On 11/9/2019 4:12 PM, Alan Grayson wrote:
On Friday, November 8, 2019 at 5:05:31 PM UTC-7, Brent wrote: On 11/7/2019 10:42 PM, Alan Grayson wrote:On Thursday, November 7, 2019 at 10:54:33 PM UTC-7, Brent wrote: On 11/7/2019 8:43 PM, Alan Grayson wrote:On Thursday, November 7, 2019 at 5:20:13 PM UTC-7, Brent wrote: On 11/7/2019 4:06 PM, Alan Grayson wrote:On Thursday, November 7, 2019 at 11:41:11 AM UTC-7, Brent wrote: On 11/6/2019 10:31 PM, Alan Grayson wrote:On Wednesday, November 6, 2019 at 11:20:23 PM UTC-7, Brent wrote: On 11/6/2019 9:00 PM, Alan Grayson wrote:On Wednesday, November 6, 2019 at 7:17:21 PM UTC-7, Brent wrote: On 11/6/2019 4:44 PM, Alan Grayson wrote:On Wednesday, November 6, 2019 at 3:46:54 PM UTC-7, Brent wrote: On 11/6/2019 12:05 AM, Alan Grayson wrote:On Tuesday, November 5, 2019 at 10:23:58 PM UTC-7, Brent wrote: On 11/5/2019 9:09 PM, Alan Grayson wrote:Crossing the horizon is a nonevent for the most part. If you try to accelerate so you hover just above it the time dilation and that you are in an extreme Rindler wedge will mean you are subjected to a torrent of radiation. In principle a probe could accelerate to 10^{53}m/s^2 and hover a Planck unit distance above the horizon. You would be at the stretched horizon. This would be almost a sort of singular event. On the other hand if you fall on an inertial frame inwards there is nothing unusual at the horizon. LC Do you mean that clock rates continue to slow as an observer approaches the event horizon; then the clock stops when crossing, or on the event horizon; and after crossing the clock resumes its forward rate? AGHe means the infalling clock doesn't slow down at all. Whenever you see the word "clock" in a discussion of relativity it refers to an /*ideal clock*/. It runs perfectly and never speeds up or slows down. It's called /*relativity*/ theory because observers /*moving relative*/ to the clock /*measure it*/ to run slower or faster than their (ideal) clock. Brent I see. So if for the infalling observer, his clock seems to be running "normally", but for some stationary observer, say above the event horizon, the infalling clock appears to running progressively slower as it falls below the EH, even if it can't be observed or measured. According to GR, is there any depth below the event horizon where the infalling clock theoretically stops?I just explained that */clocks never slow/* in relativity examples. So now you ask if there's a place they stop?? Brent I know, but that's not what I asked. Again, the infalling clock is measured as running slower than a stationary clock above the EH. As the infalling clock goes deeper into the BH, won't its theoretical rate continue to decrease as compared to the reference clock above the EH? How slow can it get? AGIt /*appears*/ (if the observer at infinity could see the extreme red shift) to /*asymptotically approach stopped */as it approaches the event horizon. This is because the photons take longer and longer to climb out because they have to traverse more and more spacetime. Brent I'm referring to two clocks; one at finite distance above the EH, and other infalling. Doesn't the infalling clock seem to run progressively slower from the POV of the other clock, as it falls lower and lower? AGI appears to run slower as seen by the distant observer. Brent As it goes deeper and deeper into the BH, does the clock ever appear to STOP? AGIt doesn't appear at all when it passes the event horizon. It appears to stop as it approaches the event horizon. Brent I know it can't be observed as it falls through the EH. That's why I referred to clock "readings" after falling through as "theoretical".Well it doesn't make much sense to call observations theoretical when it's the theory that says they can't be observed.On the other hand, LC says falling through the EH is a non-event, as if the infalling clock behaves as we expect based on a clock entering a region of strong gravitational field. But let's say the clock appears to stop as it approaches the EH, which is what I thought. How do you reconcile this prediction, which is certainly weird? AGReconcile it with what? It's a consequence of the metric which is derived from Einstein's equations. It's not as if it's some unexplained observation. It's not an observation at all. It's a theoretical prediction. Brent You don't see a problem with a theory that predicts a clock which stops as seen by an outside observer, when the observer using the clock, which measures proper time, must see it moving forward? AGNo. Why should it be a problem? You're watching the clock approach the event horizon and the photons from it come further and further apart until you have to wait seconds between photons, and then hours, and then days, and years...why because they have to travel thru more spacetime. If it's a rotating black hole, as most of them will be, each photon will have to orbit many times on it's way out. Brent If clock which is fixed some distance from the EH, and the BH isn't rotating, why must the photons traveling to the fixed observer have to travel progressively longer times? AGIt's because there is more time to traverse. It's a matter of the metric. BrentDoesn't this mean that the gravitational field of the BH becomes *infinite* at the EH? How else could the red shift become so large for photons leaving a clock at the EH, that from the pov of the fixed observer above the EH the clock approaching the EH seems to stop? AG
Look at Greg Egan's page on this: https://www.gregegan.net/SCIENCE/FiniteFall/FiniteFall.html#HOR
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