Kharakov

Hi-

The mass of a particle (A) increases as it accelerates to c in relation to another particle (B) that we will use as a reference.

This implies that the gravitational distortion of spacetime of particle (A) in relation to particle (B) increases with the velocity of (A). The inertia of (A) increases as well.

Does this mean that inertia (and velocity) is actually the distortion of spacetime relative to the 2 particles?

Attempt to restate my idea: The faster that particle (A) moves in relation to (B) the greater the distortion of spacetime the particles experience in relation to eachother- so the velocity of a particle in relation to another particle is a measure of the distortion of spacetime between the 2 particles.

-k

Abacus

What do you mean by distortion of spacetime? If by that you mean the curvature of spacetime, then in my limited understanding of relativity, there is no curvature in this case. The apparent increase in mass of the one particle is an effect of the Lorentz transformation between inertial reference frames.

Kharakov

The mass increase isn't apparent- its actual.

mass= rest mass/sqrt(1 - v²/c²)

Electrons accelerated in a CRT are close to 1 percent heavier than an electron at rest- and this has to be taken into account when guiding them to a screen.

I did use the term distortion in place of curvature, it seems to be more descriptive of what is happening.

-k

Abacus

I agree that the effect is real. The apparent increase of the mass of the particle is the result of us breaking spacetime apart into space and time. When you examine the acceleration of the particle through space, you see that the acceleration decreases as the velocity (through space) approaches a magnitude of c. One interpretation is to attribute this to an increase in mass. I guess you can do that, because it all works out mathematically.

But there is a simpler view. If you examine the acceleration of the particle through spacetime, it is constant. Furthermore, the speed (magnitude of velocity) through spacetime is always the same. That speed is c.

I guess one way to think about it is this:

You are the observer and the particle is initially at rest with respect to you. At this point, the particle is moving at the speed of light through time. Now you turn on the particle accelerator, and the particle starts moving away from you. As it picks up velocity through space, it decreases in velocity through time, but in such a way that its velocity through spacetime always has a magnitude of c. It is only when you break spacetime apart into space and time that all of those weird relativistic effects such as time dialation and mass increase show up.

So I guess, in a sense, space or time on their own will appear to be distorted as you change reference frames, but spacetime will not.

That was probably as clear as mud, but I hope that helps you out a little bit. This is a fascinating subject.

Kharakov

RNG-

The way I think about it is that you only get relativistic effects when you compare two different lumps of matter. A piece of matter hurtling through the cosmos with no other material reference point is the same as a lump at rest.

If you apply a constantly increasing force to a particle its acceleration will remain constant, to a point. The force has to increase to compensate for the mass increase of the particle. As you approach c, the amount of energy directly translated into velocity lessens and the amount of energy directly transformed into mass increases.

My main question was more aimed at whether or not someone had already come up with a mathematical system to represent (inertial) velocity of a particle as a 'curvature' of spacetime. I have to assume that people already have tried that....

-k

Abacus

I don't know if anybody has. But I don't think it is necessary. SR already adequately explains everything you talked about in terms of a flat (i.e. no curvature) space.

I'll say it again. Those weird relativistic effects are due to us, for analytical purposes, breaking up Einstein's four-dimensional spacetime into Newton's three-dimensional space and an independent time parameter.

[ July 27, 2002: Message edited by: Random Number Generator ]</p>

Friar Bellows

What is mass?

Bibliography:

<a href="http://www.amazon.com/exec/obidos/ASIN/0486299988" target="_blank">Concepts of Mass: In Classical and Modern Physics</a> by Max Jammer (1997) Dover Publications, ISBN 0486299988.