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(Somewhat related to Do different star systems experience time differently?)

In my futuristic settings1, Humanity discovered a network of portals allowing for instantaneous travel (hand-waved, their exact nature is irrelevant to this question, but these portals are miraculously exempt from science).

I want to have such a portal leading to a survivable2 planet with this special quality - time there run much faster than Earth (or anywhere else in the Solar system, for that matter), ideally, every 10 days "here" takes around 40 years "there".

Is there any set of conditions that can create such time-differential effect?

1: This is intended for a pen and paper role-playing game. Players will hear description of the setting. Their characters will start on that planet, the goal being to keep the players ignorant of their exotic state for the first chapter of the campaign.

2: To clarify, "survivable" in this context means that two-three "generations" of a tribe of "cavemen" planted there by advanced humans could survive (so around 80-120 years in their local time). These cavemen may be engineered/augmented if necessary, but only in ways that will not be immediately obvious to inquisitive players. They are transported there after any preparations already took place, including creation of a working ecosystem. The planet should have a sun, breathable atmosphere, gravity and other conditions similar to Earth's. Other than that any exotic conditions which make this time-differential scientifically possible are fair game (orbiting a black hole, rogue star system traveling at near light-speed compared to Sol or the Milky Way, exotic material composition for the entire system etc. etc.)

Bonus points if you can mention any problems your set of conditions raises (e.g. traveling at near light speed means continuous bombardment by cosmic particles), and even better if you can suggest mitigations for them (e.g. have the planet orbit around a gas giant with a strong magnetic field that will divert most of the particles).

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    $\begingroup$ Watch the movie Interstellar, note especially their experience on the first planet, Miller's Planet. $\endgroup$ – JBH Dec 4 '17 at 0:09
  • $\begingroup$ @JBH Miller's Planet experienced strong time dilation. This situation is its inverse where time runs faster on the alien planet. Of course, here from the point of view of the alien planet Earth is very time dilated. $\endgroup$ – a4android Dec 4 '17 at 11:38
  • $\begingroup$ @a4android, Oh, dang, you're right. I got it backwards. OK! Start with a planet near a black hole! Yesiree... that's the ticket! $\endgroup$ – JBH Dec 4 '17 at 16:09
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There are two tools at your disposal, as a science-based worldbuilder, that can provide answers to questions like this one. They are Special Relativity and General Relativity.

Your question reminds me of the classic Twin Paradox. In this paradox, one member of a pair of identical twins takes a trip on a rocket at near the speed of light, while the other stays at home on Earth. When the traveler returns, they will have aged less than their stay-at-home sibling. If you replace the rocket with your unusual planet and just kind of have it accelerate around the galaxy (by attaching it to a big rocket or something), you could arrange it so that 10 days there take the same amount of time as 40 years here. That's exactly the opposite of what you're going for.

Since that didn't work, let's try placing your planet in orbit around a large black hole. Gravitational time dilation causes time to pass more slowly the deeper you are in a gravitational well. As an example, the Earth's core is about 2.5 years younger than its surface. This is, once again, exactly the opposite of what you're going for.

You could solve this by attaching Earth to a big rocket or putting Earth in orbit around a large black hole, but that doesn't exactly answer the spirit of your question.

So here's what I propose: It's not relativistic weirdness that's causing time on your planet to behave weirdly; it's the planet's portal. Maybe these portals have built-in clocks that keep them synchronized, so that one hour on any planet is one hour on any other. Perhaps whoever built the portals added this feature to counteract the effects of gravitational time dilation on planets orbiting large black holes. In any case, the clock in this planet's portal is damaged, and is running some 1460 times slower than it should. As a result, if you come to Earth from this planet, stay for ten days, and then go back there, you'll arrive once the portal thinks ten days have passed... but since the portal's clock is running slow, you will actually have been gone for forty years.

This solution does horribly violate causality, but so does literally any form of faster-than-light transportation. You've already completely broken physics; this doesn't break it any more.

