[Mike Gale (OP)]

I am more interested in Penrose's entropy reset between eons in universal evolution.

I'm not familiar with that, but I seem to have falsely credited Penrose for the snapshot idea. He doesn't talk about it in that video. It must have been someone else. I'll have to dig into my archives to find the lecture I was thinking of. I remember it ended with the lecturer tossing a pile of snapshots on the floor for dramatic effect.

[Mike Gale (OP)]

Here's a good account of relativistic escape velocity:
http://www.mrelativity.net/MBriefs/Relativistic%20Escape%20Velocity%20using%20Special%20Relativity.htm

I'm not sure of that site. It seems to be promoting a personal theory stating that relativity is wrong.

Agreed. It's not peer reviewed, but he's got the math right and, although he doesn't delve into any GR, he is thinking along the same lines.

[Mike Gale (OP)]

Here's another discussion thread on this topic:
http://physics.stackexchange.com/questions/246133/deriving-a-schwarzschild-radius-using-relativistic-mass
Their expert claims that we're getting confused because the radius in the SC metric is different from the conventional one. I don't understand the distinction yet, but I intend to investigate. Do you know what he's talking about?

[jeffreyH]

Yes what John Rennie is saying is that R and r differ. Where R is radial r is an arc divided by 2 pi. The same result is coincidental. This relates to the way the unit circle operates. Which is why I am interested in David Coopers use of trigonometry in relation to relativity.


BTW If you see an answer by John Rennie it is worth taking note. I rate him highly.

[jeffreyH]

To relate r to radians read this and note the role of radians per second in the description of a simple harmonic oscillator. This becomes important when moving on to the Kerr metric.


https://farside.ph.utexas.edu/teaching/315/Waveshtml/node3.html

[Mike Gale (OP)]

Cosmological constant or cosmological variable? Wikipedia says "there is no evidence that the vacuum energy does vary, but it may be the case if, for example, the vacuum energy is (even in part) the potential of a scalar field such as the residual inflation (also see quintessence)."

[Mike Gale (OP)]

Yes what John Rennie is saying is that R and r differ. Where R is radial r is an arc divided by 2 pi. The same result is coincidental. This relates to the way the unit circle operates. Which is why I am interested in David Coopers use of trigonometry in relation to relativity.


BTW If you see an answer by John Rennie it is worth taking note. I rate him highly.

I still don't get it. I understand that a radial distance in a local reference frame is different from that measured by an infinitely removed observer, but I thought the coordinates in the SC metric correspond to the distant reference frame, not the local one.
Wikipedia defines r as the circumference of a sphere divided by 2π. If I remember my high school geometry, that's just an elaborate way of defining the radius. Is big R the radius in the local reference frame? If so, I don't see why you would use that in the gravitational potential since the local observer is in free fall. If that was not the case, there would have to be another source of energy beyond that which is provided by the gravitating mass and the SC metric does not allow for that.

[Mike Gale (OP)]

To relate r to radians read this and note the role of radians per second in the description of a simple harmonic oscillator. This becomes important when moving on to the Kerr metric.


https://farside.ph.utexas.edu/teaching/315/Waveshtml/node3.html

Yeah, I get that. But I don't see how it's relevant to the topic at hand. Have you seen the solution for waves on a string? It only works for small displacements. I find it astonishing that there's no exact solution for that in this day and age.

[Mike Gale (OP)]

I am more interested in Penrose's entropy reset between eons in universal evolution.

I'm not familiar with that, but I seem to have falsely credited Penrose for the snapshot idea. He doesn't talk about it in that video. It must have been someone else. I'll have to dig into my archives to find the lecture I was thinking of. I remember it ended with the lecturer tossing a pile of snapshots on the floor for dramatic effect.

It was Julian Barbour:

[jeffreyH]

I am more interested in Penrose's entropy reset between eons in universal evolution.

I'm not familiar with that, but I seem to have falsely credited Penrose for the snapshot idea. He doesn't talk about it in that video. It must have been someone else. I'll have to dig into my archives to find the lecture I was thinking of. I remember it ended with the lecturer tossing a pile of snapshots on the floor for dramatic effect.

