Time dilation

[Joeloki]

Accordingly to special relativity, the instant 'now' to an observer is the instant when light reaches his eyes to tell him of a distant event. This being so, it follows that if a clock moves away from the 'fixed' observer at high speed, the intervals between the swings of the pendulum will appear longer since the light from them will have progressively further to travel. In other words the time of the moving clock will appear to dilate relative to the observer.

Now my question is: if this effect occurs when the clock is moving away from the observer, will the effect be reversed - for exactly the opposite reason - if the clock moves towards the observer, thus causing a time contraction? If this is true does it not demolish the 'paradox of the twins' wherein a space-travelling twin returns to earth to find his brother older than he is!?

[gbfish]

Sounds logical to me!

[rojash]

Time dilation occurs when one body is moving relative to the other - it doesn't need to be moving AWAY from the other. But it's reciprocal. ie Each observer will see time moving more slowly for the other, and that's where the paradox lies.

[Joeloki]

Thanks for your answer rojash, but you haven't really answered the question. You say that it doesn't really have to be moving AWAY - but this is really my point: why?

[jake-the-peg]

This is discussed in some depth on Wikipedia.
http://en.wikipedia.org/wiki/Twin_paradox

The twins paradox is so called because of the belief that either twin could claim to be at rest and that both could therefore "expect" the other twin to be older.

In fact they are not equivilent one undergoes acceleration that the other does not.

I think that you may have a misunderstanding of the "cause " of time dilation. It is not simply an apparent difference due to the time light takes to convey the information to us.

An example of this is muon decay -more muons created in the upper atmosphere reach the ground than you would expect - their lifetime is longer because of their high speed
http://hyperphysics.phy-astr.gsu.edu/hbase/rel ativ/muon.html
the fact that they are travelling towards us is irrelevant it is their velocity which is important

[mibn2cweus]

Bear in mind that the Doppler effect is a separate phenomenon unrelated to time dilation. When the clock returns to the point of origin the time indicated would be �slow� compared to an equivalent clock that remained at rest.

Time dilation remains in effect even as the clock moves closer; this is true even though you might expect that the clock would appear to tick faster than normal due to the Doppler effect, indeed this is what you would observe at velocities less than about 80% of C (the velocity of light). At a velocity of about 80% of C, time dilation would have an equal and opposite effect and the clock would then appear to tick at the normal rate, but the damage has already been done and time loss would be apparent as the clock moved toward you at this velocity.

Remember that time is constrained by the cosmic speed limit C at which time ceases to elapse for objects moving at this velocity. Actually, velocities approaching C become problematic for objects possessing mass, due to the exponentially greater requirements of energy as space/time conforms to the constant velocity of light.

[rojash]

"Thanks for your answer rojash, but you haven't really answered the question." Joeloki, your question is about time dilation, as mibn2cweus points out, though, what you then go on to describe is the doppler effect, NOT time dilation. The effect you describe has nothing to do with relativity, and can be experienced at fairly low speeds. It happens with sound, too (the classic example being the change in the sound of an ambulance sirne as it passes you.)

[Joeloki]

My thanks to all respondents. You have all been most helpful. I can now sort out the problem that has been bothering my mind. The Doppler effect provides the key!