Dear Valery,

In the same way as in Restricted Relativity, the principle of relativity is very important in General Relativity. It applies in a very special way, but is well inscribed in the equations of General Relativity. I recommend you to read about the principle of general covariance (Lorentz covariance).

Best regards,

Alexandre.

Dear Alexandre,

Thank you very much. I have some idea of the general covariance of the GRT equations. I am interested in the explicit invariance of the gravitational field metric.

Best regards,

Valery

I think this principle comes in with the emphasis on the use of tensors,

which have specific transformational properties when you change coordinate systems. Use of general tensors instead of Cartesian in SR.

Perhaps deservs some inspection if this is really adequate.

Right. I distinguish a class of metrics that satisfy the principle of relativity. This metric was first used by Einstein and Fokker in 1914. This significantly narrows the number of necessary metrics to describe the gravitational field.

Philadelphia, PA

Dear Morozov & readers,

Einstein certainly seemed to think that he was generalizing the results of special relativity in GR. We still have the speed of light as a constant, for instance, and variation of measurements in relation to frames of reference.

Can you say how "preference ... given to the covariance of the equations" would de-emphasize specific characters of the special theory? What exactly do you see as being neglected?

H.G. Callaway

The question may be exactly what, if anything, is invariant in GR under general coordinate transformations, apart from the fact

general tensors remain so, such as the metric tensor, or the energy momentum tensor, or the Einstein equation itself.

(I presume the above are of invariant form, still tensors.). Conservation rules are a separate rule here? Of course there is not just one kind of transformation, different for covariant or contravarient. But some mixed combination of tensors is really invarient?

In SR the Lorenz invariants remain under transformations between inertial frames (comonly the Lorenz transformation)

xx-cctt or EE-ppcc are Lorenz invariants. So here speed of light and rest mass are really invariant.

Dear Callaway,

The subject of GR is primarily a relativistic theory of gravity. Therefore, it is not just the development of the special theory of relativity, but the spread of its principles to another area.

At the same time GR includes specialty the theory of relativity. It preserved the principle of the constancy of the speed of light, but became local. In addition, new postulates related to gravity have appeared.

Valery Morozov

The GR object is space. Therefore, GR operates with metric tensors. It is important that the theory should not depend on the coordinates. Therefore, the objects of the theory of a tensor must be equivalent after coordinate transformations, i.e. covariant.

"So here speed of light and rest mass are really invariant."

Yes, these are invariants, but only local ones.

No, it's not so. The description is always covariant, only Lorentz invariance is local, in general relativity, not global, as in special relativity.

The speed of light isn't defined, since relative velocity depends on the path in curved spacetime and Lorentz invariant quantities aren't generally covariant. All this is known, e.g. Article Lecture Notes on General Relativity

And this leads to Einstein's equations for the metric-that don't have any ``deficiencies''. Their most general form is described by supegravity.

"And this leads to Einstein's equations for the metric-that don't have any ``deficiencies''."

Nothing but the singularity and the absence of a local conservation law. It can be fixed.

Take a look. What Einstein wrote in the last year of his life.

Preprint Einstein's Last Will

my dear Valery Borisovich Morozov , you are right absolutely. might be there is a chance of this. try this you may get some new insights. nothing wrong trying of your unique idea.. as a physicist we have to continuously try all the possible chances for the better development of physics....

With regard to cosmology, I got an unexpected result.

Preprint Dark energy as zero energy of gravity field

Dear Valery Borisovich Morozov ,

"The principle of relativity is important for the special theory of relativity. In the general theory of relativity, it is read unimportant".

As per my classical perspective.----

1. As per Film theory of Universe(proposed by me), films are associated with absolute velocities and the film follows special theory of relativity and it is an ideal condition.

2. Films will change at the speed of (1/ plank time) films per second.then these absolute velocities will be turned in to acceleration and originates gravity force.

3. Since the velocity is absolute(not relative) some of the aspects of special relativity is invariant in the case of gravity(nothing but Representation of General Relativity)

Papers are available at RG for reference.

1. pubs.sciepub.com/ijp/5/4/1/

2. article.sapub.org/10.5923.j.ijtmp.20170706.01.html

Philadelphia, PA

Dear Morozov & readers,

I wonder if you will agree with the following characterization of "general covariance" in GR?

In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws.

---end quotation

See:

https://en.wikipedia.org/wiki/General_covariance

I ask because of your emphasis on this concept and your contrasting of it with "The principle of relativity" in the formulation of your question.

It seems that this comes to pretty much the same thing. Though measurements may differ, depending on the choice of a frame of reference, the laws of physics remain the same. I fail to see how the contrast you evoke will get you to a new version of general relativity--without singularities, e.g.

The way I see the matter, choice of a frame of reference is somewhat like choice of units of measurement. The (frames or) units are not physical entities, but more like intellectual means of study and observation--and should make no difference to the laws we arrive at on the basis of evidence collected. The point carries over from special relativity to GR.

Right?

