Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: A-wal on 20/03/2019 10:36:34
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Given that no amount of time is enough for an object to reach the event horizon of a black hole from the perspective of an observer at a distance can we accurately say from the perspective of an object falling towards a black hole that an infinite amount of time must pass on the watch of a more distant observer from the perspective of the falling observer before they are able to reach the event horizon?
If the answer is no then how is that resolved with the fact that from the more distant observer's perspective (assuming here a black hole with an infinite lifespan), no time on their own watch is enough for the falling object to reach the event horizon?
If the answer is yes then although there would be a time on the watch of the falling observer when they reach the event horizon, how is any lifespan of the black hole long enough for an infinite amount of time to pass on the watch of a distant observer from the perspective of the falling observer before they reach the event horizon?
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Given that no amount of time is enough for an object to reach the event horizon of a black hole from the perspective of an observer at a distance can we accurately say from the perspective of an object falling towards a black hole that an infinite amount of time must pass on the watch of a more distant observer from the perspective of the falling observer before they are able to reach the event horizon?
What happens from one perspective has little to do with the other, so be careful. For instance, for an partner coming quickly towards me, a large amount of time must pass in my frame for a small amount of time to pass on his local clock, and yet in his frame, it is my clock that is running slow. In both cases, if were were to read each other's clocks as they approach, they would appear to be running faster, not slower. That's the difference between wording it as "in frame X or Y" vs as it "appears to observers in X and Y".
That said, relativity says that time is fully dilated for an object that falls to the event horizon of a black hole. That means there is a specific time on the falling clock that it will never reach outside the horizon. Details beyond that seem to vary from one description to the next, and I am actually quite interested to hear the opinions of others on the matter.
If the answer is no then how is that resolved with the fact that from the more distant observer's perspective (assuming here a black hole with an infinite lifespan), no time on their own watch is enough for the falling object to reach the event horizon?
What needs resolution? From the outside frame, the event horizon is never reached. The clock dropped in actually stops. It also in theory appears to stop, since it can hardly move on if the next second is never reached. In reality, there are only so many photons that escape the clock in the last moment, and so the dropped clock vanishes from view in a poof of red shift.
Still, since a black hole will dissolve in a finite time due to Hawking radiation, the dropped object is still falling in at that finite time. That makes it very difficult to argue that anything actually passes the event horizon since the black hole no longer exists at that time.
If the answer is yes then although there would be a time on the watch of the falling observer when they reach the event horizon, how is any lifespan of the black hole long enough for an infinite amount of time to pass on the watch of a distant observer from the perspective of the falling observer before they reach the event horizon?
Indeed. So by this thinking, one cannot fall in. I've heard descriptions of falling into a really large black hole, one big enough that tidal forces don't kill you before you get there. What is it like? Looking back the way you came, the universe narrows to a thin band of light straight up and dark to the sides, but if there are no windows, can one detect passing over? By the logic we both express, nothing can fall into a black hole and there is no infinitely dense singularity at the middle of it. There isn't even spacetime there. All the mass is smooshed on the outside of the event horizon and is even pushed outward as new mass is added, increasing the radius of the event horizon.
So I'd like to see posts that take the opposite view and defend the idea that an object can fall in and continue its perilously brief but finite trip to the center.
Mathematically, time and one of the spatial dimensions switch inside the black hole. What was time is not space, and an object can freely move back and forth in the direction that is our past and future. The dimension that was 'down', towards the central singularity, is now time, with causality moving only in that direction. So one does not fall downward to the center, but rather moves forward in time to the singularity with is the end of time just like the big bang is the beginning of time. Mathematically, that's how the space inside the black hole sort of works, but it seems it cannot be reached. It is a totally separate universe.
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What happens from one perspective has little to do with the other, so be careful.
I'm aware. However different perspectives, although they can appear contradictory on a superficial level, can never lead to genuine paradox. In this case either answer to the first question seems to lead to a paradoxical result.
For instance, for an partner coming quickly towards me, a large amount of time must pass in my frame for a small amount of time to pass on his local clock, and yet in his frame, it is my clock that is running slow. In both cases, if were were to read each other's clocks as they approach, they would appear to be running faster, not slower. That's the difference between wording it as "in frame X or Y" vs as it "appears to observers in X and Y".
