Markus Hanke

What does this mean? Nothing has been ‘corrupted’, it’s just that now, a century later, we have a much better understanding of the foundations of GR than Schwarzschild (or any of his contemporaries) would have had. There was confusion about this only because the model was brand new back then, and it took time to figure things out. Nowadays we are in a much better position. In his original paper, Schwarzschild used a coordinate system that had its origin at the event horizon, so r=0 meant the horizon surface. However, this does not at all mean that there is nothing beyond the horizon, because in GR the choice of coordinates is arbitrary and has no physical significance. Schwarzschild used this convention simply because it made his particular way of deriving the solution mathematically easier. A consequence of this choice is that large parts of the spacetime aren’t covered by any coordinate patch, so, in his notation, there are physical events that cannot be labled by any coordinate. But again, that’s just a convention without physical significance. You can rectify this simply by choosing a different coordinate system - which does not change anything about the actual geometry of the spacetime. This is why there are so many seemingly different metrics (Novikov, Kruskal-Szekeres, Aichlburg-Sexl, etc etc) which all describe the same physical spacetime. To see whether the event horizon is a physical singularity (as opposed to just a coordinate one), and what the nature of spacetime beyond the horizon is, you can use tools that do not depend on the choice of coordinate system at all - such as invariants of the curvature tensors. That way, it’s trivially easy to show that, in classical GR, the horizon as well as all of spacetime in the interior right down to the singularity is in fact perfectly smooth and regular, just like anywhere outside the horizon. This is a standard exercise in pretty much any graduate GR course.

Interesting new paper on anomalies in physical cosmology: https://arxiv.org/pdf/2208.05018.pdf

Well, without a metric we can’t really have a discussion about this. The thing here is that you don’t start with a metric - you begin with an energy-momentum tensor plus boundary conditions, then you use these to solve the Einstein equations. That gives you the metric. All solutions to the Einstein equations are metrics, but not all metrics are valid solutions to the Einstein equations.

Ok, so what is the metric? You haven’t written it down yet.

I believe you are thinking of specific, symmetric solutions such as the Kerr spacetime. In those special cases the situation is indeed unambiguous - but that’s because these cases assume certain symmetries that remove the extra degrees of freedom. The problem referred to in the paper pertains to general regions of curved spacetime, where no symmetries or boundary conditions are assumed. Defining the total energy (not just mass) contained in such a region has been an intractable problem - which this paper now solves. I must look at this in detail, but at the moment I’m engaged in other pursuits.

That’s certainly a factor, but I suspect it’s mostly because a lot of people simply don’t have the ability to step outside the paradigm of what their sensory apparatus tells them about the world - which is essentially Newtonian. Thus, relativity and QM get rejected wholesale, because they “don’t make sense”. Also, believing that you are smarter than a larger than life figure such as Einstein props up people’s egos.

Here’s an article about this paper - it’s actually more about angular momentum (which is just as ambiguous as mass), but the problems are closely related: https://www.quantamagazine.org/mass-and-angular-momentum-left-ambiguous-by-einstein-get-defined-20220713/ I can’t offer any real details yet, since I haven’t studied the paper itself.

You’ve got this backwards - it was you who made the claim that spacetime is a mechanical medium, and that energy-momentum is always conserved. Mainstream physics says no such thing. So the onus is on you to show how your claim is right. Indeed. Yes, that’s right. The problem is that the gravitational field itself carries energy, but this energy isn’t localisable; if you try to account for it, you generally end up with expressions that are observer-dependent. A further problem is that there is more than one way around this, which is why you get different ways to define the energy content of a region of spacetime, like ADM energy, Komar energy etc etc. It’s not immediately clear how to define it in a general, unambiguous way. I believe the problem has recently been solved, though I haven’t had time to look into this new development, so I can’t comment yet.

Spacetime isn’t a mechanical medium, so this is irrelevant. Also, it might surprise you to hear that the law of conservation of energy exists only in flat spacetime - in the presence of gravity, things become rather more complicated.

First of all, spacetime isn’t some kind of physical substance that “expands” in the literal sense, like bread in the oven. Rather, it is a network of causality relations - the set of all points in space at all moments in time, and how they are related to one another. When we speak of “expansion”, then what we mean is that measurements of distance depend on time, ie they change in a certain well defined way according to when they are performed. This is an extremely useful and accurate model, but shouldn’t be reified into something like a physical “substance”. LQG deals with something called “Wilson loops”. These are mathematical objects that are solutions, simply speaking, to an equation that treats spacetime as a quantum state. These loops are not themselves “chunks” of space and time - rather, they form networks called spin foams, which, in the semi classical limit, may become curved spacetimes with a positive cosmological constant. So yes, they do actually describe an expanding spacetime. The point here is that there would be a lower limit to how small intervals of space and time can be - you can’t infinitely subdivide it. Again, this is a mathematical model - like a map of the world. But it’s something that one could, at least in principle, test experimentally, given enough energy. No. They are 1-dimensional objects that live in a background spacetime with 3 macroscopic spatial dimensions, 1 dimension of time, and 7 compactified dimensions. Of course not. It’s the spacetime they live in that expands, not the strings themselves. Physics has nothing to say on any of these issues.