H.G. Callaway

H. G.

Think you have it about right.

Some mathematicians are good at coordinate free methods, but Physicists usually have a hard time with this.

Best regards, juan

Philadelphia, PA

Dear Weisz & readers,

Thanks for the good words.

H.G.Callaway

Dear Valery Borisovich Morozov ,

"Regarding homogeneous empty space density"- I glanced it. It is very interesting.

I will go through it. Some of my ideas may support it. Let us hope a positive collaboration on it.

I have already worked out the space time densities for all fundamental forces.

My papers are available at my RG profile.

Thank you

I wrote a new note

Preprint On Einstein equation and energy of gravity field

This is a continuation of this.

Preprint On relativity principle in gravity theory

Dear Valery,

You ask:

VBM: There is an opinion that the relativity principle plays a minor role in the GR, Is it so?

It plays a very important part. It was a requirement when Einstein was developing GR that, however it incorporated gravity, it must reduce to SR in the limit of negligible masses. He achieved that and one consequence is that for any sufficiently small volume (excluding singularities), SR applies.

Dear George

Must agree with this. Does this mean that the local speed of light should be the same?

Locally, yes, though I have some views on that in relation to gravitational waves, but that involves the choice of coordinates so it's a complex topic.

I agree with that. that the theory of gravitational waves lies away from the fundamentals of GR.

Gravitational waves are a direct consequence of GR, they didn't exist in the Newtonian model because the force acted instantly.

Well yes. I would note how gravity waves differ from a quasistationary field. Usually the gravitational field has negative energy, but the gravitational wave carries positive energy.

Einstein's equation is not exact. There is evidence

Preprint On Einstein equation and energy of gravity field

You can get a uniform field metric without using equations. This allows us to obtain a new equation of the gravitational field.

Comparison of New and Old Thermodynamics

1. Logic of the Second Law of Thermodynamics: Subjectivism, Logical Jump, Interdisciplinary Argumentation.

2. New thermodynamics pursues universality, two theoretical cornerstones:

2.1 Boltzmann formula: ro=A*exp(-Mgh/RT) - Isotope centrifugal separation experiments show that it is suitable for gases and liquids.

2.2. Hydrostatic equilibrium: applicable to gases and liquids.

3. The second and third sonic virial coefficients of R143a derived from the new thermodynamics are in agreement with the experimental results.

3.1. The third velocity Virial coefficient derived is in agreement with the experimental data, which shows that the theory is still correct when the critical density is reached.

4. See Appendix Pictures and Documents for details.

How does this relate to my question?

sorry,

This is the basis of physics.

It doesn't relate at all, Bo Miao is spamming it into multiple threads with no regard to the topic being discussed.

I still try to return the topic of conversation.

The principle of relativity is a powerful tool. I tried to demonstrate this in an article where I used it to construct a metric of a general gravitational field.

Preprint On relativity principle in gravity theory

Dear V.B.Morozov,

In my opinion, the principle of relativity is more fundamental than any other thing in the theory of relativity. The law of covariance is an out come of the principle of relativity when a law is expressed in the form of a mathematical expression.I have tried to explain this property in my work:Role of the principle of relativity; An approach towards the relativity beyond physics, Jan.17.

Regards

Ramesh Chandra

Dear Ramesh Chandra,

I totally agree with you. The spread of the principle beyond the theory of relativity is reasonable, for example, the laws of physics do not change when the potentials of a system change.

Respectfully,

Valery Morozov

Dear V.B. Morozov,

Thank you very much for your reply..

I want to know your view whether, is it possible to verify the Einstein's theory of relativity by considering the principle of relativity on a law beyond the domain of physics?

Regards

Ramesh Chandra

Dear Ramesh Chandra,

I need to answer the question not related to physics. Excuse me.

Respectfully,

Valery Morozov

Well, according to Schild after the 1960 crisis (and an unnamed group of colleagues who he said agreed with him when he published his paper), special relativity and the principle of relativity applied to rotation, were geometrically incompatible.

As in, they couldn't coexist within in the same logical system.

So either the GPoR was wrong, or SR was wrong. If SR was wrong, we'd lose both SR and GR1916. Which was unthinkable. So Schild argued that SR could NOT be wrong, and that instead the GPoR had to be downgraded from being an unbreakable principle to a useful heuristic guideline, which needed to be suspended every time it would otherwise invalidate SR.

I've met this attitude a lot with GR people. They often say that the GPoR was a disposable stepping-stone to textbook GR, that the current GR equations are free-standing and more fundamental than the GPoR, and that actually, "GR" is now just a label and not a definition: the modern subject of "GR" (they say) is based on the principle of covariance, and not on the principle of relativity. The theory (they say) is a misnomer, the name is just a historical hangover, not to be taken too literally.

They also tend to drop the principle of equivalence (because this also tends to conflict with SR in rotating-body problems). Instead, they have a replacement principle (the Einstein Equivalence Principle, EEP), which says instead that gravitational theory must reduce to SR.