No, the distance between the observers has no effect on the time dilation of a clock in the frame of the other observer. Each clock would be running slowly from the perspective of the other observer and that slowed rate will always remains constant if their relative velocity remains constant. If you want to work out what they would actually see then you need to factor in Doppler shift as well but that also remain constant at a constant relative velocity but is affected by direction of motion whereas time dilation only depends on velocity.
That said, relativity says that time is fully dilated for an object that falls to the event horizon of a black hole. That means there is a specific time on the falling clock that it will never reach outside the horizon. Details beyond that seem to vary from one description to the next, and I am actually quite interested to hear the opinions of others on the matter.
So am I.
What needs resolution? From the outside frame, the event horizon is never reached. The clock dropped in actually stops. It also in theory appears to stop, since it can hardly move on if the next second is never reached. In reality, there are only so many photons that escape the clock in the last moment, and so the dropped clock vanishes from view in a poof of red shift.
No it never stops. It continually ticks at a slower and slower rate but never actually stops ticking. This is directly equivalent to a constantly accelerating object approaching the speed of light but never reaching it from the perspective of an inertial observer.
The resolution needed here is that if the answer to the first question is no then in the falling observer's frame the time on the watch of the distant observer when the falling observer reaches the event horizon would show a different time on the same watch when they reach the event horizon in the distant observer's frame. That's something that shouldn't be frame dependent.
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However different perspectives, although can appear contradictory on a superficial level, can never lead to genuine paradox. In this case either answer to the first question seem to lead to a paradoxical result.
OK, I don't see a paradox. OK, I see the title mentions a frame hovering very near the event horizon, which is a different frame in some ways than a falling 'observer', but both their clocks slow to essentially a stop from the perspective of the distant frame.
For instance, for an partner coming quickly towards me, a large amount of time must pass in my frame for a small amount of time to pass on his local clock, and yet in his frame, it is my clock that is running slow. In both cases, if were were to read each other's clocks as they approach, they would appear to be running faster, not slower. That's the difference between wording it as "in frame X or Y" vs as it "appears to observers in X and Y".
No, the distance between the observers has no effect on the time dilation of clock in the frame of the other observer.
I didn't say otherwise. I left my quote there so you can see that. Nothing is distance dependent, but the appearance of the non-local clock is dependent on the recession speed as well as the relative speed. So the arriving clock appears to run fast if watch it. This is essentially why light from approaching stars is blue shifted. The frequency of the light (which is a clock) appears to go up despite the time dilation due to the motion of the approaching light source.
Each clock would be running slow from the perspective of the observer observer
From the frame of those observers, yes, but not from appearance. I avoided the ambiguous term 'perspective' since it doesn't distinguish appearance from actuality. You're obviously talking about actuality, relative to a frame, but I'm talking about appearance, what I see when I observe the approaching clock.
If you want to work out what they would actually see then you need to factor in Doppler shift
OK, you understand what I'm talking about. Yes, appearance needs to account for that shift.
but that also remain constant at a constant relative velocity but is affected by direction of motion whereas time dilation only depends on velocity.
I disagree with both. Relativistic dilation depends on speed, not velocity. The velocity of a GPS satellite relative to Earth changes all the time, but its speed changes very little and its dilation is fairly constant due to this. As for the Doppler effect, it changes slowly or abruptly as the watched thing passes by, all without ever changing relative velocity since I presume that both clock and observer are inertial. The abruptness of the change depends on the proximity of the nearest approach.
We're not disagreeing with each other I think, just getting our terms straight.
What needs resolution? From the outside frame, the event horizon is never reached. The clock dropped in actually stops. It also in theory appears to stop, since it can hardly move on if the next second is never reached. In reality, there are only so many photons that escape the clock in the last moment, and so the dropped clock vanishes from view in a poof of red shift.
No it never stops. It continually ticks at a slower and slower rate but never actually stops ticking.
