
#37
Mar612, 11:40 PM

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#39
Mar712, 05:45 AM

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In order to qualify as an observer, his worldline must be timelike. (Which is another technial term from special relativity). An photon isn't an observer, for instance. I don't see why you say it's misguided. Though I think it may be confusing the OP, because Thorne's approach isn't based on the "clock slowing" paradigm. My basic impression is that the OP is stuck in a Newtonian view of absolute time, and is also interpreting the whole "clock slowing" down thing as some sort of scalar function that modifies how fast absolute time flows at a given position. And this is just not compatible with special relativity at all (mostly because of the absolute time idea). At the risk of possibly causing more confusion, Thorne's view is more like saying that the time doesn't really "stop" (as per the stopped time idea), it's just bent to point in a spatial direction. 



#40
Mar712, 07:22 AM

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Why is that too? We can calculate what happens when you travel at the speed of light with an equation yet right next to it have another equation that says you can never travel at or faster than the speed of light, within the same theory known as GR. 



#41
Mar712, 07:31 AM

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#42
Mar712, 12:19 PM

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I don't know what you are referring to in claiming I said escape velocities don't matter. I don't know what you are going on about traveling at or faster than the speed of light. I keep repeating this is all nonsense. The singularity is a point in time not in space. Once inside the horizon, you can shine a flashlight any direction, and fire bullets in any direction, but all light and any projectiles you fire, in any direction, move forward in time toward the singularity. Poetically, you can say the singularity is a point in time where space ceases to exist for you. (In fact, you will be subject to enormous (ultimately infinite) compression and stretching, but you can always define a tiny enough region where everything is momentarily normal  until the moment of reaching the singularity). 



#43
Mar712, 04:46 PM

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The OP thanks you all. This has been a most interesting thread and I have achieved the desired 'intuitive' breakthrough that I was seeking. Just a few notes in special appreciation starting with post #16
I won't quote quotes but I found the two in post #19 by Naty1 very helpful. In Post #20 The same statement rephrased: Were an 'instantaneous' link available from the falling clock to a slave clock held by an observer, it would indeed show the falling clock to be slowing at a rate depending on the gravitational gradient of the particular black hole. BUT IT WOULD NOT SLOW TO ZERO at the event horizon. The appearance of this effect to an observer without a simultaneous link, while real enough, is caused by the slowness of light (or other EM signal) returning to the observer from the intense gravity field. The 'simultaneously' linked clock would only approach zero rate of change as it approached the singularity. The clock itself behaves exactly as it would aboard a vessel approaching light speed, with all the same implications for local and distant observers. After all, although nothing can be seen to 'break' the speed of light this doesn't change the fact that an intrepid traveller accelerating at 1 g will subjectively do so after about three years. As I have said before, I seek intuitive understanding without math. Of course I know that simultaneous links are thought to be impossible, and that infinite anythings are rare. Indeed the only infinite 'physical' thing I can think of is the depth of a gravity well in which sits a singularity. Once again thanks to everybody who participated in this thread. You have settled demons which have been of growing concern to my intuition for some time. 



#44
Mar712, 05:10 PM

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OP here again. Not having refreshed my browser I had missed this quoted post. I now must take issue with paragraph 1




#45
Mar712, 05:55 PM

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(1) The "black hole" is not just the singularity. The term is used to refer to the entire region of spacetime inside the event horizon. When people talk about two black holes merging, they are talking about two regions inside event horizons merging into one region inside an event horizon. (Strictly speaking, there is only a single event horizon, and only a single region of spacetime inside it; that region just happens to be shaped like a pair of trousers instead of a tube, so to speak.) (2) A black hole is not "infinitely dense". The singularity itself can be thought of as "infinitely dense", but the singularity has no causal effect on anything else in the spacetime, so its characteristics are irrelevant for understanding what happens elsewhere. (Strictly speaking, the singularity is not even "in" the spacetimethe spacetime itself "ends" at the singularity, meaning there are events arbitrarily close to the singularity but none actually "at" it.) (3) The event horizon is defined "teleologically"it is the boundary of the region of the spacetime (as above, there is only *one* such region, but it may be shaped like a pair of trousers instead of a tube) that cannot send light signals to "infinity" (strictly speaking, to "future null infinity"). That definition requires you to know the entire history of the spacetime to pin down exactly where the horizon is. So when an object of nonnegligible mass falls into a black hole, the horizon starts to move outward from its old radius to its new radius even *before* the infalling object reaches it, because the horizon is defined in terms of where light signals go all the way into the infinite future. A light signal sent from outside the "old" horizon radius may still be trapped behind the new horizon even if it is sent *before* the infalling object reaches the "new" horizon radiusif it is sent a short enough time before, so that it doesn't have time to make it past the new horizon radius before the infalling object arrives. Take a look at the diagrams on this page: http://casa.colorado.edu/~ajsh/collapse.html Particularly the Kruskal and Penrose diagrams of the star collapsing to a black hole. It may help to visualize what I'm saying above. 



#46
Mar712, 06:15 PM

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#47
Mar712, 06:26 PM

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#48
Mar712, 06:36 PM

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#49
Mar712, 06:43 PM

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#50
Mar712, 06:58 PM

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Clarification:
A clock near an event horizon would appear to have slowed to almost nothing, considering redshift alone and excluding gravitational effects. In 'reality', as far as it can be applied in these circumstances, the gravitation slows the clock to near zero at the singularity. The redshift, by different means, makes the clock appear to have stopped at the event horizon. 



#51
Mar712, 07:03 PM

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#52
Mar712, 07:05 PM

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#53
Mar712, 07:24 PM

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#54
Mar712, 07:35 PM

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Others have spoken of infalling observers and I agree with them unconditionally. I also agree with eveything you said about them in your last post. But I have not mentioned them in this thread.
As for the "instantaneous link" it will be a sad day for physics when thought experiments are disallowed. 


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