# Are descriptions of relative velocity arbitrary?

1. Apr 4, 2013

### coktail

Is how we choose to describe relative velocity arbitrary?

For example, say I am floating in space with only Ball A and Ball B for reference. Ball A is moving away from me at 10mph, and Ball B at 20mph. I could say that I am stationary, and Ball A and Ball B are traveling at 10 and 20mph, respectively, or I could say that Ball A is stationary, and I am moving away from it at 10mph, and Ball B is moving away from me at 10mph.

Assuming acceleration is not involved, is how I describe this situation totally arbitrary?

Thanks!

2. Apr 4, 2013

### Mentz114

The whole point of relativity is that you can choose any of the three inertial frames to describe the setup. It will make no difference to any conclusions you deduce. So in a sense it is arbitrary.

3. Apr 4, 2013

### Staff: Mentor

(For simplicity and because we're dealing with speeds much less than teh speed of light, we won't worry about relativistic addition of velocity)

I assume that you mean the balls are moving in the same direction, so the difference in their speeds is 10 mph?

It's not totally arbitrary, because you have to choose a description in which the difference in speeds is 10 mph. But yes, beyond that, you're free to pick any description you please. Imagine that you're watching your thought experiment from a spaceship zooming by... The two balls and the interactions between them shouldn't care how fast or slow your spaceship is going, they just see each other moving apart at 10 mph.

If you want a more prosaic example: The floor of my house is 100 feet above sea level. I have a 6 foot tall shelf. When the cat knocks a glass of the shelf, I could say that the glass fell from a height of 106 feet to a height of 100 feet above sea level, or I could say that it fell from a height of 6 feet above the floor the zero feet above the floor. Someone using spherical components with the origin at the center of the earth (very convenient for calculating how hard the glass hits the floor) would probably say that the glass fell from a height of 4000 miles plus 106 feet to a height of 4000 miles plus 100 feet.

4. Apr 4, 2013

### Agerhell

If you are somewhere in space close to a massive spherically symmetric non-rotating planet you might have to take velocity relative to that planet into account.

5. Apr 4, 2013

### nitsuj

those things have positions & directions, comparatively.

ball B's "rate of displacement" from you changes, based on your arbitrary choice of who/what's at rest. So no, I can't see a way to make that symmetrical.

As would be the case if it were just you & ball A (or B).

6. Apr 5, 2013

### ghwellsjr

It's not totally arbitrary; you have to be consistent.

At first you described the setup without regard to any reference frame which is entirely OK.

Then you described the setup with regard to a reference frame in which you were at rest. No problem there either.

But then you described the setup with regard to a reference frame in which Ball A is at rest and instead of using the same terminology that you just used in the first frame, you threw yourself into the mix and got it wrong. You should have said, "Ball A is stationary, and I am moving at -10mph, and Ball B is moving at +10mph." Ball B is not moving away from you at 10 mph, it's moving in the reference frame at 10 mph. Do you understand the difference?

7. Apr 5, 2013

### ash64449

What about in the reference frame of Ball B?

8. Apr 5, 2013

### coktail

ghwellsjr, I do understand the difference, I think. It's arbitrary, as long as I'm consistent within my description.

Thanks, all!

9. Apr 5, 2013

### ghwellsjr

Ash, why don't you make a suggestion and see if you can do it yourself?

10. Apr 5, 2013

### ash64449

according to me in the reference frame of ball B, that poster is moving -20 mph and ball A is moving -10 mph.. Am i right?

11. Apr 5, 2013

Right!