民科C_Y_LO aka 鲁重贤已经基本被揭穿了

physicist Gerard 't Hooft

Poor Dr. Lo probably does not have a chance to win over the mainstrain physics community now. Maybe 50 years later...

Here is a response by a physics nobel price winer, an expert in GR Gerard 't Hooft regarding his work:

"Einstein's equations for gravity are incorrect,
they have no dynamical solutions, and do not imply gravitational waves as described in numerous text books."

Mr. L. makes this claim, and now he basically refers to a paper that he once managed to get published in a refereed journal. It is clear to me that the referee in question must have been inattentive. It happens more often that incorrect papers appear in refereed journals. Science is immune to that; false papers are simply being ignored, and so is this one; it is not being referred to by professional scientists (Spires mentions only one reference that is not by the author himself).
Dynamical solutions means solutions that depend non-trivially on space as well as time. Numerous of such solutions are being generated routinely in research papers, but most of them require some sort of approximation techniques. The gravitational waves emitted by binary pulsars are typical examples. The procedure to obtain these solutions, using routines to solve Einstein's equations, is well-known and described in the text books. L. notes that approximations are not exact, and exact solutions do not exist.
Approximations are of course used in many branches of physics. Some are reasonably accurate, some may be questionable. In the case of gravitational waves emitted by time-dependent massive objects, the approximations used are extremely accurate, and furthermore, any doubt can be removed by producing the next term in the approximation, which in many of these examples turns out to be completely negligible. L. does not have the mathematical abilities to do such calculations.

It so happens that also exact, analytical solutions exist that depend non-trivially on space and time. I showed L how these solutions can be obtained in meticulous detail. In order to present and discuss a special example, one can simply assume cylindrical symmetry. This symmetry assumes that the solution is invariant under the transformations z → z + a and φ → φ + b, where z is the third space coordinate and φ the angle between x and y. The dependence on the radius r in the x-y plane, and on time t may be anything. In a beautiful paper, Weber and Wheeler found the complete solution, where the physical degrees of freedom are functions of r and t that turn out to obey simple equations. Not surprisingly, one finds that the solutions take the form of Bessel functions, but even more to the point, one also finds wave packets in the r-t plane. Not many physical systems have cylindrical symmetry, but that's not the point. The point is now that these solutions contradict L's claim.

What does L say about this? "I have proven that dynamical solutions do not exist, so your solution is wrong". What is wrong about it? First, he ignores the wave packets and focuses on the plane wave solutions. These have infinite extension in space and time and represent infinite energy. That, indeed, is problematic in gravity. If the energy in a given region with linear dimensions R exceeds R in natural units, a black hole is formed so that space-time undergoes a subtle change in topology. This might arguably be called unacceptable. The problem is manifest in our explicit solutions (the non-linear integral describing the function γ diverges), and this is why it is important to use wave packets instead. The wave packages are identical to the ones in Maxwell theory, and since they represent only finite amounts of energy (per unit of length in the z direction), these solutions are indeed legitimate. I showed L how to construct explicit, analytical examples of such wave packets. For all such configurations, the γ integral converges.
Yet, L insists: "I have proven that dynamical solutions do not exist, so your solution is wrong. It violates causality". What? To me, causality means that the form of the data in the future, t > t1, is completely and unambiguously dictated by their values and, if necessary, time derivatives in the past, t = t1. So, I constructed the complete Green function for this system and showed it to Mr. L. This function gives the solution at all times, once the solution and its first time derivative is given at t = t1, which is a Cauchy surface. Causality is obeyed.

