1. Jul 29, 2011

### Rishavutkarsh

one twin alice is moving with 99%C another john is at rest on earth

this means 1 second of alice= 100 secs of john (approx)

suppose john runs at the speed of 1 km/s for 100 secs then for alice he is at 100 km/sec as she saw the whole what he did in sec and also, when she comes after an year she observes his twin to be of 100 years doesn't this mean that alice sees johm faster than he really is?

2. Jul 29, 2011

### ghwellsjr

At 99%C the time dilation factor is approximately 7, not 100. Where did you get the idea it was 100?

If John is running at only 1 km/s, you will not be able to discern any difference beween that and him remaining stationary if you are going to approximate the time dilation factor. You have to carry out your calculation to a lot of digits to be able to show the difference.

And when you ask about alice seeing "john faster than he really is", are you asking if she is seeing him running faster or are you asking if he is aging faster?

You also need to be clear when you say "she comes after a year" whether you mean a year on her clock or a year on John's clock or a year on a stationary clock. And do you mean she travels for a year at 99%C and then turns around and takes another year to get back or do you mean that her entire trip takes a year?

3. Jul 30, 2011

### Rishavutkarsh

i suppose you are right now i will try to use the best english i know, i made up 100 just by my mind

one twin alice is moving with 99%C another john is at rest on earth

this means 1 second of alice= 7 secs of john

suppose john runs at the speed of 1 km/s for 7 secs . but alice observes the whole phenomena in just 1 sec as she should .
alice comes in a year (her clock) and john has passed 7 years till then

suppose they kept an eye on each other the whole time then alice should see that john does 7 times faster right? if not then why?

4. Jul 31, 2011

### Pengwuino

Wait, exactly why does john need to run anywhere? If john was running for 7 seconds, yes alice would come back and say that she only saw him running for 1 second when they compare clocks.

5. Jul 31, 2011

### ghwellsjr

Thanks for the great improvement in your English.

When two observers in relative motion are watching each other, in addition to the time dilation (and length contraction), you have to take into account the increasing time it takes for the light to travel between them while they are moving apart and the decreasing time when they are finally getting back together. It's a very simple formula derived by Einstein called the Relativistic Doppler Factor. Look it up on wikipedia.org.

So for your scenario where the relative speed is 99%C, the Factor is 0.071 while they are traveling apart and 14.1 when they are finally getting back together. So if John starts running for 7 seconds shortly after Alice starts out, since she will see his clock running at a factor of 0.071 times her own, she will see him running for 7 seconds divided by .071 or for 98.6 seconds. But if John waits until just before she gets back, she will see him running for 7 seconds divided by 14.1 or for 0.496 seconds.

Of course, in the first case, she will see him running in very slow motion and, in fact, the frequency of the light will be so red-shifted that she will not be able to see him with her naked eyes and she will need some specialized optical equipment in order to actually observe him. In the second case, she will see him running in very fast motion and the light will be so blue-shifted that she will need some different optical equipment in order to see him.

6. Aug 2, 2011

### Rishavutkarsh

but isn't it true *one observes a clock fastest when they are at rest to each other* . i get the first case but what about the second like if alice watches his wrist watch (don't forget u mentioned running in fast motion) doesn't that mean that sees his clock in haste moving faster than her own ! ?

7. Aug 2, 2011

### ghwellsjr

In Special Relativity (ignoring the General Relativity effects of gravity), it is true that a clock runs fastest to those observers that are stationary with respect to it. This is called the Proper Time.

But you were asking about what observers in relative motion would "see" when they "kept an eye on each other" and I explained that time dilation isn't the only issue. There is also the issue of the light transit time. What this does is stretch out the observation when the observers are moving away from each other so it looks like they are watching a movie in slow motion and it compresses the observation when the observers are moving towards each other so it looks like they are watching a movie in high speed. But astute observers will realize that what they see is partly an artifact of the light in transit issue and will take that out to calculate what the actual time dilation of the other one's clock is and when they do that, they will always conclude that the other one's clock is running at a slower rate than their own.