I suppose that the "defensive" argument would be that when you introduce a large mass, which significantly changes the shape of the metric over a region that includes other bodies, the geodesics that we might plot in the absence of the mass no longer apply. The presence of the mass can change the geodesics, for itself and for the other bodies.

An unsatisfying and circular answer, I know. But perhsps the best that you are likely to get.

Eric Baird

Remember. The geodesics model exists because Einstein and everyone else couldn't derive from first principles the laws of nature.

They only had the empirical laws, and those laws were not consistent with reality.

You might say that the empirical laws of electromagnetism were, but you would be wrong.

Without the laws of nature, one cannot create a dynamic model.

What you are proposing is a time-dependent deformation of the metric by a body that will "follow the geodesics it creates".

I would say that is not Science.

Primarily because I provided the Force already.

Of course, if for some reason you couldn't accept Science to advance, you could try to do a band-aid to GR, but it will never work.

Eric Baird

https://youtu.be/gtss7HkVwo0

Marco Pereira ... oh, I quite agree. The geodesic argument is pretty, and elegant, but if you take it literally and exactly, then it lets us "prove" that a moving mass has zero effect on spacetime, which in turn lets us "disprove" the idea of gravitomagnetism ... and since a general theory can't exist without gravitomagnetism, the geodesic argument ... treated as a fundamental truth for the behaviour of matter ... lets us disprove general relativity!

Einstein's general theory is logically dysfunctional, and is not even a legitimate scientific theory, because it disagrees with itself. It's "not even wrong".

And it can't be fixed, because the dysfunctionality exists in its starting definitions.

The whole system needs a complete rewrite, from the groound up. At which point it's no longer Einstein's theory.

Eric Baird

You said: then it lets us "prove" that a moving mass has zero effect on spacetime,

General Relativity has been disproved already. I did it.

We don't need to hold hands and do it again. It has been done.

https://youtu.be/gtss7HkVwo0

Well, GR1916 t was logically wrong from the original days of its inception, when Einstein tried to combine the principle of equivalence of inertia and gravitation, which says that matter always has associated curvature, with a set of equaitons based on flat Minkowski spacetime, which require that mass never has curvature...

Special relativity gives us matter-physics in flat spacetime, while general relativity tells us that there's no such thing as matter-physics in flat spacetime. The presence of matter alway associated with curvature. GR1916 declares that the PoE is right, while also declaring that the principle reduces to SR physics.

His core definitions for GR1916 necessarily exist in different logical universes. One simply cannot construct a rational theory according to Einstein's specifications. It's impossible.

Eric Baird

There is nothing wrong with starting from Minkowski (zero masses and inertial reference frames) and modifying it to reflect the effect of Gravitational attraction (acceleration).

That is clear from the success in predicting the precession of Mercury.

So, the model is not illogical. What the model is, is "just a model". It doesn't correspond to reality, and spacetime is just an artificial construct.

If you make M=0 in the Schwarzschild metric, you get back the Minkowski metric (flat space) in spherical coordinates.

What makes the model useless is the fact that one can only calculate results for a single body with mass M. One cannot tackle the two-body problem.

I demonstrated this and created a replacement for GR.

It seems you are wrong about your criticism of GR. SR and GR are consistent. GR is not a theory that tackles acceleration. GR metric depends upon velocity (the Schwarzschild metric is just the Lorentz Transformation in spherical coordinates for a falling body with zero mass and zero energy at infinity).

Your criticism should have been "there is no such thing as Spacetime".

That is the correct conclusion. SR, GR, and Spacetime are narrow-scope models and not a description of reality.

Marco Pereira : " There is nothing wrong with starting from Minkowski (zero masses and inertial reference frames) and modifying it to reflect the effect of Gravitational attraction (acceleration). "

The only way that's valid is if you are using SR as a temporary disposable reference placeholder that gets replaced with a new geoemtry and equations before you start doing any actual physics.

Marco Pereira : " SR and GR are consistent. "

No, they are really not, not if "GR" is obliged to conform to the General Principle of Relativity. Because the GPoR can't coexist with the SR math. They mutually disprove each other.

You're doubtless familiar with the exercise in lots of GR and SR textbooks where they ask "Can SR deal with acceleration?" and conclude, "YES!" (in MTW, it's in Chapter 6).

Let's use that as a starting-point:

Exercise 1 Doppler shifts

If we assume flat relativistic spacetime, we can derive the SR Doppler shift equations as the only possible solution. SR = relatvity plus flat spacetime .

Now we look at the curved path of a forcibly-accelerated body. We decompose it into lots of tiny velocity-differentials, each of which is dealt with by SR. But since SR (at least for simple colinear acceleration) also deals with arbitrarily-large numbers of velocities, "stacked", through its velocity-addition formula, the light-geometry of every section of the curved line, and the entire curved line, turn out to be again a perfect fit to flat spacetime. The velocity-addition formula is derived deterministically from the shift formula, so that can't be changed independently. The accelerated body feels the effect of the relative acceleration, an inertial bystander doesn't.

So we can prove that if SR is correct about velocities, there is no such thing as acccelerative curvature, and therefore no such thing as a general theory of relativity. Because in our exercise, acceleration effects are not mutual but absolute, and the GPoR is based on the idea that acceleration forces are relative.

If an accelerated star doesn't warp spacetime, then geeforces are not due to background matter, but to some form of absolute space, and we revert to pre-Mach, pre-Berkeley physics. No GPoR

Conversely, if we want a general theiory of relativity, and need accelerative gravitomagnetism, then the accelerated mass must warp spacetime, violating the SR Doppler geometry. Within a GPoR-compatible theory, SR cannot have the right equation-set.

Exercise 2: Curvature

Similarly, the "decomposition" argument says that the spacetime curvature due to an acclerated mass is simply the aggregate of the smaller component velocity-dependent curvatures that are associated with the decomposed curve.

Under special relativity there is no such thing as a velocity-dependent curvature, and therefore, the aggregate of lots of nothings is still nothing, and there is then no such thing as accelerative grvaitoamgnetic curvature.

If we want a general theory of relativity, and need accelerative gravitomagnetism, then the accelerated mass must warp spacetime, and the relaitve velocities of objects must warp spacetiome, too. So working backwards from the GPoR, simple inertial physics cannot be a flat-spacetime problem, it has to involve the distortion of the metric by real moving masses. We can then go back even further, and say that velocity-dependent curvature also can't happen unless all particles have an underlying REST curvature, which then gets modified by velocity. So all massed particles must have gravitational fields, meaning that SR's flat-spacetime geometry automatically stops applying as soon as any matter is present. SR becomes a null solution, at best only able to nominally model matter-physics in situations where the quantity of massed particles is zero.

Exercise 3: Kinetic Energy

Einstein's GR arguments tell us that locatable energy gravitates. A spinning flywheel has a greater grvaitaitonal attration then when it is stationary, because of the recoverable KE bound up in its spin.

So we expect the increased energy of a movign particle to make its gravity-well seem to deepen (overall), and include more positive curvature (overall), than if it appeared to be "stationary". Positive curvature amounts to an increase in the amount of contained space for a region with unit perimeter -- that's how we get the "gravity-well" shape in the first place. But if the internal excess increases as a function of velocity, any wavelengths spanning the region have to stretch accordingly (when compared to SR), and the new equaitons need to be "redder" than the SR reference equations as a function of velocity, to fit the additional warped space.

So KE plus the gravitation of energy tells us that SR can't possibly be right. For space NOT to distort as a function of the relaitve velocities of objects, requires either energy NOT to gravitate, or for there to be no such thing as KE, or for there to be no such thing as gravity.

If we take the SR equaitons at face value, because they were derived from the assumption that matter has zero associated curvature, when we use those equations in a gravitational theory, the equations carry the initial assumption that matter has no gravitational fields over implicitly into our gravitational theory, pretty much guaranteeing that it won't work

Relativistic gravitation of any sort, with or without the GPoR, does not work with the SR Doppler equations. So in an SR-compliant universe, even the "simple" relativity principle does not apply to objects with gravitational fields. Which is, unfortunately, all of them.

Einstein apparently didn't do any of these background compatibiltiy checks before embarking on his GR project in 1913. He just chose to assume that the equations of his first theory would still be valid in his second. They're not.