Recent content by Geometry_dude

ZapperZ, thank you for your reply. To put things into perspective, I have to say again that a lot of this is based on my experience within academia and conversations with people I have been talking to about this issue, not careful scientific studies. Also, I live in central Europe...

Well, where to start... I do think that the foundations of physics are and have been in a deep state of crisis for quite some time now, but I do not know how far this has infested the rest of the field. My expertise is restricted to the former. The author refers to Thomas Kuhn in the article...

I think I have partially understood the correct interpretation of these quantities and I have also found some references. The interpretation: Since the velocities of the individual particles are random, ##\vec u##, ##\vec v## and ##\vec w := -D \nabla \rho / \rho## do not refer to individual...

Yes, I think you are right. Do you have a good reference where these things are treated rigorously from the point of view of stochastic equations? Well, yes, I said this above (your ##\vec u## is my ##\vec v##), but did not write it out in full: $$\rho \vec u = \rho \vec v - D \nabla \rho $$...

The vacuum Einstein equation: $$\text{Ric} = 0 $$

The issue is, the fluid interpretation is not really what I'm looking for here. In an applied math course I took we derived the 1-dimensional diffusion equation from a statistical model and then generalized it to the drift-diffusion equation (well, I did the generalizing...). We assumed the mass...

Hi, there! I was pondering on the drift-diffusion equation lately and there are some things I don't understand. I hope that some of you are more knowledgeable on the topic than me and maybe can point me to some literature. The situation: Fick's first law of diffusion is given by $$ \vec j...

There is a fundamental difference between vectors and covectors (1-forms, even though the term is usually referring to covectorfields), but it is true that one can convert one into another if one has been given a metric. Even then they are different objects, however. Intuitively, a tangent...

There was a misunderstanding here. I did not intend to ask you whether you know why the expression is constant - obviously ##c^2## is constant -, but rather why I would say that (modulo the factor) I would call this the relativistic kinetic energy. The reason is that it is the geometric...

I was trying to point out a conceptual inconsistency in Newtonian mechanics. Had Einstein ignored it, we would not have general relativity today. Yes, that's what I meant with 'forces' causing 'relative acceleration'.

Did that help or did it just make things more confusing?

If you cannot detect a universal force as the one above, how do you know that there is "zero acceleration" then?

Now, let me first say that the term under the integral including the one half is precisely the global expression of the Lagrangian in (2). If you want to be very precise, which is rare among physicists, then the term under the integral should be $$\left( \gamma^* g \right) _{s} \left(...

Well, I mean a force field like this $$\vec F = m \vec g \,$$ where ##\vec g## is (covariantly) constant. Isotropy is not an appropriate word here, but I'm sure that this is what you meant. Of course, Newton certainly viewed gravity as a force. My point is that this point of view becomes...

You read it off?