1 When a black hole moves. The incompatibility between GR and SR

The gist of the argument is that the motion of a gravitational source must affect the propagation (and energy, and momentum) of light in the surrounding region, which shows up geometrically as a gravitomagnetic curvature effect ... so the "moving" gravitational body's associated relationships (e.g. between velocity and spectral shift) can't correspond to those of SR.

The application of the principle of relativity to a moving high-gravity star has to result in a different set of relativistic equations to those of special relativity, because gravitomagnetic physics (the velocity-dependent curvature components associated with moving gravity-sources) isn't a fit to SR's idealised, simplified, flat Minkowski spacetime.

It's tempting to react to this by deciding that it doesn't matter, since SR only claims validity for cases in which gravity is considered negligible. Unfortunately there's a catch: Wave theory combined with the principle of relativity requires that //all// distant moving bodies obey a single agreed set of velocity-shift relationships, regardless of whether they are high-gravity or low-gravity. If a camera sensor images a distant galaxy and then accelerates away before taking a second picture, the change in relative velocity needs to shift //all// the components in the two galaxy images by exactly the same ratio, regardless of the different gravitational environments of the various sources. So if a distant neutron star obeys a different set of equations to those of the 1905 theory, then so must a distant hydrogen atom in the same line-of-sight. And if the same equations of motion apply to distant and nearby objects, then a nearby hydrogen atom must obey those same non-SR equations, too.

If we exist in a universe that allows gravitational masses to exist and to move, then special relativity's equations may //almost// be the real equations of motion, but they can't be quite correct.

The piece is four pages long, including pictures.

2 When a black hole moves. The incompatibility between GR and SR

You make so many errors here that I won't bother to waste more time on that.

>

The gist of the argument is that the motion of a gravitational source must affect the propagation (and energy, and momentum) of light in the surrounding region, which shows up geometrically as a gravitomagnetic curvature effect ... so the "moving" gravitational body's associated relationships (e.g. between velocity and spectral shift) can't correspond to those of SR.

Of course not! NOBODY would expect SR to apply in such a situation. So why bother to argue about it?

>

The application of the principle of relativity to a moving high-gravity star has to result in a different set of relativistic equations to those of special relativity, because gravitomagnetic physics (the velocity-dependent curvature components associated with moving gravity-sources) isn't a fit to SR's idealised, simplified, flat Minkowski spacetime.

Yes. So what? GR applies, and seems to model that quite well.

>	It's tempting to react to this by deciding that it doesn't matter, since SR only claims validity for cases in which gravity is considered negligible.

Yes, of course.

>	Unfortunately there's a catch: Wave theory combined with the principle of relativity requires that //all// distant moving bodies obey a single agreed set of velocity-shift relationships, regardless of whether they are high-gravity or low-gravity.

WHAT is "wave theory"???? It seems to be a figment of your imagination, so I cannot comment on it.

But I remark that the laws of physics must be independent of coordinates. This does NOT mean there is "a single agreed set of velocity-shift relationships", it just means the theories approximating those laws are independent of coordinates.

>

If a camera sensor images a distant galaxy and then accelerates away before taking a second picture, the change in relative velocity needs to shift //all// the components in the two galaxy images by exactly the same ratio, regardless of the different gravitational environments of the various sources.

Hmmm. This is of course modeled as an effect on the PROPAGATION OF LIGHT, not as an effect related to the sources in those galaxies.

>	So if a distant neutron star obeys a different set of equations to those of the 1905 theory, then so must a distant hydrogen atom in the same line-of-sight.

Huh???? -- why argue against a straw-man? "the 1905 theory" is COMPLETELY IRRELEVANT. For your example the relevant theory is GR plus classical electrodynamics.

>	And if the same equations of motion apply to distant and nearby objects, then a nearby hydrogen atom must obey those same non-SR equations, too.

Hmmmm. Measurement and experiment show that emissions from hydrogen atoms are extremely well modeled by QED. How they are observed from far away depends on how those emissions are affected by their propagation, and this is very well modeled by GR.

>	If we exist in a universe that allows gravitational masses to exist and to move, then special relativity's equations may //almost// be the real equations of motion, but they can't be quite correct.

And that is essentially what GR says.

>	SR requires the region to be //perfectly// flat

Again, why argue against a straw man?

No physical theory is ever "perfect", and SR is IRRELEVANT. The real issue is: are the conditions of this theory satisfied well enough so the approximation in applying the theory is smaller than the resolution of the measurements. For many experiments applying SR, the answer is a resounding yes.

>	In a fully gravitomagnetic theory of relativity, //all// physics is curvature-based

Hmmmm. "gravitomagnetic" is the wrong word. But in any case, EVERY ONE of our current fundamental theories of physics can be expressed via a Lagrangian that is an integral of the scalar curvature of the relevant manifold. For GR the relevant manifold is spacetime; for the standard model the manifold is a fiber bundle over spacetime (and the fields are quantum).

>	If the real equations were “redder and shorter” than those of special relativity by a Lorentzlike factor anywhere up to one complete additional gamma factor, then most SR testing would come out exactly the same.

This is just not true. SOME tests of SR are not sensitive to "extra factors of gamma", but not all. Particle accelerators would not work if there were "an extra factor of gamma". Kinematics in particle collisions would not work if there were "an extra factor of gamma". These are among the best tests of SR we have.

And just making up theories with "extra factors of gamma" is HOPELESS -- you need to satisfy coordinate independence, and that imposes strong constraints on the structure of valid physical theories. Indeed local Lorentz invariance is the only way known today.

>	in order to pass peer review, C.M. Will's sets a criterion which any gravitational theory has to pass to be considered credible: that it reduce //exactly// to SR physics.

This is another straw man. The true requirement is that a new theory has to pass all the experimental tests that have already been performed (and that SR and GR have already passed). The SIMPLEST way to ensure this is to have the new theory reduce to SR and GR in the relevant limits. But that is by no means the only way as you claim. Certainly any paper describing a new theory that did not reduce to SR/GR could still pass muster by describing how it agrees with those experiments.

>	Science seems to be constantly being held back by people's unwillingness to question and critically analyse and criticise popular theories.

Another straw man. ALL of the major advances in physics have come from such WILLINGNESS. If you think abut it, there is no possible way for theoretical physics to advance without discarding or modifying existing theories. Criticizing existing theories is part and parcel of theoretical physics, and has always been so.

>	SR's derivation depends on the condition of flatness.

Yes, though differently than you presume (it's due to the meaning of "inertial frame").

>

If SR hadn't assumed flat spacetime and globally fixed c, we could have implemented the principle of relativity differently, with a variable-c light-dragging model in which lightspeed was always locally measured to be c wrt any particulate body, in that body's immediate vicinity, but then transitioned to c wrt other bodies with increased proximity to those other bodies.

Hmmm. You still focus on straw-man arguments. SR is COMPLETELY IRRELEVANT -- its ONLY use is as the local limit of GR (for which it is extremely valuable, of course). GR does much of what you say here, but you seem hung up on "particulate body" and "dragging", which are not essential in GR. But indeed in GR the LOCAL vacuum speed of light is c, but over non-local distances it can vary; in the vicinity of moving massive objects, it varies in a manner similar to "dragging".

Tom Roberts

3 When a black hole moves. The incompatibility between GR and SR

As you are human, you know NOTHING about "reality", universal or otherwise; you only know about the MODELS you have made of reality. Observation is all we humans have about reality.

>	The former uses proper times, distances etc. and as such it already distorts measurements inherent in observations.

NONSENSE! Proper times are what clocks observe, and they are completely unable to measure anything else. This is not "distortion" of the measurement, but rather of your personal fantasies and conceptions.

>	More importantly, if one considers that the GR model (curved space-time) is wrong, it invites a whole new ballgame. I have not heard of anyone challenging that assertation and wonder why not.

Then you have been listening in the wrong places. Look up "string theory" or "loop quantum gravity" or "Variable speed of light [Petit or Moffat or Albrecht and Magueijo]" -- you'll find LOTS of them. (Beware of kooks and idiots, especially in the last; the authors I mentioned are serious.)

Tom Roberts

4 When a black hole moves. The incompatibility between GR and SR

You use your rules, I'll use mine. If I tried to discuss all your errors, we'd never get to the core of your claims. So I won't try.

>>>

The gist of the argument is that the motion of a gravitational source must affect the propagation (and energy, and momentum) of light in the surrounding region, which shows up geometrically as a gravitomagnetic curvature effect ... so the "moving" gravitational body's associated relationships (e.g. between velocity and spectral shift) can't correspond to those of SR.

>>	Of course not! NOBODY would expect SR to apply in such a situation. So why bother to argue about it?

>	... Because wave theory requires all distant objects to obey ==precisely the same== velocity-shift law, regardless of what local physics at the source happened to originally generate the light-signal.

First: what is "wave theory" ?????? That is a phase personal to you, and the rest of us are not privy to your thoughts. I asked before but you did not answer. I can only assume you mean a theory in which light propagates as a wave, which to me means the wave-optics approximation to classical electrodynamics (the most common way to model light in GR).

Second: nobody who understands modern physics would expect the equations of SPECIAL RELATIVITY to apply to such a physical situation. But that's OK because the equations of GR certainly do apply, even in situations where one might use SR. SR is just an APPROXIMATION to GR; a much simpler and very useful one, but still just an APPROXIMATION.

[The relationship between SR and GR is two-fold: a) SR is part of the foundations of GR, as the local limit of any manifold, anywhere and anywhen; and b) the Minkowski manifold of SR is a valid manifold of GR, so all GR equations apply to it. Thus (a) permits SR to be used as a local approximation to GR, and (b) permits the equations of GR to be used in SR, without any approximation.]

Third: I'm not certain what you mean by a "velocity-shift law" -- that phrase is also personal to you, and I am not privy to your thoughts. From context I infer that you mean what everybody else calls a Doppler-shift calculation. That's what I assume here. Your original post has expired on my server.

There most definitely is a SINGLE way to compute Doppler shift, and it applies to every known physical situation. It is expressed in terms of GR, but applies to both SR and GR. This treats light in the wave-optics approximation to classical electrodynamics:

1. obtain the 4-velocity of the source, and the proper time interval between the wavecrests of its emitted light.
2. construct a timelike displacement 4-vector parallel to the source 4-velocity with magnitude equal to that proper-time interval.
3. parallel transport that displacement 4-vector to the detector over the null trajectory followed by the light from source to detector.
4. obtain the 4-velocity of the detector.
5. compute the dot product of the parallel-transported displacement 4-vector with the 4-velocity of the detector.
6. the result of #5 is the proper time interval between the wavecrests of the detected light. The ratio of it to the interval of #1 is the Doppler shift.

>

So ... if the neutron star's light //does// change with relative motion by a velocity-shift formula that departs from the SR prediction (which the linked pieces seems to say is unavoidable), then it's a big deal, because wave theory then requires every other piece of particulate matter in the universe to follow exactly the same non-SR shift formula.

Not a problem. Why you expect SPECIAL RELATIVITY to apply is a mystery. But GR does apply, so all is well in physics, it's just YOU who needs to adapt.

>	This doesn't seem to be negotiable or fudgeable.

It isn't, as long as you use GR, not SR.

>	Either the SR relationship describes the isolated moving star's motion-shift //exactly//, or the non-SR relationship that the star follows applies everywhere, to gas clouds and galaxies and spaceships and planets and individual atoms.

Nonsense. But change SR to GR and all is well. There is no expectation whatsoever that SR applies to "gas clouds and galaxies", or any other massive objects (such as planets and neutron stars). Note that for any situation in which SR applies, GR applies also, to at least the same accuracy (nothing in physics ever applies "//exactly//").

>	Wave theory requires there to be a single, simple, universal velocity-shift relationship obeyed by all matter in the universe, and if that universal relationship is NOT the one given by SR, then SR is not correct foundation theory.

WHAT "wave theory"????? WHAT "velocity-shift relationship"?????

As far as I can see, the above calculation serves just fine, but I had to guess about the meanings of your personal phrases. In any case, your fixation on SR here is clearly misplaced, one MUST use GR.

>	If the principle of relativity applies, but the PoR plus the assumption of flat spacetime leads to the wrong equations, then SR must be the wrong theory of relativity.

Hmmmm. SR clearly _IS_ the wrong theory of relativity; GR is the right one.

Why you insist on using an approximation, and think SR should apply, is a mystery.

>	Since the PoR plus flat spacetime leads //unavoidably// to SR,

BUT THERE ISN'T FLAT SPACETIME IN THE PHYSICAL SITUATION YOU DESCRIBED.

>

this tells us that in order to generate different equations, a correct theory of relativity, which generates the correct equations, must NOT use the "reduction to flat spacetime" argument. It has to apply curved-spacetime geometry right down to the level of basic inertial physics, and must apply curvature arguments "all the way down".

This is just plain wrong. Why you think SPECIAL RELATIVITY should apply to "curved-spacetime geometry" [your phrase above] is a complete mystery. But all is well because GR does apply, and does have a SINGLE calculation for all types of Doppler shifts (see above). And GR does reduce to SR in a suitable local limit, everywhere and everywhen.

>

If you're asking "why we should bother" with these arguments, the answer is that it's because these arguments create a new generation of relativity theory that appears to be more powerful, more efficient and more logically consistent than what we currently have, and which seems to mesh with quantum theory and thermodynamics in ways that our current, creaky, patched, SR-based system can't ever hope to emulate.

Well, yes. It's called GENERAL RELATIVITY, and it's not "new" at all....

You seem to be traveling well-trod ground, and somehow think it is "new". It isn't. Except, perhaps, to you personally.

>>	[...] GR applies, and seems to model that quite well.

>

No, it really doesn't. Because wave theory plus gravity invalidates the SR relationships not just for strong-gravity bodies but for ==everything==. So when the 1916 theory says that the physics of a small free-fall region in a larger gravitational field must reduces to inertial physics, the inertial physics that it reduces to is the //wrong// inertial physics.

Whatever gives you that idea???? In any "small free-fall region", GR reduces approximately to SR, and the accuracy depends on the size of the region and the curvature of the manifold in the region. For a small enough region the accuracy can be arbitrarily good. So GR reduces to the //RIGHT// inertial physics.

>

GR1916 was designed around the assumption that the SR relationships were fundamentally correct, and this had knock-on consequences for other aspects of the theory ... for instance, if we used the redder gravitomagnetism-compatible equations, a body still had a horizon at r=2m, but it gave off indirect radiation in agreement with QM and thermodynamics. GR1916 has a different type of horizon whose shifts reduce to the SR shift relationships, and this is why it predicts that gravitational horizons must be perfectly black, in disagreement with QM and thermodynamics.

Nobody knows how to couple GR with QM. Certainly YOU do not, and neither do I. So I see no point in attempting to discuss it here.

Finding a theory that synthesizes or combines GR, QM, and thermodynamics is most definitely a current topic of intense research. But not in this newsgroup.

Tom Roberts

5 When a black hole moves. The incompatibility between GR and SR

While your reply is very different from mine, it is contained in what I wrote. You probably know this; I am mentioning it for others around here who might not.

I gave the general algorithm for computing Doppler shift in GR. If one can separate spacetime into a near field region where curvature is important, and a far field region where curvature is negligible and SR applies, then in the algorithm I described the parallel propagation and dot product in the far field region are simply those of SR. The algorithm I gave also computes the Doppler shift in the near field region.

A remark: for cosmological distances there is no far field region, curvature is important everywhere (except very close to the observer on earth). Ditto if there is gravitational lensing involved. The algorithm I gave applies in all cases.

Tom Roberts

6 When a black hole moves. The incompatibility between GR and SR

Yes. And in the wave-optics approximation to classical electrodynamics it is used (and satisfied).

>	However EM light is going so fast making that 2nd order insignificant. (would imply a speed higher than the speed of light).

NONSENSE! Apparently you don't even know what a PDE actually is. In particular, being 2nd order is ESSENTIAL for the wave equation to describe a wave. The coefficients of the equation determine the propagation speed, and here it is c (in vacuum), not "higher".

Tom Roberts

7 When a black hole moves. The incompatibility between GR and SR

Nonsense. Invalidation of SR IN A REGIME WHERE SR DOES NOT APPLY does nothing at all.

>	What you're doing by setting arbitrary domains of applicability is responding to a logical contradiction by compartmentalising.

No. Not at all. THIS IS PHYSICS, NOT LOGIC.

In physics, every theory includes a domain within which it is valid, and outside of which it is either invalid, or at least not known to be valid. In the presence of gravity, SR is KNOWN to not be valid.

This is very basic, and fundamentally simple: SR is based on some postulates, and in regimes where those postulates do not hold, SR simply is not valid. That is, the mathematical derivation of its equations are IRRELEVANT because in that physical regime the postulates don't hold.

>	* https://en.wikipedia.org/wiki/Compartmentalization_(psychology

Completely irrelevant -- this is PHYSICS. Applying theories ONLY within their domain of applicability is MANDATORY.

>	The only way that you can avoid having the two sets of arguments flatly contradicting each other in some situations where we have //both// inertial physics and gravitational physics operating is by setting up artificial barriers,

They are NOT "artificial". The "barriers" represent boundaries between regimes in which the assumptions of one or the other theory hold.

SR is the local limit of GR. SR is NOT valid throughout the universe, but only in limited regions. This is unavoidable. Live with it (you have no choice).

>	and saying that in such-and-such situation where you can get away with using SR, SR is obviously correct, and in these other situations where GR has to apply, we obviously //mustn't// use SR but GR ... but SR is still considered to be correct

NONSENSE! SR is NOT "considered to be correct" in the sense you mean. SR is considered to be VALID (not "correct"), and its domain of validity is LIMITED. Validity of a theory does NOT mean "it is how nature actually behaves", but rather "it APPROXIMATES how nature behaves is this regime ...". There are limits to the accuracy of such APPROXIMATIONS, and that determines the domain of applicability for the theory.

To one part per 1000, SR is valid throughout the solar system (yes, ALL the effects of gravity are smaller than that). But to parts per million is it valid only in much smaller regions. In the experimental halls of the LHC, for the measurements of elementary particles, SR is valid to parts per billion, which is MUCH smaller than their measurement resolutions -- so they can and do use SR in their analyses.

>	[... repetitions]

You need to learn what science ACTUALLY is. Your GUESSES are wrong.

Tom Roberts

8 When a black hole moves. The incompatibility between GR and SR

Hmmmm. "Distortion fields" could be interpreted as the particle fields of the standard model. Remember Clifford was writing long before QFT was applied to particle physics, and the nomenclature was not yet settled.

>

Sure, that's the dream of a unified field theory, but your enemy is not general relativity, it is quantum field theory (and the lack of an equivalence principle for non-gravitational forces). Actually, general relativity accomplished Clifford's dream for the force of gravity, representing it as curvature related to each particle of mass, but no one has been able to duplicate that success for the other forces of nature.

Actually the standard model does this. The standard model can be considered as a fiber bundle over spacetime, with the fibers being the various particles' quantum fields; the usual fields are of course slices of the bundle. The SM Lagrangian is just the scalar curvature of the bundle.

The problem comes when one attempts to include gravity, which affects the underlying spacetime, and it is not clear how to reconcile the curvature of spacetime with the bundle curvature. Of course in the tangent space of a given point in spacetime there is no spacetime curvature, and the standard model is locally Lorentz invariant.

Tom Roberts

9 When a black hole moves. The incompatibility between GR and SR

OK. Then we KNOW it is wrong -- light is NOT "transmitted by waves". Such waves cannot account for many observed properties of light, but the photons of QED do account for them.

There's no point in continuing to discuss "wave theory".

Tom Roberts

10 When a black hole moves. The incompatibility between GR and SR

Hmmm. GR is a geometrical theory of gravity, but it has no light waves.

>	... does pretty much require the existence of a single universal law for motion shifts, for simple motion.

And GR has exactly one that applies to all physical situations -- that's as "universal" as it gets. I gave it earlier in this thread.

Tom Roberts

11 When a black hole moves. The incompatibility between GR and SR

This is just plain not true -- there's nothing "perfect" about it. Applying SR in a local region of spacetime is an APPROXIMATION.

>	This is what puts GR1916/1960 irreconcilably at odds with quantum mechanics regarding black holes and Hawking radiation.

No. This has nothing whatsoever to do with the problems relating QM with GR, BECAUSE IT IS WRONG. The difficulties in merging QM with GR are much more subtle and fundamental.

Tom Roberts

12 When a black hole moves. The incompatibility between GR and SR

That "exactly" is YOURS, not Will's. Every physicist knows that SR is only a local APPROXIMATION to GR. But yes, SR is so solidly established as a (local) property of our world that it would be perverse to deny its validity WITHIN ITS DOMAIN OF APPLICABILITY. (Yes, there are many perverse people around here.)

Note, however, the PUN on "theory": Will uses it in the sense of creationists and science deniers: a "theory" is not established fact -- that's why he put the word in quotes. But that is not really the appropriate meaning in science: a theory is a MODEL of the world we inhabit. Once one understands this, your claims and arguments are clearly either naive or nonsensical.

Tom Roberts

13 When a black hole moves. The incompatibility between GR and SR

This is just plain wrong. You used "length contraction" where it does not apply. SR predicts a relativistic unstable particle can travel MUCH further than NM predicts.

A muon has a (proper) lifetime of 2.19 microseconds. When traveling at a speed ~ 0.9999 c it could, on average, travel 685 meters. In practice high-energy muons can AND DO travel MUCH further than that (e.g. from the upper atmosphere to the surface, ~ 12 km.

For pions the measurements are more striking: c*lifetime = 7.8 meters, but both CERN and Fermilab have pion beams over a kilometer long, in which > 90% of the pions survive. These pions have kinetic energies > 100 GeV, so v = 0.999999 c, and gamma > 714.

Tom Roberts

14 When a black hole moves. The incompatibility between GR and SR

How silly. OF COURSE Special Relativity is incompatible with gravitation -- that's what "special" means in its name, and why Einstein embarked on the long and difficult road from SR to GR (1905 - 1916).

We now know that SR is the local limit of GR, and is thus APPROXIMATELY valid in a sufficiently small region of spacetime. The accuracy of the approximation depends on both the curvature in the region and the size of the region.

Tom Roberts

15 When a black hole moves. The incompatibility between GR and SR

OK. Moreover, in this context there is no doubt about what it is: it is the algorithm I gave earlier in this thread.

>	We just disagree on what that relationship ought to be.

Only if you disagree with my previous statement. (I doubt very much that dancouriann disagrees with it.)

>	You think all simply-moving bodies must obey SR, while Tom seems to be saying that SR is only an approximation, that the motion-shift of a moving star is not an SR problem, and that nobody who understands GR would expect its shift to agree with the SR predictions.

That is a rather poor summary of what I have been saying.

First, your "motion-shift" is obscure -- such private vocabularies are hopeless. I assume you mean the Doppler shift from source to receiver. Such Doppler shifts can arise from relative motion, and also from gravitation and the cosmic expansion of the universe. The algorithm I gave handles them all. Indeed, in general it is not possible to separate such different aspects of Doppler shift, one can only compute it in its entirety (no matter, that is what one measures).

SR is MANIFESTLY an approximation to GR -- within any manifold to which GR applies, SR is approximately valid in a small enough local region of any point in the manifold, with the accuracy of the approximation depending on the size of the region and the curvature of the manifold in the region.

That is a physicist's description. A mathematician would say that SR applies only in the tangent spaces of the manifold.

In some cases that "local region" can be quite large. For instance, consider the emission of an atom on the surface of a very massive star, which propagates to a receiver on earth without passing near any other massive objects. To reasonable approximation we can consider the region from earth to near the massive star to be flat, and apply SR in this region. That is, a box around the star can enclose the region of large curvature near it, and serve as a boundary between a region in which GR must be applied, and a region in which SR can be applied with acceptable error. In the algorithm I gave, that corresponds to a region in which the parallel-propagation of the signal is complicated to compute, and a much larger region in which it is easy to compute (because SR applies).

>

My position is that the shift on a moving star is not an SR problem and the star's relationship must be non-SR, but ... since all moving bodies have to obey the same shift law, this means that SR doesn't just not correctly describe the star's behaviour, it also doesn't correctly describe the behaviour of any other moving bodies (except as an approximation).

Hmmmm. GR applies to all such objects, and one can apply the algorithm I gave earlier to compute the Doppler shift.

SR _MIGHT_ apply in some situations, but only those for which its approximation is valid. So yes, SR is not universal -- no matter, as GR is (in this context).

I have no idea why you are so fixated on SR. Switch to GR and all is well. Apply SR only in regions where its approximation gives acceptable errors.

>	IOW, it's a useful simplified "engineering theory", but not Fundamental Truth, or a correct foundation theory for gravitational physics.

This is physics, not mysticism -- YOU DON'T KNOW ANYTHING AT ALL about "Fundamental Truth, or a correct foundation theory". So attempting to discuss them is ridiculous.

But we do know that GR is a better theory than SR, in that is it more accurate in a much larger domain than is SR.

>	[... 'way too many repetitions of the same confusion]

I have no idea why you are so fixated on SR. Switch to GR and all is well. Apply SR only in regions where its approximation gives acceptable errors.

Tom Roberts

16 When a black hole moves. The incompatibility between GR and SR

I don't know what you are trying to say. Fundamental to GR is the assumption that SR applies locally (i.e. in the tangent spaces).

>	So, model-fitting might follow [...]

Hmmmm. There is no "room" for "model fitting" in GR. GR has three parameters that are in principle free to be varied, but in practice they are HIGHLY constrained by experiments:
c is the symmetry speed of the local Lorentz transform. Experimentally it is constrained to be within a few parts per billion of the vacuum speed of light.
G is Newton's gravitational constant. Experimentally it is known to about 50 parts per million.
/\ (\Lambda) is the cosmological constant. Experimentally it is constrained to be zero by experiments in the solar system; cosmological observations imply it is about 1.5E-25 kg/m^3 (far too small to be observed in the solar system).

>	but without a unified explanation there's still the deduction of one for the other and talking points (or rather, planks of the platform of what should be the foundation) at odds with each other in the combined explanation. [... more of the same]

That's just word salad without meaning.

Bottom line: GR is the physical theory, SR is merely a useful approximation to it.

Tom Roberts

17 When a black hole moves. The incompatibility between GR and SR

There isn't any here, in the relationship between SR and GR.

QM is a completely different situation....

>	About SR to GR, SR is built from its own assumptions,

RIGHT! And so SR is valid ONLY when those assumptions are valid. In the presence of gravitation (curvature) those assumptions do not hold, and SR is not valid.

>	It seems "GR the physical theory" and "GR as extending SR" aren't the same thing, here.

GR doesn't really "extend SR". Rather, SR approximates GR in local regions.

>	Because, SR is about "all reference frames" not just "locally".

YES, SR assumes its inertial reference frames can be extended throughout the (infinite) manifold. In the presence of gravitation (curvature) that simply is not possible.

Tom Roberts

18 When a black hole moves. The incompatibility between GR and SR

Reading a physicist's writings with Talmudic fervor and a lawyerish claim that his words are exact in every detail IS HOPELESS. Especially when he EXPLICITLY denies the latter:

You yourself quoted Will as denying your claim:

>	Will, 2005:: :: For most applications in atomic or nuclear physics, :: this approximation is so accurate that special relativity can be assumed :: to be exact. Claimed geometrical results and proofs are assumed to be exact, unless stated otherwise.

BUT HE STATES THIS IS AN APPROXIMATION. ASSUMING that an approximation is exact does NOT mean that it _IS_ exact. You need to read better.

>	So Will is characterising special relativity as foundation theory upon which general relativity is built. He's not characterising GR as a free-standing theory that incidentally "just happens" to reduce to SR as an approximation,

But in fact, BOTH are true: SR is part of the foundation of GR, and GR does reduce approximately to SR in a suitable local region.

>	[... 'way too much repetition]

It remains true that each physical theory is valid only in some domain. Excluding the quantum domain, the domain of SR is a subset of the domain of GR. Your arguments and claims attempt to apply SR outside its domain of applicability, so it's no surprise that you are confused.

Tom Roberts

19 When a black hole moves. The incompatibility between GR and SR

That's just plain wrong. There is no "signal-propagation logic", there are only physical theories. And your expectation of "identical" Doppler shifts is just plain silly -- GRAVITATION MATTERS.

SR is valid in a region in which gravitation is negligible. GR is valid even when gravitation is important. If the surface gravities are important (and they invariably are), then you must use GR. For computing Doppler shift that means the algorithm I gave earlier in this thread.

>	So there has to be a single universal set of equations that applies to all mutually-distant bodies, regardless of whether they're considered "strong-gravity", "weak-gravity", or "effectively-no-gravity-worth-mentioning".

Hmmm. It's an algorithm, not an explicit set of equations. I gave it earlier in this thread. It is, of course, valid in GR, including all those situations you listed, and also valid in SR. In the algorithm, the only difference between SR and GR is the form of the metric.

>	If there really is just one, single, universal velocity-shift equation that applies to everything, [...]

Why limit it to "velocity-shift"??? -- the universal algorithm I gave include that and gravitation and cosmology as well. So it completely avoids the mistake you repeatedly make by attempting to ignore them.

Note also that there is no "room" for the "extra gamma factor" you fantasize about. Experiments refute it and confirm the GR prediction. Theoretically it is nonsensical because it would completely destroy the symmetries that are the foundation of modern physics.

Go back and READ the algorithm I gave. Then ask yourself:
* Where would the extra gamma go?
* How would it "fit" into that clear and obvious algorithm?
* gamma involves a speed -- speed with respect to WHAT??? (Any choice you make will destroy the coordinate independence of the algorithm, but coordinate independence is ESSENTIAL.)

Tom Roberts

20 When a black hole moves. The incompatibility between GR and SR

That may be what he is trying to say, but that is not what he actually said. His statement above clearly includes both gravity and motion, as it discusses Doppler shifts from bodies.

In general, gravity and motion cannot be separated in the Doppler-shift algorithm, it is an integrated whole. But in cases where they can be separated, I agree that the contribution of motion is independent of that of gravity (duh! -- that's what "can be separated" means). That separation basically requires "weak" gravity, so it does not apply to the neutron stars mentioned earlier.

>	The SR Doppler formula just gives the frequency ratio, at a given point, for two different coordinate systems *at that point*.

Hmmmm. It's more general than that. Refer back to the algorithm I gave earlier in this thread. Throughout a region of spacetime in which SR is valid, the parallel propagation is trivial and does not affect the 4-vector being propagated or its components relative to any inertial frame. So the usual SR formula holds for source and detector separated by any distance within that region, not just at a single point. (Good thing, as that's how we use it.)

Tom Roberts

21 When a black hole moves. The incompatibility between GR and SR

This isn't "logic", this is PHYSICS. They are quite different. More on that below.

SR and GR are not incompatible, but you do need to understand how to "mesh" them together.

For your "atom and star" situation it is QUITE CLEAR how SR and GR "mesh together" (at least insofar as they yield identical results):

Refer back to the Doppler algorithm I gave earlier in this thread. The region outside the boxes is the region in which parallel transport is trivial (because the manifold is sufficiently flat that SR applies with negligible error).

>	Gravitational theory applied to large objects HAS to predict gravitomagnetic dragging effects,

You seem to have a VERY strange attitude: you claim "gravitomagnetic dragging effects" are important, and then bemoan the fact that SR does not include them. SO WHAT???? -- OF COURSE SR does not include them. (Whatever they are.)

SR is an APPROXIMATION. Use it when its approximation yields results at least as accurate as the measurements; don't use it when its approximation is not accurate enough. That _IS_ how physics is performed -- we have many different theories, and one can only apply those which are valid for the physical situation being investigated.

Later you said:

>	if we believe that special relativity correctly describes the shift seen on the atom, and that the star's motion-shift must obey GR rather than SR and must therefore NOT agree with SR, then we have a paradox.

This is no paradox at all. When gravitation matters apply GR; when it doesn't you can apply SR. In ANY physical situation to which you can apply SR accurately, you can also apply GR and obtain EXACTLY THE SAME RESULT (within the accuracy of SR).

As I said: you have A VERY STRANGE ATTITUDE -- you recognize that gravity is important for the star, and think it is a "paradox" that SR does not apply to the star. Your confusion will be completely resolved once you understand that physical theories are APPROXIMATIONS.

>	[... 'way too much to bother with, as it just embroiders the above confusion]

Of course GR is also an approximation. As is EVERY other physical theory. Your quest for "exact answers" is doomed.

Logic is exact, physics is NOT.

Tom Roberts

22 When a black hole moves. The incompatibility between GR and SR

Yes. And GR does PRECISELY that. Expressed as a single equation it's rather complicated and opaque, because parallel propagation is involved, so I described it as an algorithm rather than an equation. Besides, your insistence on a single equation is misplaced; all one really needs is an algorithm to compute the Doppler shift (i.e. an unambiguous way to apply the model).

>	If it can't, then we need a new general theory of relativity.

But there is no such "if".

Your fundamental problem is insisting that SR must apply, when in fact SR is only an approximation, WHICH YOU REJECT ABOVE. Your problems with the boxes are merely due to your over-simplistic attempts to apply SR to a POORLY DEFINED PORTION of the problem, while applying GR to the ENTIRE problem is straightforward.

I repeat: there is no problem here for physicists, because we know that GR applies, without approximation, within its domain (which includes everything discussed here except Hawking radiation).

Including Hawking radiation would require a theory of quantum gravity, which we don't have.

Tom Roberts

23 When a black hole moves. The incompatibility between GR and SR

Yes, that too.

>	What needs to be clearly understood is that the Doppler shift formula of special relativity is exact in the locally flat space-time of the distant observer.

I disagree, because there is no such thing as an exactly flat region in a manifold that has some mass or energy anywhere. A region of such a manifold can be APPROXIMATELY flat, to an extremely good approximation, but not exactly flat. So too, the SR Doppler shift formula can never be "exact" in such a manifold, but only approximately valid, to an excellent approximation.

Baird's quest for "exactness" of SR is doomed. Because it is never exact, but is valid only approximately (often to extremely good approximation).

Tom Roberts

24 When a black hole moves. The incompatibility between GR and SR

My point is that in any manifold with mass or energy somewhere, there is no region in which the curvature "drops to zero". It can drop to an unmeasurably small value, but never to EXACTLY zero.

>	He also seems to be saying that GR itself is only claimed to be an approximation.

Yes. We KNOW it does not handle all regimes of the world we inhabit, so GR cannot "exactly" correspond to the world we inhabit.

>	I consider this to be a cop-out on Tom's part

That's just because you obviously don't know what science actually is. This is an INHERENT limitation of scientific theories -- NONE of them correspond "exactly" to the world we inhabit.

>	To me, if someone's "talking the talk", they should be able to put up some falsifiable predictions, rather than waving about the idea that nothing's ever really exact.

GR makes myriad predictions that are falsifiable, even though it is not an exact model of the world we inhabit. All that have been tested so far have been confirmed experimentally or observationally. So GR is USEFUL, even if not "exact".

Your quest for "exactness" is misguided. What is actually needed are predictions from theories which are valid to better than the appropriate experimental resolutions. In appropriate physical situations, GR and SR can both do that.

>

Tom is saying that he has an algorithm for calculating the Doppler shifts on moving bodies, and also gravitational shifts and cosmological shifts, and seems to reckon that this algorithm represents the correct predictions for gravitational theory. I'd quite like him to be able to say which shift equation he believes the algorithm generates - Mine, Danco's, or Something Else.

It is not "my" algorithm, it is the algorithm for such a calculation in GR.

It will not "generate your equation" because you have assumed SR is exact, and SR is NOT exact for the situations you consider. But it will reduce APPROXIMATELY to your equation in a suitable region.

>	What we're discussing here is the correct equation for the frequency shift (conventionally the "Doppler shift") of light from a moving gravitational source ... just the motion-shift component, not the stationary gravitational redshift component.

But you can only "separate" those APPROXIMATELY. So your quest for "exactness" is doomed.

The algorithm I gave applies to any Doppler-shift measurement within GR's domain.

>	I want an exact solution for that that works for arbitrarily high velocities, and for sources with arbitrarily strong gravitational fields.

The algorithm I gave earlier in this thread is valid for arbitrarily high velocities and arbitrarily strong gravitational fields. But as I keep saying, your quest for "exact" is hopeless....

The algorithm is exact within the MATHEMATICS of GR. But that math is certainly not an "exact" model of the world we inhabit. In science, "exact" models do not exist.

Tom Roberts

25 When a black hole moves. The incompatibility between GR and SR

It does: The algorithm I gave earlier in this thread applies to Doppler shifts from stars, small rocks, and individual atoms (neglecting quantum aspects); also to any other physical situation within the domain of GR.

>	and the general theory should //not// reduce to the physics of special relativity.

I have no idea why you say this. In some physical situations GR //DOES// reduce to SR, approximately. And there is nothing wrong with that.

Tom Roberts