Sure. By stopped, I mean there is a time on that clock that will never be reached in the history of the universe outside. If it passes the event horizon at that time, then it enters a different universe with different laws of physics perhaps. Since the clock is moving forward in time at the same pace it was before, it seems things are not all that different on the other side. It cannot send light back to the outside any more than I can illuminate Einstein with my torch. I have no way of pointing my torch in that direction.
This is directly equivalent to a constantly accelerating object approaching the speed of light but never reaching it from the perspective of an inertial observer.
I don't think so. There is not a moment beyond which the accelerating clock will not reach, and once reached, light from that moment will makes its way back to the inertial observer after some finite time.
It could be seen as equivalent to an observer who is accelerating constantly (as opposed to the inertial observation of something else accelerating). Surely our inertial observer dropping clocks into a black hole will experience constant g force of some magnitude, else he'd fall in himself.
If I drop a clock out of the window of a continuously accelerating craft, the clock will appear to stop as seen by that observer, and will actually stop in his frame. There will be a moment in time which that clock never reaches in the accelerating frame of the observer. So the situation is very equivalent to continuous acceleration, at least from the perspecitive of the accelerated observer.
From the perspective of the inertial clock thrown out the window, it notices nothing as it passes through the ship's event horizon and happily keeps on ticking. That is sort of an argument that things do indeed pass the event horizon, even if not in any time that makes sense to the hovering observer.
The two situations are not entirely equivalent since the black hole sets up a curved gravitational field and the accelerating object sets up a flat one. The black hole clock gets torn apart by tidal forces and the one dropped out of the ship window experiences no tidal forces. That difference I think invalidates the claim that the equivalence demonstrates that objects enter black holes. But as I said, I await opinions from those taking the opposite stance. I'm no expert.
The resolution needed here is that if the answer to the first question is no then in the falling observers frame the time on their watch when they reach the event horizon would show a different time on the same watch when they reach the event horizon in the distant observer's frame. That's something that shouldn't be frame dependent.
I don't see this issue. I see the same final time as seen by both observers (the falling one and the distant hovering/orbiting one).
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However different perspectives, although can appear contradictory on a superficial level, can never lead to genuine paradox. In this case either answer to the first question seem to lead to a paradoxical result.
OK, I don't see a paradox.
If the answer to the first question is no then the paradox is (seems to me at least) that from the frame of falling observer there is a time on the watch of the distant observer when they reach the event horizon but in the frame of the distant observer that time on their own watch passes and the falling observer still hasn't reached the horizon, they can still accelerate away in this frame but in the frame of the falling observer they're inside the event horizon and can't accelerate away once the distant observer's watch reaches that time.
I said the wrong watch in my last post. I said the difference on the watch of the falling observer in the two frames when the falling observer reaches the horizon is the paradox but it's the difference on the distant watch, I've corrected it now.
If on the other hand the answer to the first question is yes then it's that an infinite amount of time has to pass on the watch of the distant observer in the frame of the the falling observer as well as in the distant observer's frame, so it can never happen.
OK, I see the title mentions a frame hovering very near the event horizon, which is a different frame in some ways than a falling 'observer', but both their clocks slow to essentially a stop from the perspective of the distant frame.
When I say 'hovering' I mean maintaining a constant distance, it can be any distance. I'll change the topic title to distant instead of hovering observer to make it clearer.
For instance, for an partner coming quickly towards me, a large amount of time must pass in my frame for a small amount of time to pass on his local clock, and yet in his frame, it is my clock that is running slow. In both cases, if were were to read each other's clocks as they approach, they would appear to be running faster, not slower. That's the difference between wording it as "in frame X or Y" vs as it "appears to observers in X and Y".
No, the distance between the observers has no effect on the time dilation of clock in the frame of the other observer.
I didn't say otherwise. I left my quote there so you can see that. Nothing is distance dependent, but the appearance of the non-local clock is dependent on the recession speed as well as the relative speed. So the arriving clock appears to run fast if watch it. This is essentially why light from approaching stars is blue shifted. The frequency of the light (which is a clock) appears to go up despite the time dilation due to the motion of the approaching light source.
Oh you just meant that Doppler shift would overpower relative time dilation, sorry, I misunderstood. It was the "as they approach" that threw me, I thought you meant 'as they approach but not before they got to a certain distance'. My mistake.
