NWSiaCB said:
Sorry, I didn't actually state it, so it may have been unclear, but what I meant was that if the immortals fell towards the black hole, time would slow as they fell towards it until they were just about to hit the event horizon, while the simple fact that black holes have a lifespan at all means that there's no need to escape the black hole; They can wait forever (with their relative time nearly frozen) for the black hole to evaporate, at which point the event horizon dissipates and it "just" becomes a decaying super-massive object. (A neutron star?) Something probably very, very difficult to escape from at that point, but being as they lived for tens of millions of years on molten Earth and escaped the expanding sun on a solar projection, this would be something actually physically possible to escape.
No.
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There are three important implications of Relativity. One, Reality is Local. Two, Space is not invariant; it is relative. Three, Time is not invariant, it is relative.
(And of course Zero, Speed of Light [in a vacuum] is always constant [when measured locally from an inertial frame of reference]. That's why everything else is all relative.)
What it means is that time dilation only applies when you have at least two observers in different frames of references, i.e. they are not Local. In the case of an entity free-falling into an eternal non-microscopic Schwarzschild (uncharged, nonrotating) black hole, (and assuming there is no accretion disk getting in the way of the view,) a distant observer will observe said entity slowing down as it approaches the event horizon, getting more progressively red-shifted and dimmer along the way, until it fades out of view. 'Extrapolating' the trajectory would then seem to indicate (to the external observer) that the entity takes an 'asymptotically' infinite amount of time to reach the EH. (Mathematically and notoriously, the calculated Schwarzschild coordinate time blows up to infinity.)
The entity free-falling into the BH, however, experiences a markedly different reality. It will cross through the event horizon in finite proper time. Or in layman terms, the entity experiences a finite amount of time as it passes into the BH, and will measure the time to be such with a clock that is attached to it (this is what proper time means, time as measured by a clock attached to a proper reference frame). Time does not slow down locally for the free-faller. From the PoV of the free-faller, there will not be anything remarkable or singular about the passage (e.g. spacetime is mostly flat, surroundings are mostly vacuum, etc.) , and the tidal forces at the event horizon can even be barely noticeable (negligibly so), if the black hole is large enough. (Sounds counterintuitive, but the Schwarzschild radius scales linearly with the mass of the BH, while tidal forces scale inversely to the cube of the distance.)
Given the assumptions above, the Hourai immortals will also free-fall into the black hole past the EH in finite proper time, exactly like the case of the hypothetical indestructible free-falling entity. What it looks like to a distant observer is completely irrelevant for the free-falling entity; Hourai time is not distant observer time. There is no absolute simultaneity. There is no global, universal NOW. Do not conflate the two and arrive at the mistaken conclusion that having a in-falling entity taking apparent infinite time to reach the EH from the PoV of a distant observer means the actual entity itself will also take an eternity to arrive at the EH (effectively never reaching it). Their times are different; spacetime is relative! Otherwise, black holes wouldn't form at all; we'll just get time-frozen stars instead since the collapsing matter would also be 'frozen in time'. (The 'frozen star' theory, common in the mid '60s, based on one interpretation of Oppenheimer's 1939 paper. This is now mostly considered 'debunked'.)
Things change somewhat if you consider quantum effects, like Hawking radiation. If we assume that BHs emit Hawking radiation (this has not been experimentally verified yet, but the math is sound, and most of the GR predictions above are also not experimentally verified either), then per Conservation of Energy this necessitates a reduction of the mass of a BH. Mass goes to zero, and poof! (or BANG!) No more black hole.
But black hole evaporation also changes the view of events for the distant observer! Effectively, you can consider outgoing light rays from the in-falling entity as being 'slowed down' by the black hole. No BH, no more 'slowdown', and hence to the external observer the in-falling object will appear (or can be extrapolated to appear) to pass through the event horizon at the 'exact' moment the BH evaporates, instead of diverging at infinity.
(The actual math are far more complicated because now you have an 'moving' apparent horizon that varies in spaceatime instead of a static event horizon, so you'll need to plot geometries [or topologies if you're a masochist and insist on higher dimensions] instead of just plugging in figures into an equation. They are multiple ways of looking at this [Penrose diagrams are a perennial favorite], but they effectively describe the above process/analogy more or less.)
