Hi Preston

Einstein's General Theory of Relativity is not even incorrect. It's geometrically invalid.

The general principle of relativity applied to rotation requires that a rotating star drags light. This dragging effect has a velocity component, in that the receding side of a star drags light away from us, and the approaching side drags it towards us.

We can then extend the argument to show that this velocity-dependent dragging effect must also apply when there is no rotation and only simple relative velocity. The back-end of a black hole receding at v has to drag light with it at exactly v, otherwise the light emitted at r=2m that was described as being frozen into the horizon for a stationary observer would either be infalling or exposed for other observers who saw the hole moving. If it's an event horizon, it has to drag 100% to avoid inconsistency, and if its not an event horizon but an apparent horizon, it then also has to drag 100% for other reasons.

So moving strong-gravity bodies have to drag light.

When they drag light, the momentum and energy of that light changes, which means that the relationship between relative velocity and light-energy cannot be that of SR. And if strong-gravity bodies have a Doppler relationship that isn't SR, then all bodies have to share that same non-SR relationship. if we look at a tiny patch of sky containing a distant galaxy, and change our velocity along the viewing path, then everything in that galaxy has to be seen to shift frequency by precisely the the same amount. The same Doppler relationship has to apply to a neutron star as to an isolated atom of interstellar gas. If the neutron star drags light, then so must the atom (and it does, Fizeau effect).

And what's more, the same departure from the SR relationships that we get due to the neutron star's motion must be precisely as the one we get for the atom's motion since we need to be able to explain the same divergence due to dragging on either the star or the atom (principle of relativity), the atom, and the neutron star and a black hole must all drag light by exactly the same amount at a sufficiently close proximity.

So all matter must be treated as if it is either horizon-bounded, or made from smaller particles that are horizon-bounded. Symmetricality then means that we aren't allowed SR-style "mathematical" observers, the only observers that are legal under a full theory of relativity are those made from other light-dragging atoms.

There's then no such thing as flat-spacetime physics – the curved spacetime relativity of a proper general theory of relativity doesn't reduce to SR or to anything else – it is self-contained, and applies right down to the level of particle physics.

The whole idea that a general theory has to reduce to a flat-spacetime physics seems to be something that Einstein just made up (because he wanted his new theory to include his older theory rather than invalidate it), and nobody really questioned whether what he was saying was really true. It satisfied an emotional need for Einstein, but wasn't obviously based on any proper scientific analysis.

People took Einstein's statement at face value, assumed that it was based on research, and didn't do their own investigations.

If you're considering things like precession, then you're overcomplicating: Einstein's GR doesn't even work relativistically for the case of an isolated strong-gravity body far from other masses, coasting in a straight line at constant velocity.

It's a turkey.

There is no GR version of Doppler that I know about.(only SR), this is not for or against GR.

Do not see why gravitomagnetism should enter this discussion.

I seem to have a slightly better view of GR than above.

Juan Weisz: " There is no GR[1916] version of Doppler that I know about (only SR), ... "

Correct with my added [1916] qualification.

So Einstein's 1916 theory of relativity uses curved spacetime, and requires massed particle curvature to be positive, but it inherits key relationships from his 1905 theory, which assumed flat spacetime and massed particle curvature being zero.

SR assumes that moving matter has zero effect on light, but the principle of equivalence says that all masses must have associated curvature, and moving curvatures then create gravitomagnetic distortions, warped spacetime, departures from Minkowski geometry and non-SR relationships.

He included a component, in a theory based on the GPoR and PoE, which was incompatible with the GPoR and the PoE, and which couldn't legally be a limiting case.

Beginning to see the problem?

Juan Weisz: " ... this is not for or against GR. "

It's against the current (failed) implementation of general relativity.

Einstein's 1916 version isn't the real deal. He wrecked his theory's logical structure by trying to use the "SR shortcut", instead of working through what needed to be the correct relationships for moving bodies according to the GPoR and PoE.

Juan Weisz: " Do not see why gravitomagnetism should enter this discussion. "

It's critical because general gravitational theory requires the existence of velocity-dependent gravitomagnetism, and so does the GPoR applied to rotation. And so does gravitational momentum exchange, and a finite speed of g, and a range of other basic arguments.

A valid general theory of relativity requires a moving star to drag light. Light-dragging alters the energy and momentum of the affected light, so that the light-geometry is warped as function of the relative velocity of the masses involved.

Minkowski spacetime's geometry is "fixed" in that it assumes the total absence of distortional effects due to moving masses. With gravitomagnetism, the spacetime geometry is instead "dynamic", and the velocity component takes the geometry further away from flatness for progressively greater velocities. Since SR is "dual" to Minkowski spacetime (we can read off SR's predictions for wavelength-change directly from the geometry of an MS slice), a velocity-dependent deviation from MS means a corresponding velocity-dependent deviation from SR.

So gravitomagnetism means that, geometrically, SR cannot have the correct equations of motion for strong-gravity bodies.

Once we know that strong-gravity physics must use non-SR relationships, we can set out to derive the Doppler relationships for the extremal case of a moving black hole. Once we have those, metric-compatibility means that the same equations must apply everywhere, even to massed particles without obvious macroscopic gravitational fields. Under a general theory, the particles making up a physical observer have to follow the same equations as a moving black hole. We then have a theory that corresponds to William Kingdon Clifford's concept that "all physics is curvature".

While Einstein's GR simply borrows the SR relationships without checking their legality in the new context, a proper attempt to derive the correct relationships from GR principles turns out to give non-SR equations, showing that Einstein's "happiest thought", that SR physics was a subset of GR physics, wasn't legal.

I do not understand anything. Excuse me.

Hi Valery!

If we start with the principle of equivalence of inertial and gravitational mass, then massed particles must have associated gravitational distortions, which aren't included in special relativity's description. When these gravitational sources have relative motion, there then also has to be an additional velocity-dependent gravitational component (gravitomagnetic effect). We then have a situation in which a pair of massed particles is associated with a deviation from flat Minkowski spacetime, as a function of their relative velocity. Since Minkowski's geometry is synonymous with the equations of SR, assigning curvature to particles therefore means that there must also be a corresponding velocity-dependent deviation from the SR equations whenever two massed particles exchange signals.

So the "flat" SR equations, geometrically, cannot be an exact physical solution of a valid general theory of relativity when real matter (and physical observers made of matter) is involved.

I've worked out what logic seems to me to require as the only possible alternative set of relativistic equations to SR's – I was wondering if you might have hit on the same solution via another route.

"So the "flat" SR equations, geometrically, cannot be an exact physical solution of a valid general theory of relativity when real matter (and physical observers made of matter) is involved."

There is such a transition from flat space. We can observe unevenly moving bodies in flat space, but our own frame of reference where these bodies are motionless will no longer be flat.

Article On bodies’ motion relativistic description