To be pedantic, you travel to the present, which is where you have always been.
Thinking about it, I do see a difference between what we’re discussing and some fictional versions of time travel. In real world “time travel” you exist as part of the universe for the entire period of “travel”. For the version used in, for example, Back To The Future, you completely disappear from the universe from the departure time until the arrival time. So if you’re going 10 years into the future, the DeLorean isn’t sitting there aging slower, it ceases to exist for 10 years. This of course violates the conservation of matter and energy.
Agreed, which is exactly why I referenced The Time Machine and not BTTF. In Wells’ novel, it takes some time for the time traveler to reach his destination, and during the trip he watches all the events around him in fast-motion: buildings being built and crumbling down, and so on.
That’s a cute quote, though it’s probably no longer true. The source for the statement is a book from 2002, and Avdeyev held the record for “most time spent in orbit” at the time. But his record was broken in 2005 by Sergei Krikalev, who probably had an extra couple of milliseconds of time travel on Avdeyev by the time of his (Krikalev’s) retirement.
You’re right. My apologies to Mr. Krikalev, the new time travelling champ.
(I’ll also take the opportunity to stick in a clarification for anyone who might have been wondering. Time travelling astronauts travel into our future, as it were, but they’re not using the gravity trick, like with the OP’s black hole. Being further away from the Earth’s surface obviously has the exact opposite effect, as you experience less gravity. However, they compensate and a lot more by using the other way to experience time dilation: The “moving extremely fast relative to us” trick.)
Actually, being in orbit, they’ve traveled less into the future than the rest of us have, not more. The effect from being in freefall is larger than the effect from traveling at high speed, for an object in orbit.
This is true. I think the “time travel” calculations for astronauts is just a whimsical thing showing how much less they aged due to speed, but gravity overwhelms it many times over. The poor buggers have aged more than the rest of us! From what I’ve read, GPS satellites have to compensate by about +7 microseconds per day due to speed and -45 due to gravity.
To be strictly accurate, though, free fall isn’t the issue, as they’re still well within the earth’s gravity well. It’s the lesser gravity due to being further from the earth’s center of mass that makes their clocks run faster.
So I got it backwards?
:dubious:
Oh, well. Good to see you guys kicking my ignorance in the balls.
Whether an orbiting observer experiences more time dilation than a non-orbiting observer depends on the radius of the orbit.
The time dilation factor for an observer held stationary in Schwarzschild coordinates is (1- 2M/r)^-0.5 compared to the earlier value I quoted for an observer in a circular orbit which is (1-3M/r)^-0.5. So, time will appear to run slower for an orbiting observer compared to an Earthbound observer for orbits up to a little less (due to the rotation of the Earth) than 1.5 times the radius of the Earth, beyond which their clocks will appear to run faster.
Just to expand on this point, in order for naked singularities to not be achievable it must get harder and harder to increase the spin parameter of a black hole as it approaches 1.
Looking up what the limit might be, Thorne places a limit on the spin parameter of an accreting black hole as 0.998. This may appear to be very closer to the extremal value of 1, but it is still woefully insufficient to achieve the time dilation factor needed for 1 hour of an observer in a stable orbit to translate to 7 years for a faraway observer.
I haven’t seen the movie, but I know Thorne was also the adviser on the movie, so maybe he knows something that I don’t (among all the other things he undoubtedly knows that I don’t).
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According to Kip Thorne’s The Science of Interstellar, which does indeed acknowledge that maximum spin limit for a black hole, the necessary time dilation is achieved simply through some hypotheticals that posit Miller’s Planet in a stable orbit sufficiently close to the event horizon. I don’t claim to understand any of these nuances, I’m just sitting here with my Kindle on my desk reading what he wrote.
The main problem he deals with is the tidal forces in such an orbit, which he says is resolved by having Miller’s planet tidally locked (well, almost – the giant waves on the planet are attributed to a slight rocking back and forth driven by the tendex lines of tidal gravity). He calculates an orbital period of 1.7 hours from an external frame of reference – about half the speed of light, but one-tenth of a second as perceived from Miller’s Planet itself.
Note that, even though that’s as high as you can get via accretion, you can still in principle get arbitrarily close to 1 via Hawking radiation. Though of course, since this relies on Hawking radiation, it’ll be glacially slow for any black hole of large enough size to be useful for a planet.
I suspect Thorne has chosen the spin parameter to be over his own limit for the sake of the story!
Just go against the black hole’s direction of rotation. It worked for Superman.
I’d have to look this up, but I’m not sure that this could be the case and Hawking radiation would carry away more angular momentum than mass from the black hole, The reason I believe this is because the Hawking process is the quantum limit of the classical Penrose process which carries away both mass and angular momentum from a Kerr black hole with the overall effect of reducing the spin parameter.
He claims not. I found this in the “Technical Notes” section at the end, although I’m at a loss as to where his relativistic approximation for α comes from, as it’s not explained further than “I have deduced a formula …”. All I can tell you is that the calculation does yield his claimed result:
In fairness, I should add to the above that Kip Thorne recounts that when Christopher Nolan came to him with the one hour to seven years time dilation requirement, Thorne told him it was impossible. Nolan insisted it was non-negotiable, as it is indeed central to the story line. So, as Thorne put it, “not for the first time and and also not the last, I went home, thought about it, did some calculations with Einstein’s relativistic equations, and found a way.”
He goes on to say, as has been said here, that a faster spin than the maximum would expose a naked singularity. He also acknowledges that a black hole with the spin rate required here is very unlikely, but the point being that it’s possible – it’s science fiction and not fantasy. Nolan writes a warm preface to the book in tribute to Thorne’s passion for keeping the movie within the bounds of scientific plausibility, noting the two-week standoff they had when Thorne refused to give in to the demand for faster-than-light travel.
Good grief, that must have been interesting. “Hey, thanks for spending a week doing heavy duty black hole physics to get the details of time dilation working realistically. Mind if we shoot every principle of physics that we know about out the window with some FTL travel?”
Sort of doing a movie about the Civil War and getting every detail of the period uniforms right, only to have the Battle of Gettysburg fought by troops riding T-Rexes with lasers.
Haven’t read the book, so I was curious if he dealt with some of the other sticky issues, like the abundance of visible light but not enough other forms of EM radiation to kill the crew (especially if the planet is tidally locked) or how they could land on the planet if it’s orbital period implied a significant fraction of c or, for that matter, why they used a conventional rocket on earth if their shuttle vehicles could hit low orbit so easily? Or was it a matter of getting the time dilation right and fudging some more on some of the other practicalities.