Physics, Astronomy & Cosmology / Re: How does time at the Event Horizon differ for approaching vs Distant Observers?« on: 20/03/2019 17:50:04 »
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.
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.Quote from: HalcFor 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.
Each clock would be running slow from the perspective of the observer observerFrom 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 shiftOK, 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.
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.Quote from: HalcWhat 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.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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