1. Jan 4, 2005

DeathKnight

I was reading about special relativity on How Stuff Works. In the article, the writer has given the following 4 points:

1. Energy must be added to the system to increase the ship's speed.
2. More of the added energy goes towards increasing the system's resistance to acceleration.
3. Less of the added energy goes into increasing the system's speed.
4. Eventually, the amount of added energy required to reach the speed of light would become infinite.

I can understand point 1 but can’t really understand the rest of them.
Can anybody please explain them in a simple way with a special reference to ‘increasing the system's resistance to acceleration’? Is it a reference to the mass of the ship?

Any help will be appreciated.
Abdullah

Last edited: Jan 4, 2005
2. Jan 4, 2005

Chronos

Energy conservancy is the answer. While it takes increasingly more energy to accelerate an object, it is exactly offset by the increased relativistic mass of the object being accelerated. This satisfies both GR and the laws of thermodynamics - upon which GR is based.

3. Jan 4, 2005

yogi

The effective inertia increases with velocity - it climbs very fast near the speed of light. To make a given change (say 10 mph) in the velocity of a relativistically moving mass requires more force than to make a 10 mph change in the velocity of a mass traveling 60 mph. When you apply a force for a given distance, you add energy to the moving mass. It is not now generally accepted to say the mass increases - but rather it is now preferred to say its resistance to acceleration increases with velocity.

4. Jan 4, 2005

Chronos

You say tamAto, I say tomatO. That is what the math says, and I am fairly comfortable with that. It takes energy to acclerate. The energy difference is conserved by mass creation in the accelerated object. A particle physics thing.

5. Jan 4, 2005

pervect

Staff Emeritus
You can look at it from a lot of viewpoints - from the energy viewpoint, the momentum viewpoint, or the velocity addition viewpoint. I prefer the second two viewoints, but the articles viewpoint is not wrong, just not the viewpoint I would have chosen.

I'll sketch out the other two viewpoints - the momentum viewpoint just says that the momentum of a relativistically moving object is mv/sqrt(1-(v/c)^2), rather than the newtonian formula of mv. Thus an object moving at the speed of light would have an infinite momentum (as well as an infinte energy).

The velocity addition viewpoint is fairly simple. Velocities in relativity add according to the relativistic velocity formula

v = v1 + v2 / (1 + v1*v2/c^2)

If you keep adding up velocities, in an infinite string, you will never reach the speed of light

i.e. .1c + .1c + .1c + .1c + .1c + ..... .1c will be less than c, no matter how many terms you add

If we do this 20 times, for instance, we get:

v := .1000000000
v := .1980198020
v := .2922330098
v := .3810961231
v := .4634348026
v := .5384797759
v := .6058556730
v := .6655339229
v := .7177642757
v := .7629989374
v := .8018201453
v := .8348779491
v := .8628412368
v := .8863622468
v := .9060531187
v := .9224722344
v := .9361179525
v := .9474275577
v := .9567796199
v := .9644983806

6. Jan 4, 2005

Gamish

I think that point 2 was inaccurate. If a ship was in a vaccume, there is no resistance towered acceleration. I can explain this is simple terns.

I am getting closer to the speed of light, my "mass" of my ship DRAMATICALLY increases, it is harder to move the ship. Obviously, it is harder to move something with a lot of mass. Therefore, when you try to move the ship by applying energy, the energy won't speed up the ship that much more, because the increase in mass is proportional to the increase in speed. More precisely, mass increases my a factor of sqr(1-v^2/c^2) (lorenz transformation).

7. Jan 7, 2005

Phobos

Staff Emeritus
I think the auther was using the phrase "resistance to acceleration" to mean inertia (not friction...unless you want to consider the behavior of spacetime itself as friction).