Markus Hanke

ADM energy is just one of many different concepts of energy you find in GR; it applies only to some very specific types of spacetime, but can be quite useful in those cases, since it is relatively straightforward to calculate. What issue specifically do you see with this? Foliating a region of spacetime into space-like hyperslices is not the same as postulating an “absolute time” axis, because there are infinitely many possible foliations. In practical terms, you can label the slices in whichever way is suitable for the given problem at hand, there is no physically preferred foliation scheme, so there is no issue with the principle of relativity. The overall model retains full diffeomorphism invariance. Just to make this clear, the ADM formalism is just a different mathematical formalism of the same theory of GR - it has all the same symmetries, makes the same predictions, and has the same physical content. It’s simply a straightforward application of the Hamiltonian framework (a commonly used a very useful tool) to GR; so you just use a different set of dynamic variables to describe the exact same thing. It is particularly useful, and routinely used, in numerical GR. P.S. If you are interested in the precise details of how this works, then Misner/Thorne/Wheeler “Gravitation” devotes an entire chapter to this formalism. Well worth a read.

I am not familiar with that particular work, so I can’t comment on it. But as for the ADM formalism itself - yes, it works fine, it’s just a different way to formulate the same model (GR).

It wouldn’t be spacetime, because there would be no concept of distance in space or separation in time. I haven’t read Eddington, but I agree with this quote. This is what I meant when I said that a collection of events without any additional structure could not manifest as spacetime in the way we experience it. So in that sense, relationships between events are more fundamental (in terms of physics) than the events themselves. Actually, it is possible to describe spacetime as an ordered set (called a foliation) of spacelike hyperslices, where t=const for each slice. The result is somewhat like the pages in a book - each page represents a snapshot of 3D space, and is labelled by a number, which plays the role of time. There is a well defined sequence of page numbers, corresponding to the arrow of time. Or you could think of it as the frames in a movie. This is called the ADM formalism, and allows you to write GR in terms of Hamiltonian dynamics. Both the (non-constant) separation between hyperslices, as well as the spatial geometry of the slices themselves, make up the curvature of spacetime. The ADM formalism is very useful in numerical GR, as well as in the mathematics of some models of quantum gravity.

It seems evident that if you had just a collection of events, without any causal relationships between them, then there would be no concept of 'spacetime' at all. So in that sense I agree, it is that interwoven network of relationships that turns a collection of events into a physically useful spacetime manifold. In practical and classical terms, you can put neighbouring events infinitesimally close together, and mathematically represent their relationships by endowing the manifold with a suitable connection and metric - which is pretty much what GR as a model does. I emphasise again that this is a useful mathematical model, a map of the terrain so to speak, not a physical something to be found 'out there'. It's really important to understand this.

Greetings everyone, I am back 😎 So what is space made of? I think we need to first upgrade the question a bit and ask: what is spacetime made of? The answer to this is that it is a collection of events, to be understood in the sense in which the term is used in physics. To be even more exact, it is made of causal networks of events, i.e. events plus information about how those events are causally related. In terms of GR this is described as a manifold with its intrinsic geometry. Space on its own would then be just the spatial part of that network. So essentially, spacetime is a way to structure and organise information. Looking at it this way opens up some interesting questions, not all of which fall under the remit of physics: exactly what kind of information underlies this concept? Can this same set of information be structured/modelled in other ways as well? Is this structure intrinsic to the information, or is it something we impose more or less arbitrarily? Etc. P.S. It is important to remember that spacetime isn’t a physical “thing”, rather, it’s a mathematical model that captures certain aspects of the universe. It’s like a map we draw of a given territory.

No such theory is possible, because EM dynamics are linear, whereas gravitation is not. They are fundamentally of a different nature. It depends what you mean by “chaos”. GR Gravity is completely deterministic, since it is a purely classical theory, but it is not always indefinitely predictable. Since gravity is highly non-linear, under certain circumstances you get chaotic systems - here “chaotic” is used in the sense that the evolution of such systems is highly sensitive to initial conditions. Even tiny perturbations of the initial conditions can have large consequences in long-term evolution of the system. This is a well known phenomenon, which is found in many other areas of physics as well. I don’t understand what you mean by this...? No instantaneous actions at a distance can occur in nature. You can only have non-local correlations, which is a different thing, because that does not allow for the exchange of information. Electromagnetism is completely local, there are no non-local interactions.

He was unsuccessful because gravity is not an electromagnetic phenomenon. His approach was basically upside down. This is not entirely true. It is in fact possible to combine GR and EM into a single, overarching model, called Kaluza-Klein gravity. The problem with this is that it can’t be done in 4 dimensions, and also that it requires extra fields for which there is no evidence in the real world.

In post #7, under the metric tensor paragraph, it should read [math]g_{\mu \nu}[/math], and not [math]G_{\mu \nu}[/math], to avoid confusion with the Einstein tensor. Just a small thing though