<p>The speed doesn't increase without bound as you move away from massive objects. It only increases to a maximum of about <span class="math-container">$1+GM/rc^2$</span> times faster. If <span class="math-container">$M$</span> and <span class="math-container">$r$</span> are the mass and radius of Earth, this factor is about <span class="math-container">$1.0000000007$</span>. 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.</p>

CC BY-SA 4.0
2022-09-20T00:21:27.563Z
suppose we live near a black hole.
WangAtChicago
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2022-09-20T00:27:32.283Z
And if massive object can increase the speed of computation, it is  amazing
WangAtChicago
CC BY-SA 4.0
2022-09-24T12:53:36.217Z
Relativity can only decrease the speed of computation (relative to the speed of a computer at rest far away from a gravity well).
Peter Shor 
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2022-09-20T00:04:06.690Z
2022-09-20T00:04:06.690Z
benrg
<p>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.</p>
<p>Is this argument true and practical?</p>
<p>Excuse me for posting such a strange question here, since I do not know where to post.</p>

CC BY-SA 4.0
2022-09-19T23:29:44.880Z
Have you consider about the time spent on being sent back to the person near the massive object?
XL _At_Here_There
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2022-09-20T21:16:22.143Z
background: https://physics.stackexchange.com/questions/25759/how-exactly-does-time-slow-down-near-a-black-hole  -- 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](https://en.wikipedia.org/wiki/Twin_paradox), with the twin that travels in space coming back younger, but with a computer replacing the twin.
Neal Young
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2022-09-21T00:14:23.000Z
@NealYoung, it's not true. see https://en.wikipedia.org/wiki/Time_dilation for more information. This is not like the twin paradox.
WangAtChicago
CC BY-SA 4.0
2023-03-02T06:55:22.243Z
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.
Yixin Cao
<time-complexity><physics>
Computational complexity and general relativity
WangAtChicago
# Computational complexity and general relativity

(Asked by: username_0 on 2022-09-19)

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.

**Tags:** time-complexity, physics
> **Comments:**
> **username_1**: Have you consider about the time spent on being sent back to the person near the massive object?  
> **username_2**: background: https://physics.stackexchange.com/questions/25759/how-exactly-does-time-slow-down-near-a-black-hole  -- 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](https://en.wikipedia.org/wiki/Twin_paradox), with the twin that travels in space coming back younger, but with a computer replacing the twin.  
> **username_0**: @NealYoung, it's not true. see https://en.wikipedia.org/wiki/Time_dilation for more information. This is not like the twin paradox.  
> **username_3**: 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.  

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## 1 answers

### Answer by username_4 on 2022-09-20. Score: 1

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.

> **Comments:**
> **username_0**: suppose we live near a black hole.  
> **username_0**: And if massive object can increase the speed of computation, it is  amazing  
> **username_5**: Relativity can only decrease the speed of computation (relative to the speed of a computer at rest far away from a gravity well).  

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