1. Apr 30, 2012

### httr

Hi,

I'm not a physicist and my idea of relativity is limited by wiki... but I have one question...

If I sit with my friend in a car and the car starts accelerating. As the speed of car approaches the speed of light, what's the relative speed of me to my friend?

2. Apr 30, 2012

### Matterwave

If he is sitting in the car with you, then his relative speed to you will always be 0.

3. Apr 30, 2012

### httr

That doesn't agree with relativity, does it? Could you explain?

4. Apr 30, 2012

### phinds

Of course it agrees with relativity. You are both in the same frame of reference so your relative velocity is zero. What would you expect it to be? Did he fall out of the car?

EDIT: It's not JUST that you are in the same frame of reference, it's that you are not moving relative to EACH OTHER.

5. Apr 30, 2012

### Fredrik

Staff Emeritus
My first thought was that what Matterwave and Phinds said is the only possible answer. If you're both in the front seat, then I don't see a reason to even suspect that another answer is possible.

However, if one of you is in the front seat and the other in the back seat, then there's the fact that the car is going to have different lengths in the inertial coordinate system in which it was at rest before you turned on the engine, and in the inertial coordinate system in which it's at rest now. In the former, the back seat will have a higher speed than the front seat, as the car is "shrinking". This could be a reason to suspect that your friend's speed relative to you will be non-zero.

If the car is doing "Born rigid acceleration" (the default behavior of a solid object that's being accelerated gently), then I think the answer is still 0. To get an answer that's significantly different from zero, the car would have to accelerate so violently that shock waves through the body of the car influence the speeds of its components parts significantly. This will tear a real car to pieces, and kill both you and your friend. So if you live to see what's happening, what you will see is that your friend's velocity relative to you is zero.

Last edited: Apr 30, 2012
6. May 2, 2012

### Naty1

Your description implies, as phinds posted:
so we all assume that the accelerations for each of you are the same and you are moving together in parallel. For example, even if you and your friend have different weights, you post implies identical accelerations and velocities.

7. May 2, 2012

### sweet springs

Hi, httr

Not only you and your friend but your belly and back or your light hand and left hand have relative speed, you expect. Are you OK in the car?

Regards.

8. May 2, 2012

### HallsofIvy

As long as you are moving at constant speed, the distance between you and a passenger in your back seat, or between your belly and back, is a constant and the relative speeds are 0. It is only if you are accelerating that you may have problems. Very high accelerations, just like being near, say, a neutron star, can cause extreme force gradients that could tear your car, or your body, apart.