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# Time Dilation

August, 2011

### Question

So if a person traveling at a high rate of speed through the universe were to stream his trip live to earth, what would be made of the difference in the way we would be experiencing time? by challengingquestions in http://www.reddit.com/r/space/

There are 3 cases to look at. Let's assume speed is 0.99c (99% of the speed of light) in all cases.

1. Traveler is moving past Earth, such that from Earth, at the moment of transmission it appears a line from the traveler to Earth is perpendicular to the traveler's direction of motion. Then, the special relativity time dilation makes the traveler appear to be moving ~50 times slower than we do on Earth. Call

$s = time at the rate the traveler experiences$

s = (1 - v2 / c2 )-1/2

s = (1 - 0.992 / 1)-1/2

s ~= 0.02

2. Next, consider traveller is heading directly away from Earth. Now, not only is there 50:1 time dilation, there is also 0.99 red shift. So visible light leaving the spaceship arrives at Earth as microwaves, and the apparent time dilation looks like 0.02 x 0.01 = 0.0002 . So a message from the spaceship that took the spaceship an hour to send, would take 5000 hours to receive at Earth.

3. Last case: Spaceship is headed directly toward Earth. Now visible light from spaceship is 0.99 blue shifted, toward UV. 1-hour message beamed from spaceship would take

$s = \left(time dilation\right) / \left(1 - blue shift\right)$

s ~= 0.02 / 0.01

s ~= 2

So the message would take 1/2 hour to receive at Earth, the people talking in the message would sound like Donald Duck or the chipmunks, and would appear to be moving at double speed.