Recent content by pervect

There's a couple of different questions here. Basically, using devices that spin (such as the Forward Mass detector), can detect nearby massive bodies. The forward mass detector works by detecting tidal forces. There's a short reference to the forward mass detector in the wiki entry on...

Thank you. Untangling this in terms I can more fully understand will be quite a problem. I'm suspecting the issue is fundamental in that I'm viewing curvature as being defined by a metric. Which isn't necessarily how mathematicains view it. But I think the discussion has moved outside of...

Two dimensional

Not a paradox, but a rather hard problem. To deal with the problem with special relativity, I'd suggest replacing gravity due to mass due to the "artificial" gravity crated by an accelerated platform. The "paradox" then becomes the description of the accelerated platform with a different...

Sorry for this very late response. My first thought was that you had a good point, but as I was thinking about this more later, and I realized that this is not a counter-example to my argument. Specifically, the argument doesn't claim that you can't embed a 2-sphere in a flat 3-space. It...

I've been assuming the answer to this question is, informally, "the shortest path". The mathematical term is the "Levi-Civita connection". A straight line, more formally a geodesic in a more general treatment is a line that continues "in the same direction". The general concept of a...

I have not read anything definitive on that, but my current thinking is that it's not possible in general, but it may be possible in specific cases. The usual approach is not about embeddings. Instead, one starts with some curved manifold, and specifies a pair of vectors at this point. The...

My intuition leads to a similar conclusion, but I think we would need to clarify what a "beam" is in this context. I am not sure I have a solid enough definition of what mathematical properties a beam has to make a mathematical argument about why this should be so. The beam being elastic (so...

I'll start out by giving some (I hope) interesting references on the topic of sector models, which describe an approach to learning about curvature based on the simple idea of cutting and gluing. There's a whole series of papers by Kraus and Zahn, for instance https://arxiv.org/abs/1405.0323...

It's unclear to me what mathematics models a "large sheet of paper" in the current context. So I don't have anything rigorous. But I'll talk about the "small piece of paper" case. A "small piece of paper" will have a sectional curvature that can be computed from the Riemann tensor, wiki has...

As I think about the issue more, I h ave to note that my calculations were NOT based on an experimental defintion for energy (or momentum), but rather on symmetry principles, i.e. Noether's theorem. Most active posters in this thread are already familiar, but for any lurkers who may not be...

In the context of my favorite easy-to-understand (though not necessarily most accurate) test of relativity described in "The Ulitmate Speed", , if the speed of light is anisotropic, so should the speed of a relativistic electron beam. For a sufficiently high energy, in fact, we should observe...

I like the definition of measuring the energy with a calorimeter - or by the ability to penetrate an armor plate if one has a militaristic bent. Momentum measuring is less common, but one could measure the velocity of a large stationary sandbag after an inelastic collision to find the momentum...

I'd agree that the momentum is some constant times the (1, beta,0,0), where beta is the normalized coordinante velocity. (in this context, it's normalized to the average speed of light for a round trip). This is because for an object moving at some velocity beta,we want x = beta * t by...

Well, it looks like I was overcomplicating the analysis. Unless I've made an error (quite possible), [1,0,0,0] and [0,1,0,0] are both killing vectors. Or if you prefer ##\partial/\partial T## and ##\partial / \partial X##. And all the Christofel symbols vanished, too. I wasn't expecting...