Correct My Misunderstanding of Special Relativity

[guldurkhand]

If you are going fast enough, time will be slowed down. I have two questions about it:

1. If someone takes a videocamera in a spaceship and let him filming while sending the film with lightsignal, will the video be slowed down or will you see it at the same speed as the man who is filming it?

2. If you will see it on the same speed as the man who is filming it, than you can see in future.
Now you kill the man who is filming it. That means that there are 2 almost the same worlds. And why it isn't one world: if you go back in time and kill yourself, than you have never been back in time so it can't be right.

 

[Mentz114]

In order to define 'going fast' you need at least two people, say one on Earth and another in a spaceship, who is flying away. The observer on Earth would see the video slowed down compared with his clocks. The man on Earth would only see the pictures after they had traveled back to earth, which takes time.

That means your second conjecture ( as I understand it ) can't happen.

 

[smallphi]

The video is going to be slowed down because of the time dilation: a time interval between two events happening at the same place in the spaceship, appears dilated in the Earth frame. The light signals will just transfer that slowing down from one place in the Earth frame where the current position of the spaceship is to the observer on earth.

 

[guldurkhand]

Thanks, I get it.

 

[pervect]

If you transmit the video, both time dilation and a changing signal propagation delay will affect the rate of playback.

The rate of playback of the video will be the same as the apparent motion of clock hands watched through a telescope - it will be the relativistic doppler shift factor

$$k = \sqrt{\frac{1+v/c}{1-v/c}$$

http://www.astro.cornell.edu/academics/courses/astro201/doppler_rel.htm

This implies that an observer will see actually the video playback [edit] for an approaching object [/end edit] (or the hands on a clock watched with a telescope) faster than normal, for instance.

 

[smallphi]

The slowing down when the rocket is going away from Earth is caused by two effects: time dilation of time intervals in the Earth frame with respect to the spaceship and also time delay between signals emitted at different places on trajectory. The second effect is present even in Newtonian treatment and is given by non-relativistic Doppler effect formula.

The total of both effects is captured by the relativistic Dopler effect formula. If the source(on the rocket) is going away from the Earth then the Earth would observe a redshift i.e. longer wavelength and smaller frequency hence slowing down of the video.

It's interesting that if the rocket is going towards earth, then we have blueshift i.e. speeding up of the observed video. In this case we still have time dilation but the other effect -shortening of time intervals between signals emitted at different places on trajectory - overcompensates.

 

[blumfeld0]

I'm being dense but how is
"This implies that an observer will see actually the video playback (or the hands on a clock watched with a telescope) FASTER than normal(by normal do you mean as compared to someone on earth??), for instance"
the same as saying
"The video is going to be slowed down because of the time dilation" which is it?
is the observer from the Earth going to see video in slow motion or fast motion?

 

[robphy]

Take a look at the spacetime diagrams on http://www.csupomona.edu/~ajm/materials/twinparadox.html

 

[guldurkhand]

You will see the film slowed down(so there is lower frames per second)

 

[JesseM]

I'm being dense but how is
"This implies that an observer will see actually the video playback (or the hands on a clock watched with a telescope) FASTER than normal(by normal do you mean as compared to someone on earth??), for instance"
the same as saying
"The video is going to be slowed down because of the time dilation" which is it?
is the observer from the Earth going to see video in slow motion or fast motion?

If the ship is moving towards you, you'll see it in fast motion, not slow motion. But the speed you see things moving in your telescope depends on two things--firstly time dilation, and secondly the doppler effect, which is based on the fact that photons from successive ticks of the ship's clock have different distances to travel to reach you because the ship is moving towards you or away from you. In the case of a ship moving towards you, time dilation slows things down and the doppler effect speeds things up, and the net effect turns out to be that you see things sped up, but by a smaller factor than you'd expect if there was no time dilation and you were just using the classical doppler shift equation. And if you correct for the different travel time of each photon, figuring out the time at which each event on the ship was "really" happening in your coordinate system as opposed to the time you received light from each event, then you'll find that events on the ship were slowed down by the amount predicted by the time dilation equation.