Recent content by pervect

You seem to be stuck on the idea that "time slows down". One can ask "Slows down relative to what? To me, your words suggest you believe in some sort of "absolute time" in which things can be at "absolute rest", this viewpoint has been presented by you several times and hasn't changed through...

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...

My understanding of quantum mechanics is not good. But I've been under the impression that "ordinary" quantum mechanics is not compatible with special relativity. Specifically, Schrödinger's equation is not compatibility with special relativity, and neither is the idea of instantaneous wave...

I concur with Pallen's observations. MTW goes into the explicit geometric details of how to construct a proper frame of reference. And I agree one can get an inertial proper frame by setting the acaceleration and rotation to zero - Pallen has quoted the relevant section of MTW on this so...

Measuring pressure is certainly possible. Even in Newtonian mechanics, pressure is only as simple as a single number when the pressure is the same in all directions (i.e. isotropic). I could say more about how anisotropic pressures wind up being represented, but I think that would drift off...

You can't move at the speed of light, but it turns out you that relativity depicts what you describe. There's another way of saying this - given a head start, a rocket with a constant acceleration can outrun a light beam. In the case of a rocket accelerating at approximately 1g (the exact...

I barely said anything, but if you have a chance and ability to read the reference I cited, it's the best treatment of accelerated frames of reference that I know of. I will add that it starts out with a good discussion of why said "frame of reference" is limited in extent. I'll add that from...

It looks more like you are trying to understand the relationship between two inertial frames of reference rather than the concept of a "proper reference frame". My graduate level textbook, Misner, Thorne, Wheeler "Gravitation", has a discussion of proper reference frames of possibly accelerated...

I'm not doubting your word on this, but a reference would be handy.I thought "extremal" and "stationary" were synonyms. For an I level example, f(x)=x^2 and f'(x)=x^3 are both extremal at x=0, because the derivatives df/dx and df'/dx both vanish. But the first is a minimum, the second is a...

It's always safer (though less understandable) to say that geodesics (of the Levi-Civita connection) are extremal rather than maximums or minimums. But for the Riemannian case, where one is not also dealing with time (and distances are always non-negative), it's a common simplification to say...

For a general way to get an intuitive feelings for geodesics that is not too advanced, I'll put in a plug for the "sector model" approach of Kraus and Zahn. There are a number of papers on sector models, the one that google finds specific to geodesics is https://arxiv.org/pdf/1804.09828...

A limited notion of parallel transport that works on a sphere is, IMO, a good place to start. One start with the notion that great circles are geodesics of the sphere. (If I'm being pendatic, which is sort of required to avoid having someone point out the oversimplification, I'll add that a...