Travel (how far?) into the future using a black hole and light-speed space craft?

Question

A person is traveling in a space craft that was designed and built by sufficiently advanced aliens. This space craft left from Earth and is capable of traveling infinitely close to the speed of light. His/her journey takes him/her into space where the craft then orbits a black hole before sling shooting itself back to Earth. Is it feasible (through combined time distortion of both light speed travel and the proximity to the extreme gravity of the black hole) that when the traveler returns to Earth, millions of years have passed on Earth, despite the journey having only lasted no more than 10 years for the person inside the craft?

If so, depending on how close to the speed of light the space craft is traveling and the size of the black hole, how many millions of years is it reasonable to expect to have passed on Earth for a 10 year journey relative to the traveler? 5 million years? 50 Million? 500 Million? Less? More? etc.

For the sake of this question we can assume there is a black hole approximately 5 light years away from Earth.

EDIT: Thank you E Reid, Hyperion, user25972 and Justin Eiler for helping me realize my misunderstanding of the perceived time for our traveler and how a distance of 5 light years would be too short for him to experience 10 years of travel at near the speed of light.

Answer 1

Forget the black hole. Just from travelling arbitrarily close to the speed of light,the time dilation is arbitrarily high. This Article includes formula:

$$\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$$

You state that ∆t is 10 years. Pick a v to get any ∆t′ you like: millions of years or more!

Answer 2

There is no real-world physical mechanism that can make almost-light-speed travel work like you are describing. If the black hole is five light years away, and the space-craft travels at almost-light-speed, the space-craft will take just a little over five years to travel to the black hole from the point of view of an observer on Earth. Depending on how close to light speed the space-craft was traveling, there will be relativistic time dilation effects, so the astronaut in the space-craft will experience a briefer time (perhaps much briefer).

The black hole, on the other hand, can produce effects like you describe. This is also a case of relativistic effects--mathematically speaking, high gravity acts just like any other form of high acceleration. So you could feasibly have a space-craft travel to the black hole, spend a (to the astronaut's frame of reference) fairly brief time in the gravity well of the black hole, yet have an observer on Earth experience millions of years. This could happen--theoretically.

The problem is, it most likely could not happen practically. For a stellar-sized black hole (a black hole created from the collapse of a massive star), a space-craft that is close enough to the black hole to experience that degree of time dilation will also experience massive tidal effects. These effects will be enough to shred any space-craft no matter what materials it is made from: no material humanity can or could possibly make could withstand that degree of force. And if the space craft did not shred from the tidal forces, the people inside most certainly would. Now, you could get around this by making the black hole a super-massive black hole (billions of times the mass of our Sun), but with most black holes that readers may be familiar with, that is less workable.

Now, if you are writing a story or creating a setting for an RPG campaign, you could (of course) completely ignore the tidal effects. You could decide the tell the audience that the ship is made from some material that ignores the force, or that blocks gravity. That's up to you--tell your story, and if the physics doesn't work, ignore or explain away the parts that don't work for you. But for a hard-science campaign or story, this may not be what you're looking for.

Now, you could completely ignore the black hole, and simply have the intended destination be millions of light years way. Traveling very close to the speed of light, the astronaut may only experience ten years in transit back and forth, but on Earth millions of years will have passed. That gets you the same results, is a LOT easier to calculate, and still gets you the setting you need.

Answer 3

1. As of right now, the closest black hole we know of is V616 Mon. It's located about 3,000 light years away. So from an outside observer a space craft going near c (.95c) will take about 3k years to arrive. Taking into account time dilation, aboard the craft, the riders would experience 900 years. If we want to hit your 10 year mark, the black hole would need to be about 32 light years from earth (My math maybe wrong). None of this is taking into account the time dilation effects of being so close to a black hole. I would say yes, its feasible depending on the conditions.
2. I have no knowledge of how orbiting a black hole effects time dilation, but if I had to give you my close guess, taking into account the distance of the black hole being not 10,000 light years away, would be in the thousands of years.
3. Worm holes are very theoretical but based off the assumption that they are essentially holes in space-time, I would say they would take you to some place instantly. Since nothing can go faster than light, this wouldn't break that law because its simply a hole in space-time.

An idea to think about for FTL travel would be a craft that could distort or bend space-time. Basically a craft could shirk space-time in front of the vessel and expand it, behind the craft. This could (in sci-fi) enable a ship to move from an outside observer faster than light.

Hope this helped.

Answer 4

I'm sorry that the site won't allow me to post this bit as a comment: You have described the novel "A World Out of Time" by Larry Niven. (Niven's story took more time on board the ship; the occupant was in suspended animation for most of the trip.) I assume this is intentional?

There are two important factors in the answer. Gravitational time dilation at the black hole and special relativistic time dilation during the bulk of the journey. I'm too lazy to get into general relativity but SR by itself answers your question: You can make the ten years that the traveller arbitrarily large for the Earth by simply getting closer to the speed of light. Specific answers will of course depend on the distance travelled but the calculation is available on Wikipedia: Twin Paradox

(Edit) HOWEVER

After your edit I think that you may misunderstand something. A ten-year return trip would cover ten lightyears in the reference frame of the traveller. You have described a black hole ten lightyears away in an inertial reference frame. In order to get the required time from SR alone, you will need to make a longer journey. I only mention this because you chose the specific number of 5 lightyears distance; gravitational time dilation near the black hole can make up the difference if the black hole is large enough that the tides aren't too extreme to survive at the appropriate periapsis.

Answer 5

Time dilation from travelling near light speed or from passing close to a black hole could extend arbitrarily far depending on how close you travel to the speed of light/the event horizon of the black hole.

The only limiting factor I can think of is the acceleration of the ship. If your ship (or your passengers) can only withstand an acceleration of 1g there will be a limit on how far you can stretch this 10 years from the point of view of your travelers. I'm afraid I don't know enough about GR to give an upper limit based on this acceleration, or what acceleration would be required to allow millions of years to pass on Earth, but if you find someone who knows more, they could tell you what acceleration is required for your scenario.

Edit: If you are using time dilation close to a black hole there will be other things for your ship and crew to withstand (tidal forces, strongly blueshifted radiation, other nasty stuff) depending on how close you want to go. You don't necessarily need to use the black hole though if your ship can accelerate close enough to the speed of light, you'd just need to fly further than 5 light years.