# Time dilation thx!

1. May 26, 2007

### say_physics04

Hi to all! I’m just curious about something in time dilation. This is the case: IMAGINE you are a passenger in a trolley moving as fast as the speed of light. Then there is a very huge clock capable of being seen wherever the viewer is. The velocity of the trolley is c and moving away from the huge clock. The current time in the huge clock is 12 noon, the same as the time in YOUR watch before you start moving. As the trolley moves, if I’m correct, you infinitely see the time in the huge clock as 12 noon, but you see the time in your watch running normally- 60 seconds per minute. If your trolley keeps moving at this pace for 1 hour, based on an outside observer looking at the huge clock, then suddenly stops and you look immediately at the huge clock, will you see the huge clock having a time of 1 pm, meaning from 12 noon then 1 pm immediately? I know time dilation but I would appreciate if you’ll discuss how it happens in this case.

Thanks a lot!

2. May 26, 2007

### Alabran

From my very limited understanding of the subject, seems that the period of 1 hour, as seen by the outside observer, will take no time whatsoever for the person in the trolley. So, say the trolley moved at c in the opposite direction for an infinitismilly small amount of time and the person on the trolley car was turned around to watch the clock the whole time. When the trolley starts going, he'll see the clock at 12 noon, and then an amount of time equal to d/c, where d is the car's distance from the clock, he'll see it jump to one. Depending on the initial distance between the huge clock and the trolley, there will be an increasingly large interval of time between when the trolley stops and when the clock is observed to be 1. This is because an hour on the clock takes a negligable amount of time on the trolley and, hence, it will have travelled a negligable distance.

3. May 27, 2007

### pervect

Staff Emeritus
There is a problem with this. One can't imagine a trolley moving at the speed of light from the standpoint of relativity theory because such a thing does not exist. Perhaps you would like to know what happens if you imagine you are in a passenger in a trolley moving NEARLY as fast as the speed of light?

For a trolley moving at nearly the speed of light, you'd see the clock ticking very slowly. This is described mathematically by a doppler shift factor k.

Suppose we make the doppler shift factor k equal to 12 - then you see the clock ticking at 1/12 its normal rate. What you see includes relativistic time dilation and the fact that as you get further away from the clock, it takes longer from the light from the clock to arrive.

If your trolley keeps moving at this pace for 1 hour, in the ammended problem 5 minutes pass on the clock. (1/12 of the 60 minutes you experience). If you suddenly stop, the time you visually see on the clockface will not change, but the clock will start to advance at its normal rate. So when you stop, an hour later, the clock reads 12:05, and as soon as you stop, it starts to appear to tick at the normal rate.

One of the best ways to see this is to draw a space-time diagram. To do this successfully, you need to know one fact - that the doppler shift factor k, the interval between transmission and reception, depends only on the relative velocity between the emitter and the receiver.

For more details, try googling for "bondi k calculus".

Last edited: May 27, 2007
4. May 27, 2007

### Alabran

I had thought, taking the equation $$T=\frac{T_0}{\sqrt{1 - v^2/c^2}}$$ one could multiply said equation by the denominator and result in $$T \sqrt{1-v^2/c^2} = T_0$$. Since $$T_0$$ is the time the trolley would observe and $$T$$ is the time the outside observer would observe, it would seem that if the velocity were c then one could say that however long the outside observer watches the clock, the observer on the trolley will not see time pass whatsoever. Since under that understanding no-matter what T is, the lorentz transformation is zero and thus, so is the time period of the trolley. What's wrong with this understanding?

Last edited: May 27, 2007
5. May 27, 2007

### cristo

Staff Emeritus
Relativity states that a body with non-zero rest mass can never travel at the speed of light. The formula for time dilation does not hold in the case of a body travelling at the speed of light, since this makes the denominator of the right hand side equal to zero-- this is not mathematically defined.

6. May 27, 2007

### say_physics04

I think you can conclude that the clock will stop tickling when you're moving at c even though you can't imagine it well, cant we? I know it will be really IMPOSSIBLE for anything to travel at c except EM waves, I'm just thinking "if ever" you will be at that speed. So let's focus on the time dilation on the clock and how you'll view it if you stop suddenly from the trolley.. and not on the impossibilty of traveling at c.. thx!

Last edited: May 27, 2007
7. May 27, 2007

### cristo

Staff Emeritus
The point is that SR is a theory based on inertial frames. There is no such thing as an inertial frame that is "sitting on a photon" i.e. moving with speed c. Therefore, the time dilation equation does not hold, and therefore you cannot draw any conclusions from it.

8. May 27, 2007

### say_physics04

9. May 27, 2007

### George Jones

Staff Emeritus
I don't understand this.

If a clock moves away from me such that the Doppler shift factor is 12, then I see the image of clock ticking at 1/12 its normal rate

Last edited by a moderator: May 27, 2007
10. May 27, 2007

### pervect

Staff Emeritus
The best you can do is take the limit as you approach the speed of light. You can't actually travel at the speed of light.

This may seem like a fine point, but one runs into actual mathematical contradictions if one pursues the idea of "moving at the speed of light" further. Fortunately, the answer to these issues is very simple - material bodies don't move at 'c'.

Last edited: May 27, 2007
11. May 27, 2007

### pervect

Staff Emeritus
Right - I'll revise the original so it actually makes sense. (The only way 5 enters into the picture is that 5 is 1/12 of 60). One does in fact see the clock ticking at 1/12 it's rate as you point out. Thus on a 1 hour trip, the clock, ticking at 1/12 its rate, only appears to advance 5 minutes.