I've read enough of Ronald Hatch's stuff to figure out that all he has done is built an elaborate mathematical reformulation of GR and SR and *insisting* that they're not GR and SR and that everything observed is merely "apparent." He does not contest that the effects of SR and GR are observed, he merely insists that they are only a seeming. But his physics is no more Newtonian than Einstein's relativity.

...

I think physicists can see through the little mathematical games he's playing and are thinking, "How cute!"

The above judgement was based on snippets gleaned from abstracts behind a paywall (I refuse to shell out money for an internet battle). Since then, I've managed to track down some equations that our friend Hatch is using from a slideshow presentation from 2000.

The first thing to remark is that Hatch does not understand GR on its own terms. This is clear from his own attempts to characterize the "gravitational scale factor" of GR. In GR, the metric plays a central role in the physics of spacetime. Instead, what he expresses as the scale factor is just the gravitational redshift for a Newtonian potential, z = exp(-GM/rc²)-1, plus 1. But we don't use this expression or any similar one for deriving the kinematics of free-falling particles; we derive it explicitly from the metric.

Speaking of the weak field, Hatch's scale factor for his "revision" looked awfully familiar to me, so I checked in my copy of

*A First Course on General Relativity* by Bernard Schultz, and lo and behold, I found it (or rather, its square, but it's in a d_² term) in the metric expression for the weak field approximation. Specifically, in the time component, which is the dominant component of the weak field approximation for a Newtonian potential, ϕ = -GM/r. From this, you can recover Newton's gravitational force law, dp⃗/dτ = F = -m∇ϕ = -GMm/r², for a particle free-falling in this metric.

No, Dr. Hatch, GR does NOT derive F = -GMm(z+1)/r² as you claim!

Thing is about the weak field approximation, it's been kicking around since Einstein, and is derivable from GR with the assumptions that the gravitational field is weak (with escape velocities well below light) and for small velocities (again, well below light). Under the assumptions of the weak field/small velocities, the metric can be treated as straight Minkowskian perturbed by a very small matrix, h, and under the Lorentz transformation, the metric transforms in such a way that our h transforms as if it were a tensor itself, and leads to what Schultz calls a "convenient fiction" that h is a background field on flat spacetime. Hatch claims his is an "ether theory," and this is part of the reason why it works after a fashion. The other thing is that we can derive the weak field approximation for the Newtonian potential completely in GR. I don't know how Hatch derived his expression for his gravitational scale factor, but if his calculations are in any way sound, I wouldn't be surprised that he somehow recapitulated the result of GR's weak field approximation.

As such, I'm able to put a finer point on that little thing that physicists say when they see Hatch's stuff: "How cute! He re-derived Einstein's gravitational weak field approximation!" So it's no wonder physicists aren't taking him seriously. He's literally coming up with stuff that has been known for almost a century and treating it as if he's come up with a brand new interpretation. It'll even sorta work for weak fields.

**Addendum:** I have just now learned that Hatch's scale factor, s, comes

*exactly* from the weak field approximation. Just straight rips it off. It's called an "approximation" for a

*reason.* So, yeah, it really is just a recapitulation of an approximation that physicists have known about for almost a century. ⑨

Oh, and he's derived the full spherically symmetric external field in GR wrong. We know what it is. It's the Schwartzschild metric, which does NOT have exponentials in its expression. ⑨ /Addendum

Now, his alternate Lorentz transformation? That's more difficult to fathom, because I have yet as this writing to track down an explicit expression. He does make reference to an absolute frame, though how one's supposed to find the absolute frame (and thus get the "really correct" value of c) is beyond me. However, Hatch does reference the apparent speed of light in tranverse and parallel (along-side) directions as c

_{t} = c/γ; c

_{p} = c/γ², and a length contraction along the parallel direction is l

_{p} = l/γ, while transverse length is unaffected. (As always, γ = sqrt(1-v²/c²).)

Let's work out a Michelson-Morley type experiment here. Figuring the lengths of the two arms in Earth's frame, E, and translating to the "true frame" will allow us to avoid parallel and transverse speed of light shenannigans. The parallel moving tube is measured to be L = l'

_{p} in E, so it's "true length" is l

_{p} = γL, so it takes light t

_{p} = 2γL/cγ² = 2L/cγ to travel this distance. For the transverse moving tube, measured at L = l'

_{t} in E, its "true length" is l

_{t} = L, so it takes light t

_{t} = 2L/cγ*. The difference is ∆t = t

_{t} - t

_{p} = 2L/cγ - 2L/cγ = 0, so it appears that it replicates the Michelson-Morley experiment and no fringing is detected.

But * indicates an incorrect derivation: the light does NOT travel l

_{t} = L along the transverse path, because the ends of that tube are MOVING forward at v — the light that gets reflected from the far mirror has to be traveling along a diagonal outward, and takes a similar diagonal back. In fact, the actual path traveled by the light can be shown to be γL each leg, not L. This gives us t

_{t} = 2γL/cγ = 2L/c, which gives us a ∆t = 2L/c - 2L/cγ = 2L/c (1-1/γ) ≠ 0. Ergo, Hatch's derivation of transverse and parallel length contraction does NOT produce an equal time along both tubes.

Taking it from E, this becomes t'

_{p} = 2L/c

_{p} = 2Lγ²/c; t'

_{t} = 2L/c

_{t} = 2Lγ/c, so ∆t' = γ∆t = 2Lγ/c - 2Lγ²/c = 2Lγ/c (1-1/γ), which gives us ∆t = 2L/c (1-1/γ) the same magnitude of fringe shifting.

But of course, Michelson and Morley and other experiments of its type show no such fringing. Hatch's equations make the wrong predictions. Too bad, so sad.

And the nail in this coffin comes in the form of his conclusion, which predict that "LIGO experiments should indicate failure of GRT model within 10 years." Except that LIGO detected their first gravitational wave on 14 September 2015. While five years late, it does mean that Hatch's prediction is wrong, and six have been detected since. Womp, womp.