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I wish to clarify my doubts regarding time dilation

Is it possible for a planet to be habitable like Edmund's planet from interstellar, which has somewhat similar gravitational force as Earth (9.8 m/s^2) and has time dilation with the time on that planet slower in the rate when compared with the time on Earth. If it is possible, what could be the reasons for it to happen?

Note:

  1. The planet is not orbiting any black holes.

  2. Let us consider that 1 day on that planet would be 2 on earth.

  3. Similar g force is for the reason that humans could even inhabit that planet.

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Peaceman
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    at sea level your head is older than your toe while standing... thanks but no thanks time dilation! – user6760 Nov 30 '17 at 08:59
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    Not an answer, a recommendation: In sci fi, most stuff involving time makes absolutely 0 sense. It only makes sense in the rare cases where it happens to be convenient to the plot. If you have to justify it, say an ancient alien device did that. Never mind how it works, nobody cares ;) – Raditz_35 Nov 30 '17 at 09:19
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    @Raditz_35 agreed. I have not seen interstellar, but i have heard conflicting opinions on whether it makes sense or not. Either way: you're right. Ancient alien device is the #1-go-to when you want supernatural effects in a sci-fi scenario. Also does not make you have to explain it, as non of the people in the story know how it works. – ArtificialSoul Nov 30 '17 at 10:42
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    Earth is orbiting a black hole -- Sagittarius A. What, exactly, do you mean by "not orbiting"? – Yakk Nov 30 '17 at 18:15
  • I've asked a similar question (not a duplicate by any means) on having time dilation for an entire star system. Unfortunately that system has to be moving silly fast for anything noticeable. https://worldbuilding.stackexchange.com/questions/4962/do-different-star-systems-experience-time-differently – Twelfth Nov 30 '17 at 23:34
  • Does the fact that time passes faster at higher altitudes in real life count? =) – jpmc26 Dec 01 '17 at 00:25
  • Why does it matter if it's orbiting a black hole? If you're worried about the lack of light, just have it be a binary star system where one is producing enough light for photosynthesis, while the other is a black hole. – Golden Cuy Dec 01 '17 at 06:59
  • What @Raditz_35 said. The Mulians did it. – R.. GitHub STOP HELPING ICE Dec 01 '17 at 16:37

4 Answers4

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Time dilation comes from gravity and/or velocity.

Since the planet is not orbiting a black hole it would either have to orbit another super heavy mass or fly through space with a lorentz factor of 0.5 (when seen from earth) as that would equal time dilation of a factor 2.

$t_{planet} = \gamma * t_{earth};$ with $\gamma$ being the lorentz factor of $\gamma = \sqrt{1-(v/c)²}$

with $\gamma = 0.5$ the velocity is $v = 0.866 * c$
This means your planet would have to travel with 86.6% times the speed of light.

EDIT:
as Raditz_35 pointed out

It should be worth pointing out however that there is absolutely no way that planet would be habitable. Let's forget about the event that made it go that fast, space is not a vacuum and stuff would bombard that planet at insane speeds

EDIT:
Bridgeburners pointed out that since it's time dilation by velocity and not gravity you have to take into account that it is a more difficult scenario and the perceived time changes strongly depending on the observer.
I did not properly clarify that this might not be the effect you were going for.

