# Time dilation question for a sci-fi story premise

lendrick
Greets!

Sorry for the random question... I realize this forum is about real physics, so I apologize if this post is inappropriate. I'm not speculating that this is possible -- it's more of a thought experiment about how it would appear if it were. :)

I'm pondering a sci-fi plot where some aliens are using an unknown technology to slow down time by roughly 20% on their planet, relative to the surrounding universe. They're doing this in order to make their planet habitable, because otherwise it's the outside of their star's habitable zone, and would be too cold for them. I'm trying to speculate what the effects would be on the appearance of the planet from the outside, and the appearance of the rest of the universe from the planet. Here's what I've come up with thus far:

* Viewing the planet from space, everything would be red-shifted (such that plants would be red-orange instead of green).
* Viewing their star from the planet, it would be blue-shifted. There would also be more ultraviolet radiation than one would expect.
* The planet would be warmer than expected from the perspective of people on it.
* Here's where I'm really guessing: If you were to orbit the planet, you would discover it is lighter than you expect.
* It would be orbiting the star faster than expected.

Am I handling gravity right? If an object is moving away from you fast enough to be red-shifted, is the intensity of its gravity less than it would be if it were stationary relative to you? Also, assuming the "time warping" field ends at the edge of the atmosphere, would it look like the atmosphere is refracting light in an odd way?

Thanks!

Bart

## Answers and Replies

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Fredrik
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I'm pondering a sci-fi plot where some aliens are using an unknown technology to slow down time by roughly 20% on their planet, relative to the surrounding universe. They're doing this in order to make their planet habitable, because otherwise it's the outside of their star's habitable zone, and would be too cold for them.
First let's see what you mean by "slow down time". If a person was to leave the planet (slowly), spend a few years away from it, and then come back, would he have aged more or less than the people he left behind. My guess is that you mean that the people on the planet are aging slowly from his point of view, so that he would be the old one.

I don't see how this would make the planet warmer. If the idea is to capture more sunlight, keep in mind that the rate at which the planet radiates energy into space will increase by the same factor (or at least it seems that way to me). So the net effect seems to be zero. And the energy required to do something like this would probably be astronomical, perhaps more than the sun radiates in billions of years. If they have an energy source like that, they could probably find easier ways to heat their planet, or at least their houses.

It's hard to tell what exactly the effects would be. We would have to find a solution of Einstein's equation that actually describes this scenario. My guess is that the energy you input to curve space around the planet would make the planet, or rather the region of "space" it occupies, significantly heavier than before.

JesseM
Science Advisor
One way to slow time in the region of a planet (relative to the outside universe) without creating deadly tidal forces (as would happen if you put a big black hole at the center) would be to enclose the planet in a massive shell, in which case anything inside would feel no gravitational effects from the shell. In a sci-fi story you could probably get away with saying that the shell was made out of some form of matter that didn't interact electromagnetically (dark matter, say) so that it was transparent to light (to explain how the shell stays up if there are no electromagnetic bonds between its particles, perhaps you could say all the particles in the shell are in circular orbits around the planet)(edit: actually this is probably thermodynamically impossible, random gravitational disruptions to the orbits would likely convert the collection of particles from a shell to a solid sphere in fairly short order, so you'd need some non-electromagnetic force to hold the matter in a shell shape, but probably neither the strong or weak nuclear forces would really do the trick). The light from the star would in this case be blueshifted and more energetic, I'm not sure if Fredrik is correct to say that this wouldn't warm the planet since the planet would just radiate back more energy (after all wouldn't it also be true that if you just moved the planet closer to the Sun, it would still radiate back the same amount of energy as it received? It would obviously get warmer in this case though) And such a shell would make the gravitational pull of the planet/shell to those outside become greater, not smaller. Also this should have no effect on the speed at which the planet orbits as seen from outside, since the speed at which an object orbits a star doesn't depend on its own mass (though people on the planet would of course see a year go by more quickly because of the time dilation effect).

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bcrowell
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The amount of mass-energy your aliens would have to manipulate in order to carry this out would be many, many orders of magnitude greater than the amount of energy it would take simply to heat their planet.

JesseM
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The amount of mass-energy your aliens would have to manipulate in order to carry this out would be many, many orders of magnitude greater than the amount of energy it would take simply to heat their planet.
Well, once you built it you wouldn't have to continue to expend energy, so maybe they want to be on the safe side in case their civilization goes into a new dark ages at some point (although you could probably think up better ways of permanently warming a planet which would require less energy, like moving it closer to the sun or building a dyson sphere around it). Maybe the aliens are just eccentrics and did it because they though it was cool even though it's not really an optimal solution.

K^2
Science Advisor
Let me rephrase bcrowell's statement. The amount of mass-energy you'd need to cause such time dilation is many orders of magnitude greater than amount of energy you'd need to heat the planet until the star it orbits burns out to a dwarf or goes out in a supernova.

The amount of mass-energy your aliens would have to manipulate in order to carry this out would be many, many orders of magnitude greater than the amount of energy it would take simply to heat their planet.
Well he *is* writing a sci-fi story, and I assume that the slowed down time is meant as a plot device that is central to the story.

The "amount of energy required to do X" problem is usually where suspension of disbelief plays in sci-fi, so this is the part that can be overlooked, IMO.

Think of:
The amount of energy required for warp drive. (But oh, we can use antimatter!)

Then:
The amount of energy required to create enough antimatter, (whoops!)

Or: The amount of energy and the storage requirements required for teleportation.

The questions about redshift, blue shift, heat, etc. are good ones if he wants to make his story a bit more "harder" sci-fi. So I respect that. If he just goes with the time thing and doesn't consider the other consequences then he's writing a fantasy story.

He just needs to invent some kind of time slowing thingy the same way Star Trek invented inertial dampers and "Heisenberg Compensators" and write his story around it.

-DaveKA