It was Julian Barbour:

I only watched the video halfway through. Interesting that the square root removes time from the action. I removed time in a different way. The annoying point about the video was that as he is describing the mathematics is when focus is taken away from the screen. This is very unhelpful. He is also talking away from the microphone. It's a pity since I would have watched it all the way through otherwise. I may try to watch it again when I have some free time.

[Mike Gale (OP)]

Yes what John Rennie is saying is that R and r differ. Where R is radial r is an arc divided by 2 pi. The same result is coincidental. This relates to the way the unit circle operates. Which is why I am interested in David Coopers use of trigonometry in relation to relativity.


BTW If you see an answer by John Rennie it is worth taking note. I rate him highly.

I still don't get it. I understand that a radial distance in a local reference frame is different from that measured by an infinitely removed observer, but I thought the coordinates in the SC metric correspond to the distant reference frame, not the local one.
Wikipedia defines r as the circumference of a sphere divided by 2π. If I remember my high school geometry, that's just an elaborate way of defining the radius. Is big R the radius in the local reference frame? If so, I don't see why you would use that in the gravitational potential since the local observer is in free fall. If that was not the case, there would have to be another source of energy beyond that which is provided by the gravitating mass and the SC metric does not allow for that.

Okay, I think I get it now after sleeping on it. The idea is to define radius in terms of circumference because the latter is invariant (in Flamm's parabaloid) and the former is not. It's akin to setting G=c=1 to simplify notation. It's a neat trick in both cases because it reduces complexity, but it makes it easier to lose track of the physical significance of your results and I think this is a case in point. It is little r that belongs in the potential energy equation, not big R. The correspondence between escape velocity and the SC scaling distance is no coincidence, The scaling factor (1-rs/r) is in fact (1-(v/c)^2), where v is escape velocity as opposed to coordinate velocity. These are one and the same in the (radial) free fall case, which is really all the SC metric can cope with aside from orbital dynamics.

[PmbPhy]

I disagree. Nothing penetrates the horizon, not even light. The local reference frame is completely decoupled from the external one at the event horizon. From a local point of view at that location, the gravitating mass is infinitely far away.

That is quite incorrect. If you were in a space capsule and were falling into a super giant black hole then from your frame of reference you would most certainly pass through the event horizon. This is a well known fact from general relativity. Two great texts to learn about this are Taylor and Wheeler's texty Exploring Black Holes and the book by Kip Thorne (THE black hole expert) Black Holes and Time Warps - Einstein's Outrageous Legacy.

Regarding your other assertions where you disagree with what I wrote, please point to a derivation from a good text on GR. Until then I see no point in merely stating that the other person is wrong. Thanks.

[JohnDuffield]

Okay, I think I get it now after sleeping on it. The idea is to define radius in terms of circumference because the latter is invariant (in Flamm's parabaloid) and the former is not. It's akin to setting G=c=1 to simplify notation...

It might simplify the notation, but setting c=1 is absolutely wrong. It flatly contradicts Einstein, who said "a curvature of rays of light can only occur where the speed of light is spatially variable". If it wasn't, you wouldn't fall down.

I suspect the problem you're having here is that you're getting mixed messages. I recommend you focus on what Einstein said, and be a little sceptical about what people like Kip Thorne says. He's the sort of guy who comes up with "wild theories" and attempts to justify them by appealing to Einstein's authority even though he's contradicting Einstein.

[JohnDuffield]

Cosmological constant or cosmological variable? Wikipedia says "there is no evidence that the vacuum energy does vary, but it may be the case if, for example, the vacuum energy is (even in part) the potential of a scalar field such as the residual inflation (also see quintessence)."

See the Einstein digital papers and note this: "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". Vacuum energy varies in the room you're in. The spatial energy density is greater at a lower elevation.

[jeffreyH]

Below is a link to the wikipedia article on Kip Thorne. Before deciding whether or not to follow a charlatan I suggest the intelligent reader review the article first.


https://en.m.wikipedia.org/wiki/Kip_Thorne

[jeffreyH]

So John what are your qualifications? We could compare them to Kip Thorne's.

