# Approaching speed

1. May 11, 2012

### moatasim23

Are approching speed and relative speed different quantities in all circumstances or only for photon?

2. May 11, 2012

### HallsofIvy

What, exactly, do you mean by "approaching speed"? My interpretation would be that it is the relative speed of an object, measured relative to some other object it is nearing ("approaching").

3. May 11, 2012

### Staff: Mentor

Do you mean closing speed? (The rate at which two things approach each other as measured in some third frame.)

If that's what you mean then, yes, closing speed and relative speed are different in general, not just for photons.

4. May 11, 2012

### HallsofIvy

Ah, thanks, Doc. Yes, that would be different.

5. May 11, 2012

### harrylin

As you know, Einstein disagreed with that. But nowadays it has become popular to mean with "relative speed" the same as what commonly is meant with "speed" - the speed of an entity relative to a reference system. Those who use such a definition for "relative speed" then must use such expressions as "approaching" or "closing" speed for the speed of one entity relative to another one, as measured with a reference system in which both are moving. That is generic, for all entities and not only for photons.

Last edited: May 11, 2012
6. May 12, 2012

### moatasim23

If we consider a car A moving with speed v towards another car B travelling with speed 2v towards A.What is the relative speed and what is the closing rate?

7. May 12, 2012

### yuiop

The relative speed of A according to B (or vice versa) is (v + 2v)/(1+v*2v/c^2) where v<c and the closing speed is 3v.

8. May 12, 2012

### ghwellsjr

Yes, the so-called "closing speed" is the incorrect answer when you simply add the two speeds together without doing the division part of the correct formula. It doesn't represent anything real. It's not the speed of anything, just two numbers added together and given a name so that we can talk about how wrong it is.

9. May 12, 2012

### yuiop

It does have one practical application. If the distance between the two objects is d, then the time to collision is d/(closing speed) but as you correctly point out it is not the speed of any single tangible object and is not a violation of SR or an example of superluminal speed.

Last edited: May 12, 2012
10. May 12, 2012

### m4r35n357

If I'm paraphrasing correctly, effectively special relativity only "applies" when the observer is actually one out of the two. Is there a technical term for that?

11. May 13, 2012

### harrylin

Special relativity effectively applies for all these cases (see my earlier reply). The technical term for measurements "when the observer is actually one out of the two" objects that are in relative motion, is that object's "rest frame".

12. May 13, 2012

### moatasim23

But the answers of the two are almost identical at low speeds.Arent they?

13. May 13, 2012

Yes.