Ah I see. The Klein-Gordon equation is the quantum version of the energy-momentum relation (not the tensor though), and is generally used to describe relativistic fields/particles without spin - scalar particles.

How do you know that they don’t?

Apologies, you are of course correct, “fusion” was what I meant to say (I typed that in a hurry). I’m not sure what you mean here - could you elaborate?

You can’t isolate it (the concept of a single quark doesn’t even make sense), but you can probe its properties by letting it interact with other particles, even while it is bound up in a composite particle. This technique is called deep inelastic scattering.

It’s a bit more complicated than that - a fission bomb fuses hydrogen atoms into heavier elements. Initially you need to supply energy to do this, in order to overcome the electromagnetic repulsion between protons (among other things). However, once the protons are close enough for the residual strong force to kick in, they “fall” into its respective potential well, forming a stable nucleus - which is structured such that you end up with a net surplus energy at the end of the interaction. There’s actually a lot more going on, but that’s the gist of it. I reiterate again that E=mc^2 works only for massive particles at rest - it’s a special case of the energy-momentum relation, which is in turn just the magnitude of the energy-momentum 4-vector.

The source of gravity isn’t just mass (whatever its form), but all sources of energy-momentum. Even an electromagnetic field (which isn’t composed of quarks), and things like pressure, stress and strain have a gravitational effect. Same goes for particles not composed of quarks, such as electrons and neutrinos. These all gravitate.

Elementary particles don’t have an internal structure, because they are local excitations of quantum fields. Such fields don’t have structures. In tech speak, elementary particles are irreducible representations of symmetry groups. There is no physical principle requiring all particles to have internal structure. E=mc^2 has nothing to do with potential energy, which is what you must be referring to in this statement, or else it doesn’t make sense. It’s the energy equivalent of the particle’s rest mass, and this relationship is true only in a massive particle’s rest frame. This has nothing to do with any potentials or internal structures. E=mc^2 has nothing to do with potential energy, nor internal structure. Only with rest mass. No, see above. No, I am saying that there is no internal structure, according to current understanding of the Standard Model. Elementary particles are irreducible - and that’s true for all of them, irrespective of whether they carry electric charge, colour charge, flavour, isospin, or mass. To experimentally verify the elementary-ness of such particles, you use a technique called deep inelastic scattering. This is, however, limited by the available energy of the accelerator. Proposing internal structure for these particles means you need to introduce new physics.

That’s because elementary particles - as opposed to composite particles - do not have any internal structure; that’s why they’re termed ‘elementary’.

I’m afraid I’m getting that same impression, so I don’t feel it is worth my while to volunteer any more of my time in this thread. Good luck.

I’m beginning to see where it is that you’re stuck, I think. You see, the form of the geodesics themselves is already completely determined by the geometry of the underlying spacetime, which has nothing to do with velocities. There are really infinitely many geodesics in any spacetime - this is called its ‘geodesic structure’. So, in order to find the correct geodesic for a given particular situation, you need to specify initial and boundary conditions for the problem. And that’s where velocity comes in - it serves as an initial condition to select the correct geodesic out of all possible ones. It doesn’t actually determine what that geodesic looks like - only the geometry of spacetime does that, and that follows from the presence of sources of energy-momentum. In practice, you start by solving the Einstein equations - you input what and where sources of gravity are, and out comes a description of the geometry of spacetime. For our purposes here you can think of that description as a big bundle of free-fall geodesics - all possible ones for all possible cases, and what each of them looks like is already determined in that description. So, as a second step you need to find and select that one geodesic out of that big bundle that applies to your problem at hand; so you need selection criteria. These are your boundary conditions - initial velocity being one of them. But it isn’t a case of velocity determining the geodesic structure of spacetime - it simply helps you find “your” geodesic in an infinite pile of possible ones. The pile itself depends only on the distribution of energy-momentum. Note that velocity alone isn’t enough though, you need at least one more boundary condition. It doesn’t. It simply tells you which geodesic is followed, the ‘shape’ of which is already determined by the geometry of spacetime. See above. Gravity is defined as being geodesic deviation, in GR. It doesn’t really, it presents only one specific aspect of gravity. And it isn’t a model either, it’s just an analogy. The rubber sheet visualisation is what is called an ‘embedding diagram’ - the form that’s usually depicted uses Schwarzschild coordinates, and plots changes in the radial coordinate against changes in proper distance. That’s all - it shows just this one relationship. It doesn’t depict the time coordinate, nor the angular coordinates - so you can’t see the tidal components of gravity (or any other gravitational phenomena) in that plot. Generally it also only shows the region outside the central body, and ignores the interior part. You can deduce some of these things from what you see - but that’s only because you are dealing with the simplest of all geometries, Schwarzschild spacetime, which is highly symmetric. For something even slightly more complicated, such as Kerr spacetime, this kind of visualisation fails badly, since you can’t easily deduce any of the other aspects, such as frame dragging. Are you actually aware that in everything you’ve said so far you are tacitly assuming a very specific spacetime geometry, being Schwarzschild? It’s the simplest of all solutions to the Einstein equations - it’s spherically symmetric, static, stationary, asymptotically flat, and depends only on the mass of the central body. This solution is great for academic purposes, since it’s pretty simple and works well as an approximation. But actually, really world gravity is vastly more complicated - it may involve angular momentum, gravitational radiation, sometimes electric charges, non-linear self-interactions, and a whole host of other things. If you account for these, the geometry of spacetime very quickly becomes vastly more complex. Please don’t think that what you find in Schwarzschild is all there is to gravity. That’s not the case at all.

