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Assume we have a super-computer working on an important problem, and we estimate it will take about $200$ years to solve. But, we need the answer in $20$ years.

Could we ship the super-computer into space at $1/10$ of our speed to get the answer in $20$ years?

Edit We want the super-computer to age, so it gets $200$ years of production while we age $20$ years. Is this not possible? This would be the opposite of the twin paradox: the traveling twin would be traveling much slower. Edit2 The goal is to over-clock the computer by sending it on a slower journey. The $200$-year solution takes $x$ computer cycles, so the check-points should send results from more cycles, regardless of how its clock compares to ours.

Fred Daniel Kline
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    1/10 our speed in what reference frame? – The Photon Sep 17 '19 at 18:55
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    OP, Remember in the twin paradox, it's the twin who stays home that ages (experiences more time, and does more calculations) and the one who goes on the spaceship who stays young (and if she took a computer along, it'd have less time to do computations). – The Photon Sep 17 '19 at 18:57
  • @ThePhoton, I want the super-computer to age relative to us. If we can get it to go 1/10 of our speed, I think that should do it. Unless time-dilation only has an affect on living things. – Fred Daniel Kline Sep 17 '19 at 19:07
  • FWIW, you need a speed difference of about 0.995c to get a Lorentz factor of 10, i.e. 10× time dilation. And as everyone has said, you need to be the one who goes away, turns around, and comes back. If you send the computer, it ages 2 years over the journey that takes 20 years Earth time. That's just the way spacetime geometry works. – PM 2Ring Sep 17 '19 at 21:10
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    Please make your post one cohesive question. An edit history is available for those who are interested. – BioPhysicist Sep 17 '19 at 21:31
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    Also, see my edit. I think you have some misunderstandings of relativity. – BioPhysicist Sep 17 '19 at 22:59
  • Related: https://physics.stackexchange.com/q/375333/109928 – Stéphane Rollandin Sep 17 '19 at 23:27

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As mentioned in the comments, your conclusion is backwards (haven't checked the validity of your calculations. I am not sure what you mean by 1/10 of our speed). We know from the twin paradox that the traveling twin is the twin who has aged less when they return to Earth due to changing inertial reference frames during the trip.

Therefore, if you wanted a calculation done "quickly" you would have to be the one who hops on a spaceship, goes on a long journey, turns around, and then comes back.

I suppose there is nothing wrong with this in theory. I guess you would need to have sufficient justification that the use of resources to do this trip outweighs the time it would take to just wait on Earth.

Or you could go hang out by a black hole for a little bit.

Based on your edits I think I understand what is going on here. You are taking "the universe" to be some "absolute reference frame", and you are thinking that the Earth has some speed relative to this frame. Then you send the computer at a speed relative to the universe that is less than the Earth's speed relative to the universe. So you say that the time dilation of the Earth relative to the universe is then greater than the time dilation of the computer relative to the universe, so we get faster calculations relative to us.

This is not how relativity works. There is no absolute reference frame that has the "true time", and there is no moving relative to this absolute reference frame that changes your own experience of time. All that matters in this scenario is the relativity between you and the computer. This is why saying "the computer is at 1/10 our speed" is meaningless. The computer can only have some speed relative to us.

BioPhysicist
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  • The traveling twin is going faster than us. Maybe the question should be: can we have the twin travel slower and thus age more? – Fred Daniel Kline Sep 17 '19 at 19:09
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    @FredKline Saying the traveling twin is going faster than us is not a well-defined statement. What reference frame are you referring to with this statement? And your question didn't mention anything about traveling faster or slower. Therefore, I am not sure I understand your comment – BioPhysicist Sep 17 '19 at 19:16
  • I got the idea from: https://physics.stackexchange.com/q/74543/15901, where the traveling twin was less productive. – Fred Daniel Kline Sep 17 '19 at 19:17
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    @FredKline Right... So you would want to be the traveling twin. You would not want your computer to be the traveling twin – BioPhysicist Sep 17 '19 at 19:21
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No.

First of all, $1/10$ of your speed doesn't result in $10$ times faster clock — the Lorentz's transformations are a bit more complex.

Second, the true effect of such great time dilatation is able only in speed very very close to speed of light, so it's practically impossible.

Third, to obtain the result, you have to meet supercomputer again, and the duty of changing velocity (to accomplish this) would (mainly) be on you — in the opposite situation the supercomputer would appear as a slower one, and not a faster than a supercomputer placed just next to you (in your reference frame).

MarianD
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  • I'm thinking super-computer transmit check-points during its journey. – Fred Daniel Kline Sep 17 '19 at 19:25
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    During your journey. As the distance between you and computer permanently increases, the regular information (let's say, every month) from the computer point of view) you obtained in longer period (let's say, every 10 mohths). (From your point of view, the computer clock is slower.) – MarianD Sep 17 '19 at 19:40
  • That's what I was afraid of. Thanks. – Fred Daniel Kline Sep 17 '19 at 19:44
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Adding to the previous answers - it is correct that you got the twin paradox the wrong way around - it is the travelling twin that ages less. Nonetheless there is a bizarre use for this, it is not in making calculations more efficient, but one could build a relativistic freezer.

Does your produce go off before you eat it? Easy, just ship it on a rocket moving close to the speed of light away from the earth and then back - the produce will be still fresh even after a long time has passed in your rest frame. Of course, the timing of the delivery and the energetic requirements make this use a little bit far-fetched.

Akerai
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  • +1 for the freezer. I didn't have it backwards, I just had the traveler going slower, which doesn't work. See the penultimate paragraph of Aaron Stevens' answer. – Fred Daniel Kline Sep 18 '19 at 11:07