[Mike Gale (OP)]

well, we have Pete here at times. You could PM him with a link, or the whole idea and see what he thinks about it.

I don't have his user ID, but feel free to bring him in on this. I love his videos.

[Mike Gale (OP)]

Your photon sphere is going to be out as 1/2r_s instead of 1.5r_s.

Since this is all theoretical anyway I don't suppose it's a concern.

The photon sphere is where orbital velocity reaches light speed. The orbital speed limit is found by setting ds = dr = 0.

[yor_on]

That one wasn't that bad It' seems perfectly correct, and discuss it from a local as well as from a 'far away' perspective. But saying that the light 'freeze' is still a observer dependent definition, not a local. And placing a mirror just outside that event horizon light should still be at 'c' as I expect.

Maybe I missed something though? I do not expect the guy to really believe light to 'freeze' due to using his local 'far away' reference frame, comparing clocks though? The only way I imagine one to get it to 'freeze' would be to assign this 'far away observer' a universal 'golden standard'. And that should then mean no more relativity, and at last somewhere from where one can "Give me a lever and a place to stand and I will move the earth."  But as you say, it's mathematics.

[yor_on]

Relativity 11d - spherical bodies and black holes IV

[Mike Gale (OP)]

That one wasn't that bad It' seems perfectly correct, and discuss it from a local as well as from a 'far away' perspective. But saying that the light 'freeze' is still a observer dependent definition, not a local. And placing a mirror just outside that event horizon light should still be at 'c' as I expect.

Maybe I missed something though? I do not expect the guy to really believe light to 'freeze' due to using his local 'far away' reference frame, comparing clocks though? The only way I imagine one to get it to 'freeze' would be to assign this 'far away observer' a universal 'golden standard'. And that should then mean no more relativity, and at last somewhere from where one can "Give me a lever and a place to stand and I will move the earth."  But as you say, it's mathematics.

"Far away" observers cannot "see" light freeze on the event horizon. They must infer that by observing transit time and distance from different (free-falling) reference frames.

[yor_on]

Agreed, but what I said before still stands. It's a question of reference frames, and there you get to one result treating it as a 'whole universe', looking at the implications of your equations and what different observers find. But if defined locally it really doesn't matter. In the local frame 'time' never stops, well, as long as one is alive at least

[Mike Gale (OP)]

Agreed, but what I said before still stands. It's a question of reference frames, and there you get to one result treating it as a 'whole universe', looking at the implications of your equations and what different observers find. But if defined locally it really doesn't matter. In the local frame 'time' never stops, well, as long as one is alive at least

Correct, but note that there is a point in the new metric at GM/2c^2 where special relativity breaks down. It's not clear what the universe looks like from that perspective.

[yor_on]

Yes Mike, a pleasure to have you aboard btw

[Mike Gale (OP)]

Note that, although the Schwarzschild metric does indeed define a preferred reference frame, it does not permit you to move the Earth with a lever because it excludes all sources of energy beyond that of the gravitating mass.

[yor_on]

heh

[Mike Gale (OP)]

Light speed as perceived by the infinitely removed observer is found by setting ds and angular displacement to zero. The result from standard SC metric is:
dr/dt=(1-2GM/rc^2)*c
The result from new SC metric is:
dr/dt=(1-GM/rc^2)^2*c

[Mike Gale (OP)]

That's the radial speed limit. Orbital speed limit is found by setting ds=dr=0. Standard solution is:
d(angle)/dt=sqrt(1-2GM/rc^2)*c/r
New solution is:
d(angle)/dt=(1-GM/rc^2)*c/r

[Mike Gale (OP)]

These guys seem to be puzzling over the same problem:
http://physics.stackexchange.com/questions/147417/advantage-and-disadvantage-of-weak-field-approximation

[yor_on]

Well Mike, maybe because you ask interesting questions. And that one reminds me of the hen and the egg
This one seem to have a relevance to your ideas Derivation of the linearized Einstein equations, and applications of their solutions (in the limit of weak and static fields) to discuss two classical tests of general relativity: the bending of light rays and the radar-echo delay. A special topic (not available in the current textbook literature) discussed in this chapter is the shift of mean velocities induced by gravity, and the effective “slowdown” or “speedup” of light signals, depending on the observer position and on the given kinematic configuration

The problem with it is the usual for us paupers, it's behind a paywall.

