# Isn't time dilation relative?

1. Jan 9, 2007

### paintonfire

Please forgive if this question is not up to snuff. Indeed, I am a painter, and very much the amature physics enthusiast.

One of Einstein's classic thought problems that interested me was the idea of two astronauts passing each other at a high velocity in open space. The idea was that in this case motion was completely relative... it was equally proper to say astronaut A was zooming by astronaut B as it was to say the opposite.

If motion is completely relative in this sense, then how does this figure into the time dilation problem (i.e., the space traveler who leaves earth at a high rate of speed. For those left on earth, time passes much more quickly than for our intrepid traveler.) Sadly, if our astronaut ever returns, all of his or her loved ones are all long dead, etc.

If motion through the universe is completely relative, indeed, if it is equally proper to say that the earth left our astronaut at a high rate of speed, then does time dilation not cancel out? Or is there some objective way to measure the relative velocities and distances involved so that we know who is aging more quickly than whom?

Any feedback regarding this question would be greatly appreciated.

2. Jan 9, 2007

### Hurkyl

Staff Emeritus
This question is relative too. The answer depends on how their ages are being compared -- it depends on which reference frame you consult to answer the question.

3. Jan 9, 2007

### nakurusil

There are two main situations and they are indeed very different:

1. If the twins observe each other from passing rockets that are in uniform rectilinear motion they will each see the other's time as being dilated by the same amount

2. If one twin flies away and turns around and comes back to compare clocks with the twin that continued in rectilinear and uniform motion, then, the twin that turned around would notice that less time has elapsed on his clock. The mathematics of this situation are shown nicely here.

4. Jan 9, 2007

### DaveC426913

Yes. In short, the key to the paradox is that one of the subjects (twins/spaceships/planets/whatever) changes its acceleration, thus distinguishing itself from the other, inertial objects.

5. Jan 10, 2007

### Littlepig

don't cancel:

you must think something like this: you have a person in earth, he is moving at speed v1(as earth is moving) for that person, time is passing "normaly".
another person goes to make a space trip, before spaceship starts moving, time is passing normaly to both persons, when spaship start moving at a v2 speed, happens that v2>v1. the diference betwen then, is the velocity that person in space is from the person on earth, so that diference, is what you need to take in count...

the expression to calc that is: $$t_1= \frac {t_2}{ \sqrt{1-v_2^2/c^2}}$$ (1)

where t_1 is the time in inertial observer, and t_2 is the time in moving body.
v_2 is moving body speed...

if v_2=0, t_1=t_2, if v_2=c, is impossible as t_2/0 is inf...(the prove that bodys can't go faster than c)

so, for the guy in earth who is counting time t_1, t_2 is bigger, as denominator is always smaller or equal to 1 and bigger than 0

for the guy in spaceship who is counting time as t_2, $$t_2= t_1 \cdot \sqrt{1- v_2^2/c^2}$$

and he knows that t_1 for him, is smaller, as product is always smaller or equal to 1 and bigger than 0

Last edited: Jan 10, 2007
6. Jan 10, 2007

### ranger

t_2 should be the time lapse at rest while t_1 is the time lapse of the moving body relative to t_2.

But shouldnt it be t_2*0? Which would establish the fact that no time would pass for the object traveling at c when compared to their earthly counterparts as opposed to t_2/0. The reason why we cant travel at v_2 >= c is becuase no matter how much energy we add, v_2 would only creep towards c. We can add more and more energy but v_2 would only seem to stand still as it gets closer and closer to c.

Last edited: Jan 10, 2007
7. Jan 10, 2007

### Littlepig

ups, in tex i made a mistake, puted \fract and forgot a } instead of \frac...so it hapears t_2*Y factor instead of $$t_1= \frac {t_2}{ \sqrt{1-v_2^2/c^2}}$$