jcsd
You are right in saying that we have a 4 dimensional structure. By imposing a null displacement condition in 5D we are reducing by 1 the number of independent dimensions. The advantage is that we are left with a choice for describing this 4D structure in either Minkowski or Euclidean...
Hi Doug,
Well, yes and no. The Schwarzschild metric in isotropic coordinates is
\label{eq:isotropic}
\mathrm{d}\tau^2 =
\left(\frac{\displaystyle 1-\frac{M}{2r}}{\displaystyle 1+\frac{M}{2r}}\right)^2
\mathrm{d}t^2 -
\left(1+ \frac{M}{2r}\right)^4 \left[...
Doug
I agree; no matter which metric one uses the main thing is that velocity is basically determined by
\frac{v^2}{r} = -\frac{\mathrm{d}V}{\mathrm{d} r},
where V is the gravitational potential; the metric introduces a correction which is significant only for very small r and large M.
You...
Doug,
I had a quick look at the paper and I now realize there are a few mistakes, none of them serious and all easy to correct. The main difference after correction will consist on doubling the exponent in Eq. (7), but that will have no consequences for the discussion and conclusions.
Jose
Hi Doug
Actually I wrote about this a few years ago with someone who has since passed away. We never agreed that the paper was fit for even placing in arxiv, so it remaind in my hard disk until now.
Note that I had not yet got the exponential metric quite right at that time, so now the paper...
Hi Doug,
Pardon me for hopping in like this but I thought you could possibly use one little piece of information about the exponential metric. You may or may not know that the exponential metric seems to have been first proposed by Houssein Yilmaz in "H. Yilmaz, New approach to general...
Introducing General Euclidean Relativity
I believe we are now ready to start addressing GR and its Euclidean counterpart; this post will introduce the subject.
In a curved space displacements are evaluated by a quadratic form which we write as
(d \tau)^2 = m_{\mu \nu} d x^\mu d x^\nu...
If you allow non-geodesic movement you have then different paths linking any two points in 3+1-space, so you get different evaluations for the proper time difference between them. Each path could then be separately mapped to 4-space but their endpoints would not coincide. I want to make sure I...
This message was edited to correct a serious mistake; the editing is clealy marked with bold.:redface:
Dear Hurkyl,
I'm very happy because finally someone is really paying attention to what I write
(...)
Put in those terms I can't but agree with you. Actually \tau is a line integral in...
I can see your point but I don't think it apllies here. I wrote about an alternative way of looking at problems but I did not say relativity was wrong. My position about this is that no physical theory is ever final and so no physical theory is ever absolutely right, which does not mean it is...
I believe we are on the right track now, so let us take a few more steps.
Quite right. I would like to rephrase that to make sure we understand exactly where we are: Although geodesics can be mapped from 3+1- to 4-space and back, the same thing cannot be done with points, that is, if three...
I plan to place special and Euclidean relativity side by side, being able to translate between the two. One always gains perspective by looking at a problem from diferent angles. When the 5D null displacement principle is replaced by the more fundamental concept of 5D monogenic functions we get...
I don't reject Einstein's convention but I find Bondi's more natural and easier to work with; if I have only one measuring instrument I can avoid all synchronizations. That Bondi's approach works for special relativity is a fact generally accepted.
It is telling us that \langle x, y, z, \tau...