[yor_on]

Mike, as I said I blame the lights disappearance primary on geodesics, not time dilations per se. Both phenomena are definitely connected though.

"The gravitational redshift is a phenomenon based on gravitational time dilation, don't we want to exclude definitely any loss of energy of photons? The gravitational Redshift is a phenomenon which is directly related to the time dilation of the atomic clocks in a gravitational potential. Somebody still gives the interpretation of an energy loss of photons in a gravitational potential. If the interpretation is due the exchange of net amount of energy with the gravitational field while crossing  different gravitational potentials, treating the radiation as being massive while travelling, such hypothesys has to be excluded. The results of the PRS experiments verify (1+gh/c2) as being the frequency shift ratio, and since in both cases (lossive and clock hypothesys) the same shift is predicted, one of the two interpretation has  to be discarded.

Lev Okun invited to perform such a sharp distinction more than 15 years ago, discarding forever the gain or loss of energy of the photons as measured always in the same RF. The two interpretations cannot be considered alternative views of the same phenomenon and the  net electromagnetic energy exchange with the gravitational field during the transit has to be discarded and is not certainly supported by the GRT.

The Clock hypothesys is verified also  in the experiment of Vessot and Levine by testing the Schwartschild solution . 

It is also verified that when clocks are in sync in a gravitational potential, due to the compensation of the kinetics, there is not  redshift at all, In  other words, although there is a different gravitational potential between the emitter and the observer, there is a specific point along the ballistic motion where no redshift is observed or present, and no time dilation between the emitter and observer is present according to GRT." 

I'm not thinking of the clock hypothesis there, just the assertion that "although there is a different gravitational potential between the emitter and the observer, there is a specific point along the ballistic motion where no redshift is observed or present, and no time dilation between the emitter and observer is present according to GRT."

Makes for a interesting reading, doesn't it? The gravitational redshift is a phenomenon based on gravitational time dilation, don't we want to exclude definitely any loss of energy of photons? 

[jeffreyH]

Everything else changes but the photon stays the same. The conditions in the local frame at the time of emission are important.

[Mike Gale (OP)]

The simplest geodesic to analyze is the one in which dr=0 (i.e. circular orbit). In that case, observers in different reference frames are stationary with respect to one another so SR predicts no frequency shift. GR begs to differ:
(ds/dt)^2=(1-rs/r)-v^2/c^2=1-2v^2/c^2~sqrt(1-v^2/c^2)
This is the first step in the GPS clock drift calculation for example. As in SR, the dilation is the same in both reference frames. That is, the surface dweller perceives the satellite clock to run slower and the satellite perceives the surface dweller's clock to run slower. It seems paradoxical, but it's not. It's analogous to the Twin's Paradox.

[Mike Gale (OP)]

There is no red-shift between free-falling reference frames.

I was wrong about this. There is red-shift in that case, but it's due to time dilation, not variable speed of light.

[Mike Gale (OP)]

Makes for a interesting reading, doesn't it?

Stephano seems to be debunking the model in which a photon has a tiny, but finite mass. I don't understand why.

[Mike Gale (OP)]

This one seem to have a relevance to your ideas Derivation of the linearized Einstein equations, and applications of their solutions (in the limit of weak and static fields) to discuss two classical tests of general relativity: the bending of light rays and the radar-echo delay. A special topic (not available in the current textbook literature) discussed in this chapter is the shift of mean velocities induced by gravity, and the effective “slowdown” or “speedup” of light signals, depending on the observer position and on the given kinematic configuration

Perhaps. Sounds like they're focused on the weak field domain, but it does exemplify the variable light speed phenomenon.