# Relativity problem thats been bugging me

1. Jul 9, 2010

### mm06sk

Firstly, im sorry if a similar question has already been posted, but I couldnt find the answer anywhere.
Im not an expert by any means, and my confusion might be caused by my complete misunderstanding of special relativity, so Ill start by explaining what I think an example of special relativity is, which could be complete rubbish, I dont know.

Take 2 people, A and B. A is standing stationary, and observing B, who is travelling at 0.99c, aswell as a beam of light travelling in the same direction to B. Person A observes for 1 year (relative to himself). He observes that the light beam travels exactly one lightyear, and person B travels 0.99 of a lightyear. However, according to person B, the beam of light has only travelled 0.01 of a lightyear further than him, and as light always travels at 1lightyear/year the time that has passed according to Person B is 0.01 of a year (3.65 days). I hope this makes any kind of sense.

My question is, say both people A and B are also observing a beam of light travelling in the opposite direction to person B, starting at the same position as the starting point of person B. person A would observe a total distance between Person B and the new beam of light after a year to be 1.99 lightyears. But we know that if it takes a year for person A to observe something, it takes person B only 3.65 days, therefore the relative speed of the new beam to person B is 199c. This makes no sense. What have I done wrong?

sorry if this is a silly question/already been answered/the ramblings of a madman, but id be very grateful if anyone could explain this problem to me

thanks

2. Jul 9, 2010

### Staff: Mentor

OK.
Actually, it's according to person A that the beam only traveled 0.01 ly further than B. And the time dilation factor is about 7, so while A says the trip took 1 year, B says it only took 1/7 of a year according to his clocks.

According to observer A, B and the light beam separate at a rate of 1.99c. No problem there. Of course, both observers A and B observe the light beam to travel at the speed c with respect to themselves.

3. Jul 9, 2010

### mm06sk

Sorry I wasnt aware of time dilation factors. Ok i'll think about it in terms of positions. Take the direction Person B and the first beam of light is travelling as +ve, and the other beam of light to be travelling -ve direction. After person A has observed for a year, Person B will be at +0.99lys, The first beam of light will be at +1 lys, and the 2nd beam of light will be at -1 lys. I (now) know that when the objects reach these positions, 1/7 years have passed for person B. However, the position between person B and the 2nd beam of light will be 1.99 lys, and this was acheived, according to person B, in a seventh of a year. So the 2nd light beam was travelling at 6.93c. Still confusin. Thanks for telling me about time dilation factors though, i'll read into it.

4. Jul 9, 2010

### espen180

Nope, sorry. B will observe that the beams are +1/7ly and -1/7ly relative to him.

I think the point of confusion here is that you are mixing measurements from different reference frames. Take a look at the lorentz transformation equations and use these when doing these kinds of problems.

http://en.wikipedia.org/wiki/Lorent...ormation_for_frames_in_standard_configuration

Remember to never mix measurements from different frames. For example, in your post, you took x/(t') as a measurement for the speed of one of the light pulses.

Last edited: Jul 9, 2010
5. Jul 9, 2010

### Staff: Mentor

Positions are affected as well.
Careful. These three positions are reached simultaneously according to A only. Observer B will not agree.
Careful: According to B, the trip takes 1/7 y. But when he gets there, he observes that each light beam has traveled exactly 1/7 ly with respect to him. According to B, the light beams are at different positions from what A thinks.

No. As I said above, observer B will measure each light beam as having traveled 1/7 ly during his trip that lasted 1/7 yr. So he measures the speed of each beam as being the usual c.
As espen180 said, you cannot mix measurements made in different frames. In addition to time dilation, you'll need to worry about length contraction and the relativity of simultaneity. That last one is the trickiest to understand; different observers will disagree as to where the 'objects' were at the same time, because simultaneity is relative.

6. Jul 9, 2010

### espen180

Maybe phrased less ambigously; Different observers generally disagree on the order in which events take place. Each frame has a plane of simultaneity which is perpendicular to its time axis in a Minowski diagram. (http://en.wikipedia.org/wiki/Minkowski_diagram) These diagrams are very useful when doing these problems.

Observer A measures that the events:
1: B is at +0.99ly (All measurements made relative to A)
2: Pulse 1 is at +1ly
3: Pulse 2 is at -1ly
occur simultaneously. However, according to B, these events will occur (when the events are lorentz transformed to B's rest frame) in the order (2,1,3) (if I am not mistaken).

7. Jul 9, 2010

### Staff: Mentor

That's a perfectly fine way to put it, but I think it's equivalent to what I was saying. The question "Where are the light beams at the moment when B reaches his destination?" will be answered differently by the different frames.