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If I have a very computationally expensive task that no current computer can solve in less than 100 years, I could start the task on a powerful computer, get on board my Super Hyper Extravaganza Space Ship ©™, fly at 0.99999 the speed of light for a while, and when I return to Earth the time dilation effect means that I would have aged much more slowly than my computer. In fact, if I flew long enough, my computer would have aged a few hundred years more than me and the task would be completed.

However there is the issue that everything else on Earth would also have aged a few hundred years more, and the computation that I was solving would no longer be relevant.

If I was to put the computer on the space ship instead that would be silly because, being back on Earth, I would be aging faster than the computer, and from my perspective the task would take thousands of years instead of hundreds.

Is there a way to 'invert' this time dilation? Can I make time pass faster for just the computer, and essentially 'skip forward' to when the task is complete?

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Yes, But You're Not Going To Like It

Time dilation is all down to frame of reference. So, if you don't want everyone on Earth to age during the computation, you just have to take Earth with you. You already have an unreasonable Super Hyper Extravaganza Space Ship ©™ that can reach and maintain absurd speeds, so...

Make Earth into a spaceship. Will there be technical challenges? You bet. But you will accomplish your desired effect. You will have new, exciting problems, but your initial one will be solved!

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    $\begingroup$ I love this absurdist answer and look forward to your hitchhikers guide style book on the concept 😄 $\endgroup$ – Fred Stark Apr 1 at 8:08
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    $\begingroup$ This is my favorite kind of answer. $\endgroup$ – The Square-Cube Law Apr 1 at 10:20
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    $\begingroup$ Kurzgesagt has an interesting video about that topic youtube.com/watch?v=v3y8AIEX_dU $\endgroup$ – SigmaSoldier Apr 1 at 12:30
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    $\begingroup$ @jdunlop You would, of course, need to leave the computer behind, as close to the comoving frame as possible, and you would need to come back to pick it up later. Even a K-II civ would find this a challenge... $\endgroup$ – J... Apr 1 at 18:24
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    $\begingroup$ @JohnDvorak - Robert said "take the sun along. So you have all the problems involved with bringing the Earth and a million times the mass (in Fermi numbers). $\endgroup$ – jdunlop Apr 1 at 19:49
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The resolution of the twin paradox rests on the principle that there is an asymmetry between two observers. The observer on the spaceship must, for some amount of time, undergo an acceleration$^{\dagger}$ opposing its velocity so that it doesn't simply keep moving away from the observer on the planet. Therefore, the spaceship is, while accelerating, no longer in an inertial frame. If you do the calculations, you find that this leads to the observer in space experiencing time dilation when it returns to the planet. (For more details, see John Rennie's explanation on Physics Stack Exchange.) In short, when it comes to the twin paradox, time flows slower for the observer doing the accelerating.

Therefore, your suggestion would require keeping the computer in an inertial frame while putting the entirety of the universe (or at least Earth and everything else you cared about) in a non-inertial frame, which seems unfeasible with current technology! It's possible that we'll eventually figure that out, but by then, the supercomputer you need (i.e. from the year ~2121, as per your question) will already have been built.


$^{\dagger}$ Here, "acceleration" refers to any change in velocity, whether involving an increase in speed or a decrease in speed.

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    $\begingroup$ Note that the twin paradox doesn't rely on acceleration. $\endgroup$ – nwp Apr 1 at 9:47
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    $\begingroup$ @nwp It relies on the asymmetry between the two observer because of that acceleration. $\endgroup$ – fishinear Apr 1 at 12:03
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    $\begingroup$ @nwp In some cases, no, but does in scenarios that resemble the ones applicable to our situation. All of the situations mentioned there either involve significant departures from Minkowski spacetime or don't allow for the fact that, initially, the computer and everything else are stationary relative to one another (because they're all on the same planet!). $\endgroup$ – HDE 226868 Apr 1 at 13:55
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No. There are other ways to get a 100yr algorithm done faster than 100 years.

The physics of this answer have been answered already (no), however theres an engineering answer to how to do 100years of work in less than 100 years.

Firstly algorithms with these kind of runtimes need to be specially designed to be as parallel as possible, fault tolerant and resumable. Every hard drive this algorithm touches for storage is going to fail and need to be replaced over this time period, and when this happens, you need to not lose the progress you've made, or any data you're yet to process.

Apparently this consideration comes up at Google-levels of data, a single pass over all the data in a single database table takes so long, and the number of hard drives and server clusters involved is so large, that statistically one drive will fail per pass over the data. For your algorithm, every hard drive will fail and need replacing. Multiple times.

Because of this already-existing design consideration on your algorithm, and becuase you need to replace hardware anyway (and why buy antique hardware?), you will inadvertently upgrade the hardware over time as new hardware comes out. If computers double in power every 2 years, you can process 2% of your algorithm in 2 years, then upgrade and process 4% in the next 2 years, then 8% the next 2 years, then 16%, then 32%, then the final 38% in the last year. The algorithm will complete after 11 years and 5 hardware upgrade cycles.

Also due to the fault tolerant and resume features of the algorithm, you can upgrade the algorithm over time too, making it faster and more efficient as developers micro optimise every last detail of it over the years, putting out new versions, which the super computer starts using on the next reboot / hardware replacement. Sit a team of developers in a room for a year and theyll be able to speed anything up eventually, making the next year slightly more efficient. They could improve the compiler or 3rd party code to speed up the runtime too. They could discover new maths to totally rewrite the approach. How much this returns depends on how optimised the algorithm already was, I'd be surprised if it was below 100% speedup.

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  • $\begingroup$ At every point you mention, errors will be propagated into the system, not to mention bit flipping errors which will become even more significant as your machine sizes descend to the quantum limit. Also, what about the halting problem? This is programming as fantasy, even if this is not a halting problem, how can you have any faith in the answer? $\endgroup$ – chiggsy Apr 1 at 16:45
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Yes, but it has side effects

  1. If you have a wormhole and let one end travel on a relativistic round trip, you will get a wormhole connecting the time-dilated end in the future with the "stationary" end in the "present" - a time machine. Using CTC and information from the future for hypercomputation is trivial. Sadly, wormholes might just not exist in this universe, and if they do, CTCs might be disallowed.

  2. a Malament–Hogarth spacetime describes a (general) relativistic configuration that allows (potentially) for infinite computational task to be carried out in a finite observer's time. You set up the computer on a worldline that lies completely in your past, receive a signal from there after the sufficient number of computational steps has been taken (and if you never get a signal, you know that the machine carried out an (countably) infinite amount of steps without finding the solution or whatever). Unfortunately, in practical terms, you probably have to drop the Earth into a black hole to achieve this. Nevertheless, the coolness of having infinite computational power likely outweighs the disadvantages.

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    $\begingroup$ Notes on the MH solution: a Kerr black hole looks like it can be used for hypercomputation in this way but a) you can't perform an infinite amount of computation in a black hole because the things evaporate in a finite length of time (and even extremal charged black holes will ingest oppositely charged particles and be neutralised in a finite length of time) and b) readout is performed by crossing the inner event horizon which in the absense of FTL travel is a one-time trick and the results can't be communicated to the rest of the universe. $\endgroup$ – Starfish Prime Apr 1 at 9:12
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    $\begingroup$ Slightly less extreme: an impatient civilization could orbit a (probably rather large) black hole very close to the event horizon, with production, computation and observation moved to a more distant orbit. Just, uh, avoid building any skyscrapers, I suppose. $\endgroup$ – Ruther Rendommeleigh Apr 1 at 9:39
  • $\begingroup$ @Starfish Prime Can you weasel your way around this by keeping an extremal black hole stored somewhere until the universe is so old that no charges exist in your light comes to cancel the extremal parameters. I think I have a new terminal goal for the human species. $\endgroup$ – alessandro Apr 2 at 19:34
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    $\begingroup$ @alessandro I don't think that's a thing you can guarantee except in a universe undergoing accelerating expansion. We may not live in one of those, and even if we do there's an outside chance that the dark energy driving the expansion could evaporate black holes. I could easily be wrong, though. $\endgroup$ – Starfish Prime Apr 2 at 20:42
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In a fashion yes, but not really, and you're really not going to like it.

Time dilation effects are caused by gravity as well as speed & gravity effects reduce with distance.

The higher up a mountain you are the faster time flows compared to elsewhere on the planet.

Put it in space (the further from any large bodies the better) & it's even faster.

You're only going to get a small boost this way though.

So park the Earth in really close orbit around a black hole at the same time & that slows everything down for everyone on Earth compared to your space computer, the closer the orbit the faster it has to be to avoid falling in so you get your relativistic effects of speed at the same time.

The added bonus of course is we can then watch the heat death of the universe unfolding around us in apparent (to us) real time, should be interesting.

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    $\begingroup$ The restaurant at the end of the universe. $\endgroup$ – fishinear Apr 1 at 12:06
  • $\begingroup$ By the standards of this website, it would be reasonable to just position the computer high up some kind of "gravity tower" (close to a white hole or whatever). $\endgroup$ – ShapeOfMatter Apr 1 at 18:40
  • $\begingroup$ @ShapeOfMatter OK, I've taken the time to actually read up on white holes properly (deleting other comments on them as they're now excess to requirements) // they're not theorised to 'spew time' // you've taken the 'opposite of a black hole' bit & run with it in the wrong direction // if a white hole can exist in this universe it will spew matter out // so time will be just the same as anywhere in deep space & maybe a bit slower than a completely empty bit of space because of time dilation from that matters mass. $\endgroup$ – Pelinore Apr 5 at 21:39
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The energy required to accelerate a 100 metric ton mass to 99.995% of c is about $8.9\times10^{23}J$, which is about 1000 times our yearly energy consumption. I'd wager that for 1000x our current GDP, you can build a pretty big and powerful computer instead.

