Recent content by pervect

If you were to use tensor methods, you would calculate ds from the formula $$ds^2 = g_{\mu\nu} dx^{\mu}dx^{\nu}$$ (So, to get ds, you need to take the square root of the right hand side). Use of the Einstein summation convention is assumed, which means you sum over all 16 value pairs of...

So far, so good. You have described the symmetry principle of relativity well. And it is indeed puzzling how this is possible - at first glance, it does seem paradocixal. OK, here's where you made a giant logical leap. I'm not sure what you're trying to say here. Symmetrical motion is...

Are you familiar with the concept of dual vectors? I suspect that this may be the underlying issue you are struggling with. Here's the way I interpret things. Hopefully my memory isn't off too much, I haven't gone back to the textbooks to double check my memory, though, be warned. ##x^a## is...

As others have pointed out, it's a bit more complicated than that. I'm guessing that you are assuming there is some state of "absolute motion", and those "moving fast" have slow time, while those moving "normally" have normal time. But motion is relative, which means that an observer on the...

I ran across the very interesting https://arxiv.org/abs/quant-ph/0302081, "Geometry of the 3-Qubit State, Entanglement and Division Algebras" which goes a long way to answering my own question. The extra phase factor is not eliminated

In my opinion arguments over or about the one way speed of light are pretty much a dead end, but rereading the post I see Peter was right in commenting that this was the original question. Somehow I thought the OP was interested in whether the radial speed of light was the same as the...

Is clock syncrhronization actually important to your question? It's not obvious to me why it's relevant to your problem, and it'd be a lot easier to analyze the problem if you could get rid of it. I'd suggest about thinking why you need it, and the approach I'd take to that is to try and...

Because to OP is talking about "reference frames", they are most likely doing Newtonian physics and not actually doing GR. If they were doing GR, they would be talking about what metric they were using rather than about "reference frames". But I'll try to answer the question both from a...

Consider the Euclidean metric of a plane, dx^2 + dy^2 = 0. Formally, this would actually be called a line element, mea culpa. Any linear transformation of this metric, which we can perform algebraically or by other means (such a the tensor tranformation rules) provides an equivalent metric...

In https://web.cecs.pdx.edu/~mperkows/june2007/bloch-sphere.pdf, Ian Glendinning describes a derivation of the Bloch sphere for one qubit. To paraphrase his basic argument, one qubit in a pure state can be represented by 2 complex numbers, ##\alpha= a + bi## and ##\beta = c + di##. This yields...

Can you really read the formulae and the diagrams on the Kindle version? I would think it'd be tough to get much out of it :(.

I would say that your characterization of GR as saying that "the planet is stretching" is flawed. But lets move on to your question, perhaps the answer to that will help clear up your confusion and lead you twoards a less-flawed understanding of what GR is saying. The closest approximation...

A recap of what others said. If one defines coordinates on a manifold, (to be more formal, one might talk about a coordinat chart), one automatically define a coordinate basis. But, that's not the only possible basis one might use. Frequently, one is interested in some other basis, such as an...

When talking about directions, I've had arguments in the past about whether a "spacelike" direction is a vector, like ##\partial / \partial x##, or a dual vector, like dx. This doesn't make much difference in a true orthonormal basis, but it does in other cases and can cause arguments. The...

I can quote some of the equations you need for a Schwarzschild black hole, I don't know how good an approximation that is for Sag A*. From "Oribits in Strongly Curved Space-time", https://www.fourmilab.ch/gravitation/orbits/, which is the same eqautions as MTW's textbook "Gravitation" we have...