, which is why we still learn it at school. But go outside of its domain, and it fails miserably. You yourself just quoted a paper that provides an example of some of these local effects being measured. But like I said, they are very small compared to the z~10 cosmological redshifts.

Redshift measurements are not done by observing anything “getting smaller”, so you don’t need to look for millions of years. Also, it’s not that things recede only from us - everything recedes from everything else. The distances between all systems not gravitationally bound will increase over time, equally in all directions. Well, it’s just that cosmological redshift is of a vastly greater magnitude than any local gravitational or kinematic effects - eg frequency shift due to the relative motion of galaxies is on the order z ~ 0.005 or so, whereas typical cosmological redshifts for very distant objects is of the order z ~ 10. That’s many orders of magnitude (due to the maths relations involved), so local effects such as the ones you mentioned can be safely ignored on very large scales.

As I said, it is only one single data point in among many others. There is really no “main” one, as they all need to fit.

I think you are forgetting several things here. First and foremost, what we are looking for in cosmology isn’t just an explanation for redshift - it’s a model that can explain all the available observational data in a coherent framework that is compatible with known physics. Of course cosmological redshift is a key data point, but there are other important observations: - the cosmic microwave background and its polarisation - the ratios of heavy and light elements (nucleosynthesis) - the large-scale structure of the universe (filaments and voids) - gravitational wave background (g-waves with wavelengths on the order ~Ly) - acoustic baryonic oscillations - the accelerated expansion rate Among many others. Secondly, whatever model we use in cosmology must be fully compatible with the laws of gravity, since that is the predominant force on large scales. At present, this is General Relativity, which has been extensively tested on solar system scales, and found to be correct within that domain. We’re making a working assumption here that it remains equally valid on larger scales too. Right now, the only model we know of that fits all these criteria really well is the Lambda-CDM model. It’s a valid solution to the gravitational field equations of GR for a certain set of reasonable conditions, and it provides the current best fit for the available observational data. Metric expansion is a natural part of this - it necessarily follows directly from the laws of gravity. This isn’t to say that Lambda-CDM is without its problems - there is a certain tension with some observational data, and there are a few things it struggles to explain at all. That is why a variety of alternative models have been (and continue to be) explored; see here for a very quick overview: https://en.m.wikipedia.org/wiki/Non-standard_cosmology But once all is considered, the Lambda-CDM model still remains the one model that provides the best fit to the largest set of currently available observational data, which is why it is the accepted consensus at present. But as more data becomes available to us, this may well change in the future - the last word is most likely not spoken here, especially since for now we can only observe the universe in the electromagnetic spectrum, and to some limited extent in the g-wave spectrum; the neutrino spectrum is as of yet almost entirely missing, since we haven’t got sensitive enough detectors. We’d expect to find a cosmic neutrino background with very specific properties as well, so this will be an important future test of our models. So there’s a whole lot more going on in cosmology than just light and redshift - you can’t either embrace nor reject any model just on the basis of this alone.

We know perfectly well the laws of physics that describe electrons, protons and neutrons (quantum mechanics), as well their interactions. We also know how neutrons and protons come to be composed (quantum field theory), plus a lot more. It’s just that those laws aren’t the same as the classical mechanics we learn at school, but they are still well understood and extensively tested.

This statement is extremely misleading to the point of being just simply wrong - yes the initial state was “dense”, but “tiny” is a difficult to define term here, and it most certainly wasn’t a “fireball”, and there was no “explosion”. This statement comes from a really bad source. It’s not a sphere. That’s a common misconception, the Lambda-CDM model only meaningfully describes how the universe evolved after a certain point in the very early universe. It has little to nothing to say about how the initial state came to be, since this requires physics that we do not yet have. Yes, but it does so from every point - all distances increase over time, so there wasn’t one central point where everything started.

Probably not, for the simple reason that relativity isn’t just some abstract mathematical theory, but a framework that we actually apply everyday in all manner of practical engineering applications - from MRI scanners, to chemistry, to electrical engineering, to navigation systems, to nuclear power plants, to particle accelerators…the list is endless. In short, we know the theory works because we use it everyday. So if someone comes along and says “relativity is wrong”, then he will be bound to be met with a very large amount of healthy scepticism.

