Would computers accelerated to high speeds compute "faster" from our point of view? I woke up to this thought yesterday:
Lets say Computers A and B have exactly the same specifications and at time T both are set to process an algorith that would normally take exactly 1 year and exactly at T the A computer is accelerated to 0.5c (or anything c). Both are set to automatically broadcast the result to a central computer. 


*

*Would A finish processing first from my point of view? 

*Would we be able to receive the broadcast from A?   

*Would it matter if A were travelling at a straight line or orbiting a
planet or even a star system?

*Would it be feasible to accelerate a computer to "compress time" on a
Machine on the likes of the LHC.


Excuse me part: I'm sorry if this question is not fit for this StackExchange , I'm sure someone asked that , but I don't know how to look for this- I'm really new to all things physics.
 A: Since you only mention acceleration to 0.5c, we'll assume we're dealing with special relativity alone.  In this case, your accelerating computer 'loses time' -- its clock moves slower.  Computers ultimately work on clock cycles.  Thus it is fair to say that, as its clocking is ticking slower -- from your point of view -- the computer on your desk will finish first.  


*

*As its clock is ticking slower, it'll take longer to perform the same calculation...from your point of view.  The Lorentz transformation gives the ratio by which the travelling clock will slow:
$\gamma^-1 = \sqrt{(1-v^2/c^2)} = (\sqrt{1-0.5^2}) \approx 0.86$, (or $\gamma \approx 1.154$)

*Second question meaningless given the above; if it landed back on your desk after a year's round trip, your desktop machine would be finished, it wouldn't (from the above, if you start 1 Jan one year, start looking for an answer midway through Feb the year after).

*Here it gets interesting.  If it was orbiting a planet, gravitation comes into play, and with it general relativity.  For example, Wikipedia says GPS satellites lose ~7ns/day due to special relativity, but gain ~45ns a day due to general relativity.  So instead of cruising at 0.5c, you might want to fling your computer off to 'park' far away from really big planets.  

*Possible?  Yes.  Feasible?  Depends on the length of your calculation, the cost of building the equipment needed to achieve it, and the benefits of the -- possibly marginal -- decrease in calculation time.  I suppose one might conceive of some futuristic 'space station supercomputer receiving station' in orbit around a black hole.

A: You're thinking about gravitational time dilation.
Time machines do exists. If you go in a space ship and travel around the supermassive blackhole in the center of Milky Way, close enough to not fall in it, and then come back to Earth, you just traveled to the future (relative to the space further from you). So in that thinking line, if you want to make a computer run faster by gravitational time dilation, you must be living in an environment of extremely high gravity and put your computer outside this environment, where time runs faster relative to you. A computer orbiting the Earth will be faster than a computer here, but just by a few nanoseconds.
Would we be able to recieve the broadcast from this computer? Yes, the same way we are able to receive pictures sent from Jupiter by Voyager 1 and 2, we would need to count the interference in the transmission but nothing more than stretching/shrinking waves.
A: 1) No, because it's actually going slower from your perspective. In special relativity, "the fastest wristwatch is always your own".
2) Yes, but remember that it's farther away from us now, so it will take some time to get to us (if it was travelling at 0.5c it will take 50% longer to get to us).
3) Mostly in that as an observer the redshift effect would be different. 
4) It would be feasible to accelerate to dialate time, but that wouldn't be useful.
