Markus Hanke

Exactly +1 And in reverse, there are also issues being portrayed as moral choices that in reality have little to nothing to do with morality, eg drug addiction. Also, the title of this thread has it exactly backwards - it is awareness of these issues that ensures society can continue to improve and thus remain stable, rather than such awareness being a destructive influence. Historically, many of the great empires (eg the Romans, the Ottomans, the USSR,…) failed and collapsed precisely because they didn’t address their issues of inequality and moral inconsistency. History provides us with all the necessary data points.

The Friedmann equation is just the 00-component of the Einstein equations for the case of FLRW spacetime with a perfect fluid taken as the source term; essentially it gives a relationship between expansion rate and its second derivative, which needs to be fulfilled in order for the model to be consistent with the laws of gravity. Thus, it describes what form the scale factor a(t) can have. Or to put it differently - this equation states that spacetime in the interior of an isotropic, homogenous perfect fluid has an intrinsic tendency to metrically expand, unless counterbalanced by just the right kind and amount of background curvature. This is a direct consequence of the laws of gravity, and not some idea that got inserted into the model post-hoc. Here is a good non-technical overview over where the Friedmann equations come from.

If you consider it “fun” to mock minorities within your society and events in history that caused a lot of suffering, then you are clearly lacking an appropriate moral compass. The point of this whole movement is fundamentally to raise awareness of those social dynamics that perpetuate suffering and inequality, thereby hopefully working towards a more fair, just and equitable society. This is an important and necessary self-correcting function within all civilised and developed communities, and the sad part is that this needed to take on the form of an “-ism” at all in the US. Any society that does not have this function will over time fracture, divide, degrade, and arguably fail as a last consequence. Unfortunately all “-isms” have the potential to also be misused and/or pushed too far on occasion, so it isn’t ideal that it had to take this form; but honestly, I think you’ve got only yourselves to blame for that. Just my own personal opinion as an uninvolved outside observer.

Note that such photon orbits would be unstable, ie any small perturbation would lead to the photon to either in-spiral, or escape to infinity. This is because these orbits are on a local maximum of the effective potential function for the photon. This is true for all four basic BH types. Whether it is possible to construct a more complicated spacetime in which stable photon orbits can exist, is an interesting question; I don’t immediately know the answer to that.

But this is entirely irrelevant to Dark Matter. The mathematical relationship we are talking about here (Tully-Fisher relation and Faber-Jackson relation) are statistical statements; they relate the average rotational velocity of a large collection of stars in a galaxy to their total combined mass. Notions of simultaneity for an arbitrary observer as to the position of a single star at any given time never come into this at all, so this entire discussion is pretty much mood. The other thing of course is that DM is needed for a lot more than just galaxies’ rotation curves; you cannot just ignore all the other evidence we have for its existence when discussing this subject.

Maybe place a tethered buoy into the zone where the waves break? You could then just use an ordinary theodolite to determine how high the buoy is lifted by each breaking wave above standard sea level. Or even simpler, just place a precision GPS device on the buoy to read its height.

In fairness, it has given us some very useful insights and techniques (think eg AdS/CFT), even if it hasn’t been successful in its original goal as a TOE. So I wouldn’t say the resources were wasted. It also is still possible that an actual viable model can emerge from it, though personally I don’t think so. String Theory had its heyday back in the 90s and early 00s, but nowadays it seems to me that fewer and fewer people are seriously working on it full time; it has fallen somewhat out of favour. I think unless some unexpected breakthrough happens, it will just fizzle out over time.

String Theory is perhaps best understood as a framework, rather than a specific model, in the same way as in quantum field theory. Whether it is in fact possible to formulate a model within that framework that corresponds at all to the particle zoo we see in our real universe is still an open question, because no one has been able to do that so far.

Well, one of these issues would be that the energy-momentum tensor, being the source term in the Einstein equations, cannot be promoted (to the best of my knowledge) to a Hermitian operator in the QM sense.

Just for the record though - there are things in GR where the concept of commutativity is meaningful and useful. An obvious example would be the directional covariant derivative, which doesn’t commute - this is precisely how Riemann curvature is defined in the context of GR.

I don’t understand this comment - in GR, these things aren’t operators (or even observables in the QM sense), so it isn’t clear to me what you even mean by “non-commuting” in this context. We just have a differentiable manifold with four locally linearly independent basis vectors, plus a connection and a metric; there’s nothing in this basic structure really that is meaningfully relatable via Fourier transforms. Even in quantum mechanics, specifically for your last example, the correct pairing would be time and energy. Time and position do commute, with the caveat that treating time as an operator comes with its own complications in QM. I think it’s also important to remember that GR is from the ground up designed to be a purely classical theory, and classicality precisely implies that there are no non-commuting observables.

But this is functionally identical to the ordinary field equations with cosmological constant, thus \(E_{\mu \nu}=\lambda g_{\mu \nu}\). There is nothing new here. This is not a valid tensor equation, and thus quite meaningless. The other thing of course is that we know from experiment and observation that the motion of free-fall particles outside local masses (eg Earth) is very well described by vacuum solutions to the ordinary Einstein equations without cosmological constant. This puts very stringent limits on whatever modification to the field equations you propose. PS. The forum software here supports LaTeX, I’d suggest you use it instead of embedded pictures.

