Markus Hanke

You’re still not getting this - the point I was making was that the structures you are using already presuppose and require some combination of the things you have initially rejected as unnecessary, and I have highlighted some specific examples. Others here have attempted to point out the same. What you do with these criticisms we offered is up to yourself, it’s your hypothesis after all.

Exactly, and herein lies the issue - you explicitly said you weren’t going to use any coordinate systems, yet you talk about areal radius measured in meters. To meaningfully define the notion of “distance” between points, you need a metric space structure; the same is true for angles, and thus orthogonality. My question about gradients you haven’t answered at all; in short, you need a notion of derivatives to define the gradient, and, if the basis is not orthonormal, you explicitly need a metric as well. The point of all this isn’t numbers, but to show that you are tacitly using the very notions you are rejecting; that is why I asked about that scenario. You are literally going in circles, pun intended - and I note explicitly that the very notion of “circle” is meaningful only if you already have a metric space. Just throwing around the word “relational” doesn’t change these facts.

What is an “areal radius”? Since it is in units of meters, it sounds suspiciously like a distance (length) to me. What is an “algebraic output of a field measurement”? And how do you mathematically define the gradient of a scalar field without recourse to any derivatives? How do you even have a scalar field if there’s no manifold for it to live on? A field on what, exactly? What is “intrinsic orthogonality”? How do you tell if two directions (vectors) are orthogonal, in the absence of an inner product? What does “source of geometry” mean?

Thanks, but unfortunately that quote thingy never appears for me at all, not even for a single dead-Center word selection :/

I’m sorry, but this is utter nonsense. You said you aren’t going to use coordinates or metrics, but then you talk about radial and tangential directions, lengths and orthogonality, gradients, areas, components, conserved quantities, Killing vectors…none of which can meaningfully exist without a spacetime manifold endowed with a connection and a metric. Some of these things are also observer-dependent, which you’re not taking into consideration at all. Furthermore, nowhere do you actually take into consideration the nature and strength of the energy-momentum distribution; there’s only talk of some nebulous scalar, defined via a Schwarzschild radius, though this is most certainly not a Schwarzschild situation. if this were an EM field, where do you encode the specifics of the field? In reality the EM field cannot be represented by a single scalar. Also, real-world gravity isn’t linear, but nowhere do you account for that non-linearity - the overall gravity of this situation is not simply the sum of all gravitating sources. If I were to model this situation in standard GR, the result for the trajectory of the test particle is very different - not surprisingly, because it accounts for all relevant relativistic effects. It seems obvious to me that all you’re doing is to pull random stuff out of some LLM-AI. So I agree with the other posters on this thread that there’s not much of value here. My honest opinion.

I know, and I’m not at all blaming the mods here - I think you’re all doing a fantastic job :) It’s just a sign of the times I guess. Sure I will, I’ve no intention of disappearing, it’s just that I find it frustrating that everyone is suddenly the new Einstein, just because whatever LLM they’re using is designed to not outright tell them that their ideas are nonsensical. Science cranks have always been around, but since LLMs came along the issue has taken on a different quality - it often looks like they know what they are talking about, while in fact they don’t understand much of the subject matter, because they’ve never taken the time to study it in-depth. It’s just harder and more frustrating to debunk, because these LLMs are good at talking people into having the perception that they’re onto something, with superficially plausible-looking maths and all, even if they’re not. At least in the old days, the maths weren’t quite as easy to come by, you needed to actually make a real effort to develop it - nowadays, Lagrangians and tensor equations are a dime a dozen, even if they’re meaningless.

Unfortunately neither of these suggestions work for me - I’ve tried on Safari, Opera, Chrome and Firefox, scrolled and reloaded, but the partial quote button never appears. I haven’t actively posted here in a while (the flood of AI-generated posts/answers we’ve been seeing have spoiled the fun for me), but last time I did, this still worked fine :/

Does anyone have problems with the quote function? I can quote an entire post using the button underneath, but when I select just a snippet out of the post, I no longer get the option of just quoting that snippet…?

