[Scourge of Ages]

(the following questions are not the question:) Could I just google this? Probably, but I like the interaction. What makes me think there's physicists here? It worked last time, and I just need a general understanding.

My question regards relativity, and it is:

Are two objects traveling in the same direction at the same speed - even if they're separated by a long distance - in the same frame of reference?

Imagine a scenario where two space ships are moving through space at, let's say, 0.5C. They're separated by... 50,000 km. How would radio communication between these two ships work? Would it be roughly normal but with a little extra lag due to the extra distance traveled? Would it be identical to if they were both stationary? Would there be some sort of frequency weirdness like redshift due to them both moving so quickly?

[ShadowsOfLight]

It's been a while since I took my last class relating to special relativity, but here's my take (also without Googling): if they are travelling perfectly parallel, in straight lines, at the exact same speed, they would be in the same frame of reference (for the context of this question). The speed of light always looks like c (in a vacuum) to the observer. I don't think there would be any difference in their communication from being stationary from their points of view.  I bet things would get weird if you tried to analyse the situation from a stationary observer's point of view...

Redshift/Blueshift only relates to travelling away from or towards the source of light, because of a perceived change in frequency (but not speed).

Once again - it's been a while so I might be misremembering. Special relativity is weird 

[Scourge of Ages]

Special relativity is weird 

I don't know much, but I do know that

[Mongoose]

Yeah, vaguely-remembered classes from 15 years ago (God I'm old) make me think ShadowsOfLight is correct. If both ships are traveling at the same constant velocity, they'd be in the same inertial reference frame, and there would be no discernible difference compared to if they were viewed as stationary.

[Colonol Dekker]

Now if two trains are travelling on parallel tracks 20 meters apart, at a full speed of say 125mph, and you try to throw a ball between them, will it make it?

[The E]

Now if two trains are travelling on parallel tracks 20 meters apart, at a full speed of say 125mph, and you try to throw a ball between them, will it make it?

Depends. Can you make an accurate throw when there's a 125 mph wind around?

[perihelion]

How far apart do these parallel trajectories need to be before the accelerating expansion of the space between them due to the expanding universe becomes significant enough to measure?

Taken to the nth degree, can ANY two objects actually occupy the same identical frame of reference? 

[Fearless Leader]

I don't think there would be any difference in their communication from being stationary from their points of view. 

This sounds right. I think there would be blue/red shift on any radio communication if the ships are still accelerating or decelerating, just because the radio waves would have a constant speed but the ship would be accelerating or decelerating.

Even though space is a vacuum, there is still something there, and your communication is going to have to pass through it. 

Im gonna get sloppy with the math because its 12:30am here.
 You're traveling at 149,896,229ms and want to do a 1 second burst transmission on your 1m wide antenna, over a distance of 50,000,000m. That transmission will be spread over a volume of about 749,481,150,000,000m3. Deep space has an average density of maybe 1 atom per cm3 but might be as high as 1000 atoms/cm3. (This is where I know Im too tired for this) because I converted it to 749,481,150,000,000,000cm3, the most common element in the observable universe is hydrogen with an atomic weight of 1, that equals  1.6735 x 10^-24 grams, or as I like to type it out  0.0000000000000000000000016735g. If you take the next steps you're trying to transmit through anywhere between 1.25mg at the high end and 0.001mg of hydrogen on average. Hydrogen, although flammable, is actually capable of insulating against radio signals, so you're going to have signal degradation just due to the amount of particle you're passing your communication through. How much radio signal can 1mg of hydrogen block? I dont know. Maybe all of it. Maybe none of it.

Im not sure if any of that is right, but it sounds good to me right now

[Scourge of Ages]

That is a very good point!

[Fearless Leader]

Thank you! I was worried that sleepy me was just talking out of my ass.

There were a couple other things I though of while trying to type that. Like, what kind of signal noise the energy source and/or drive systems would be generating, but that's all theoretical.

On a practical level there would be a few issues that would be problematic at our current technology level. Just aiming a directional antenna at something that far away would take extremely sensitive equipment. It's been a while since I messed with satcom anything, but its extremely slow speeds even for low earth orbit satellites that are 2,000km away and all my experience is getting data links from Earth. But that's through atmosphere and with equipment built by the lowest bidder. I imagine that whoever had two space ships traveling at that speed would be able to overcome the practical problems and filter signal noise before traveling that fast and trying to talk to each other.