The original equivalence principle had a habit of invalidating SR (which was unacceptable), so they replaced it with a new thing with a similar name, which could never conflict with SR by definition.

I've also had discussions with GR people who feel that the general theory doesn't have to conform exactly to laws of geometry ("Nobody ever claimed the theory was exact"). When one points out apparent geometrical failures of the theory, they say, "but the theory is only meant to be an approximation".

----

While GR was originally proposed as an "unfudgable" principle-based theory that lived or died on the basis of logical consistency (which is why Popper said such nice things about it), some modern GR folk seem to have accepted that under Popper's criteria, GR1916 would have to be classed as falsified. Their response is that Popper's criteria were too severe, that Einstein's original characterisation of the theory as being a principle-based theory was naive, that the GPoR and Mach's principle were also naive, and that "pragmatic" fudging is perfectly normal and acceptable behaviour. They say, it's quite normal for a theory to evolve and change over the years as our understanding improves.

----

Personally, I'm more of a purist. I think that if "modern GR" is functionally indistinguishable from a failed theory, then we call it a failed theory. I think that if the GPoR disagrees with SR, then instead of throwing away the GPoR, we investigate what a general theory of relativity would look like that does not include SR. If we jettison SR from GR, does GR get better or worse?

That seems to me to be the more scientific approach.

But it would mean that a lot of GR people would have to get off their arses and actually do some proper investigative research, which they seem to be reluctant to do.

"The principle of least work" seems to apply. The attitude seems to be, "Why bother with a new theory of GR when we are happy with what we have now? Non-incremental research is disruptive and troublesome. Scientific breakthroughs are dangerous, one can't always tell beforehand who's going to be the winners and who's going to be the losers! Change is bad!"

I think a lot of these people basically need to retire and take up gardening.

SR does not work for non-inertial systems. This is the task of GR. There are no unsolved problems with the rotating reference system. See for example THE THEORY OF RELATIVITY BY С MØLLER.

The principles of general relativity do not yet cause objection. The problems of general relativity are not problems of theory, they are problems of understanding. The main question is the understanding that the classical GR is not complete. The gravitational field equation, i.e. Einstein's equation is not exact or definitive.

This is a physical task. Popper and methodology will not help here.

D earV.B.Morozov,

SRdoes work for non-inertial systems.

In SR we define acceleration and force.Also,in the derivation of mass energy relation,we consider the rate of change of mass with velocity.These are possible only when we consider non-inertial systems in SR.

Regards

Ramesh Chandra

Dear Ramesh Chandra,

SR does not describe non-inertial systems. But SR can describe the motion of accelerated bodies in inertial systems. Non-inertial systems consider GR. Regards, Valery

Valery Borisovich Morozov: " SR does not work for non-inertial systems. This is the task of GR. "

But GR1916 does not work properly even for inertial systems! It cannot consistently relativistically describe what happens when two inertial bodies with different gravitational characteristics have (effectively) constant relative velocity. Gravitational theory gives one answer, special relativity another. The two descriptions are not reconcilable with the principle of relativity.

Valery Borisovich Morozov: " There are no unsolved problems with the rotating reference system. See for example THE THEORY OF RELATIVITY BY С MØLLER. "

There might well be no unsolved problems in the textbooks. That's because they tend not to describe the problems that they don't know how to solve, or the problems whose only known solutions seem to invalidate standard theory (either that, or they leave them as exercises for the student!).

If you really want to know what's wrong with general relativity, the "forensic", scientific approach approach is to make a list of the problems that are mysteriously missing from the textbooks. Those are the ones that nobody can get to work. Note the pattern of voids, look for the underlying patterns and themes linking the spaces.

Start by looking for a chapter in a GR textbook that describes and explains gravitomagnetism's dragging component for simply-moving inertial bodies with gravitational fields, and the consequences. What's the gravitomagnetic motion shift as a function of velocity and gravitational field intensity?

If you'd prefer a rotating-body problem, then try this: what's the gravitomagnetic shift on light reaching the observer from the receding and approaching edges of a rotating star? See if you can work that out from the textbooks.

Or how about calculating the position of the effective horizon for a receding black hole. The result is incompatible with the SR Doppler equations.

Valery Borisovich Morozov: " The problems of general relativity are not problems of theory, they are problems of understanding. "

Actually, they are problems of definition (and perhaps of gullibility). Einstein's definitions for GR1916 simply cannot be used to construct a legal theory.

For SR to be correct physics, our universe must assign zero curvature to massed particles. For a general theory of relativity to be correct, the PoE requires that our universe assigns positive, non-zero curvature to particles.

These are two mutually exclusive conditions. they cannot both be supported in the same universe. GR requires that any moving mass must drag light , while the SR derivations require that light-dragging doesn't happen. One physics is not a subset of the other.

Valery Borisovich Morozov: " The main question is the understanding that the classical GR is not complete. "

Classical SR-based GR can never be complete – because its fundamental architecture based is impossible, based on contradictory starting assumptions. You can't extend and complete a pathological structure without running into the pathologies.