Each clock would be running slow from the perspective of the observer observer
From the frame of those observers, yes, but not from appearance. I avoided the ambiguous term 'perspective' since it doesn't distinguish appearance from actuality. You're obviously talking about actuality, relative to a frame, but I'm talking about appearance, what I see when I observe the approaching clock.
Yes true. I tend to completely ignore Doppler shift because it's purely an optical effect due to an increase or decrease in lag time for the light to reach them but I should definitely have said frame, not perspective.
but that also remain constant at a constant relative velocity but is affected by direction of motion whereas time dilation only depends on velocity.
I disagree with both. Relativistic dilation depends on speed, not velocity. The velocity of a GPS satellite relative to Earth changes all the time, but its speed changes very little and its dilation is fairly constant due to this. As for the Doppler effect, it changes slowly or abruptly as the watched thing passes by, all without ever changing relative velocity since I presume that both clock and observer are inertial. The abruptness of the change depends on the proximity of the nearest approach.
I'm not quite sure I fully follow either point to be perfectly honest but both are irrelevant to the issue at hand.
No it never stops. It continually ticks at a slower and slower rate but never actually stops ticking.
Sure. By stopped, I mean there is a time on that clock that will never be reached in the history of the universe outside. If it passes the event horizon at that time, then it enters a different universe with different laws of physics perhaps. Since the clock is moving forward in time at the same pace it was before, it seems things are not all that different on the other side. It cannot send light back to the outside any more than I can illuminate Einstein with my torch. I have no way of pointing my torch in that direction.
Yea that's extremely awesome and is what really caught my eye, sparked my imagination and inspired me to properly think about relativity. The reason you can't escape from inside the event horizon of a black hole is that a direction in space that leads out of the black hole simply doesn't exist, every direction leads to the singularity eventually. It actually makes me disappointed that I can't see how it's possible to reach an event horizon.
This is directly equivalent to a constantly accelerating object approaching the speed of light but never reaching it from the perspective of an inertial observer.
I don't think so. There is not a moment beyond which the accelerating clock will not reach, and once reached, light from that moment will makes its way back to the inertial observer after some finite time.
I think there is a moment that the accelerating observer's watch won't reach if they continue to increase their acceleration at an exponential rate to mirror the acceleration of falling towards an event horizon.
It could be seen as equivalent to an observer who is accelerating constantly (as opposed to the inertial observation of something else accelerating). Surely our inertial observer dropping clocks into a black hole will experience constant g force of some magnitude, else he'd fall in himself.
If I drop a clock out of the window of a continuously accelerating craft, the clock will appear to stop as seen by that observer, and will actually stop in his frame. There will be a moment in time which that clock never reaches in the accelerating frame of the observer. So the situation is very equivalent to continuous acceleration, at least from the perspecitive of the accelerated observer.
From the perspective of the inertial clock thrown out the window, it notices nothing as it passes through the ship's event horizon and happily keeps on ticking. That is sort of an argument that things do indeed pass the event horizon, even if not in any time that makes sense to the hovering observer.
You be talking about the Rindler horizon. :)
The two situations are not entirely equivalent since the black hole sets up a curved gravitational field and the accelerating object sets up a flat one. The black hole clock gets torn apart by tidal forces and the one dropped out of the ship window experiences no tidal forces. That difference I think invalidates the claim that the equivalence demonstrates that objects enter black holes. But as I said, I await opinions from those taking the opposite stance. I'm no expert.
I'd like to comment on that but we're not supposed to discuss personal models in this section, which is fair enough.
The resolution needed here is that if the answer to the first question is no then in the falling observers frame the time on their watch when they reach the event horizon would show a different time on the same watch when they reach the event horizon in the distant observer's frame. That's something that shouldn't be frame dependent.
I don't see this issue. I see the same final time as seen by both observers (the falling one and the distant hovering/orbiting one).
Yep, that's the bit where I said the wrong bloody clock.
I re-read the OP, and if the event horizon is never crossed, then yes, the black hole eventually fades with Hawking radiation and the observer there (who cannot exist any longer since he has also faded away with the same radiation) will experience in no time a sort of finite discontinuity.
