Time DIlation and Observation

1. Mar 1, 2015

julianwitkowski

If an observer was traveling with a Lorentz factor that would make that observers time slower than someone's on Earth, what would that observer see watching a live video feed, or if it was possible to observe Earth with a telescope, and vice versa?

I understand that either party would only see light that's been reflected, or being broadcast from Earth (which is moving faster than and at the same relative speed for both parties),

However, relative the moving observer's time would be slower... What effect does this have on the perception of the light thats moving relative for both observers?

I'm trying to come to terms with whether the moving observer would see Earth in fast forward, or normal, and what Earth would observe if they had a live video feed or magic telescope looking at the moving observer?

Would Earth see the moving observer moving normally as they did at that point in the distant past wrt to the Lorentz factor?

2. Mar 1, 2015

stevendaryl

Staff Emeritus
I think maybe what you're asking about is the "relativistic doppler shift". If you have a source broadcasting radio signals that is moving toward you, the frequency is shifted higher:

$f' = f \frac{\sqrt{c+v}}{\sqrt{c-v}}$

If you were watching a TV signal, you'd see the video running faster by that same factor. If the source is moving away from you, the frequency is shifted lower:

$f' = f \frac{\sqrt{c-v}}{\sqrt{c+v}}$

The relativistic Doppler shift can be thought of as due to two different factors:
1. The frequency is shifted lower by time dilation: $f_1 = f \sqrt{1-v^2/c^2}$
2. Also, if the source is moving toward you, then the distance each peak of the signal has to travel gets shorter and shorter. If the source is moving away from you, the distance each peak of the signal has to travel gets longer and longer. This causes the apparent frequency to rise or drop: $f' = f_1/(1\pm v/c) = f \frac{\sqrt{c \pm v}}{\sqrt{c \mp v}}$

3. Mar 1, 2015

Staff: Mentor

If the earth-bound station was transmitting one frame every second, more than one second would elapse between receipt of each frame on a spaceship moving away from earth so the video feed would be slow. Conversely, if the ship were approaching earth, the video feed would be fast; frames would reach the ship at a rate greater than once per second. This happens because when the ship is moving away from earth each transmission has farther to travel to reach the ship, while it's the other way around if the ship is approaching the earth.

A transmission from the ship to the earth behaves the same way - the video looks fast if they're approaching and slow if they're moving apart.

However, when the observers remember to correct for the light travel time (if the frame was transmitted when they were six light-seconds apart, then the time of reception is six seconds after the time of transmission) both observers will correctly conclude that time is running slow for the other one - they aren't generating frames at the one-per-second rate that you'd expect if there were no time dilation.

Google for "relativistic Doppler effect" for more.

4. Mar 1, 2015

UVCatastrophe

Try this at home:

Suppose B is moving with a speed of .6c away from A in A's rest frame. In B's rest frame, A is moving at .6c in the opposite direction away from B. They are both collaborating in an effort to observe a space-time paradox.

After one year elapses in A's frame, A sends a beam that says "Hi B---One year has elapsed here. From, A". Of course, this will take some time (it turns out, another 1.5 years, in A's frame) to get to B since B is moving away. By the time the message gets to B, 2.5 years have elapsed (in A's frame).

If you do the time dilation calculation, you'll find that only 2 years will have elapsed in B's frame. From B's perspective, A has been moving away from B at a constant speed of .6c. Thus, B does their own calculation, and finds that it took .75 years for the message to travel from A to B. A had sent the message "One year has elapsed" after 1.25 years had elapsed in B. In other words, everyone on B had aged 1.25 years in the time A's passengers aged 1 year.

B has confirmed that A's clocks are moving slower, with the exact gamma factor that you'd expect for a moving frame of .6c. They fire back, "Got ur message -- 2 years have passed."

A, however, knows how long light takes to catch up to its moving target: 1.5 years. Back in A's frame, 2.5 y had passed when their "One year" message was received by B. It'll be another 1.5 years before A receives B's "2 year" message. When everyone on A has aged 4 years, they realize that, in the time it took them to age 2.5 years, the passengers of B had aged only 2 years.

Why have I gone through this whole spiel? I want to make it plausible that both A and B observe each other's clocks running slower than their own. I'd also like to point out that there's nothing special about the Earth's frame -- Earth could be, say A (or B) in the example above. In fact, this idea that there's nothing special about Earth's absolute motion is what makes special relativity such a success.

The next step is to imagine overloading this process, so A is sending a square wave pulse now with a given frequency. This pulse will end up red-shifted when received by B, meaning fewer pulses in the same amount of time. Likewise, pulsed waves sent from B will arrive at A with the same time dilation. You might imagine each pulse containing an image file, and the result is a movie. The movie would play slower, regardless of whether B is broadcasting to A or vice versa.

Note how transmission across space (and time) plays a role here. I think a lot of students imagine that reference frames are like magic boxes that alter the passing of time. The temptation is then to somehow merge them together, or to be in two places at the same time to observe a paradox. But you can't do that without violating some physical principles.

5. Mar 1, 2015

bcrowell

Staff Emeritus
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