Does Time Dilation Make Earth Clocks Look Faster from a Spacecraft?

[Ziggity]

If someone leaves on a spaceship from Earth at near the speed of light, the clock on the spaceship will appear be moving slowly when viewed from the earth.

When the guy on the spaceship looks at the clocks on Earth, they will appear to be moving fast, right? This makes sense since when the guy on the spaceship returns to Earth more time will have passed for the Earth than for him.

I just wanted to make sure since it seemed that some people in the "time dilation" thread were saying that the clocks on Earth will appear to be moving slowly when viewed from the spaceship. I might have been misinterpreting what people were saying.

Thanks,
Ziggity

 

[HallsofIvy]

No, people have been saying exactly what you thought. Since speed is "relative", in the frame of the person on the spaceship, the person is not moving while the planet is moving at high speed. The person on the spaceship will see people on the planet moving slowly relative to himself just as people on the planet would see time moving slower for him.

That is applying special relativity while the spaceship is moving a constant speed relative to the planet. In order for the "twin paradox" to come into play, you have to have the person accelerate away from the planet initially, then accelerate to turn around and finally accelerate to land on the planet. All that acceleration takes you out of special relativity and into general relativity.

 

[selfAdjoint]

Umm, Halls, you don't need GR to handle simple acceleration cases in SR. You can do calculus on the SR background. Indeed all quantum field theory, and most of string theory too is done on the SR background! Manifest covariance they used to call it; not only relativistic, but in-your-face relativistic.

 

[DW]

Originally posted by Ziggity
When the guy on the spaceship looks at the clocks on Earth, they will appear to be moving fast, right? ...
Thanks,
Ziggity

Observations are not about "appearences", but are about how things actually "are" according to the observer's coordinate frame. As observed from the spaceship, the Earth clocks will only advance fast when the ship accelerates toward it at the far end of its round trip. This is due to a break in simultaneity between the initial and final inertial frames with respect to which the ship is at rest before and after acceleration. Durring portions of the trip for which the ship is not accelerating the ship frame observer finds that the Earth clocks run slow just like the Earth frame observers find that the ship clocks run slow. In a round trip both observers will agree on how much less the ship clocks will read than the Earth clocks only once this acceleration effect concerning relative simultaneity is accounted for.