Recent content by pervect

The organizational structure in MTW actually illustrates why there are 20 degrees of freedom and 21 unique (up to sign) nonzero components in the Riemann. MTW start with the Riemann ##R^{\hat{a}\hat{b}}_{\hat{c}\hat{d}}## as per MTW's exercise $14.14, Note that this is presumed to be in an...

I was doing some more reading, and apparently the "modern" approach to the topic involves decomposing the Weyl tensor rather than the Riemann tensor. The process I was refering too, which I described colorfully as requiring "the flow of time of an observer" is more formally called the "3+1...

It seems to me you are asking, at least in in part, about the self-force problem. "How does a particle, the thing that you are calling a constituent of your larger body, move taking into account the field it itself generates". This is a simple question to which AFAIK we don't have a...

There is a way to break down, or decompose, the curvature tensor in General relativity (called the Riemann tensor) into parts, which can be loosely interpreted as an "electric part", a "magnetic part", and a "topological (curvature) part". This is a bit different than the GEM formalism, also...

If you do an experiment in a small sealed box where you only look at things inside the box, the laws of physics according to special relativity don not allow you to tell whether you are moving or not. If your question is about general relativity, you might be able to detect motion relative to...

I'm on board with this - I regard it as the theory of timelike congruences, which I first stumbled across in Wald, and later read more about in Poisson's "A Relativists Toolkit". Before that, I went with using Fermi Normal coordinates to gain a physical understanding. At that point I couldn't...

I have espoused that idea, and met a lot of resistance in certain instances. When I have the energy, I still do sometimes like to advocate for the idea that the fundamental idea of physics "should be" presented independent of conventions. But that is more from idealism than practicality. I...

I would use much simpler (but also less precise) language to convey a similar thought. I would call "causal diamonds", light clocks. It's just a matter of a different name choice, I am thinking that the idea of a "light clock" might be more familiar for the typical PF reader. I am somewhat...

I'm not sure what the best tools are to treat the relativity of simultaneity. I find space-time diagrams (Minkowskii diagrams) convenient, but I think much of the value lies in learning to draw them, and less in looking at diagrams others have drawn. Looking at diagrams others have drawn can...

Yes - I agree. I suspect that a full classroom environment, with homework and grading of the homework to provide feedback to the audience/students studying the material is a huge help in the success rate of understanding. Some of the pedagogical literature I've seen suggests that the...

MENTOR NOTE: This thread is a continuation of the following thread and focuses on Relativistic Simultaneity and it's effects on time. https://www.physicsforums.com/threads/true-static-equilibrium-and-effects-on-time.1083728/#post-7296784 —- You seem to be stuck on the idea that "time slows...

I would suggest learning about quantities, called invariants, that are independent of the frame of reference. In special relatiavity, his would be, for instance, the Lorentz interval. This would be discussed in textbooks such as "Space time physics" by E.F. Taylor. An older edition is...

That's correct. And in the context of special relativity, neither a material body nor a frame of reference can move at the speed of light. This should not be surprising, since if a frame of reference could move at the speed of light, light would be stationary in said frame of reference. But...

I don't know if this is standard, but I think of a vector, in tensor notation written as ##u^a## as a column vector in matrix notion, represented graphically as a little arrow with magnitude and direction, and a one-form, ##u_a## in tensor notation, as a row vector in matrix notation...

My $.02. Intuition is great, but - it's just not reliable. The only way to know if your intuition is correct or not is to look at the facts. Using your intution to try and guess at the facts is just not going to be reliable. We don't actually have a lot of facts relevant to your questions...