Accelerating trajectories in relativity

[twinsen]

Hi

I am trying to write a code to find the minimum time until a sphere of expanding light interacts with a set of N particles moving at speed. These particles are acted on by forces which remain constant over the time period.

My problem at the moment is that these particles have a mass and therefore should be restricted to v<c.

At higher speeds am I right to say that it takes relatively more energy to add speed, where an infinite energy/force would be required to get to c??

What would this acceleration velocity dependence be?? I presume I can then just integrate this along with the initial velocities to get the position as a function of time.

I am really just unsure as to how to apply relativity in this case where the particles are accelerating under a force..

Thanks in advance.

Alex

 

[Mike_Fontenot]

[...]
What would this acceleration velocity dependence be?? I presume I can then just integrate this along with the initial velocities to get the position as a function of time.

I am really just unsure as to how to apply relativity in this case where the particles are accelerating under a force..
[...]

Basically, you need to use a quantity (often called "rapidity") that is related to ordinary velocity (it's just a one-to-one non-linear transformation of velocity) that has the useful property that it adds linearly across inertial reference frames (ordinary velocity DOESN'T).

Taylor & Wheeler use it in their SPACETIME PHYSICS book, and I imagine most other good special relativity books do too. I think T&W used rapidity in an example showing how far a traveler could get, if constantly accelerating at 1g, in one human lifetime.

I also use rapidity in my paper on accelerating observers:

"Accelerated Observers in Special Relativity", PHYSICS ESSAYS, December 1999, p629.

If you don't already have T&W's book, that would be a good purchase no matter what. As I recall, the very first edition may not have had all the worked examples that later versions had, so try to get the latest one.

Mike Fontenot

 

[Mentz114]

twinsen, you might find this helpful

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

and this

http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

 

[twinsen]

Yeh that's great. Exactly what I was looking for :)

I will try and find Wheeler's book when I go back to uni! Really should remember all this stuff but sometimes it's quicker to ask.

Cheers

Alex