Indeed. Which brings up another issue, in that it is actually very difficult to extract specific predictions from this model, since it lacks much of the symmetry of FLRW (and is thus not analytically solvable), so you’re stuck with numerical simulations that are computationally complex, and rely on precise knowledge of the exact distribution of matter and radiation in the cosmos.

Of course not. But why would you want to do such a thing?

Indeed. We should also remember that the finding referenced in the OP regarding the ‘timescape’ model only fits the 1a supernova data to a confidence level of 3 sigma, which is below the necessary threshold. But yes, I do think it’s worth further study.

I also agree that these are interesting proposals. However, the devil is in the details, because it seems these models need to make a number of their own assumptions to actually work, and it also seems that it is not at all clear that they actually really do produce the correct effective dynamics. Here are some more technical details about inhomogenous cosmologies in general: https://ncatlab.org/nlab/show/inhomogeneous+cosmology Maybe it can work, but I just think this requires more study before jumping to any conclusions.

Tbh, this doesn’t sound like something Einstein would have said. Well, a ‘manifold’ is fundamentally a mathematical model that’s intended to represent certain elements of reality, so no you can’t ‘observe’ it as such. But you have to remember that whatever observations you do make in the real world always involve time, no matter how short - so in that sense it is in fact impossible to perceive reality in anything less than (3+1)D, because any measurement of something that is spatially extended inevitably requires time as well.

Actually yes, they do. The spacetime distance between two events - which is the geometric length of a world line connecting these events - is precisely the total amount of time physically accumulated on a clock carried by an observer tracing out this world line. You can directly measure and observe this, without needing any fancy equipment or calculations. All you need is a simple clock. The entire concept of spacetime is set up such that it connects to physically measurable and observable reality in this neat and direct way. That is what makes it so useful as a model.

The geodesic structure of any particular spacetime (thereby also expansion) follows from the connection and the metric, both of which are tensorial quantities - and thus these are not observer-dependent.

This is a particular example of a class of inhomogenous cosmological models. While interesting in principle, there are several fundamental issues with such models, which are important to note here. In particular, to actually make the model fit observational data, one has to make several assumptions, among them that the universe has globally non-zero spatial curvature; that we are located near the center of a low-density region; and that a particular choice of gauge is made in the model. It is also not at all clear that the model actually does produce the correct behaviour, since it isn’t analytically solvable, and numerical simulations have proven challenging. Here is a more thorough overview.

My understanding of this is that in order to measure the graphing distance, you have to first foliate the hypergraph into slices of simultaneity, which is to say you need to have a convention to decide in which sequence the nodes and edges get updated, since in general there’s more than one possibility. Different observes will do this in different ways since they belong to different subgraphs, which is essentially just your ordinary relativity of simultaneity. The graphing distance is then measured within one slice of that foliation only, since we wish to consider spatial length contraction. Thus, even if all observers are part of the same hypergraph, they can still obtain different graphing distances between the same nodes, because they count nodes along different paths within the graph. The graph’s symmetry of causal invariance ensures that the causal structure is always the same, regardless of which sequence the graph gets updated in. That’s how I understand it anyway. Wolfram’s own explanation of this is found here.

All observers are themselves a part of the hypergraph, so I don’t think this question is very meaningful. I think the better question to pose is whether SR and GR follow from this framework (ie can you recover the spacetime interval from the hypergraph), and the answer is apparently yes - with the caveat that I haven’t studied the technical details of this, so I don’t know how watertight Wolfram’s derivation actually is. I should perhaps explicitly state that it isn’t my intention to make any claims as to the viability of this framework - it might well turn out to go nowhere. I merely think it’s a very interesting approach that is worth pursuing further.

The idea is that space is discretised, ie a geometric volume would consist of a finite number of points (which increases with time), each of which corresponds to a node in the hypergraph. By measuring graph distance, you’d thereby have a measure of how a volume relates to an emerging space’s dimensionality. There’s apparently also a mechanism which ensures that the number of dimensions in the emerging spacetime remains stable after a certain point, but I haven’t fully wrapped my head around the details of that yet.

Yes, that’s the big question. The thing with this model is that the underlying discretisation of spacetime has potentially got consequences on larger scales, which can at least be estimated, eg here: https://arxiv.org/abs/2402.02331 So essentially, accretion disks of some black holes would be more luminous than expected from ordinary physics alone. The precise values will depend on the underlying model, which of course hasn’t been finalised. But the point is that yes, these models make specific predictions that can at least in principle be falsified.

I’m wondering if anyone here has followed the Wolfram Physics Project? If so, what are your thoughts on it? The text in the link is a long-ish read, but well worth it. When I first heard of this I didn’t think much of it, but I must admit that the idea has really been growing on me. It’s a fascinating approach to a TOE (if one can call it that), and those of you who have known me for a while will notice that it contains many of the elements I have been advocating for some time now, such as chaos/complexity, graph theory etc. And some of the preliminary results are tantalising. I know this thing isn’t so popular in most of the physics world, but I’m curious to hear what others here think.