Yes, I know I’ve been sloppy in my choice of words in that statement. The actual definition of a constant is more along the lines of a quantity that does not vary wrt to any relevant variable, particularly not in space or time within this context. The main point was though to contrast this against the notion of invariance, which is a different concept. And then of course there’s the notion of covariance, which is again a different concept.

It would probably be described by some variant of Cauchy’s equations of motion for inhomogenous media; see for example paragraph 3.1 in this article: https://www.mdpi.com/2624-599X/3/4/45

You don’t seem to appreciate just how fundamental SR is to modern science and engineering - it underpins everything from the behaviour and properties of elementary particles (the entire Standard Model is a relativistic quantum field theory), to chemistry and all its uses, electrodynamics and all its engineering applications (including whatever device you use to make your posts here), to classical mechanics in the high-velocity regime, to everything to do with gravity, to cosmology. Our everyday world is full of relativistic phenomena - CRT screens, the colour of metals such as gold, particle accelerators and the interactions they observe, MRI scanners, the chemical properties of the materials in your smart phone…the list is endless. So the suggestion that SR is somehow “wrong” is just silly - we use it every day, and have done so for some time, and hence know that it is a good model from experience. So you’ll have to excuse when people call you out on some of your more egregious statements.

There is no such implication at all - no exchange of information takes place here. There is no such incompatibility - the combination of SR and QM gives you quantum field theory, which is perfectly well established, and extensively tested too. There are also simpler relativistic generalisations of the QM wave equations, such as the Dirac equation.

It changes by a factor \(\gamma^{-1}\), due to transformation of 3-forces perpendicular to direction of motion.

I think it depends exactly what you mean by determinism. What is stochastic about QM is only the outcome of specific measurements - but given some quantum state of a system, plus necessary boundary conditions, its evolution is entirely deterministic.

That’s principally invariance - but so long as you specifically talk about c in vacuum, and so long as there is no gravity involved, then it is also constant. Just bear in mind that it won’t be constant if you go from vacuum into another medium. No, sound is different from light, it’s neither invariant nor constant. The thing is this - even if you didn’t know anything about the theory of relativity, and just worked off Maxwell’s equations alone, you would still find c to be invariant. You can derive the electromagnetic wave equation from Maxwell, and solve it for a fast moving emitter - the resulting wave still propagates at exactly c. Special relativity simply describes the logical consequences of this fact in a coherent and simple way - something which Newtonian mechanics fails to do. Of course, we now know that Maxwellian electrodynamics is essentially a relativistic phenomenon, but Maxwell himself didn’t know this.

Constancy means that c always has the same value under all circumstances - which it evidently does not, since its value depends on the permittivity and permeability of the underlying medium. For example, c is different in glass than in vacuum. This is a direct result of Maxwell’s equations. Invariance means that its value remains the same irrespective of the relative state of motion between emitter and receiver. For example, light emitted from high-velocity particles (e.g. northern lights) propagates at the same c as light emitted from a stationary flashlight. In other words, the form of the laws of physics do not change if you introduce relative motion. No, these are independent concepts. For example, kinetic energy in an inertial system is constant, but not invariant; mass of that same system is invariant, but not necessarily constant. You can’t conflate these terms. That’s not how it works. A model is considered valid and successful if it is able to produce correct and accurate predictions for the largest possible domain of applicability. Newtonian physics works just fine for classical, low-energy, low-velocity scenarios (which is why we all still learn it at school), but it fails miserably in the quantum realm, are for high-energy, high-velocity situations. Relativity has a much larger domain of applicability (ie it works for a much wider range of situations), which is why it has been adopted as a useful model. Remember, physics makes models, not ontological claims. You are welcome to disregard relativity and try to describe the world in Newtonian terms, if that’s what you wish - but you’ll find that you very quickly run into major problems with this.

It’s invariance of the speed of light, not constancy. That’s an important difference. All aspects of SR have, over the past 100+ years, extensively tested in hundreds, perhaps thousands, of different experiments - it is arguably among the most well-tested theories in all of physics. At the heart of SR lies the symmetry of Lorentz invariance, so ultimately the aim is to look whether this symmetry is ever violated or not: https://en.m.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation No such violations have ever been observed within the domains we are able to experimentally probe, so SR stands firm.