The free-falling observer will still fall through the event horizon at finite proper time. BH evaporation is mostly inconsequential from his perspective, and in fact the free-faller will not observe any (appreciable amount of) Hawking radiation at all; this is, remarkably, an effect of the different reference frames. A static local observer will experience Unruh radiation instead (as a consequence of accelerating against the gravitational pull of the BH). Free-falling entities do not 'accelerate' and will hence experience no Unruh radiation.
See this paper and this blogpost (The blog post explains things in a more intuitive manner, but there are some misrepresentations there. For one, Hawking doesn't claim the antiparticle-particle virtual pair phenomenon as a theory; he carefully notes it as a "heuristic" analogy. But most pop science authors will quote him otherwise, so Ethan is rebutting the pop science version of Hawking.)
So yes, the same thing happens for the Hourai Immortals — they'll tumble through the horizon in finite proper time. They'll get a finite (and short) time to adapt, not an eternity.
To summarize, you are in effect assuming one set of conditions that hinges on eternal blackholes to arrive at 'infinite' 'relative' time, assuming the opposite that blackholes are now finite (contradicting the prior assumptions that the calculations hinge on), then further wrongfully applying the conclusion on the WRONG observer. Or, to put a spin on the old Physics joke, you're (metaphorically) assuming a spherical cow in a frictionless vacuum, then concluding that if you kick a four-legged cow on Earth it will roll on infinitely. It doesn't work that way.
XionGaTaosenai said:
Okay, something that has always bugged me about black holes.
To an outside observer, something falling into a black hole would fall gradually slower and slower as they approach the EH, because of how gravity affects time. The outside observer will never, in all eternity, see that thing actually cross the event horizon.
So to an observer falling into a black hole, wouldn't the rest of the universe seem to move faster and faster, as their personal perception of time slows down? And then as they approach the event horizon, all of eternity would happen around them, increasingly quickly, before they crossed the EH. But before they crossed the EH, all of eternity would pass around them... including the part where the black hole evaporates. How does anything actually cross the event horizon? Even if black holes didn't evaporate, you would hit a point right as you crossed the event horizon where time for the universe around you would pass infinitely fast. What happens then? What happens after that, when you've gone through at what seems to you your normal speed but a literal infinite amount of time has passed outside?
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No. You're assuming some kind of reciprocal opposite effect like NWSiaCB, that if Observer A sees Observer B's apparent time as slowing down to zero, then Observer B also sees Observer A's apparent time as speeding up infinitely. This is not the case. You can consider it as somewhat analogous to a similar example in Special Relativity, where you have two observers traveling at different velocities. Here, Observer A will see Observer B's apparent time (imagine a light ray coming out of B's clock to A's position) as slowing down, but from B's perspective A's clock is likewise slowed down, NOT sped up!
Of course, the General Relativity case isn't as simple, as the time dilation effect is not symmetric unlike in the case of SR. So, you have to work them out both separately. For the purposes of the motion of a entity free-falling into a black hole, refer to my response to NWSiaCB typed up above. (To sum it up, the entity will fall through the event horizon in finite proper time, as measured from its frame of reference.)
Now, as for how the rest of the universe appears to the free-falling entity... that's more complicated. The short answer is no, not for a Schwarzschild (uncharged, nonrotating) blackhole, because you can only see light that actually get to you (within your finite proper time). And light from events that are sufficiently far away in distance and in the future from you will never get you in time, i. e. they cannot arrive in your past light cone. (To use that terminology.) So, you can't see into the arbitrary future, or to an arbitrary distance either. (And this is before taking metric expansion of the universe into account.)
The long answer is pretty much the same as the above, but with a shit-ton of math and topology involved, which I'm not going to bother here (especially without LaTeX). So, first I'm going to point you to Andrew Hamilton's excellent modeling (and image resources) of what things look like when you fall into a Schwarzschild blackhole. This should give you an intuitive understanding of sorts, and if you have the necessary mathematical background you can follow some of his calculations and diagrams, which should prove very illuminating.
(Note you'll see both blueshift AND redshift depending on where you are and where the light is coming from.)
Next I'll point you to this excellent Stack Exchange question that answers your, well, question precisely. In particular pay attention to the answers made by Michael Brown, John Rennie, Alfred Centauri, Rob Jeffries, Pulsar and Colin MacLaurin. (Especially Rennie's). Basically, to sum it, events past a certain point of 'time' are no longer visible to the free-falling entity because it only sees a finite amount of light.
