Video camera links in Special Relativity

[YellowTaxi]

There's a video camera at a railway station. It can see the driver in the front of a fast moving train going past in the distance. Another camera is on the train itself, again filming that driver. v= (whatever it is)? so that gamma = 3

The train's own camera is filming the driver making a coffee, and he knows it takes him exactly one minute to do so. This guy's video is transmitted to the railway station.

The station camera films the same scene for itself, but naturally observes that the pilot took 3 minutes to make the coffee.

Questions:
1) Is there any difference between the 2 video images when they're fed into a monitor at the railway station.

2) If the video that was made inside the train and transmitted to the station is then re-transmitted back to the train, what will the train driver see, Will he see himself time dilated in his own film. If so, then by what factor ? ie 0, 3, 6 or 9

 

[PeterDonis]

The station camera films the same scene for itself, but naturally observes that the pilot took 3 minutes to make the coffee.

No, it doesn't. What the station camera films is not determined by the $\gamma$ factor, but by the relativistic Doppler shift factor. The $\gamma$ factor does not tell you what is directly observed, but what is calculated after correcting what is directly observed for light travel time.

If we assume that the train is moving away from the station, then the Doppler shift factor will be $\gamma(1+v)$, which will be larger than $3$, so the station camera's film will show it taking longer than 3 minutes for the pilot to make the coffee.

Is there any difference between the 2 video images when they're fed into a monitor at the railway station.

You mean, other than the difference in rates due to the Doppler shift? Obviously there will be differences in the images because they are taken from different viewpoints. There is also something called Penrose-Terrell rotation [1] which will affect the station camera's image.

[1] https://en.wikipedia.org/wiki/Terrell_rotation

If the video that was made inside the train and transmitted to the station is then re-transmitted back to the train, what will the train driver see

It depends on how the video is encoded and transmitted. If the video is encoded digitally (like an MP3 file), for example, it would not change at all from the original, either at the station or when re-transmitted back to the train, because the process of decoding would restore the original video as recorded, regardless of Doppler shift or any other effect during transmission.

A better way of getting at what I think you're trying to ask would be to imagine the raw image from the train's video camera transmitted towards a mirror at the station, where it is reflected and then received back at the train. Then, when observed at the train, this reflected image would be "running slow" by a factor equal to the square of the Doppler factor (one Doppler factor for the motion of the transmitter relative to the mirror, times one Doppler factor for the motion of the receiver relative to the mirror).