# Another question on time dilation

1. Aug 27, 2007

### Luke987

It is my understanding that, as an example, a spaceships (traveling close to the speed of light) inhabitants would appear to be moving very slowly to us on Earth as a result of time dilation yet would the ship be moving monstrously fast?

Also, if two ships at said speeds above were to pass each other would the inhabitants of both see one another moving in slow motion? If so, why; if both ships are the same speeds should there not be a discrepancy but rather motion speeds as we know on Earth in our day to day lives?

Thanks.

2. Aug 27, 2007

### JesseM

You have to be careful about wording like this, there is no absolute notion of "speed" in relativity, only speed relative to a particular frame, and thus whether or not something is "traveling close to the speed of light" depends on what frame you choose. If an object is traveling at 0.99c relative to the Earth, you can look at things from the point of view of a frame where the object is at rest and the Earth is moving at 0.99c, and this frame is as valid as any other inertial frame.
See above, since speed only is meaningful relative to a particular frame, your question doesn't really make sense--in the Earth's frame the ship would be measured to be traveling whatever its velocity is relative to the Earth. And the amount by which its clocks were slowed down, as measured in the Earth's frame, is just a function of its speed in the Earth's frame--if the speed of a clock in a given frame is v then the time dilation factor of the clock as measured in that frame is always $$\sqrt{1 - v^2/c^2}$$.
They would both measure the other one's clocks to be slow; what they would see using light-signals would also be affected by the Doppler shift (which happens because light signals from successive ticks of a moving clock have a different distance to travel to reach your eyes, thanks to the clock's motion), so that as the ships were moving towards each other they'd each see the other ship's clock ticking fast, and as they moved apart they'd see the other ship's clock ticking slow by an amount greater than the time dilation factor. But if they correct for the time-lags of light signals from successive ticks, in both cases they will find that the other ship's clock is ticking slowly in their frame by the amount predicted by the time dilation equation.
"Same speeds" relative to what? In each ship's own frame, they are at rest while the other ship has a high velocity. Certainly it's true that if you pick a frame where both ships have equal speeds, then in that frame both ships will be measured to have their clocks slowed down by identical amounts, but this wouldn't be the frame of either ship.

3. Aug 28, 2007

### Luke987

Thanks for the post JesseM. As you may have guessed I'm new to physics so sorry for any badly strung sentences.

So if the ship has nothing to compare its velocity too, no 'frame', then the passengers feel at rest and another ship too flying near to c, relative to Earth say, would look to be in slow motion?

I think my main query was that if both travel at 0.99c relative to Earth then why would they both see each other in a slow motion state as opposed to a normal motion state?

Last edited: Aug 28, 2007
4. Aug 28, 2007

### JesseM

The convention is that each observer always defines themself to be at rest in their own frame, it doesn't matter whether or not they have something to compare their velocity to.
Not sure I understand, what is the speed of the second ship relative to the first, or the speed of the first relative to Earth?
If they're both traveling parallel to one another, then each one is at rest in the other's frame so the clocks aren't measured to slow down. But I thought you were talking about a situation where they were both traveling at 0.99c relative to the Earth, but in different directions, so each one would measure the other to be moving at a substantial fraction of c in their own frame.