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  • $\begingroup$ Thanks for a first answer :). There's something I'm a bit confused about, though - in the twins paradox, what makes Earth's frame of reference the "fast timed one" (you can always view yourself as static and have the whole universe accelerate in the other direction)? $\endgroup$ – G0BLiN Dec 3 '17 at 20:20
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    $\begingroup$ @Goblin; relativity is not about speed relative to you so much as energy level relative to you. In this context, the person in the rocket is travelling faster because he has more ENERGY applied to his situation. He's actually felt the acceleration of energy being added to his rocket in the form of increased kinetic energy, which means that his speed is always the 'higher' one, relatively speaking. $\endgroup$ – Tim B II Dec 3 '17 at 22:33
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    $\begingroup$ @G0BLiN The difference, in the case of the twins paradox, is that the Earth is not accelerating, while the rocket accelerates quite a lot. And it's the acceleration that causes the time dilation. You can't get around that by measuring things relative to an accelerating reference frame, because accelerating reference frames are fundamentally different from non-accelerating ones. If you're in a sealed, windowless box, you can't tell how fast you're moving, but you can tell how fast you're accelerating. Acceleration feels just like gravity, because, in GR, they're literally the same thing. $\endgroup$ – Someone Else 37 Dec 3 '17 at 23:48
  • $\begingroup$ Sorry this would be a good answer, but you gotten the situation completely around the wrong way. It is the alien planet where time runs faster not planet Earth. For this solution to work it would have to be our Earth orbiting the supermassive black hole. $\endgroup$ – a4android Dec 4 '17 at 11:52
  • $\begingroup$ @a4android if you read the whole answer you would see that the answer demonstrates that the two possible solutions that do not violate physical principles are, as you pointed out, backwards. It then posits a third solution, that can give the required answer, but violates physical principles (namely causality). $\endgroup$ – Snyder005 Dec 4 '17 at 21:53
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The other world might not be real (a computer simulation) or it might have some unusual TBD biology that enables the quicker perceived time (such as mosquito or bacterial life times and evolutionary quickness). The portal might do the work of translating the biology of a traveler to be suited for the destination.

Had another thought. What you might want is a white hole. A white hole might be negative mass, and cause time inflation (instead of dilation) close to the Schwarzchild radius. You've asked for a roughly 1:1,200 time inflation, so the planet would need to orbit very close to that edge (R-planet ~ 1.0008 R-schwarzchild) Moreover, the gradient between one edge of the planet and the other shouldn't be too large, or the gradient would cause all sort of odd effects. So, 6,000 kilometers should be about 0.001 Rs - at a minimum Rs = 6 million kilometers. That's a big white hole (about ten times the diameter of the sun), but not huge. The white hole could be inside-out, where the negative energy portion interacts with the rest of the universe, or outside-in, which would be very different. The planet would somehow have to fight the force of gravity pushing it further away - maybe the aliens that seeded the planet or built the gateway have something.

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  • $\begingroup$ Time inflation! Time dilation is called time dilation because geometric representations in Minkowski diagrams shows time intervals expanding with increasing velocity. This could be just as easily called 'time-inflation'. The equivalent geometric representations of faster time in a Minkowski diagram would be smaller. The more accurate term for such a phenomenon would be 'time-contraction.' That said, your white hole would have negative gravitational mass to create a time-contract region containing the planet. [to be continued] $\endgroup$ – a4android Dec 4 '17 at 11:46
  • $\begingroup$ [in our exciting episode] The planet could remain in orbit around the white hole if it was composed of matter with negative inertial mass. This would have problems for visitors & explorers made of positive mass matter. But that only makes life more interesting. Plus one for an interesting concept in your answer. $\endgroup$ – a4android Dec 4 '17 at 11:49
  • $\begingroup$ @a4android Actually, if the "planted" cavemen were "manufactured" from negative mass, that'll resolve another issue with the campaign world (why they shouldn't use the portal to physically travel to Earth) $\endgroup$ – G0BLiN Dec 4 '17 at 16:41
  • $\begingroup$ @G0BLiN That's fine with me. It solves the problem, possibly two problems since you have moved things to the next level. Well done, sir. $\endgroup$ – a4android Dec 5 '17 at 8:01
  • $\begingroup$ James - I think that after the edit, the first paragraph of this answer isn't adding much (thanks for the out-of-the-box suggestions, but I'm trying to find an answer to this question, not circumvent it). Also - can you please expand a bit about the negative mass (I'm not sure it have to be a white hole to have negative mass and vice versa, but I'm no physicist...) $\endgroup$ – G0BLiN Dec 5 '17 at 8:48

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