# Time dilation

1. Nov 24, 2007

### fire100_anand

If two persons are wearing the same watch showing the same time say 5 Am...one person remains in earth and the other person goes to space at the speed of light ....After one hour the watch on person on earth will show..what will be the time on the watch worn by the person who went to space...please explain time dilation

2. Nov 24, 2007

### JesseM

It's impossible for any observer to reach the speed of light in relativity. But suppose someone is on a ship which moves away from the Earth at some speed v that's smaller than c (c is the speed of light), and then turns around and returns to Earth at the same speed v. In this case, if the person on Earth has aged by some amount T between the time the ship left and returned, then the person on the ship will only have aged by a smaller amount $$T * \sqrt{1 - v^2/c^2}$$. For example, if the person on Earth aged 10 years, and the ship was moving at 0.8c (80% the speed of light), then the person on the ship will have only aged by $$10*\sqrt{1 - 0.8^2}$$ = $$10*\sqrt{0.36}$$ = 10*0.6 = 6 years.

3. Nov 24, 2007

### slider142

As an alternative reply, if one uses continuity, one can argue that objects traveling at the speed of light do not experience any passage of time, so omitting the impossibility of a massive object accelerating to the speed of light, they will read their time as 5AM, no matter what time the person left back on Earth reads.

4. Nov 24, 2007

### robphy

Can you use continuity?
If so, can you show this explicitly?

5. Nov 24, 2007

### slider142

This is just assuming that the equation t' = t*(1-v2)1/2 holds when |v| = 1 (geometrized units) where v is the velocity of the primed frame as measured by the unprimed frame. Note how it doesn't make sense to input a non-zero t' and be able to solve for a t when |v|=1, even if we allow complex numbers.

Last edited: Nov 24, 2007
6. Nov 24, 2007

### robphy

You see, it seems to me that:
given two distinct events P and Q on a photon's worldline,
either P is to the future of Q, or vice versa.
So, I question whether time-measurements by massive particles (and conclusions drawn from them) can be applied in the massless case.

7. Nov 24, 2007

### slider142

Given two events P and Q, it is not at all necessary for one to be in the future light cone of the other (the interval may be space-like, not time-like. Indeed, the third possibility is that the events are light-like, which is the case since they are connected by the worldline of a photon). Photons, as measured from our reference frame, have future and past events with respect to our reference frame. As we know from our study of relativity, simultaneity is relative to each reference frame. It may just be the case that all events are simultaneous as measured from the frame of a photon.
Indeed, the idea of measurements *in* the frame of a photon is rather silly, but the interpretation of time in that frame is so common that it would be an omission to leave it unmentioned. :)

Last edited: Nov 24, 2007
8. Nov 24, 2007

### robphy

Yup.

Causality is a relation between events, regardless of any choice of reference frame.

Well... one needs definitions to make things work.
I know of no consistent set of definitions that will extend the notion of a massive particle's reference frame that of a photon.
Here's my earlier post on this matter: