Steven Crothers , against BB

[NotEinstein]

Believe that if you wish - that particular issue is dusted and done as far as I'm concerned.

OK, then let's get back to more important things!

It's quite straightforward. While from a coordinate basis the radial spacing of transverse grid lines compress closer to the source mass, radially oriented ruler shrinks by exactly the same fraction. The two cancel at any given radial location. Hence a 1cm proper radial displacement at one elevation is always transmitted as a proper 1cm radial displacement at any other elevation (we ignore 'practical' matters like mechanical stress/strain, and of course that elevations are always above the dreaded 'EH').

Do you have, or can you please link to, a mathematical derivation of this?​

 

[Q-reeus]

Can you please point me towards a post where you established the truth of this claim, or to some other reference that verifies it? I am coming to this discussion later, and admittedly have not read the entire thread.

It builds over the entire span of my relevant contributions this thread. Therefore I suggest reading through all my posts beginning at #79, and then see if that question still needs to be asked. Relevant links were given in #84 & #96 re standard predictions. Consider checking them out.

At first glance, it seems to me that the electromagnetic field tensor transforms just like any other tensor in curved spacetime. Why would it not respect the metric?

See examples of transmitted quantities given in #119 that do logically 'respect the metric' by violating flat spacetime expectations. A universal trend bucked according to GR only by static E & B fields.

My second inquiry is: supposing you are correct, and E and B fields don't "respect gravitational metric fields at all". Would that have any practical or experimentally-verifiable implications? If so, can you direct me towards experimental results which confirm your claim?

Very unlikely experimentally detectable. Even in gravitational extremes with large static B fields like afaik still only theorized magnetars, observational evidence would have to be evaluated against many model dependent interacting factors.

 

[Q-reeus]

Do you have, or can you please link to, a mathematical derivation of this?

What further do you need? The problem was your thinking extra radial space created in SM somehow results in a leverage advantage of sorts. It doesn't. It's a matter of basic logic. What you quoted is sufficient. Let me throw this back at you. How could there not be a 1:1 radial displacement correspondence between two different elevations?

 

[NotEinstein]

What further do you need?

As I said: a mathematical derivation.

The problem was your thinking extra radial space created in SM somehow results in a leverage advantage of sorts. It doesn't. It's a matter of basic logic.

Basic logic is quite tricky to get right in the theory of general relativity, due to all kinds of non-intuitive things happening. I'd like to go step-by-step through a rigorous mathematical derivation, so that I don't have to depend on possibly faulty logic.

What you quoted is sufficient. Let me throw this back at you. How could there not be a 1:1 radial displacement correspondence between two different elevations?

How about that link I posted in post #157? It explicitly states that measured lengths can be stretching due to gravity.

 

[Q-reeus]

...How about that link I posted in post #157? It explicitly states that measured lengths can be stretching due to gravity.

It says there is more radial distance generated between spherical shells of given area than would exist in the absense of gravitating mass. So? The g_rr metric component operates on both the connecting rod and the space in which it is immersed - equally. There is no differential logically possible. What that means overall is - sure you have to feed out more tape measure to initially go from station A at r1 to station B at r2, wrt flat spacetime case. But once connected, any further proper feeding motions are recorded equally at A and B. This is surely obvious.

 

[NotEinstein]

It says there is more radial distance generated between spherical shells of given area than would exist in the absense of gravitating mass. So?

In your (spherical) scenario radial distances and intervals pop up. So if there's some subtly involved when handling such cases, I'd like to make sure those subtleties are taking into account properly before I move on to other parts of the scenario.

The g_rr metric component opeates on both the connecting rod and the space in which it is immersed - equally. There is no differential logically possible. What that means overall is - sure you have to feed out more tape measure to initially go from station A at r1 to station B at r2, wrt flat spacetime case.

So that raises the question I already asked in post #157: does this also affect the "dr" in your calculation?

But once connected, any further proper feeding motions are recorded equally at A and B. This is surely obvious.

As I already said: I don't trust any argument that simply says something is obvious, without any mathematical derivation to back it up, especially in the quantum and GR realms. However, in this case, yes, it's obvious.

 

[James R]

Q-reeus:

Without delving into this further, I don't think I can make much sense of the content of this thread. It's been quite a while since I studied GR.

It's unfortunate that przyk bowed out of this discussion before it was resolved. He generally had a good handle on this stuff.

Anyway, thanks for your reply, but I'm out of this thread.

 

[Q-reeus]

Q-reeus:

Without delving into this further, I don't think I can make much sense of the content of this thread. It's been quite a while since I studied GR.

It's unfortunate that przyk bowed out of this discussion before it was resolved. He generally had a good handle on this stuff.

Anyway, thanks for your reply, but I'm out of this thread.

OK no problem. Thanks for asking.

 

[Schmelzer]

Ah, OK, so you were talking about some non-inertial frame of reference you didn't mention, and/or some non-local values from a location you didn't mention. Got it.

Hm, there is no such animal as an "inertial frame" in GR. In GR we have only systems of coordinates, and no system of coordinates is preferred as being inertial. So, Q-reeus behaves correctly if he presupposes "non-inertial frames" without mentioning them - all "frames" (better: systems of coordinates) are non-inertial.

The "constant speed of light" in GR makes sense only if understood as an approximation, where one uses some system of coordinates which locally approximates an inertial SR frame, and adds the hypothesis that the guy who uses this system as "inertial" and, moreover, decides to use Einstein synchronization (which makes sense only if he assumes that it is he who is in rest, despite his inability to identify the rest frame by observation and the fact that he has probably a quite large speed relative to the CMBR frame, which is the most plausible candidate for the true rest frame) to measure the length, using the two-way time light needs.

 

[Q-reeus]

Hm, there is no such animal as an "inertial frame" in GR....

How would you describe use of Fermi coordinates then?: https://en.wikipedia.org/wiki/Fermi_coordinates
Not a global chart obviously but handy to adopt for local purposes.

 

[NotEinstein]

Hm, there is no such animal as an "inertial frame" in GR. In GR we have only systems of coordinates, and no system of coordinates is preferred as being inertial. So, Q-reeus behaves correctly if he presupposes "non-inertial frames" without mentioning them - all "frames" (better: systems of coordinates) are non-inertial.

The "constant speed of light" in GR makes sense only if understood as an approximation, where one uses some system of coordinates which locally approximates an inertial SR frame, and adds the hypothesis that the guy who uses this system as "inertial" and, moreover, decides to use Einstein synchronization (which makes sense only if he assumes that it is he who is in rest, despite his inability to identify the rest frame by observation and the fact that he has probably a quite large speed relative to the CMBR frame, which is the most plausible candidate for the true rest frame) to measure the length, using the two-way time light needs.

You're right, I should have been more careful with my wording: I meant a freely falling reference frame. I apologize for the confusion, and not correcting it sooner.

 

[Schmelzer]

How would you describe use of Fermi coordinates then?: https://en.wikipedia.org/wiki/Fermi_coordinates
Not a global chart obviously but handy to adopt for local purposes.

And even as a local chart, it is not really inertial. The nice properties mentioned in you link hold only on a particular geodetic. Which is a single trajectory, of measure zero, not even an environment of a point. It nonetheless remains useful for some local purposes, but it is of no fundamental importance for GR. You can do GR without using Fermi coordinates at all. At least I have never used them.