# Computational complexity and general relativity

According to general relativity, the time that a Turing Machine near a massive object spends on computing every step is longer than the time that the Turing Machine far awayfrom a massive object spends on every step. Of course, the former TM cann't speedup on computational complexity, but can speedup on the same time. So, if we are near the computer and massive object, we can get much earlier result from computer far away from us and other massive objects, equivalently, we may make speedup of Turing Machine in this way, or make computational complexity relative.

Is this argument true and practical?

Excuse me for posting such a strange question here, since I do not know where to post.

• Have you consider about the time spent on being sent back to the person near the massive object? Commented Sep 19, 2022 at 23:29
• background: physics.stackexchange.com/questions/25759/… -- it seems plausible to me that light appears to slow down near a black hole only relative to a far-away observer, because (in that explanation) in some sense "distance" around a black hole is increased. can you explain why you think that this would, in any way, result in slower computation? this seems similar to the twin paradox, with the twin that travels in space coming back younger, but with a computer replacing the twin. Commented Sep 20, 2022 at 21:16
• @NealYoung, it's not true. see en.wikipedia.org/wiki/Time_dilation for more information. This is not like the twin paradox. Commented Sep 21, 2022 at 0:14
• When we talk about the "time" a Turing Machine uses, we mean the number of steps, right? This is not the time in the physical sense. Commented Mar 2, 2023 at 6:55

The speed doesn't increase without bound as you move away from massive objects. It only increases to a maximum of about $$1+GM/rc^2$$ times faster. If $$M$$ and $$r$$ are the mass and radius of Earth, this factor is about $$1.0000000007$$. In the time that a CPU on Earth does 4,000,000,000 cycles of computation, a CPU far from gravitating bodies does about 4,000,000,003. So it isn't worth it.

• suppose we live near a black hole. Commented Sep 20, 2022 at 0:21
• And if massive object can increase the speed of computation, it is amazing Commented Sep 20, 2022 at 0:27
• Relativity can only decrease the speed of computation (relative to the speed of a computer at rest far away from a gravity well). Commented Sep 24, 2022 at 12:53