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If you figure this out, you have solved P v NP

This would no longer be an old joke:

Humor: Einstein and Lorentz Play Marbles

Einstein begins, “You know, Hendrik, people say we think so much alike we must be twins, but we are obviously different ages.” Lorentz responds, “Yeah, I know, it sort of a twin paradox – I think Siggie started that one. Forget it, let’s play marbles.” Lorentz said, “Here’s the rules: From a 50/50% mix of red and blue marbles we each have to put the blue marbles in a blue container and the red marbles in a red container.” Einstein responded, “I’ve done something like this before, and I noticed I get worse and worse as the number of items to sort gets larger and larger.”

Being the mathematicians they are, they decided to give each other a 50/50% chance of winning. That meant doing some preliminary games to develop a handicap – like in golf. First Lorentz tried it. Given 2 marbles to sort, he completed the task in 2 seconds. 4 marbles, 4 seconds; 10 marbles, 10 seconds, etc. Now, for Einstein: 2 marbles, 2 seconds; 4 marbles, 24 seconds; 10 marbles 3628800 seconds, etc. Lorentz said, “Looks like I scale linearly as x, as the number of marbles, increase … But, wow, Albert, you scale as a factorial, x!”. They both realized the handicap was x! / x, with Albert’s nonpolynomial rate (x!) on top of Hendrik’s simple polynomial rate (x).

Einstein said, “I think I know how to normalize for our respective handicap using a new vehicle I just invented that runs on an E=mc^2 engine and dilates time (t) to t’ based on division of t by that equation you just discovered with ( 1 – (v^2 / c^2))^-0.5. We will have to neglect F = ma because it will be crushing and W = fd because of the consequential heat at the launch site.”

Lorentz agreed and added, “Let’s play for the best rate, after normalization, because I don’t want to do all the integrals for total velocity and time!” Einstein fret that he had problems naming the vehicle, “I found that Folks-Wagon is taken, so I called it a You-Van. In fact, I’ll ride first because you are so slow.” They worked out the math and found the necessary velocity for the handicap to sort 100 marbles:

t’ = t (( 1 – (v^2 / c^2 ))^-0.5) solve for v, with c = 1: v = ( t’^2 – t^2)^0.5) / t’ substitute the scaling factors: v = (((x!)^2 – x^2)^0.5) / (x!) enter actual numbers: v = (((100!)^2 – 100^2)^0.5) / (100!)

Lorentz looked again and said, “Too bad Cook and Levin haven’t been born yet!” Einstein added, “Oops, we have to wait for Wolfram, too, as we need a lot of precise digits for this calculation. Another day …”

In other words: As Velocity Approaches Light Speed, P Becomes Equivalent to NP for Computations Using Zero-Mass Particles

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    $\begingroup$ NP is nondeterministic polynomial, not non-polynomial. $\endgroup$ – Ray Apr 1 at 20:31
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    $\begingroup$ Yes, the problem here is not time but number of computation steps - as in Big O notation, but for sci-fi engineering, I think time and steps are the ~ same. BTW, the WP article is unreadable. $\endgroup$ – Youvan Apr 1 at 23:35
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If you know how to contain a black hole, you shouldn't even need the Super Hyper Extravaganza Space Ship ©™. You could just make a black hole, contain it, park the computer near it, and due to the time dilation from the black hole, the equation could be solved relatively quickly.

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    $\begingroup$ "the equation could be solved [really slowly]." fixed it for you, black holes slow time, so, more time passes for everyone outside it's influence, so the computer will take longer to do the calculations, relatively. $\endgroup$ – Pelinore Apr 1 at 14:10
  • $\begingroup$ How about, then say you park earth around the black hole in the habitable zone of the accretion disk? $\endgroup$ – Madman Apr 1 at 15:00
  • $\begingroup$ @TheMadmanandtheFool - several people have proposed putting Earth nearer the event horizon than the computer in their answers, yes. $\endgroup$ – jdunlop Apr 1 at 16:08
  • $\begingroup$ @Pelinore Thanks for the correction. This is venturing into theory here, but you could replace the black hole with a "white hole" instead. $\endgroup$ – random internet person Apr 5 at 13:36
  • $\begingroup$ @randominternetperson OK, I've taken the time to actually read up on white holes properly (deleting other comments on them as they're now excess to requirements) // they're not theorised to 'spew time' // you've taken the 'opposite of a black hole' bit & run with it in the wrong direction // if a white hole can exist in this universe it will spew matter out // so time will be just the same as anywhere in deep space & maybe a bit slower than a completely empty bit of space because of time dilation from that matters mass. $\endgroup$ – Pelinore Apr 5 at 21:33

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