GR and Brans-Dicke theory are both relativistic theories of gravitation. It is true that BD can explain the precession of perihelia. However i was referring mainly to the impossibility of explaining this precession using Newtonian mechanics.
I realize that physicists can declare any legal physics theory of gravitation to be “General Relativity” if they wish to do so. Even Newtonian mechanics is General Relativity given appropriate semantic conditions. The way a circle is an ellipse with 0 eccentricity any physics theory is General Relativity with a suitably chosen X = Y condition.
1. The difference between GR and other gravitation theories is academic
The relativistic theory of gravitation (RTG) disagrees with the Einstein’s general relativity (GR) in the crucial point: it denies the total geometrization and considers the gravitation on the basis of the classical Faraday-Maxwell’s field approach.
In theoretical physics, the Brans-Dicke theory of gravitation is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein’s more popular theory of general relativity. It is an example of a scalar-tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general relativity. The gravitational constant G is not presumed to be constant but instead 1/G is replaced by a scalar field φ which can vary from place to place and with time.
In reality, the difference between these theories and General Relativity is academic. General Relativity is so flexible, malleable, plastic and semantic that it can be molded into any shape to prove anything and everything including the existence of god. Physicists use general relativity to map the mind of god into their own careers. Molding General Relativity into a specific shape to prove a physicist’s preferred doctrine is where physics at.
2. General relativity as cargo cult
When physicists talk about the relationship of General Relativity to Mercury’s perihelion they always repeat standard physics mythology without applying even the smallest amount of scientific skepticism to it. But even a superficial questioning of physicists’ interpretation of the precession of Mercury’s perihelion reveals that we are faced with a cargo cult.
In general, any statement that claims that “General Relativity predicts” a natural phenomena is a lie. Einstein’s general theory of relativity is a rubric for an immense collection of statements. Rubrics cannot make quantitative predictions. To say that “general relativity predicts correctly the perihelion of mercury” is as meaningful as saying that “English language predicts that tomorrow it will rain.” Same thing.
3. Only the final unique single formula used in the computation is relevant to the computation
As a rational scientist I ignore derivations physicists use to navigate between legal physics nodes. I look at the operational equations. Philosophical ruminations invented by physicists to rationalize their derivations or their starting point in legal physics have no practical value. I look at the formula that is used to compute astronomical quantities. An astronomical quantity is not computed with a rubric but with one single formula. In this case the formula used to compute the perihelion of Mercury is the equation of the ellipse with an extra term Delta phi. No vestiges of General Relativity remains in the equation of the ellipse after the derivation.
Equation of the ellipse:
Equation of the “general relativistic ellipse!”
The magical Delta phi:
4. Where is General Relativity in the ellipse equation?
To endow this Delta phi with general relativistic properties is charlatanism, shamanism and political doublespeak all combined into one. Or legalese.
And where is the famous spacetime of general relativistic physics in this simple equation of the ellipse with a Delta phi? No such thing exists. Physicists talk about spacetimes and fields and geodesics and so on but they eliminate them in order to obtain a practical geometric formula. Physicists tell us that they’ve discovered a fundamental thing called spacetime but when it comes to calculating astronomical motions they will eliminate their spacetime with all the other philosophical furniture they’ve ascribe to nature.
To repeat: physicists will lie through their teeth to defend their faith. In a professional sense, a physicist is a combination of a politician, a cardinal and a lawyer combined into one! The common characteristic of these professionals is that they are all master wordsmiths using semantics to prove their ideology. Mathematical semantics used by physicists is no different than prose semantics used by the others. This fact can be gleaned from the ugliness of the theories designed by physicists. And human knowledge is entrusted to these professional bureaucrats.
I realize that physicists have the authority to define the equation of the ellipse as a relativistic equation. There is nothing to be done about this at this point because we don’t know to whom to transfer physicists’ illegitimate authority on human reason. Yes, professional physicists will call the geometric equation of the ellipse a general relativistic equation because they added their own constants to it and there is absolutely nothing you can do about it.