So let's say the black hole lives only for a billion years. As I observe the universe as I fall in, outside time speeds up and abruptly jumps a nice finite billion years, and it turns out I never left the universe at all. There isn't even a gravity well here anymore. The black hole is gone, and my clock ticks at the same rate as the patient clock watching all this from a distance, except we're a billion years out of sync now.
So the answer is that the time of the rest of the universe is finite, not infinite. The infinite answer is only a mathematical idealization which assumes black holes don't evaporate.
Yes that's exactly how I see it. No amount finite amount of time is enough, the rest of the universe (including the end of the life of the black hole) will always happen before the event horizon can be reached.
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If the answer to the first question is no then the paradox is (seems to me at least) that from the frame of falling observer there is a time on the watch of the distant observer when they reach the event horizon but in the frame of the distant observer that time on their own watch passes and the falling observer still hasn't reached the horizon, they can still accelerate away in this frame but in the frame of the falling observer they're inside the event horizon and can't accelerate away once the distant observer's watch reaches that time.
I don't think the question asked is a yes/no thing since it assumes that the event horizon is reached after finite (no) or infinite (yes) time. It seems it is not reached at all, and perhaps the paradox is real if the event horizon is actually reached, as some claim.
If on the other hand the answer to the first question is yes then it's that an infinite amount of time has to pass on the watch of the distant observer in the frame of the the falling observer as well as in the distant observer's frame, so it can never happen.
It seems there is never an infinite time for anybody, and the event horizon is never reached. That's my story at least.
When I say 'hovering' I mean maintaining a constant distance, it can be any distance. I'll change the topic title to distant instead of hovering observer to make it clearer.
The distant observer is hovering either way. No distance will keep him out of the black hole forever without some acceleration or orbital motion keeping him out. OK, he could go so far away that the falling clock isn't visible, but what's the point of that?
Yes true. I tend to completely ignore Doppler shift because it's purely an optical effect due to an increase or decrease in lag time for the light to reach them but I should definitely have said frame, not perspective.
Agree. I don't ignore observational effect because our guy is observing out of a window as well as computing in a closed room what is actually going on in his frame. Two different answers to what is going on from his 'perspective'.
Relativistic dilation depends on speed, not velocity. The velocity of a GPS satellite relative to Earth changes all the time, but its speed changes very little and its dilation is fairly constant due to this. As for the Doppler effect, it changes slowly or abruptly as the watched thing passes by, all without ever changing relative velocity since I presume that both clock and observer are inertial. The abruptness of the change depends on the proximity of the nearest approach.
I'm not quite sure I fully follow either point to be perfectly honest but both are irrelevant to the issue at hand.
I think I'm being picky with the difference between speed and velocity. I try hard to use the correct word for the context because they're different things.
Yea that's extremely awesome and is what really caught my eye, sparked my imagination and inspired me to properly think about relativity. The reason you can't escape from inside the event horizon of a black hole is that a direction in space that leads out of the black hole simply doesn't exist, every direction leads to the singularity eventually. It actually makes me disappointed that I can't see how it's possible to reach an event horizon.
Every spatial direction leads not-out. The direction out is to the past, and you can't go that way, gravity or not. But this all assumes anything is in the black hole in the first place. I suppose it could, but how would it get there? There are laws of physics in there, but without matter, does it matter? (Pun intended I think)
There is not a moment beyond which the accelerating clock will not reach, and once reached, light from that moment will makes its way back to the inertial observer after some finite time.
I think there is a moment that the accelerating observer's watch won't reach if they continue to increase their acceleration at an exponential rate to mirror the acceleration of falling towards an event horizon.
That's not a continuously accelerating frame. That is an increasing acceleration frame. It isn't equivalent because the artificial one involves acceleration and local g force, and the falling one is a geodesic with no local g force. Hence my analogy of tossing a clock out of the window of a continuously accelerating ship. It isn't perfect, but the clock does at least stop from the ship perspective.
You be talking about the Rindler horizon. :)
Yes. You can explain Unruh radiation to me while you're at it.
