# Alice and Bob on the Tracks

1. Jul 23, 2011

### TimDubya

I'm sure many will cringe at the mere sight of this question. I've only had a brief introduction to relativity so I am having difficulty conceptually with a problem a professor posed to me. His question is of standard Bob and Alice form.

"Bob is on a flatbed train, Alice is in the station. When bob passes Alice (x=0) he flashes a flashlight."

Now we both agree Alice and Bob independently will observe the wavefront moving away at c. My issue is I can not conceptualize how in Alice's frame she also sees the wavefront moving away from bob at the speed of light and simultaneously away from herself at c while Bob is clearly moving with some velocity along the direction of propagation of the light flash.

Any insight will be much appreciated.

2. Jul 23, 2011

### Hurkyl

Staff Emeritus
It looks like you haven't mentally separated the notions of "how fast the distance between two things is increasing in Alice's frame" and "how fast the distance between two things is increasing in Bob's frame".

3. Jul 23, 2011

### TimDubya

How might one go about mentally separating such notions.

4. Jul 23, 2011

### Staff: Mentor

She doesn't. The second postulate of relativity says that in every inertial frame the speed of light is c. It does not say that in every frame the separation speed with every object is c. The separation speed between two objects is not the speed of any object, and so it is not limited to be less than c, etc.

5. Jul 23, 2011

### TimDubya

Then do you and Hurkyl disagree?

6. Jul 23, 2011

### Staff: Mentor

Not at all. We are taking slightly different approaches to answering your question, but our answers are not in any disagreement.

7. Jul 23, 2011

### TimDubya

Ok then my original intuition was correct, thank you.

8. Jul 23, 2011

### Hurkyl

Staff Emeritus
Unlearning something is always a tricky thing.

Math often helps. By writing things out explicitly, it is difficult for the matter to be clouded by errors in your intuition. And in the process of writing things out, you might find something you didn't know you were missing.