Markus Hanke

I think it suffers from the same problem as the opposing claim - you cannot ever disprove the existence of a designer. The best we can do is show that the laws and processes of physics as we see them arise without need for outside intervention - but at the moment we can’t really do that yet. But even if we can do this, the mere absence of such a need still does not necessarily rule out a designer - it could have been designed even though there wasn’t a need for a designer. So I think looking for evidence for either claim is ultimately a waste of time, unless the alleged designer chooses to reveal himself in indisputable and unambiguous ways.

The actual definition of a geodesic is a curve that parallel-transports its own tangent vector. This requires a connection, but not necessarily a metric - IOW, a manifold that is endowed with a connection but not a metric, will exhibit a geodesic structure. Of course, if you have both a connection and a metric (as is the case in GR), then the geodesic equation can be written in terms of derivatives of the metric tensor. But that is not its fundamental definition. I don’t know what you mean by this. A metric is a structure on a manifold that has a very precise definition, which has to do with fiber bundles and tangent spaces, but not with any particular coordinate choices. What, exactly, do you want to replace here? The Einstein equations are a covariant tensor equation, so its form is the same irrespective of what geometry the manifold has. That’s the entire point of general covariance. IOW, you are quite free to use a different concept of time (coordinate basis) to describe your scenarios, but that doesn’t change the laws of physics, and thus all tensor equations remain unaffected. In that case you will obtain incorrect predictions for the polarisation states of gravitational waves, which cannot be modelled by any rank-1 model. You need at least a rank-2 model to correctly account for all relevant degrees of freedom, so gravity cannot be a force in the Newtonian sense. It’s not absolute, it’s just a convenient choice of coordinate basis that makes certain astrophysical calculations easier. You are always free to choose your coordinates and units as is convenient - that doesn’t change anything about the laws of physics, in particular not their form when written as tensor equations.

No, it’s a religious belief you have chosen to adopt. As I have shown you, patterns can arise independently of any intentional creator, so this is not evidence for your claim.

Actually, I’m hoping that there might be some convincing reason to once and for all rule out superdeterminism (I don’t like the idea) - but I can’t find any, and a number of quite esteemed physicists seem to pursue this line of research.

A pattern is not evidence of intent. Consider the action of wind blowing across sand (beach, desert etc) - the motion of individual grains of sand is chaotic and cannot be predicted past the characteristic Lyapunov time of that system, yet after a while a well-ordered wave pattern emerges on large scales from the chaotic motion of many billion grains of sand. No intentional creator is required for this. And that’s just one random example.

I’m not trying to convince you, since I myself am not convinced that superdeterminism is a viable way to go. I’m saying only that it shouldn’t be readily dismissed, since it does reproduce the same results as ordinary QM. I’ll have to do more study myself regarding the precise details, though.

No he wouldn’t. The distance from horizon to horizon would explicitly depend on where it is measured, when it is measured, and also how it is measured (since the horizons are not spherical). The spacetime in between these black holes is not stationery and admits very few spatial symmetries, so figuring out what any one observer would measure here is highly non-trivial. But he certainly wouldn’t see any perfectly circular orbits. You cannot use Newtonian forces to describe or visualise this, since the radiation field here couples to a rank-2 tensor as its source. This really does require the full machinery of GR.

How do you know this? The metric in close proximity to a BH merger is complicated enough so that it cannot be written in closed analytical form - it can only be modelled numerically. Given that such a spacetime would admit at most one spatial Killing field (and even that only approximately), and is not stationary, I think it is highly unlikely that any observer there would measure a perfectly circular orbit for the black holes. Maybe it is possible to find some coordinate system where this might be approximately the case over a short span of time only, but even that I’m not convinced of.

Two black holes in close proximity cannot be of the Schwarzschild kind - so their event horizons would be nowhere near spherical. Also for a single Schwarzschild BH, no stable orbits exist at the horizon.

For a BH merger, there is only one wave field, not two, so I’m not sure what you mean by ‘phase difference’. Also, gravitational waves and the energy-momentum they ‘carry’ do not add linearly (GR isn’t a linear theory), so the argument wouldn’t hold anyway.

I would disagree with this, since - as mentioned - several “toy models” exist that do just precisely this. Genady has mentioned ‘t Hooft, and another example is the model by Donadi/Hossenfelder: https://arxiv.org/abs/2010.01327 I think the key here is the distinction between correlation and causation - the necessary correlations exist from the beginning, but the measurement outcome is still caused purely locally by the detector settings only, just like in ordinary entanglement. The very fact that such models can be written self-consistently while demonstrably reproducing all predictions of standard QM makes it difficult to outright dismiss the concept as nonsense. Experimentally, superdeterminism would show up as small deviations from Born’s rule under specific circumstances, so it might be possible to experimentally distinguish it from QM.