Suppose there’s a region filled with some form of energy-momentum distribution, perhaps a radiation field, not necessarily assumed to be uniform, plus some extended body with given mass located at a given point within that region. Suppose further a test particle enters this region, at some given point and instant, with some given initial velocity vector. Assume further that the test particle moves under the influence of gravity only. Can you show us exactly how you calculate the trajectory of this test particle? Does it hit the body, or not? Remember you cannot use any concept of coordinates, you don’t have a field equation, you don’t have a metric, you don’t have a concept of geodesics, nor do you have access to tensors or any other type of covariant object. I’m interested to see how you encode the gravitational sources, and how you find the trajectory of the particle, as test whether or not it hits the solid body.

PS. One more thing to consider is that for an outside stationary observer lowering a rope, its loose end would never appear to reach the horizon, even if he lets go and allows it to free-fall. The loose end would just appear to move downwards more and more slowly, while getting dimmer and dimmer, until it eventually fades out. Actually hitting the horizon would take infinitely long on his own clock. For a clock moving downwards alongside the rope, on the other hand, the (freely falling) rope would cross the horizon in finite time. So nothing about this seemingly simple scenario is quite straightforward.

The crossing of the horizon would happen in a tiny fraction of a second, orders of magnitude shorter than even the electrochemical signals in your nerves could propagate. So no, you wouldn’t notice anything special. Below the horizon there are no stationary frames, so if you lower a rope through it, it would simply break. In practice it would in fact break quite a bit before it even reaches the horizon, since at the horizon itself only massless particles could remain (at least in principle) radially stationary under the right conditions, though this would not be an equilibrium. So no, you can’t pull it back out. What you pull back towards you will be the broken, shortened end that hadn’t crossed the horizon yet. Actually, your head and legs won’t share a common notion of simultaneity in this situation, so it’s rather more complicated than you think. What’s more, for your head the horizon is below, whereas for your legs the horizon is in the past.

You’re right, the two are not necessarily the same - you can eg have “false vacuums”. So long as you assume that the laws of nature also apply to a “perfect void” of the type you describe, then yes, the void must have these properties.

Of the top of my head, so probably not an exhaustive list, and assuming you mean actual physical space: Topology, ie properties such as dimensionality, connectedness, orientability etc Geometry. Pick any set of points in your space, and there will be well-defined notions of distances, angles, volumes etc. IOW, a metric. Note that the absence of gravitational sources does not necessarily imply that this geometry is trivial. Permittivity and permeability, ie an ability to support EM fields, as well as a particular value of c. Yes. In an empty universe all quantum fields are in their ground (vacuum) state, and that state may be associated with non-zero vacuum energy. Could one conceive of a universe that does not contain any quantum fields? I don’t know. Possibly.

They could show themselves.

I think euthanising a living being for no good reason other than that is “unwanted” is ethically problematic. If you can’t or don’t want to keep your pet any longer, there are more appropriate options available. Also, keeping animals locked up in zoos just so we can gawk at them, is likewise ethically questionable.

Thanks for the recommendation! I haven’t heard of this story, but I do like Clarke in general, so I’ll try to find it somehow :)

Yes, and I still do. Well, what is “it” that you think is “going” someplace? I don’t know, it’s not something I’ve thought about much (and I haven’t been following developments in AI too closely) - but this is a good question. In my tradition, and at this point, it plays no role at all, and probably never will; but it may be different in other religions.

I’m not yet that old, but yes, I’ve found my way in life. That didn’t happen over night though, and took some doing.

It’s generally unwise to disclose too much personal information on social media, so I can’t comment on these.

Yes, I live in a small forest monastery together with some other monastics.

Because I’m an ordained monastic, and in our contemplative tradition we (the individual monks and nuns) live entirely without owning or handling money. Thus, accessing things that aren’t free is complicated for me.

I have not been following developments in this area, so I’m wondering, what AI’s that are specifically designed for symbolic maths (other than Wolfram Alpha) are freely available (ie no payments) out there?

This is not a valid tensor equation.

Because it’s pretty much standard textbook material, and thus already well known. There’s simply not a lot to discuss here.

You can’t start with “photons” and “collapse” processes at all, since these are meaningless concepts in the absence of an already well defined spacetime. As I said, you’d need to start with something that does not itself require any notions of space or time, so particles or any kind of “process” are out of the question.