The two situations are not entirely equivalent since the black hole sets up a curved gravitational field and the accelerating object sets up a flat one. The black hole clock gets torn apart by tidal forces and the one dropped out of the ship window experiences no tidal forces. That difference I think invalidates the claim that the equivalence demonstrates that objects enter black holes. But as I said, I await opinions from those taking the opposite stance. I'm no expert.
I'd like to comment on that but we're not supposed to discuss personal models in this section, which is fair enough.
How wacky is your personal model? I think there are physicists on both side of the 'does it fall in' question, so both are mainstream enough. Not sure what you have in mind. You seem to be able to follow what I'm describing, so I'm interested.
Yes that's exactly how I see it. No amount finite amount of time is enough, the rest of the universe (including the end of the life of the black hole) will always happen before the event horizon can be reached.
Well heck, then we need to get somebody else in on this discussion to take the other side, although I bolded a grammatical confusion.
I'm going to go look at your other thread.
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There is actually another very good reason to think that an event horizon can't be reached. I didn't want to start another topic for it and appear to be spamming.
Gravitation is supposed to be time reversible, it's an attractive force either way. This doesn't hold once an object crosses an event horizon because then that object has to reemerge from inside the event horizon if the arrow of time is reversed and that shouldn't be possible either way.
There is not a moment beyond which the accelerating clock will not reach, and once reached, light from that moment will makes its way back to the inertial observer after some finite time.
I think there is a moment that the accelerating observer's watch won't reach if they continue to increase their acceleration at an exponential rate to mirror the acceleration of falling towards an event horizon.
That's not a continuously accelerating frame. That is an increasing acceleration frame. It isn't equivalent because the artificial one involves acceleration and local g force, and the falling one is a geodesic with no local g force. Hence my analogy of tossing a clock out of the window of a continuously accelerating ship. It isn't perfect, but the clock does at least stop from the ship perspective.
Continuously increasing rate of acceleration. I think the equivalence of that accelerating observer relative to an inertial observer and an observer falling towards an event horizon relative to a distant observer does hold but that's going into my model.
You be talking about the Rindler horizon. :)
Yes. You can explain Unruh radiation to me while you're at it.
I thought Unruh radiation was a quantum mechanical effect, not a relativistic one. Could be wrong though.
How wacky is your personal model? I think there are physicists on both side of the 'does it fall in' question, so both are mainstream enough. Not sure what you have in mind. You seem to be able to follow what I'm describing, so I'm interested.
I was under the impression that the mainstream was well and truly in the yes they do reach the horizon camp. They definitely used to be not long ago but maybe that's changed.
My model is on the most recent page in the new theories section.
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I didn't want to start another topic for it and appear to be spamming.
The two-object argument also belongs in this thread. You don't need a separate thread for each contradiction you think you've found.
Gravitation is supposed to be time reversible, it's an attractive force either way. This doesn't hold once an object crosses an event horizon because then that object has to reemerge from inside the event horizon if the arrow of time is reversed and that shouldn't be possible either way.
A time-reversed black hole is a white hole with the event horizon running the other way.
An interesting thing would be a white-hole spontaneously forming from next to nothing as it un-Hawking radiates into existence.
I thought Unruh radiation was a quantum mechanical effect, not a relativistic one. Could be wrong though.
It seems to occur where the two models meet. Since we've no unified field theory, the exact description of such effects might have to wait. Still, an object falling to a black hole event horizon is destroyed and the one falling through the Rindler horizon notices nothing. The two seem not equivalent in that way, but equivalent enough to get the Unruh radiation.
How wacky is your personal model? I think there are physicists on both side of the 'does it fall in' question, so both are mainstream enough. Not sure what you have in mind. You seem to be able to follow what I'm describing, so I'm interested.
I was under the impression that the mainstream was well and truly in the yes they do reach the horizon camp. They definitely used to be not long ago but maybe that's changed.
Feel free to argue otherwise then, because I'm also in that camp. Yes, I think your examples (yes and no questions) suggest contradictions either way.
My model is on the most recent page in the new theories section.
The unified relativity thing? That's a lot more than just nothing-falls-in argument. Parts of that might well qualify as non-mainstream. I didn't particularly see this topic isolated in there.