The thing here is that no experimenter has the freedom to choose the parameters of his experiments - in some sense, all experiments and their outcomes are preordained from the very beginning, so it isn’t possible for these constituents you mentioned to not be exactly correlated in the right way. One might say that it is the correlation that reveals the experiment, not the other way around. There is no freedom of choice in superdeterminism. Unfortunately I do not understand all of it, since this is not an area of physics I have reliable expertise in. So I’m not in a good position to evaluate its scientific merit. It should be mentioned though that this isn’t the only such proposal - there are several superdeterminism candidate models in existence, all of which are consistent with QM and the known Bell experiments. Personally I dislike the idea greatly; it even scares me a little, since a superdeterministic universe would be one in which no one possesses any degree of free agency. But I struggle to find a decisive argument against it, since the maths appear to be consistent, and I must acknowledge that it would eliminate some difficult issues, not least of which the measurement problem.

I wouldn’t look at it this way. What it means is that there are in fact correlations between observer and system that are not accounted for in standard QM, which fundamentally assumes statistical independence. I don’t like this idea much either, but the fact of the matter is that the universe started off very small and very dense, and has a finite age - so the concept perhaps isn’t so absurd after all. But of course, this would have serious implications for the philosophy of science, since one could no longer cleanly separate an experimenter from his experiment. How much could we reliably know about a universe where this is the case? Here’s a very recent and quite interesting paper on this - see under ‘conclusions’ at the end for a quick summary. https://arxiv.org/pdf/2308.11262.pdf

Bell’s inequality can fail to hold in another way, too - namely, by virtue of one of its underlying assumptions to be false. In particular, it assumes statistical independence of observer and system, meaning the experimenter actually has completely free choice in how he sets up his experiments. If this is violated, you get some version of superdeterminism, which can preserve local realism even if Bell’s inequalities don’t hold. I personally don’t like this idea, but the more you think about it, the less easy it becomes to dismiss it outright, especially since it also provides a solution to the measurement problem.

The MTW method has one limitation though - it assumes that all dimensions are of equal size. If that’s not the case, then the result obtained by this procedure may become scale-dependent. We all know about compactified dimensions (ref String Theory). I’m wondering though - is the opposite possible? What I mean is - could one configure a spacetime manifold such that one of its dimensions becomes detectable only at large scales, but is hidden at smaller scales? I can’t think of a way to do that, but would like to hear others’ opinions on this.

I don’t quite understand what you mean here - vectors, forms and scalars are themselves just tensors, so all of these objects are already on equal footing from the beginning. The slots (indices) simply tell you what mappings are possible, and what the rank of the resulting tensor will be.

I’m with MTW - I look at it as a map that maps vectors and forms into real numbers (or other maps).

Another way to look at this is that in curved spacetimes (of which FLRW is a specific example), energy-momentum is not - in general - a globally conserved quantity, even though it remains conserved everywhere locally. Thus it is not surprising that light does not retain its original frequency when traversing large regions of non-flat spacetime. I personally think this is a better way to view this, since, after all, these galaxies remain in free fall and do not undergo proper acceleration at any time, despite the velocity-distance correlation.

There’s also the matter of the star’s shape to consider - in the frame of the particle, the star isn’t spherical, but a flattened disc along the direction u. Thus both the time and the space parts of the gradient must be considered, and treated in the same way (for covariance) - therefore (2.37) is indeed reasonable so far as its general form is concerned.

I would have answered the same. Does anyone see a reason why this would be incorrect?

Are we not perhaps overthinking this a little? After all, the quote given is from MTW, which is a book about spacetime. My feeling is that what the authors had in mind was a physical space, as well as physical procedures to determine its dimensionality. The more abstract notions mentioned here are all good and well in pure maths, but they don’t necessarily relate to GR.

Very nicely put +1

I’m sorry, maybe I’m being a bit thick here, but I’m still not 100% sure what ‘structure’ were are talking about exactly. The definition says it locally resembles a Euclidean space - so can we assume the presence of a connection and a metric, or just a connection, or neither?

On manifolds with curvature, covariant derivatives do not, in general, commute; thus, again in general, they wouldn’t end up at the same place. But answering this question requires that your manifold is endowed with a connection.

Yes, it would appear so…but I’ll defer to what the real mathematicians here have to say on this.