You are right, an orbit is a geodesic in curved spacetime, where it is the “straightest” possible connection between events, in a certain precise mathematical sense. But the geometry of spacetime (more precisely: geodesic deviation) is gravity. That’s the definition, and the current consensus. I don’t quite understand why you feel there is any kind of contradiction to “convention”? I think you may be referring to Newtonian gravity, which uses forces. This is a much older model than GR, but it still works really well in situations that deal with slow motion and weak fields. In such cases it is often unnecessary to employ the full machinery of GR, which is mathematically much more complicated than Newton. So Newton is a good approximation to Einstein in the right circumstances - which is why it’s still taught in schools.

You had to get that in, didn’t you Either way, I’m familiar with it under its original name Swordy-Abbasi spectrum, from when this was first published - but you seem to be right that it appears to be called “the knee” and “the ankle” nowadays. See, I learned something new today! And no, my area of expertise is General Relativity (mostly its theoretical foundations), not HEPP, which is why I haven’t followed latest developments on this particular issue. Exactly why do you think this is even relevant to theories of gravity? Yes. The fundamental grounds are rock solid.

The speed of light is invariant, not constant. That’s an important difference. Furthermore then it is directly related to the electromagnetic properties of the underlying medium: \[c=\frac{1}{\sqrt{\epsilon_{0} \mu_{0}}}\] Since these are fundamental constants, irrespective of anyone’s state of motion, c has to have the same numerical value in all reference frames.

Sure. But that’s not due to forces, because these stars in free fall. Of course. Coincidentally though this is not a gravitational phenomenon. I don’t know what you mean by “knee shift” - can you provide a source? GR is a purely classical theory, so it does not predict any gravitons. I have explained this in my previous post. Also, GR only indicates that there is an additional source of gravity that is distributed in a certain way - it does not say anything about the nature of this source. In particular, GR does not say that DM is particulate matter. The search for DM is currently underway, but not finding DM particles does not mean that DM isn’t there; there are options other than it being made of new particles. Lastly, if it turns out that DM isn’t there, then that still doesn’t mean that GR is wrong - it means only that GR’s domain of applicability is limited to shorter scales, and needs to be modified for longer scales. Either way, your idea is not a contender, since it is ruled out on fundamental grounds, as I’ve explained. This is what MOND tries to do - unfortunately the resulting model is inconsistent with observational data, so this approach does not work. It also requires extra vector and scalar fields, for which there is no evidence. No, see above. DM is a prediction about there being additional sources of gravity, but GR says nothing about their nature. So it doesn’t predict new particles. How could it? It’s a purely classical model that has no concept of quantum fields.

Well, that’s the problem with your idea, because objects going at different velocities with respect to the galactic center still experience gravity in the same way. The laws of gravity do not depend on any reference frame whatever, and thus they don’t depend on any velocity with respect to anything. This fact is already inherent in the formalism of GR, and borne out by all observational data. Gravity depends solely on sources of energy-momentum, and the non-linear self-interaction of gravity itself. Consider the SMBH at the center of our galaxy - its velocity with respect to itself is zero. So does that mean, according to your ideas, that no gravity exists there? And what about objects outside our galaxy, which don’t move around any central point? Like other galaxies? Or entire galaxy clusters? What does their gravity depend on, according to your ideas? Or consider the Cavendish experiment (which you can do yourself at home) - the gravitational interaction between the balls demonstrably depends only on their masses, but not on the Earth or its relative velocity to anything else.