The biggest issue I see is the fact that gravitational time dilation is considerable on the surface of the Miller's planet, but not so much in the relatively close proximity of the planet, where the mothership is. I just don't get that part.
Calculations about time dilation become enormously more complicated in a system where the black hole is spinning, because you get effects like frame dragging that influence the orbits and time. For the purposes of the parent poster, a ball-park number of distance is enough, they don't need the whole shebang.
At this point a few issues arise. The first is that what you’re describing is a feature of the Schwarzschild metric, which applies to a model black hole, which is time-independent and eternal. There is no particular reason to believe that this accurately describes black holes in nature. For example this metric can not describe the merger of two black holes, but we now have observational evidence that this does indeed take place.
The biggest issue, aside from the model, is that time dilation is something which only matters when two observers “compare clocks.” Neither observer alone ever experiences a difference. The crew of a 99.9% lightspeed ship doesn’t experience time dilation... until they return home. It makes no sense to talk about the effects of time dilation from the point of view of a one-way trip to the event horizon.
If interstaller thought us anything, the closer you are to a black hole the slower time gets. When they got close to the black hole they only spent a few hours there but lost years compared to our frame of reference.
Our solar system is rotating within our galaxy, presumably you have to travel quite a bit before being „away from a gravity well“. But at that „location“, there may be a lot of relative velocity to our solar system, so there will be time dilation effects - for us or them, depending on your reference frame.
...One of the first things you learn in special relativity is that there are no preferred reference frames, I still have trouble wrapping my head around that one.
Assuming these people 10000 lightyears away from the black hole are also on a planet, their reference frame is almost the same as ours - the relative speed of different planets is very small compared to the speed of light. So they'll agree on when 24000BC is.
Now is the part where someone brings up even with the low relative velocity, you haven’t accounted for the simultaneity issues we’d have if the earth collided with a black hole while the rover landing was happening.
wow thanks! this was super fun, do you happen to have some souce about the calculations that go into determining the time dilation based on different velocity? i'm aware about black holes being capable of well, doing time dilation thingy due to their massive gravitational force but nothing else.
edit: souce as in something a regular average joe can make sense of haha
Yes, but doesn't that ignore the gravitational acceleration? Time dilation isn't just speed, it's also acceleration. Even if you could hover very near the event horizon the time dilation would be severe.
I’m not claiming that they can’t recognize that their relative velocity is much greater than their surroundings. You can even calculate the degree of time dilation you’re experiencing relative to another observer, but I’m not talking about that either.
The biggest issue, aside from the model, is that time dilation is something which only matters when two observers “compare clocks.” Neither observer alone ever experiences a difference. The crew of a 99.9% lightspeed ship doesn’t experience time dilation... until they return home. It makes no sense to talk about the effects of time dilation from the point of view of a one-way trip to the event horizon.
That has to do with the experience of their frame of reference. Time does appear to “slow down” for them, rather everything else will seem to “speed up.” You can infer the difference, but you can’t sctually communicate that or compare with anyone else until you decelerate. In the extreme case of a gravitational event horizon, there will be no ability to ever communicate again. The fact that external observers will see you infinitely redshifted doesn’t imply anything about your experience of subjectively falling past the horizon. Both are valid frames of reference, but ultimately will develop spacelike separation which prohibits further communication.
As it relates to the issue st hand, you can’t make accurate statements about mass never passing through the EH based on observations from a distant from of reference.
> Time dilation isn't just speed, it's also acceleration.
That's not correct. Gravitational time dilation isn't a function of acceleration, it's a function of gravitational potential, i.e., how deep you are in the potential well of the source.
(Also, an object that is in a free-fall orbit has zero acceleration in GR, since in GR acceleration is proper acceleration--what is measured by an accelerometer.)
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