Neither is the speed of light - it explicitly depends on the permittivity and permeability of whatever medium it travels through. But that is irrelevant, since SR is only about its invariance, not any notion of constancy.

I don’t see how it would be possible to separate out just the non-linear contributions, so it is difficult to test this directly, other than to compare the exact solutions against the linear approximation.

The non-linearity of the model is encoded in the structure of the field equations themselves, and means simply that you can’t just add two valid solutions (metrics) together, and expect the result to also be a valid solution to the equations for the particular physical scenario you are interested in. For example, in the aforementioned case of a binary BH merger, the metric of the spacetime containing the in-spiralling black holes is thus not just the sum of two “ordinary” black hole metrics, but a new and different solution in its own right, which has to be obtained from scratch by solving the field equations (which in this case can only be done numerically). The degree by which solutions fail to be linear will increase the more you move into the strong field regime - e.g. when your binary BH are still very far from each other, the overall spacetime almost (depending on your required levels of accuracy) looks like two ordinary BH spacetimes joined together; but as they continue their in-spiral and get closer together, the error of the linearised approximation becomes very large very quickly. Since, in this scenario, the form of the gravitational wave field far away depends explicitly and directly on the geometry of the spacetime close to the in-spiralling black holes, the difference (relative to a linearised approximation) is directly observable here. In general though it is difficult to separate out the effects purely due to non-linearity, since this self-interaction is encoded in the structure of the equations themselves, and thus does not appear as a computational term that can be isolated and separately measured. The basic idea is this - you treat the gravitational metric as a small enough deviation from flat Minkowski spacetime, so you make an ansatz of the form \[g_{\mu \nu}=\eta_{\mu \nu}+h_{\mu \nu}\] and demand that \(|h_{\mu \nu}|\ll 1\). Also introduce the convention that an upper bar means trace removal, ie \[\overline{h}_{\mu \nu } \equiv h_{\mu \nu } -\frac{1}{2} \eta _{\mu \nu } h\] Without loss of generality (this can be formally proven, but I’ll obmit that here), one can then impose a gauge condition to simplify the maths, such as \[\overline{h}{^{\mu \alpha }}{_{,\alpha}}=0\] Setting all of this into the original Einstein equations and working through the considerably cumbersome expressions, everything decouples and simplifies into \[-\overline{h}{_{\mu \nu ,\alpha}}^{\alpha}=16\pi T_{\mu \nu}\] Unlike the full original Einstein equations, this equation is fully linear, and obviously far easier to solve.

The non-linearity of GR only really shows up in the strong field regime, so there’s no real way for us to experimentally test it. We can, however, test it observationally - in particular, gravitational wave forms observed from collisions of black holes and other heavy objects are consistent with full strong-field non-linear GR, but not with linearised GR. Generally speaking, most (not all) weak-field regimes can be quite accurately modelled with linearised GR, but strong-field scenarios generally require the full non-linear theory. The non-linearity of the GR equations is very well understood mathematically - ref any text on systems of differential equations. As for perihelion precession, the non-linearity would only show up for very elliptical orbits (not the case for Mercury), or for orbits in highly curved spacetimes.

It’s a real shame, I have many fond memories of my years on TSF. But that’s how it goes sometimes. This here is a good place though. Lol yes, I copied this across when I first came here. I still think it is one of the most beautiful (and important) results in all of maths :)

@KJW Well, mark my words…I remember you from the good old days back on The Science Forum…great to see you again

Yes, but this isn’t the point here. Stellar black holes start off with ordinary stars, which are described by energy-momentum tensor fields that always satisfy the positive energy condition. Then they undergo collapse, which can be described by an appropriate interior solution to the EFE. None of these solutions lead to a geometry below the horizon such as the one you describe, at least not as far as I am aware. You might be able to manually construct such a geometry be glueing together patches of suitable spacetimes (though I doubt even that is possible), but whether such a construct is a valid solution to the field equations for a physically reasonable collapse process is an entirely different matter. I very much doubt this, but I would also encourage you to actually go and try to derive such a geometry - it would be very instructive. If you do find something, then please present it here, I would be curious to take a closer look. I don’t quite understand - you said you want to apply a full Lorentz transformation to the 4-vector, so this already affects all four components, and guarantees that the vector norm is preserved.