Note that the above apply in the case of a free-falling observer. Now, if you were to try to stay at a 'static' point above the event horizon instead, fighting against the black hole's gravity (a "shell observer", so to speak), then things work markedly differently. The rest of the universe away from the black hole will then appear to move at 'fast-forward', and you can speed this up arbitrarily by maintaining a position arbitrarily closer to the event horizon. The key difference is that you're no longer free-falling, so your earlier intuition is now valid (for the static shell observer case, not the free-falling one). Do be aware that the amount of acceleration you need to fight gravity also becomes arbitrarily higher (blowing up to infinite) as you set up camp closer to the EH though, so this becomes physically impossible past a certain point. And of course, incoming light will also be blueshifted up by a similarly arbitrary factor, so you'll get fried by the incoming radiation if you try to speed up time too much.
(Mathematically, since you're now static with respect to the BH [like the distant observer], Schwarzschild time now also applies to your case, like the distant observer (and unlike the free-faller), except you experience a relative time dilation. This is why there's now a 'reciprocal timewarp effect', so to speak.)
Or you could just fire your jets in a flat region of flat time anyway and achieve time-traveling into the future that way, like in Special Relativity. No need to worry about getting fried by blueshift (but you'll also see significantly far less stuff, as trade off).
Also note that all the above assume a Schwarzschild black hole. Things again become different (and complicated, see a pattern here?) with charged and/or spinning black holes. The idealized solutions for those kinds of black holes permit wormhole solutions, including timelike wormholes, so mathematically you can in theory travel to the future with those. Conventional view holds that you'll get fried by blueshift when you reach the entrance of the wormhole (in effect an inner event horizon, called the Cauchy horizon), somewhat similar to the shell observer case above (but without requiring physically-impossible amounts of acceleration). There's a recent paper by Hintz et al. that factors in metric expansion of the universe in their simulations to arrive at a surprising and interesting conclusion.
NWSiaCB said:
There was one of those Kurzgesagt videos discussing that... I can't remember if it was in the ones I linked earlier, but...
First, all light would seemingly recede into a sphere "above" you (away from the black hole), while at the same time increasing massively in intensity. (All the light coming from across the universe would be bending in towards you/the black hole and millions of years of light would seem to be arriving within a second, so you'd be seeing space as increasingly brighter the more time was slowing down for you. Basically, it would look like the black hole was expanding to envelop everything around you, while the light grew brighter as it shrinks to a pinprick of laser-like focus. Note this still occurs after crossing the event horizon - light's still coming in from outside, after all. Also note, everything in front of/below you redshifts to invisibility, while everything behind/above you blueshifts.)
No. You're making a common mistake here. The light "receding and growing brighter" stuff only happens in the case of a static "shell observer" maintaining a certain distance from the event horizon (by firing jets to continually accelerate against the BH's gravity). This is not the case for an entity free-falling into a black hole (any kind).
Refer to Andrew Hamilton's simulated images for what a free-falling observer is expected to see. Or refer to Taylor and Wheeler's book on Exploring Black Holes (ISBN 9780201384239), IIRC there's a section that deals directly with your misconception.
NWSiaCB said:
But as for the actual crossing, it's hypotehtically possible, it just takes infinite time to do so. This is kind of one of those cases where you're matching up an infinity against another infinity and they cancel out. To an outside observer, it takes infinite time to cross, but to you, if you're heading towards it, you don't notice time slowing down, so it all happens instantly. The thing is, however, that Hawking radiation means the black hole doesn't live forever, so the black hole will shrink and dissipate as you get infinitely close to the event horizon until it turns into a neutron star or whatever.
No, NO! Stop assuming a spherical cow! (and then generalizing it for non-spherical ones!)
See my earlier response to your prior post, at the top of this post. Or see John Rennie's answer here.
NWSiaCB said:
Oh, and because basically nothing could survive the incomprehensibly titanic forces at play here unless magic, this is all kind of academic. The radiation alone would boil you before the spaghettification would rend your atoms asunder.
As noted earlier, tidal forces can be negligible up to the event horizon for large enough black holes. Surviving the radiation from the accretion disk is, while improbable, still possible depending on the black hole, the entry path, and the technology available.