"You are a mathematician, not a good physicist", L then says. "You can't add a physical source, so your solution is not causal", L says, without explaining what that means. My guess is that what he means is that cylindrically symmetric sources "are unphysical". Indeed, you won't find many such sources in the universe, but that's totally besides the point. The point is that any kind of sources might occur in Nature, and the solution I am discussing is the one that can be constructed without any need for approximations, if the source would happen to have cylindrical symmetry. This particular case thus disproves L's claim. His complaint that the solution I wrote down explicitly is the sourceless one is strange; just like in Maxwell's theory, you can add as many cylindrically symmetric sources as you like, and indeed, this may be an instructive exercise for students. In my solutions, one might assume the sources to be at the boundary of the system. But you can also read the solution as follows: it describes how any kind of cylindrically symmetric ingoing gravitational wave converges to the centre, and smoothly bounces outward again. It is a dynamical solution disproving L. He stubbornly continues claiming that I don't understand wave packets, and illustrates this by writing down an expression that does not obey decent boundary conditions. My solutions obey the boundary conditions as required. Remember that there might be (weak) sources at the boundary. Cylindrically symmetric wave packets are generated by cylindrically symmetric sources. Unlike wave packets that are only functions of x - t , these wave packets are functions of r and t that tend to spread out in space. There is nothing wrong or unphysical about that.
"That's because you don't understand the equivalence principle, that would have implied that gravitational fields carry no energy", L continues. Now this is perhaps the real reason of his beliefs. Apparently, he fails to understand where the energy in a gravitational wave packet comes from, thinking that it is not given by Einstein's equations, a misconception that he shares with Mr. C. Due to the energy that should exist in a gravitational wave, gravity should interact with itself. Einstein's equation should have a term describing gravity's own energy. In fact, it does. This interaction is automatically included in Einstein's equations, because, indeed, the equations are non-linear, but neither L nor C appear to comprehend this.
One way to see how this works, is to split the metric gμν into a background part, goμν, for which we could take flat space-time, and a dynamical part: substitute in the Einstein-Hilbert action: gμν = goμν + g1μν . The dynamical part, g1μν , is defined to include all the ripples of whatever gravitational wave one wishes to describe. Just require that the background metric goμν obeys the gravitational equations itself; one can then remove from the Lagrangian all terms linear in g1μν. This way, one gets an action that starts out with terms quadratic in g1μν, while all its indices are connected through the background field goμν. This is because both goμν and g1μν transform as true tensors under a coordinate transformation; all terms in the expansion in powers of g1μν are therefore separately generally invariant. The stress-energy-momentum tensor can then be obtained routinely by considering infinitesimal variations of the background part, just like one does for any other type of matter field; the infinitesimal change of the total action (the space-time integral of the Lagrange density) then yields the stress-energy-momentum tensor. Of course, one finds that the dynamical part of the metric indeed carries energy and momentum, just as one expects in a gravitational field. As hydro-electric plants and the daily tides show, there's lots of energy in gravity, and this agrees perfectly with Einstein's original equations. In spite of DC calling it "utter madness", this procedure works just perfectly. L and C shout that this stress-energy-momentum tensor is a "pseudotensor". Indeed, its transformation properties are subtle, and one might wish to claim that splitting gμν in a background part and a dynamical part is "unphysical". But then, indeed, one should accept the fact that the notion of energy is observer dependent anyway. An observer who is in free fall in a gravitational field may think there's no energy to be gained from gravity.
Actually, one can define the energy density in different ways, since one has the freedom to add pure gradients to the energy density, without affecting the total integral, which represents the total energy, which is conserved. Allowing this, one might consider the Einstein tensor Gμν itself to serve as the gravitational part of the stress-energy-momentum tensor, but there would be problems with such a choice. The definition using a background metric (which produces only terms that are quadratic in the first derivatives) is much better, and there's nothing wrong with a definition of energy, stress and momentum that's frame dependent, as long as energy and momentum are conserved. In short, if one wants only first derivatives, either frame dependence or background metric dependence are inevitable.

L furthermore claims that the "established theory" uses Einstein's equivalence principle incorrectly, as if there were several versions of it. Pauli had it all wrong, according to him, which is his explanation of our "mistakes".

When all other arguments fail, L accuses me of doing "undergraduate physics". Indeed, our discussions rarely transcend that level, but there's nothing wrong with undergraduate physics. Another interesting accusation one gravitational dissenter threw at me was that I am "at the wrong side of the history of science". Well, we'll see about that.