ArtificialSoul
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    Yes. It should be worth pointing out however that there is absolutely no way that planet would be habitable. Let's forget about the event that made it go that fast, space is not a vacuum and stuff would bombard that planet at insane speeds – Raditz_35 Nov 30 '17 at 09:16
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    @Raditz_35 that is correct. I'll add that. – ArtificialSoul Nov 30 '17 at 09:17
  • Would it even be possible to be on an orbit at that speed? I would assume that (even if it goes around a supermassive black hole) the orbit would have to be so big that you would have multiple black holes inside the orbit, just by random chance because it goes around multiple galaxies. Which would then not be an answer to the give question. – Fabian Röling Nov 30 '17 at 12:16
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    @Fabian It's possible to orbit at that speed. The sun you are orbiting would have to travel at roughly the same speed. – Taemyr Nov 30 '17 at 12:46
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    Things bombard our planet at insane speeds all the time. Time dilation is why we can observe certain particles at ground level that should have decayed before traversing our atmosphere. – chepner Nov 30 '17 at 13:24
  • If we observed a planet moving away from us at 0.86c, it would observe us moving away from it at 0.86c as well, and Earth is certainly habitable. – chepner Nov 30 '17 at 13:28
  • What if that planet is revolving at the habitable zone of a star bigger that sun? Is it possible for time dilation to occur since the gravitational pull would be large because of that star. Even if there is a chance. What would be the Lorentz factor? @ArtificialSoul – Peaceman Nov 30 '17 at 14:27
  • @MohmedShahid You seem to lack the perception of scale. A regular sun is not just a bit lighter than a black hole. Not even a gigantic version of it is even close to it. A black hole has a significantly higher gravitational pull than any sun. To my knowledge only neutron stars come even somewhat close to the high density of black holes. Not sure if they have a realistic chance of having habitable planets. – ArtificialSoul Nov 30 '17 at 15:03
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    The most feasible way for this to be the case is if the galaxy is also moving at that speed relative to the Milky Way. The most feasible way for that to be the case is if the relative speed is due to ordinary cosmic expansion via Hubble's Law. Using Hubble's constant, this would put the galaxy at a distance of roughly 12 billion light years. So it cannot be accessed by normal travel means. But possibly a wormhole. – Bridgeburners Nov 30 '17 at 16:03
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    It must be noted that Lorentz time dilation (unlike gravitational time dilation) goes both ways. That is, if somebody made the trip to this planet (from Earth) and back, they will have aged half the time that Earth has. However, if someone made the trip from this planet to Earth and back, they will also have aged half the time of that planet, not twice as you might expect. This may seem like a paradox but the key is based on the acceleration required for the person to make the trip. – Bridgeburners Nov 30 '17 at 16:07
  • @Bridgeburners yes, correct. I have not made that clear. I'll edit the answer accordingly later or tomorrow. – ArtificialSoul Nov 30 '17 at 16:09
  • @chepner Those particles that hit Earth at near C speeds are tiny relative to Earth. I think what the answer is saying is if your planet is moving at 0.86C, asteroids / comets / dust clouds are going to do lots of damage to your planet because of the speed difference and the larger mass of those objects. Although if your plant is going that fast then the whole solar system is too, so only extra solar objects would do extra damage. – Caleb707 Nov 30 '17 at 16:13
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    The issue here is that Lorentz time dilation, like the velocity that causes it, is relative, so the time dilation factor would depend rather heavily on where you were observing the planet from. For example, if this planet had a moon (which was somehow orbiting it and not being pulled out of its orbit by the things they're flying past), then you could travel to and from that moon with no more time-dilation-related effects than we experience when travelling to our Moon. – anaximander Nov 30 '17 at 16:42
  • A planet could be moving that fast relative to earth with no real issues as long as the interstellar gas around it is also moving at that speed. That’s the trouble with relativity: nothing is stationary. – Joe Bloggs Nov 30 '17 at 22:38
  • @ArtificialSoul "A black hole has a significantly higher gravitational pull than any sun" is a misleading way to look at it. You could replace the Sun with a black hole of the same mass as our Sun, and all the other bodies in the solar system would feel the same gravity and have the same orbit (including Earth). Black holes are incredibly dense, not necessarily incredibly massive. The gravitational pull near the event horizon of the black hole is much greater than you can experience near the Sun, but only because the same distance from the Sun's centre of mass puts you deep inside the Sun. – Ben Dec 01 '17 at 06:01
  • However I'm not sure a star would need to be really massive to cause significant time dilation out to planets orbiting in its habitable zone. I'm not sure whether a start that big could remain stable. – Ben Dec 01 '17 at 06:03
  • @Ben though theoretically "lightweight" black holes could exist they, but to my knowledge they do not exist. They are always by several magnitudes heavier than our sun. If i am correct then it is not misleading as the scenario you describe is not realistic. – ArtificialSoul Dec 01 '17 at 07:25
  • @ArtificialSoul Stellar mass black holes can be only 5 times the sun's mass, hardly several orders of magnitude. According to https://en.m.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit the maximum size for a neutron star is only 1.5 to 3.0 solar masses. Stars can be more than 100 solar masses, so there are certainly black holes and stars of similar mass. – Ben Dec 01 '17 at 11:32
  • @Ben okay, then i was incorrect. Sorry. Thanks for correcting me. – ArtificialSoul Dec 01 '17 at 11:33
  • If you get your velocity by orbiting something very quickly it could still work for story purposes. – Christopher King Feb 14 '18 at 00:21
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Your universe has a much, much lower speed of light than ours. Say, 1000 meters per second. Relativistic effects become dominant at attainable speeds.