XionGaTaosenai said:
I mean, I understand all that - the stuff about light intensity was even covered in an earlier page of this comic. It's specifically this part that trips me:
"It all" meaning everything, all of space and time, happening before you cross the event horizon. So then what happens after? If you were to look up at the light entering in behind you (and not be blinded by the aforementioned intensity), what light would you be seeing? Light from the universe after an infinite amount time had passed. But that's impossible - you can't have anything after an infinite amount.
The answer to that question is Hawking Radiation - specifically that the Black Hole will evaporate while the "infinite" time is passing and you will never actually cross the event horizon. But that means that nothing ever truly crosses the EH. So how do black holes gain mass? Do they just gather matter right past the edge of their EH until that shell of matter itself pushes the EH outwards with it's extra gravity? If so, then what happens when the event horizon pulls a Russia and crosses you? Wouldn't you still have the "witness an impossible universe after infinite time" problem? And what happens to the matter that is already inside the black hole's event horizon when it forms?
Refer to my earlier response.
NWSiaCB said:
You'd be seeing the light that was flying in from "above" (relative to the black hole) you in space.
You see light from all over. Refer to Andrew Hamilton's simulated images or Taylor and Wheeler's book on Exploring Black Holes.
NWSiaCB said:
Light is bombarding you as a continuous stream, and would continue coming in for billions of years after the stars that emitted that light have burned out. (Think of how the Hubble Space Telescope can see events from near in time to the Big Bang by just looking across the universe from where the Big Bang took place.)
No.
NWSiaCB said:
The problem is, I see conflicting information on this sort of thing. Strictly speaking, it doesn't seem like the singularity itself should gain mass if time slows down infinitely near the event horizon, and hypothetically actually flows backwards inside it. If the event horizon gained mass and expanded the event horizon because of that to engulf you, and time was flowing backwards within it, and you were somehow not crushed to sub-atomic particles, you'd still not notice a thing, however, as you'd be going backwards through time, un-thinking your thoughts and having all the light you were looking at before fly out of your eyes back towards the stars they came from, at least until the event horizon evaporated back down to exclude you again. (Although that evaporation would probably be ejecting "you"/the mass that made you up as particles.) If your eyes still existed at that point, the light "previously" eject would then be traveling back towards them and enter your eyes again...
Black hole science is an emerging field, with new innovations and discoveries made. Strictly speaking, until someone can figure out a unified theory of quantum gravity, most of the theories will be incomplete and 'conflict' with each other. (Or rather, they start with different assumptions.)
You are also mixing up a lot of PopSci distilled-down explanations that apply to different scientists' particular models of black holes. (By taking the colloquial semantic meaning of said explanations purely at face value, devoid of technical context, like applying RAW in DnD with zero consideration for RAI). They don't mix well because they start from different assumptions. (Again, spherical cow!).
NWSiaCB said:
Strictly speaking, it doesn't seem like the singularity itself should gain mass if time slows down infinitely near the event horizon, and hypothetically actually flows backwards inside it. If the event horizon gained mass and expanded the event horizon because of that to engulf you, and time was flowing backwards within it, and you were somehow not crushed to sub-atomic particles, you'd still not notice a thing, however, as you'd be going backwards through time, un-thinking your thoughts and having all the light you were looking at before fly out of your eyes back towards the stars they came from, at least until the event horizon evaporated back down to exclude you again. (Although that evaporation would probably be ejecting "you"/the mass that made you up as particles.) If your eyes still existed at that point, the light "previously" eject would then be traveling back towards them and enter your eyes again...
No, no, no! Time does not slow down infinitely near the event horizon! Relativity doesn't work that way!
Time maybe-kinda-sorta flow 'backwards' inside the event horizon, but not the way you're thinking. There's 'inversion' of r and t in Schwarzschild coordinates past the event horizon, but that's an artifact of the coordinate system used, like 90 degree latitude in spherical coordinates at the north pole. Then there's a new law, the holographic screen area law, which implies reversal of thermodynamic time, but what it means (despite the catchy title) is that entropy tends to decrease inside black holes, not that biochemical processes flow backwards and your worldline reverses until you fly back out of the black hole! This flies in the face of every general relativity theory, with or without quantum effects considered.
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