Markus Hanke

Yes, that’s a very good point too +1

That’s because the human psyche is still the same; we are still subject to and affected by the scourges of greed, hatred and delusion to varying degrees. Our technology and culture has evolved, but not our minds, so no matter what political system we put in place, the same human tendencies will continue to crop up, and thus things like fundamentalism, extreme nationalism etc etc will continue to manifest themselves when the conditions are conducive.

Yes, China indeed has its own serious systemic issues too, I didn’t mean to imply anything different. But still I see it becoming a much more influential global player in the near future. Btw, the surveillance state has always been there in China, it’s just that this has become a lot easier now in the digital age. I love Canada, especially the Western states, have been there several times. But for now I’m quite happy in the Nordic countries

Indeed. As someone who grew up in the former Eastern Bloc, and whose family fled to the West as political refugees in the early 80’s, the US used to be something we looked up to and admired, a beacon of hope somewhere beyond the bleak grey concrete of communist suburban plattenbau (literally and figuratively). Needless to say these illusions have been thoroughly destroyed over the past 30+ years, and what I see now in the US just fills me with sadness and a sense of despair. Are we soon going to see people fleeing the US, like we once fled from the East? Oh how the tables have turned. I anticipate the rest of the world turning more towards the Asian powers in the near future, particularly China, mark my words. Time to dust off my rather rusty Mandarin (it’s been 25 years since I lived in China), me thinks.

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.