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I didn't want to start another topic for it and appear to be spamming.
The two-object argument also belongs in this thread.
I thought there was more than enough of a difference between the two to keep them separate and not have one thread becoming too cluttered and messy with different scenarios but I don't mind if a mod wants to merge them.
I thought Unruh radiation was a quantum mechanical effect, not a relativistic one. Could be wrong though.
It seems to occur where the two models meet. Since we've no unified field theory, the exact description of such effects might have to wait. Still, an object falling to a black hole event horizon is destroyed and the one falling through the Rindler horizon notices nothing. The two seem not equivalent in that way, but equivalent enough to get the Unruh radiation.
I view the Rindler horizon as the exact opposite of an event horizon. If you think about it, a Rindler horizon has to form behind an observer falling towards an event horizon just as it does for other accelerating objects and if that observer were able to reach the event horizon then their own Rindler horizon would have caught up with them so the two horizons would meet at the position of that observer. After that the two horizons would have crossed over and would both be the on the opposite side of the observer and if you know how the Rindler horizon works you'll understand just how silly it would be for their Rindler horizon to be in front of them. I think it's equivalent to an event horizon being behind them.
My model is on the most recent page in the new theories section.
The unified relativity thing? That's a lot more than just nothing-falls-in argument. Parts of that might well qualify as non-mainstream. I didn't particularly see this topic isolated in there.
It goes into that model when we start talking about certain equivalences.
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If you want to work out what they would actually see then you need to factor in Doppler shift as well but that also remain constant at a constant relative velocity but is affected by direction of motion whereas time dilation only depends on velocity.
Is there a parallel, here, between trying to work out what each observer would see on the other’s clock; and trying to work out what an observer, travelling at “c”, would experience? Neither is possible, so the issue becomes more philosophical than scientific. Just a thought. :)
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If you want to work out what they would actually see then you need to factor in Doppler shift as well but that also remain constant at a constant relative velocity but is affected by direction of motion whereas time dilation only depends on velocity.
Is there a parallel, here, between trying to work out what each observer would see on the other’s clock; and trying to work out what an observer, travelling at “c”, would experience? Neither is possible, so the issue becomes more philosophical than scientific. Just a thought. :)
It's perfectly possible to work out what the observers see and in fact quite straight forward because the time dilation and Doppler shift caused by relative motion are entirely predictable, you just need to combine the two effects.
It becomes trickier when one or both are accelerating, whether gravitationally or otherwise.
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.....It's perfectly possible to work out what the observers see....
It's perfectly possible to work out what the observers would see, if they could; but my point was that neither observer could actually see the other's clock.
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Well, that's one of the reasons 'time' as in your wristwatch became ephemeral. Looked at from the opposite direction your wristwatch never lies. If I may. Define from where you look at it before questioning it.
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Rereading your original question A-wal.
" how is any lifespan of the black hole long enough for an infinite amount of time to pass on the watch of a distant observer from the perspective of the falling observer before they reach the event horizon?"
That one is perplexing, and some people define it such as all mass infalling never will reach a 'center'. Others define it as time, as a clock defined 'globally', doesn't exist. What exist is your 'local clock', and everyone's else local clock. And if so, locally defined, all mass infalling must reach a 'center'. It's strongly related to 'frames of reference', and from the viewpoint of something hovering at a 'event horizon' 'things' should just 'appear' as it seems to me to then slow down to a more normal speed, to then just 'disappear' passing the event horizon.
The reason I'm thinking this way is that for the hovering observer the 'universe outside', relative its own frame of reference, should be perceived as evolving extremely fast, which should mean that to the hovering observer infalling mass more or less should 'appear' above the event horizon, to then slow down as it approaches, and finally 'accelerate' again into oblivion passing the event horizon, all from the perspective of the observer. If it now makes any sense :)
Because a Black hole is represented of a infinity of gravity at its 'center' it seems reasonable to presume that somethings final speed as defined by the observer should approach 'c'.
What should be noted there is that no one expect 'time' to move backwards for any observer. There is only one arrow of time.
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Thanks!