Markus Hanke

As a silent reader not actively involved in this thread, allow me to offer an observation. Your initial post had one or two points in it that are relevant and worthwhile, but unfortunately your tone and general presence here comes across as arrogant and condescending, You made at least one good point (and some not so good ones), but you failed to communicate them in a proper manner. Please take this as constructive criticism, i.e. an opportunity for growth.

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, linear momentum is the conserved quantity that arises from spatial translation invariance via Noether’s theorem.

SR is far more general than just a relationship between inertial frames; it describes how events are related in regions of spacetime where gravity can be neglected. As such, it applies to any type of reference frame, not just inertial ones - it’s just that the relationship between inertial frames takes on a particularly simple form (Lorentz transformations), since the world lines of such local frames represent the longest possible separation between given events. Of course it also works with accelerated frames, but naturally the relationship between such frames has a more complicated form than a simple Lorentz transformation (i.e. such frames are in general not symmetric). To “derive” SR, all you need to know is that the metric of spacetime is diag{-,+,+,+} or diag{+,-,-,-}.

I am unsure what you mean by “amount of movement” - you would have to provide an exact mathematical definition of this term. In general though, you can obtain the equations of motion for a system from its action by plugging the action into the Euler-Lagrange equations. Solving the equations of motion then gives you the “movement” of the system, in the sense of some quantity changing with respect to some other quantity. This general approach is often used for field theories of various kinds. To answer your original question - no, the relationship between action and “motion” is somewhat more complicated than a simple gradient.

Yes, dimensional reduction on small scales is a distinct concept. I don’t know what - if any - observable consequences would arise from such a small scale structure, on macroscopic scales. Note that dimensional reduction is not what the OP suggests here, though.

Macroscopic spacetime being (2+2)-dimensional can be ruled out on a number of observational grounds (over and above the obvious fact that there are evidently three spatial dimensions that we can observe). To give just one example - in such a spacetime, electrons would not be stable particles, and would decay rather quickly. This is evidently not what we observe.

Of course it does not physically exist - it‘s just a mathematical artefact of the fact that GR is a purely classical model, and hence cannot account for quantum effects.

We already have such a framework: quantum field theory.

Yes, it is invariant under rotation about some real-valued angle (i.e. under a U(1) symmetry); the corresponding conserved current in Noether‘s theorem is called the probability current.

The angular momentum of a black hole is a property of the entire spacetime, and not of the singularity (which only arises in our models in the first place because we can‘t yet account for quantum effects). Furthermore, while spin can be considered a form of angular momentum, it is quite different from the one of macroscopic bodies.

A geometric relationship between reference frames in spacetime. In the simplest case of inertial motion, two reference frames being in relative motion quite simply means that they are rotated by a (hyperbolic) angle wrt each other in spacetime. Motion is purely a geometric phenomenon.

The gravitational field in the interior of a mass distribution such as a galaxy is not equivalent to the sum of gravitational interactions between discrete point masses arranged in a disk pattern. Also, I am pretty sure that General Relativistic effects cannot be neglected in this scenario, so Newtonian gravity is not the right theory to use. The model’s basic assumptions are fatally flawed, which is why no one in the scientific community is using it.

It’s battery operated (as I suspected), so the green light indicates that the battery is fully charged.

Distinction between what?

Yes, the magnitude and precise direction of the frame dragging effect does depend on the mass and the total amount of angular momentum of the central mass. It also depends on the exact shape of the central body, since rotating bodies are not perfectly spherical.

No. Causation does not imply intention. But then, it also does not preclude intention either - the question of whether or not there is a creator deity is outside the domain of the natural sciences. It is seldom a good idea to try and conflate fundamentally different domains of enquiry.

充饱 is usually used in the context of a battery being fully charged. So I guess this means that, when the green light comes on, the charging process is complete.

You will find all relevant answers in this excellent resource: http://stopmasturbationnow.org/

What SR says is that all observers agree on the separation between events in Minkowski spacetime. That physically means that all inertial observers experience the same laws of physics, which implies that such observers must be related via Lorentz transformations, and hence that measurements of space and time are observer-dependent, and not absolute. There is no absolute “past”, “future”, or “present” - there are only light cones associated with events, and their relative orientation in spacetime. This makes a concept such as “time travel” pretty much meaningless in this context.

The laws of the universe are found in statistical correlations between measurement outcomes. We perform experiments, measurements, and observations on aspects of the world around us - for example, we might measure the electrostatic force some distance from an electrical charge, and then do the same again at some other distance from the same charge, and so on. Given enough data points, a statistical pattern emerges, and that pattern is exactly the physical law that governs electrostatic forces for this particular setup. You repeat the same for more general setups, und you get more general laws. So the laws of the universe reside precisely in patterns that emerge from our observation of it.

The only way to “know” something is to go and experience it yourself. And even then you get only a subjective experience, filtered by your senses, and the way the mind processes information. So in that sense, there is only ever opinions and views. Since direct experience of something is not always possible, one can use logic to infer things. For example, I have not myself experienced the Second World War, but based on a various physical and non-physical traces it has left behind in the human world, many of which are accessible to me, I can infer with reasonable confidence that such an event has in fact happened. I still don’t “know” that it has happened, but the likelihood of it being just an illusion based on false inferences is negligibly small. The same is true in the sciences.

Actually, no. Being able to label the structure in the room as “table” relies on a lot of supporting conditions, some of which are very much subjective. For example, a member of some indigenous rainforest tribe who has never before seen a table, and does not even understand the concept of “table”, or has a word for table in his/her language (having no use for such a thing in his/her native environment), will not see a “table”. He/she sees only pieces of wood arranged in a certain fashion. Unlike you yourself, who sees a “table”. So clearly, a “table” being a “table” is not an objective fact, but a subjective perception, which is dependent upon prior knowledge and experience of the observer; if you’ve never before seen a table, you won’t recognise one as such. An objective description of the world would be one that is completely independent of the physical and mental structure of the observer who perceives that world. That is a very non-trivial undertaking, and arguably not really achievable in its purest form. This may seem like nitpicking, but actually has pivotal consequences.