That's why GR people have to hide behind talk of approximations and incompleteness. It's because, when we try to calculate certain things under GR in different ways, the predictions we get don't line up.

For people who've never studied failed theories, this is what a failed theory is supposed to look like. This is the behaviour that we're supposed to look out for as tell-tale evidence that a theory doesn't actually work.

"If you really want to know what's wrong with general relativity, the "forensic", scientific approach approach is to make a list of the problems that are mysteriously missing from the textbooks. Those are the ones that nobody can get to work. Note the pattern of voids, look for the underlying patterns and themes linking the spaces."

I am quite aware of the problems of GRT. My knowledge and skills allow me to work successfully. The problems you are talking about do not exist. Rather, these are your problems, the origin of which is probably in the lack of knowledge of the subject. I do not have the time and opportunity to retell the entire course of GTR and SRT, therefore I recommend that you familiarize yourself with the course of Möller, which most fully covers your questions.

I am sure that the field of how you get acquainted with the book our conversation will be meaningful.

"That's why GR people have to hide behind talk of approximations and incompleteness. It's because, when we try to calculate certain things under GR in different ways, the predictions we get don't line up."

It would be correct to back up this statement with your specific calculations.

Eric Baird: "That's why GR people have to hide behind talk of approximations and incompleteness. It's because, when we try to calculate certain things under GR in different ways, the predictions we get don't line up. "

Valery Borisovich Morozov: " It would be correct to back up this statement with your specific calculations. "

Oh, there’s multiple ways that GR fails.

• 1: SR is commonly described as “GR with gravity switched off”. But according to the principle of equivalence, you can never have inertia without gravity. “Switching gravity off” to get SR from GR is an illegal operation, violating the PoE.

If SR’s derivations relying on massed particle curvature being zero, and general relativity requires particle curvature to be non-zero, then SR physics is not a valid subset of GR physics. The two classes of theory are founded on mutually exclusive assumptions and operate in different logical universes.

Einstein’s claim that one could attempt to combine the GPoR/PoE and SR all in the same theory was … optimistic. And according to (Schild 1960), wrong.

• 2: MTW’s Gravitation (early 1970s) gives three criteria that any competing gravitational theory has to meet in order to be considered worth testing. It has to (A) agree with the experimental evidence (B) mesh with other theory, including QM, and (C) must be logically inconsistent (as it’s possible to produce theories that look good at first sight, but that under scrutiny turn out to be logically pathological). Einstein’s 1916 theory fails criterion (B) for failing to mesh with QM, which means that under the MTW criteria, it can safely be dismissed as wrong, and not worth testing. It also fails the test of strict logical consistency, and I’ve never yet come across anyone who claims to know of GR being sanity-tested for logic, and passing. SR yes, GR no. This is where people start talking about approximations and the theory being unfinished.

Not yet finished to the point that it can stand up to “internal consistency” testing, after a century? Seriously? Again, according to MTW, “Insufficiently credible to be worth testing”.

• 3: Gravitomagnetism. A moving gravitational source couples with nearby matter and light to produce a dragging effect. There’s probably about six different ways of calculating the effect, we can use momentum conservation arguments, gravitational timelag, work backwards from the slingshot effect, relativise the concept of refractive index, work forwards from general displacement arguments, generalise the Fizeau effect, work backwards from the idea that horizons appear frozen, or derive the effect as the velocity component present in rotational dragging required by the general principle of relativity. Actually, that’s eight.

When we drag light, we change its energy and momentum. So if a dense star aims light at us, if it recedes it drags the light away from us reducing its energy, and if it approaches, it drags light towards us, increasing the signal’s momentum and energy. Redshift for recession, blueshift for approach.

• If this gravitomagnetic shift applies on top of the SR shift, then the total motion shift for a body with a gravitational field is non-SR. And according to the PoE, all inertial masses have gravitational fields, meaning that they all must obey a non-SR motion-shift relationship.
• OTOH, we might argue that the gm shift doesn’t act in addition to the motion shift, but is the motion shift, smeared out across space with the body’s gravitational field. But in this case, the lightbeam geometry must include velocity-dependent deviations from flat Minkowski spacetime, and since the Minkowski geometry is inseparable from SR, a velocity-dependent deviation from the Minkowski geometry means a velocity-dependent deviation from the SR relationships. In which case, again, bodies with gravitational fields (which the PoE says, means all bodies with inertia) must again obey a different set of relativistic equations to SR.

So if we start from the “gravitational” side of GR, we can prove that a moving star’s motion-shift must deviate from SR, while if we start from the SR end, we can prove that in order to have the same Doppler equations as a moving atom, the star must exactly agree with SR.

Before we even do the calculations, there’s a qualitative/logical disagreement – the two predictions don’t line up.

When we can use the same theory to prove two opposite outcomes, the theory is said to be logically inconsistent, or pathological.

Valery Borisovich Morozov: " The problems you are talking about do not exist. Rather, these are your problems, the origin of which is probably in the lack of knowledge of the subject. I do not have the time and opportunity to retell the entire course of GTR and SRT, therefore I recommend that you familiarize yourself with the course of Möller, which most fully covers your questions. "

No, it really doesn’t. It took me maybe half an hour to skim through that book. Nothing particularly interesting, or original, or anything I wasn’t aware of.

I’d said: “ Start by looking for a chapter in a GR textbook that describes and explains gravitomagnetism's dragging component for simply-moving inertial bodies with gravitational fields, and the consequences. What's the gravitomagnetic motion shift as a function of velocity and gravitational field intensity? ”, and your response appears to be a bluff. What I asked for isn’t in there.

So … have you read the book? :)

Moeller: Page 288: “ Since the tensor equations of the special theory are assumed to hold in a local system of inertia, … ”

Note: assumed, not derived within the new context of curved spacetime.

Moeller, page 299: “ Strictly speaking, the particle itself will create a gravitational field, which should also be described by the functions gik … ”

Good. Excellent, in fact. And the principle of relativity then requires that we obtain the same results irrespective of whether the observer-particle or the observed object is moving. This then places severe constraints on the number of relativistic equation sets that could possibly operate symmetrically between any combination of particles and/or masses. In fact, there only appears to be one solution that meets this criterion, if the particle has a positive, non-zero gravitational field.

This is potentially exciting. It's Moeller standing on the edge of a major scientific breakthrough. What he has to do next is to derive the strength of the particle’s own gravitational field. And this is possible from first principles thanks to the principle of relativity.

In order to satisfy symmetricality, the observer-particle’s curvature-based motion effects must somehow be able to perfectly replicate/mimic/reproduce the curvature-based motion effects results of any other object it might ever exchange signals with, whether that’s a moving grain of sand, a planet or star, a neutron star or a black hole.

The options here are limited:

• If all particles have zero curvature (violating the principle of equivalence), we get the same equations for all massed particles, and also for all larger objects, because those zero fields combine to produce a zero field. We get special relativity, but also a proof that our universe is flat and devoid of gravitation. Which is wrong.
• If fundamental massed particles have very small (identical) gravitational fields, then we can have the principle of relativity apply to signals sent between those particles, but not for larger composite bodies, where the gravitational differential between empty space and an emitting atom is different depending on the larger-scale properties of the body that the atom is a part of. So assigning "weak" gravitational fields to particles doesn’t work, it breaks the PoR.
• The only way to get to a fully viable theory of relativistic gravitation is for all massed particles and bodies to present precisely the same apparent gravitational differential along the signal path when at rest, regardless of their composition and mass, which is only possible if all particles already show the maximum possible deviation from flat spacetime (=are horizon-bounded). Then, a particle can exchange signals with a black hole, and the thing is symmetrical, and it can exchange signals with small rock, and the thing is still symmetrical, because the rock is constructed of particles that each already have the same maximum curvature at extremely small distances. When we bunch rocks together, and they combine their external fields, making the differential between free space and the particles’ surfaces greater, the particle’s curvature horizon simply extends … if we identify a particle’s nominal surface with its curvature horizon, we then have a self-regulating system.

So this is Moeller standing on the very brink of greatness. All he has to do now is present the argument that all massed particles and bodies must present the same apparent curvature, which means that according to the PoE/PoR all particles must present maximal curvature, and calculate the equations of motion assuming that those particles act like little black holes, and he will have a replacement for Einstein’s general theory that meshes with quantum mechanics. So what does Moeller do next?

Moeller, p290: “ In the present sections we assume, however, that the field is weak in comparison with the external field so that its influence on gik may be neglected. ...”

FAIL!!!!!! This is why Moeller is not remembered as one of the world’s great theoretical physicists. He had an opportunity to revolutionise relativity theory, and he copped out. It’s like, in soccer, a striker approaches the goal of the opposing team, and its an open goal, with no defending players in his way, and all he has to do is gently tap the ball across the line to win the match and the championship, and instead he loses his nerve, turns around and faces the other way, and kicks the ball back to his team captain … at which point the other team intercept the pass and gain possession.

Moeller assumed that the field was weak in order to get the result he wanted, he didn’t calculate or derive it. If he’d tried to derive the field strength using geometry and logic and the principle of relativity, he’d have found that the particle curvature had to be maximally strong, to the point of particles being horizon-bounded.

This result might have seemed crazy in 1950 (because how could a horizon-bounded particle ever emit radiation?). But if he’d worked though the exercise further, he’d have found that the necessary gm equations for black hole light-dragging don’t generate a Wheeler black hole, they generate an “effective” horizon rather than an “event” horizon, and effective horizons radiate indirectly, fluctuating and leaking massenergy and information in a way that statistically corresponds to Hawking radiation. Classical relativity theory done properly gives us Hawking radiation.

All Moeller had to do was to be a scientist and follow his own argument to the logical conclusion, and we’d have a new general theory, Hawking radiation would be called Moeller radiation, and we’d have had a theory of quantum gravity in 1950.

But Moeller was too much of a slave to orthodoxy. Instead of following through, he recognised that strong particle-curvature undermined the pro-SR result that he was aiming for, so he said that we know the particle curvature is weak, and then he approximated that weakness by putting in a zero.

He "fiddled" the expected answer instead of deriving the real one.

The result is junk theory. It’s faking one of the most critical stages in the calculations in order to get the standard result instead of the correct one.

This is why Moeller was only at best a second-division theorist. He used schoolboy tricks to get “the result that the teacher wanted” rather than do a valid derivation and arrive at a valid and exact (but revolutionary) answer.

To wrench this discussion back to the original question, " Does the relativity principle play a minor role in GR? ", the answer would seem to be, "according to some people"

Gravitational theory plus relativity generates a different set of equations of motion to flat spacetime plus relativity, making GR1916 logically inconsistent. As a result,

if we take three features that Einstein wanted to include in general relativity: (A) gravitation/curvature, (B) the principle of relativity (in its widest sense), and (C) SR, then a valid theory can only include two out of those three:

Some members of the mainstream tend to drift towards option (1): they say that SR is compulsory, gravity obviously exists, and that the general principle of relativity is therefore only an approximation or guide. They'll say that Mach’s principle is naive and outdated, and that when push comes to shove, the EEP replaces the original principle of equivalence.

Others will say that all three conditions are met by GR, but only approximately, because the theory only claims to be an approximation, and/or is unfinished.

Personally, my preference is for option (3), an exact implementation of the GPoR and relativistic gravitation, which downgrades SR to being a flat-spacetime approximation of curved-spacetime physics. But while this would be "general relativity", it wouldn't be Einstein's 1916 version, or the current textbook version.

Dear Eric Baird,

I do not always understand you. In my opinion, everything is much simpler. GTR deals with the local principle of relativity. Those. legitimate natures are the same in the limit of a small area. Until not seen violations of this principle.

In your reasoning you use the concept of "black holes". This defect of GR is caused by the imperfection of the Einstein equation. The problem is solved by replacing the Einstein equation: Preprint New version of the general theory of relativity (Initial pri...

Regards, Valery

"Personally, my preference is for option (3), an exact implementation of the GPoR and relativistic gravitation, which downgrades SR to being a flat-spacetime approximation of curved-spacetime physics."

So it is precisely this way one must understand the relation of theories. That is what Einstein said.

Valery Borisovich Morozov: " In your reasoning you use the concept of "black holes". This defect of GR is caused by the imperfection of the Einstein equation. The problem is solved by replacing the Einstein equation: "

I'm using the term "black hole" loosely, to mean anything that has a gravitational curvature horizon. I know that it used to mean specifically a Wheeler black hole, but the QM folk have since muddied up the definitions by referring to a radiating QM black hole as still being a black hole, even though it isn't black. :(

I suppose I could use a more general term ("horizon-bounded object", HBO?), but most people just say "black hole".

Some people object to the idea of a black hole based on the craziness that happens around a curvature horizon. But these things also happened under Newtonian theory: see John Michell’s original derivation of the r=2m horizon radius, published in in 1784.

in fact, the Newtonian “dark star” was even crazier than a Wheeler black hole, because the horizon position was observer-dependent, which meant that particle-events that weren’t directly visible to one observer could still affect an intermediate region of spacetime, and create consequences that could be seen indirectly. So the 1780s dark star can produce the same definitional crazinesses of "virtual" and "real" particles as QM – the 1780s theory generates classical Hawking radiation.

Einstein was kinda correct to reject the idea of Wheeler black holes based on his conviction that a region should never be entirely causally disconnected from the outside world – but once you change the basic shift equations away from SR to a gravitomagnetically compatible set, and start to get indirect radiation through the horizon, the region is not causally disconnected, eliminating Einstein’s objection.

Other people object to the idea of a black hole due to the idea of there being a central singularity, which is commonly regarded as being a defect in a geometrical theory.

But once a theory supports Hawking radiation, the hypothetical central singularity seems to dissolve:

If we look at a stationary stellar-mass black hole from a long way away, its Hawking radiation is extremely weak, and the horizon is extremely cold. Almost none of the hole’s mass exists outside the horizon as HR.

But if we let ourselves fall into the hole, the situation changes. Once we’ve fallen through the r=2m horizon, there’s still expected to be a "censoring" horizon between us and r=0, but this "sub-horizon" radius is smaller, and smaller black holes radiate more strongly. The further we fall towards r=0, the smaller the intervening horizon seems to be, the greater the temperature, and the greater the flux of Hawking radiation. As the apparent radius of the horizon goes to zero, the radiation rate goes to infinity, which means that before we get to r=0, the amount of radiation that we encounter really should at some point equal the mass of the hole, so that when we reach r=0 there’s nothing left.

Smaller holes have shorter lifetimes, shrinking and eventually radiating away all their remaining energy in an final explosion. So we fall towards r=0, it’s as if we are watching the process accelerate, so that by the time we reach r=0, we find that the hole has already exploded. The interior of the hole then represents a sort of frozen explosion in equilibrium.

That’s the “hand-wavy” description: things might not be quite so simple in full calculations, due to, e.g., the restriction on how fast radiation can leave a tiny hole with a tiny surface area, or the apparent existence of significant mass above the sub-horizon, changing the field “drop-off” with distance away from that of a point-mass. Some people might also argue that we might find a tiny particle-like quantum remnant that one can’t “fall into” due to the exclusion principle.

And there’s lots of trading off different sizes of infinity against each other. But as soon as we have classical Hawking radiation, the standard proofs that a hole's mass must all reside at the centre disappear, because we now have to take into account the Hawking radiation pressure, which although incredibly puny outside a decent sized hole, becomes infinitely strong towards r=0. QM people also talk about degeneracy pressure - I don't know what the classical counterpart of that might be.

If we solve the other problems with GR (like support for velocity-dependent gravitomagnetism), the solution might well also solve the singularity problem.

Dear Eric Baird,

The problem of "black holes" is not that someone does not like them. Schwarzschild's decision has a meaningless feature, the space does not exist there. This is not the abnormality of GR, it is a feature of the Einstein equation. The problem is solved only by rejecting the Einstein equation. The new gravitational field equation has no singularities in the solutions. It's just an extremely fast growing gravitational field , faster than Newton or Schwarzischild.

Regards, Valery

EB: "Personally, my preference is for option (3), an exact implementation of the GPoR and relativistic gravitation, which downgrades SR to being a flat-spacetime approximation of curved-spacetime physics."

VBM: “ So it is precisely this way one must understand the relation of theories. That is what Einstein said.”

Not quite. Einstein said that as we zoomed in on a region of spacetime, and the background field gradients faded away, what we were left with was flat-spacetime physics and special relativity as a nominally exact solution. So under Einstein’s scheme, SR physics lives on within GR as an exact subset of the larger physics.

I’d counter-argue that while zooming in on a region containing particles removes the background curvature, it doesn’t remove the curvature of the particles themselves. Einstein’s reduction argument only yields SR physics if we said that these particles had zero associated curvature … which isn’t allowable, as this would violate the PoE, which was supposed to be one of the cornerstones of GR.

So Einstein’s “reduction to SR” argument is illegal.

Some physicists would shrug and say that they don’t care about technical illegalities, and as long as special relativity is vanishingly close to reality, they’re happy. They’re not going to worry about nit-picking technicalities, or the difference between a "true" zero and something really, really small.

Trouble is, iF we bother to try to work out the gravitomagnetic equations of motion, the SR equations aren’t even that close. They’re off by an entire additional Lorentz factor.

I don’t blame Einstein for being emotionally attached to special relativity, and for wanting it to live on within general relativity. It would be very difficult for him not to be attached. But the fact is, if we try to derive the properties of inertial physics from the GoR and PoE, they don’t give us special relativity.

"So under Einstein’s scheme, SR physics lives on within GR as an exact subset of the larger physics."

This is true, but Einstein considered the totality of the initial principles of the theory, and not the theory itself. It is clear that in real space is curvilinear, But we can consider the approximation of the special theory of relativity. There is no contradiction. By combining mechanics with electrodynamics, Einstein received a special theory of relativity. Further adding the principle of equivalence, the theory began to describe the gravitational field.

Einstein: "According to the law of inertia, a material point, on which no forces act, moves uniformly in a straight line. In the four-dimensional continuum of the special theory of relativity (with a real time coordinate), this is the usual straight line. The most natural, that is, the simplest, generalization of the line lines in the concept system. The Riemannian general theory of invariants is a “straight line” or geodesic line. "

"The introduction of coordinate systems accelerated relative to each other as equal, prompted by the identity of inertia and gravity, combined with the results of the special theory of relativity, leads to the conclusion that the laws governing the location of solids in the presence of gravitational fields do not correspond to Euclidean geometry. A similar result is obtained for the clock. Hence the need for another generalization of the theory of space and time, since the direct interpretation of the space-time coordinates as measurement results obtained with the help of scales and clocks, now disappears. This generalization of the metric, which was already obtained in the field of pure mathematics in the works of Riemann and Gauss, is based mainly on the fact that the metric of the special theory of relativity is preserved for small domains and in the general case."

Einstein: " This generalization of the metric, which was already obtained in the field of pure mathematics in the works of Riemann and Gauss, is based mainly on the fact that the metric of the special theory of relativity is preserved for small domains and in the general case. "

But it's not preserved for small domains, if those small domains contain two or more massed particles with relative motion.

If a domain contains a pair of particles exchanging signals, and they have relative motion, and mass, the PoE requires them to have associated curvatures, and the relative motion of those curvatures is then associated with a velocity-dependent deviation from flat spacetime along the path taken by exchanged signals.

The energy of the signals exchanged then no longer corresponds to the relationships of Minkowski geometry, or the SR equations. The sheer perfection of SR's match to fixed flat spacetime means that if we switch the geometry to a dynamically curved spacetime, the relativistic relationships have to NOT be those of special relativity.

For a counter-example to the usual "geometrical reduction" argument, consider the hypothetical case of a relativistic acoustic metric, in which there's no preferred frame, and all moving curvature-sources drag light. An r.a.m. is a classical system that generates Hawking radiation and therefore a cannot be described by the SR equations of motion. Its geometry is non-Minkowski, and its physics is qualitatively different to SR's. But if we applied Einstein's "small domain" argument, we could still zoom in sufficiently far on an empty region, obtain effective flatness, and apply the PoR to that flat region to get SR!

Since the reduction argument appears to prove SR even when SR isn't correct, there would seem to be something wrong with the logic. On investigation, the flaw in the reduction argument (in the a.m. example) is the assumption that the limit of geometrical physics is still physics. In applied math, some limits are inclusive limits, the furthest we can go and still have system work, and some are exclusive limits, the point at which a system no longer works (or no longer applies).

In the case of an acoustic metric, the physics is described by the curvature. The limit at which this curvature disappears (to give SR) does not describe "simple" physics, it describes a metaphysical set of relationships that can only be said to apply (to nothing!) when matter isn't actually present, or even nearby. Put the particles back, the curvature reappears, and the SR solution vanishes again.

The Einstein reduction argument only gives SR as physics if we presuppose that particles don't have associated curvature. And since that assumption violates the PoE, a PoE-compliant theory cannot use Einstein's argument. If a valid general theory wants to incorporate the SR relationships it has to use a different, PoE-compliant set of arguments ... and I would strongly suggest that no such arguments exist, or can exist.

Einstein later concluded that the path that he had taken to get to the 1916 general theory wasn't entirely legitimate. It had been the best that he'd been able to manage at the time, but it was no longer objectively justifiable.

The components used to construct a general theory needed to be able to demonstrate that they were indeed compatible with the GPoR before being allowed to be accepted as part of the theory (special relativity fails this test). It was wrong to divide physics into gravitational and nongravitational sections, and to use GR just to handle obviously "gravitational" problems and to leave SR to deal with everything else, in the hope that everything would fit together and work out in the end (it doesn't).

The very concept of a "nongravitational" physics was something that Einstein said he no longer believed to be legitimate.

Einstein (1950):

" ... all attempts to obtain a deeper knowledge of the foundations of physics seem doomed to me unless the basic concepts are in accordance with general relativity from the beginning. This situation makes it difficult to use our empirical knowledge, however comprehensive, in looking for the fundamental concepts and relations of physics, and it forces us to apply free speculation to a much greater extent than is presently assumed by most physicists. I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified. The comparative smallness of what we know today as gravitational effects is not a conclusive reason for ignoring the principle of general relativity in theoretical investigations of a fundamental character. In other words, I do not believe that it is justifiable to ask: What would physics look like without gravitation? ... "

Einstein essentially said that the whole idea of an SR-based general theory was unreliable, unsafe, and (with hindsight) indefensible. We could not assume (as he had, previously) that curved-spacetime physics reduced naturally to flat-spacetime physics, because we could not be sure that there was any such thing as a correct flat-spacetime physics. It might be that the reach of curved-spacetime geometry extended into regions where its presence had not been fully appreciated, and where the application of curvature-based arguments had not yet been fully explored.

Einstein's role here is of the architect of a building, who had also overseen its construction, announcing to the general public that the building was not to be considered safe. He was "blowing the whistle" on his own theory, as the guy who knew more about its origins than anyone else on the planet. He was the guy who was there.

Einstein's warning was something that the community didn't want to hear, or to have to deal with – their reaction seems to have been either to pretend that he hadn't said any such thing (the piece is missing from a number of otherwise quite thorough bibliographies), or to go around telling people that Einstein had "lost his marbles", and that the things he said were no longer to be taken seriously.

Einstein's misgivings turned out to be well founded. Ten years later, in 1960, Schild said that the community now (mostly) accepted that SR was incompatible with the GPoR and PoE, and then in the early 1970s, we found that the 1916 theory was also incompatible with QM.

It's also incompatible with gravitomagnetism and with modern cosmology, and ... with almost everything else, if you look hard enough. Particle physics, statistics, information theory, topology applied to cosmology, horizon theory, conservation of momentum ... Even the PoE and GPoR. It's incompatible with almost everything, including itself.

Thank. I read with great interest (for some reason I did not read before).

I do not perceive SR as something alien to GR. The equation of motion now looks the same in both cases. Accelerated reference systems allow you to go continuously to GR.

The problem of combining GR with quantum mechanics is really important and serious. But now I am focusing on classical general relativity. There is something to do.

Regarding Einstein’s Opinion

Preprint Einstein's Last Will

Time has passed, now we can say that the problem has been solved.

Preprint Gravitational Field Equation and the Structure of Black Holes