# Yet another question that is supposed to turn SR on its head

1. Sep 10, 2006

### neutrino

This is something that arose out of a section in Richard Mould's Basic Relativity.

He begins SR with his so-called "Physical Threorms (PT)," which are gedanken experiments used to show the effects time-dilation, length-contraction, and the concept of simultaneity in relativity, in that order.

I'll give a gist of his second PT: An observer, in whose frame a rod of length L is at rest, obserevs a clock that reads 5:00 as it passes the left end of the rod (event A) with velocity v to the right. By the time (say, an hour) it reaches the other end, the moving clock reads $5:\frac{L}{\gamma v}$ due to time dilation(event B). Both observers must agree on the "facts" (events A and B).

Now, the second observer agrees that his clock does read $5:\frac{L}{\gamma v}$ when the moving rod's end B passes him. But according to him, it is because a rod of length $\frac{L}{\gamma }$ is moving with a velocity v to his right.

Mould does not talk about how the first observer's clock appears to the second.

Now here's my question: If I were to replace the rod with two asteroids (assumed to be moving at the same uniform velocity) seperated by a distance L, with event A and B corresponding to passing asteroid 1 and 2, respectively. How would I explain the fact that both observers agree that the second observer's clock reads $5:\frac{L}{\gamma v}$ when passing asteroid two, since there is no contraction of length involved.

I hope my question is clear.

2. Sep 10, 2006

### JustinLevy

Look at the thought experiment more closely. Follow through what the book describes. Does it really matter if the length is a material object or just empty space between two objects/points?

Thinking this out yourself will help you learn SR better, but if you'd prefer, one of us can just tell you the answer (although ultimately the answer probably won't settle well unless you think it through yourself anyway).

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3. Sep 10, 2006

### neutrino

That's the question which has been nagging me. If I had known the answer, this thread probably won't exist. ;) Moreover, I'm trying to answer this with what is already known (in the book), viz. the principles of relativity and the 1st PT (time-dilation).

4. Sep 10, 2006

### DaveC426913

Why would replacing the rod with two asteroids change anything? Space contracts as much as materials do.

eg. At near the speed of light, the distance to Alpha Centauri is greatly contracted.

(In fact, if you extrapolate 'near c' to 'at c', you can see what a photon "sees". Which is that every point in the universe has contracted to be zero distance from every other point, which is why it takes "no time" from a photon's perspective to get from A to B - i.e. a photon doesn't experience time.

Last edited: Sep 10, 2006
5. Sep 10, 2006

### neutrino

The photon's perspective is something I thought about earlier which shows that a material is not needed for the lenth between two points to contract.

Now that my doubt is more or less cleared (it will never be completely clear), I can continue reading the book with a lot less clutter in my mind. Thanks.

6. Sep 10, 2006

### pervect

Staff Emeritus
It seems to me that neutrino may have missed the key element of the relativity of simultaneity.

The first observer has not just one clock, but two clocks. He has a clock on the left end of the rod, which was used to measure event A, and a clock on the right end of the rod, which was used to measure event B.

The first observer has synchronized his clocks, of course. But, what do we know about clock synchronization in relativity?

....

....

....

It's frame dependent. Clocks that are synchronized in one frame are not necessarily synchronized in another frame.

So take a closer look at the problem with the "relativity of simultaneity" in mind. I'd be rather surprised if the author doesn't discuss this, but I don't have the book in question.

7. Sep 10, 2006

### neutrino

As I said in the first post, simultaneity is dealt with after length contraction. Infact, the author never talks about the first observer's clock in this part.