[jeffreyH]

In special relativity the velocity addition formula is:



This precludes superluminal motion for massive objects.

[timey]

Special relativity holds the speed of light relative to a static length second, where time dilation is velocity related.
General relativity says that differing gravity potentials have differing length seconds.
(Note: A combination of both are used to calculate general relativity gravity potential time dilation and special relativity centripetal motion time dilation for time dilation of longitude in relation to equatorial bulge)

So this special relativity velocity addition formula - is it talking about velocity related time dilation? Calculating a velocity related time dilation that affects the velocity is a catch 22.  And where it is saying /c^2, this is not taking into account differing length seconds at differing GP's.  Is it?

[dutch]

Where did I say the speed of light was faster than c?

Nowhere.  Why do you think I am under the impression that you did?

Sorry I thought I was writing "where did I say anything was going faster than c" (the speed of light).

So when the speed of light is always measured as c 'locally', which local's rate of time is the observer holding 299 792 458 m/s relative to?  The observer observes (hypothetically) that the rate of time is occurring 18% slower at rs=3.  If a second is 18% longer at rs=3, then at the local of rs=3 the speed of light will be 299 792 458 m/second that is 18% longer than the observer's length of second.

Local Lorentz Covariance means (in part) a volume surrounding any point will measure the speed of light as c using rulers and clocks defined at that point. How large this volume is depends on how much curvature there is. If I measure the speed of light in a lab on Earth I expect to measure exactly c (the lab is relatively small and the curvature is low). However, because of curvature if I measure the speed of light of a light beam passing near the Sun (and crossing much of the solar system) I would measure a value slightly different. To my rulers and clocks the light beam would curve and appear to slow down a bit depending on r (r is the distance form the center of the Sun). If you use locally defined measuring rods and clocks you always measure c (this works at all points except for singularities where curvature goes infinity in theory).

So the speed of light is the same distance traveled held relative to the time period of a second.  If a second in one part of the universe, lets say rs=3 for instance, can be 18% longer, then the speed of light at rs=3 is 299 792 458m/second that is 18% longer that the speed of light at the observers location, which is 299 792 458 m/s.  At both locals the speed of light travels the same distance in the time period of a second, but each local is inherent with seconds that have an 18% difference in length.

Time AND space change. If I get what you're saying it seems somewhat correct (Maybe?) but you're not including the spatial part (a Lorentz "Contraction" effect).

If the observer holds the speed of light relative to the time period of a second in his own local where the 'observed" motion is 98% of the speed of light, then when he takes into consideration that it is taking the matter between 18% and 11% longer to travel from rs=3 to rs=5 in that local than it is in his own local, he will realize that the matter must be travelling between 18% and 11% faster from rs=3 to rs=5 than 98% of the speed of light of his own local...
If it has taken the matter longer to travel between point A and point B, then clearly the matter must be moving faster than 98% of the speed of light.  The matter will be moving between 18% and 11% faster than 98% of the speed of light held relative to the time period of a second of the local of the observer.

No, I still don't get this line of reasoning. A large amount of matter may be moving at >50% the speed of light starting at about 3rs from the event horizon in the accretion disk (again as stated before the disk should start at about this distance as orbits become unstable closer and at 1.5rs only light can orbit). Sure, there's time dilation because the matter is moving fast and it's close to a massive object. However, this does not preclude the ability of the blackhole to eject some of the matter using magnetic fields and frame dragging. For example, gravity may "pull" a rocket downwards on a launch pad before it takes off but this does not preclude the ability of the rocket to accelerate upwards once the engines fire. The Penrose Process tapping into the energy stored in the angular momentum of the blackhole and magnetic fields seem to have the ability to accelerate some matter to high speeds in jets. It's interesting and very complicated but not a paradox.

So this special relativity velocity addition formula - is it talking about velocity related time dilation? Calculating a velocity related time dilation that affects the velocity is a catch 22.  And where it is saying /c^2, this is not taking into account differing length seconds at differing GP's.  Is it?

