Recent content by pervect

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...

Just to clarify - this is the geodesic Lagrangian of a free particle, not the relativistic Lagrangian of a free particle, is that correct? As I review the material, it seems that the geodesic Lagrangian corresponds to the square of the proper time (sometimes I've also seen it multiplied by a...

Yes, I personally think it would be simpler to introduce relativity by means of proper velocity, or as you write it ##dx/d\tau##. Do you have an attribution for where Einstein actually wrote that? I was trying to make a case for introducing relativity by means of proper velocity, which as you...

I'd like to expand on my earlier point. Suppose we have some frame in which Newton's laws work. Two equal masses moving in opposite directions at the same velocity as measured by the two-clock system of measuring velocity collide, and come to an exact stop. Now, let's change the clock...

A cautionary note is needed here I think. High school and introductory physics has been known to be formulated and taught in such a manner that certain conventions NEED to be followed for the results to be valid. For instance, Newtonian physics as taught in an introductory level only works in...

As long as you don't believe that your clock synchronization has any physical significance, in particular as long as you don't address the issue of the laws of motion in your supposedly inertial frame, I don't see any issues. If you were to make further assumptions like assuming that your clock...

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