Emilio M Bumachar
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    I'm not sure what affect such a low speed of light would have on every day experience, but I'm sure it would be drastic. – chepner Nov 30 '17 at 13:30
  • @chepner There should be a sweet spot speed, high enough for a familiar breakfast and shower, low enough for completely different fighter jet dogfighting. – Emilio M Bumachar Nov 30 '17 at 13:48
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    Does your every day experience involve molecules of any kind by any chance? The electrons in there exhibit quite strong relativistic effects. This would also have to be an universe where matter for example works completely different. One would have to invent a completely new physics for this one. You would have to handwave so much that explaining that one particular time travel detail feels strange. Not saying this wouldn't be ok, it's just strange to solve one problem by creating a million new ones – Raditz_35 Nov 30 '17 at 13:51
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    i agree with Raditz_35. It's certainly more dramatic to ignore all the side-effects from changing the speed of light than ignoring the implausibility of a habitable planet with twice the time dilation of earth. – ArtificialSoul Nov 30 '17 at 14:02
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    The question is, given such a universe, would 1000 m/s actually be an attainable speed? The reason the speed of light isn't attainable is not simply because it's so fast, it's because the energy required to accelerate increases the faster you go until it moves toward infinity as you approach the speed of light. All else being equal, a universe with a slower speed of light would simply result in all matter in the universe moving at a slower rate; you still wouldn't be able to get to the speed of light just because it's slower than our universe. – Simba Nov 30 '17 at 14:55
  • @Simba you missed the point of that. If the speed of light is 1000m/s it is by definition not attainable. The idea is that lorentz contraction/dilation effects start at way lower speeds. And 900 m/s would be 0.9c resulting in a dilation of roughly 0.45. – ArtificialSoul Nov 30 '17 at 18:53
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    @ArtificialSoul You missed the point of Simba, to accelerate to 0.9c in both universe should take the same amount of energy which would mean it is just as impossible in both universe. Which means any time dilation would be relative to c in both universe. Which means lower speeds relatively across universe means nothing. – A. C. A. C. Nov 30 '17 at 19:01
  • @A.C.A.C. then he is simply incorrect as the speed of light has huge implications for everything electromagnetic and thus quatum mechanics including it's impacts on chemistry. I am very certain nuclear physics as well as chemistry would look different with a different speed of light. – ArtificialSoul Nov 30 '17 at 19:04
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    @ArtificialSoul His point doesn't conflict with any of that.. – A. C. A. C. Nov 30 '17 at 19:22
  • A.C.A.C. is correct. My point is that if the speed of light is attainable, then it .. uh... isn't the speed of light any more. Yes, everything changes if you change the speed of light, but even ignoring all other side-effects, the speed of light is unobtainable by definition. Making it slower doesn't change that definition, because if you do change that definition it has immediate implications on the concept of time dilation that would fundamentally break the assumptions that the question is based on. It would break the universe anyway, but even if it didn't, it would break the question. – Simba Dec 01 '17 at 12:51
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ArtificialSoul gave a great answer. But there might be another way.

The planet could rotate really fast, like REALLY REALLY fast. Obviously centripetal forces would tear it apart unless... the planet is also really really massive. Being massive and dense would negate the requirement that the planet has similar surface gravity to Earth, however you could make it so that at the equator the combination of centripetal forces and gravity gave out at least an apparent Earth gravity.

I'm not sure this extreme Mesklin-like planet could physically exist (let alone naturally develop), I might come back later with the math when I have time, I didn't really give it much though.

If possible, only the equator could be habitable, with gravity increasing and time dilation decreasing the more you move toward the poles. No freaking idea what the sky would look like, or what the consequences of having part of the planet age faster than others. Will think about it

SilverCookies
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  • The sky would probably look like this: https://worldbuilding.stackexchange.com/questions/97177/is-a-long-exposure-like-night-sky-possible – Fabian Röling Nov 30 '17 at 12:19
  • Might be possible, but i doubt a planet rotating that quickly could hold an atmosphere. Not sure though. – ArtificialSoul Nov 30 '17 at 12:21
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    You'd certainly have some quite exciting Coriolis effects. – Sobrique Nov 30 '17 at 14:05
  • @Fabian Much worst actually, day and night would be indistinguishable; combine that with time dilation and everything would permanently look like a perpetual redshifted dawn – SilverCookies Dec 01 '17 at 21:20
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How hard does your science have to be? Because if the answer is "not at all," then there's the ever-popular hand-waving effect:

The deep, in-universe, answer can be something like:

Some millions of years ago, an advanced and unknown alien race required a laboratory with specific pseudo-relativistic conditions. They used an unknown technology to generate a localized time-like metric and tied it to the world (or solar system) at a quantum level, to ensure that the planet (or solar system) didn't travel outside the time-like metric for the duration of the experiment.

When the aliens were done with the experiment, the forgot to switch the effect off, so today we use the world because X.

Or maybe the experiment isn't over yet, and the mice are going to be really hacked when they come back and find out we've skewed their results...

While the answer that the characters know can be:

We don't know why it's like this, but boy it's useful for X!

The difference between the two can be the story in itself.

Ultimately, unless the how is crucial to the story, it's a minor detail and can be hand-waved away. It's not my favorite method as a reader, but it does occasionally help to make the implausible into the plausible.

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