The special relativistic velocity addition equation just like the constant speed of light holds exactly in GR at all points but only in a small enough volume around a point anywhere outside the event horizon (again part of Local Lorentz Covariance; it should also hold inside the event horizon everywhere but the singularity). If spacetime is flat the volume of space the velocity addition equation holds in is infinite.

[timey]

Local Lorentz Covariance means (in part) a volume surrounding any point will measure the speed of light as c using rulers and clocks defined at that point. How large this volume is depends on how much curvature there is. If I measure the speed of light in a lab on Earth I expect to measure exactly c (the lab is relatively small and the curvature is low). However, because of curvature if I measure the speed of light of a light beam passing near the Sun (and crossing much of the solar system) I would measure a value slightly different. To my rulers and clocks the light beam would curve and appear to slow down a bit depending on r (r is the distance form the center of the Sun). If you use locally defined measuring rods and clocks you always measure c (this works at all points except for singularities where curvature goes infinity in theory).

The Shapiro effect.  A test of general relativity that holds with the Schwarzschild, and is compatible with special relativity.

Time AND space change. If I get what you're saying it seems somewhat correct (Maybe?) but you're not including the spatial part (a Lorentz "Contraction" effect).

Yes (chuckle) - I did rather leave out the 'contraction effect'... Dum de dum...

No, I still don't get this line of reasoning. A large amount of matter may be moving at >50% the speed of light starting at about 3rs from the event horizon in the accretion disk (again as stated before the disk should start at about this distance as orbits become unstable closer and at 1.5rs only light can orbit). Sure, there's time dilation because the matter is moving fast and it's close to a massive object.

But now you are talking about time dilation that is velocity related.  What about the gravity potential time dilation at the location/s?

The Penrose Process tapping into the energy stored in the angular momentum of the blackhole and magnetic fields seem to have the ability to accelerate some matter to high speeds in jets. It's interesting and very complicated but not a paradox.

Is that Penrose's twister theory?  Yes it is interesting to wonder how the jets get so fast, but that "is' complicated and beyond the remit of my capabilities tbh.  Sticking for the mo to the observation of 98% of the speed of light motion of the jet...

The special relativistic velocity addition equation just like the constant speed of light holds exactly in GR at all points but only in a small enough volume around a point anywhere outside the event horizon (again part of Local Lorentz Covariance; it should also hold inside the event horizon everywhere but the singularity). If spacetime is flat the volume of space the velocity addition equation holds in is infinite.

But spacetime is not flat.  It is curved and rippled and wavy... 

[dutch]

The Shapiro effect.

Yes.

But now you are talking about time dilation that is velocity related.  What about the gravity potential time dilation at the location/s?

I'm really not sure what your writing about. Both affects occur. A full mathematical treatment of a rotating blackhole would be needed and that's quite complicated.

Is that Penrose's twister theory?

No, it's the Penrose Process (look it up).

Sticking for the mo to the observation of 98% of the speed of light motion of the jet...

What's the issue with this? I'm not understanding. I think you're assuming velocity adds in a classical way and it doesn't. You're clearly not taking into account the length contraction effect with your objections. Remember space changes as well as time.

But spacetime is not flat.  It is curved and rippled and wavy...

Well yes it is curved but in a small enough region of spacetime it's flat. This is similar to how the Earth's surface is flat in a small enough region. Spacetime is approximately flat in a volume around all points (the size of the volume depends on the curvature in the location; at a singularity the curvature is infinite so this rule fails).

[timey]

I was wondering... Perhaps if I listed all of the physics books that I've read on my profile page,..

I just asked you to consider a simple translation of general relativity gravity potential time bases that are 18% different to each other in relation to 'a remote observation' of matter travelling at 98% of the speed of light.

If you are using special relativity or Shwartzchild you are calculating with a speed of light held relative to a static length second.

The physics books tell me that these theories/calculations are open to discussion 'because' the maths break down at black holes.  I did not forget to incorporate Lorentz contraction.  I omitted mention of contraction on purpose in that we consider a general relativity calculation without it.

Penrose discusses the Penrose process in his book Cycles of Time.
(It occurs that each and every thread could be answered with the reply "Look it up".  The point of a thread is discussion - isn't it?)