[Mike Gale (OP)]

I disagree. Nothing penetrates the horizon, not even light. The local reference frame is completely decoupled from the external one at the event horizon. From a local point of view at that location, the gravitating mass is infinitely far away.

That is quite incorrect. If you were in a space capsule and were falling into a super giant black hole then from your frame of reference you would most certainly pass through the event horizon. This is a well known fact from general relativity. Two great texts to learn about this are Taylor and Wheeler's texty Exploring Black Holes and the book by Kip Thorne (THE black hole expert) Black Holes and Time Warps - Einstein's Outrageous Legacy.

Regarding your other assertions where you disagree with what I wrote, please point to a derivation from a good text on GR. Until then I see no point in merely stating that the other person is wrong. Thanks.

Don't be offended if I disagree with your opinion. I'm only trying to find the truth. I base my assertion (that nothing penetrates the horizon) on the fact that proper time abruptly enters the imaginary domain at that location. Viascience gives an excellent example of this. The worldline of an in-falling object just stops in mid flight. One can presume that this is inconsequential to the local observer, but that means abandoning the SC solution for something entirely different. It is also demonstrably true that light can't penetrate the horizon so it's hard to imagine anything else doing so.
I am not aware of any established texts that adequately address this issue, but from what I've seen of the Susskind lectures, he is of the same opinion. It is the basis for his holographic principle for example. Also his theory about elephants. I can't imagine what he would make of the new metric, but I like to think he would give it due consideration before having me strung up and quartered.
Note that proper time is always real with the new metric, but as with the old one, penetration of the horizon is still impossible due to infinite spatial dilation. There's no way in or out from the bottom of Flamm's parabaloid. I expect that's part of Susskind's justifcation for this premise, not just that proper time is ill defined. Since I bring it up, I suppose it's part of my justification, too.
Note also that, although penetration is a prerequisite for black hole formation (by a collapsing star), that process is speculative at best.

[jeffreyH]

The photon leaving the near vicinity of an event horizon is much like an in falling object. It undergoes a positive coordinate acceleration. So things appear to slow down since the light takes a longer time to get to the remote observer. The local observer on the other hand will experience his fall to the singularity in a shorter period of time than  they would expect. No magic and no smoke and mirrors. What Susskind says about entropy and the holographic principle is entirely unaffected by this.

[Mike Gale (OP)]

The photon leaving the near vicinity of an event horizon is much like an in falling object. It undergoes a positive coordinate acceleration. So things appear to slow down since the light takes a longer time to get to the remote observer. The local observer on the other hand will experience his fall to the singularity in a shorter period of time than  they would expect. No magic and no smoke and mirrors. What Susskind says about entropy and the holographic principle is entirely unaffected by this.

I suppose it's true that the Susskind theories I identified only require penetration to be impossible from the point of view of a distant observer. What happens in the local reference frame is immaterial. The smoke and mirrors happen when you derive equations of motion in the weak field domain and apply them in the strong field domain. That's what Viascience does (https://youtu.be/OF7dyka7FEs?list=PLF56602BAC693237E). Although the equations break down at the horizon, it looks for all the world like the test mass is going to carry on all the way to the central singularity (as Newton predicts) even though photons do not (Newton is silent on that point.) That makes no sense to me. I think Flamm's paraboloid paints a more realistic picture, which is that nothing ever reaches the horizon in any reference frame. In any case, I probably should have nipped this part of the discussion in the bud because it is getting off topic. Like Wilson said, the new metric doesn't change any of this. What I'm looking for is a reasonable argument against the viability of the new metric. I haven't heard any yet.

[jeffreyH]

You are making the mistake of confusing frames. Locality and non-locality cannot be mixed. That is why Lorentz transformations are used. If you believe that a photon never reaches the horizon then you have made a mistake. Because of tidal forces the direction of a trajectory is critical. More so at the horizon. For a photon the photon sphere is the point of no return. Simply because of its path. I derive the radius to the photon sphere for the Schwarzschild solution before I knew of its existence without field equations of any kind. Then I started to look at the Kerr metric and thought better of it! Keep going. You are making some interesting points.