Might is right. This is true in politics and also in physics.
Physicists have the monopoly on human reason and they use their monopoly to prove their dogma. Physicists are the Doctors of Philosophy who trace their ancestry to the Medieval Doctors of Philosophy against whom a Scientific Revolution was necessary to emancipate human reason from their monopoly.
Let’s look at how physicists obtain the equation of the ellipse from Einstein’s equations.
5. Derivation of the relativistic ellipse for the purpose of saving Mercury’s perihelion
As usual physicists start by writing down a piece of legal physics, in this case, the legal version of non-linear Einstein’s equations. After displaying Einstein’s authority prominently physicists start to eliminate one by one any term, concept or principle that they do not like; pick and choose solutions; cherry pick spacetimes, and add new terms as necessary. All legally, of course, everything is done according to the book.
In physics, the science of physical semantics, non-linear equals linear. In physics, a non-linear equation is simultaneously a linear equation. So these semantic wordsmiths start by writing non-linear equations and then say “let’s assume that our non-linear equations are linear” and work in the “weak field approximation” which is the semantic justification of the principle of equivalence for linearity. The relativistic ellipse equation is built upon many ad hoc but legal hidden assumptions. It is a piece of polemical semantics.
So after a long string of legal assumptions including linearity, spherical symmetry of Schwartzchild and what not, physicists eliminate all of the functionality of Einstein equations and find the ellipse equation with an ad hoc term Delta phi. The ellipse equation is to Einstein’s equation what a bicycle wheel attached to a New York light pole is to a bicycle. Yet, physicists still claim general relativity saves the perihelion because physicists stripped Einstein equations into the ellipse equation.
6. Same formula was derived by Gerber before Einstein
The same equation associated with Einstein’s name that saves the precession of Mercury’s perihelion was found by Gerber prior to Einstein. Einstein claimed that he never heard of Gerber’s solution. So here we have a formula derived from totally nonrelativistic assumptions by another German physicist and dismissed by Einstein and subsequent physicists because Einstein was on the first page of the New York Times but Gerber was not. This is how physics works.
Charlatanism? Yes. But this is just the tip of the iceberg.
7. Le Verrier and Newtonian mechanics
Physics propaganda claims that
1) Nineteenth century French astronomer Le Verrier could not predict Mercury’s small anomalous motion with Newtonian mechanics and
2) Einstein discovered an equation with his miraculous General Relativity and saved Mercury’s precession.
This story of Einstein explaining Mercury’s unexplained precession is mythology. Or fraud. Because we cannot prove the opposite no matter how strong our case is.
Let’s look at what Le Verrier actually wrote. Here’s his theory of Mercury’s motion. What do you see? I see that Le Verrier is not using Newtonian mechanics to model Mercury’s motion. He is just using standard practical astronomy methods to fit observations to a trigonometric model. That’s TRIGONOMETRY. I realize that physicists have the authority to read TRIGONOMETRY as NEWTONIAN MECHANICS but I can’t do anything about that. (Trigonometrical dynamics was invented by Newton himself.) The historical fact is that Le Verrier is not using Newtonian F = GMm/r^2 as physicists assert to compute the precession of Mercury’s orbit. No. He is just fitting observations to trigonometric expansions.
So what does this mean? It means that the cargo cult physics assertion that Einstein’s General Relativity explained something that Newtonian mechanics could not explain is wrong.
Einstein added an ad hoc term to the equation of the ellipse and pretended to derive it from his philosophical principles later to be sanctified under the rubric of General Relativity.
8. Physics is a secular religion
All this proves that physics is a secular religion. Physicists use semantic methods to manipulate mathematical symbols to prove their dogma. General relativistic explanation of the precession of the perihelion of Mercury proves this fact.
As mentioned above, Alberto wrote that there are alternative theories that save the observations equally well. There are alternative theories, yes, and also observations are saved best by the usual method of trigonometric expansions. So why do physicists attribute the perihelion of Mercury issue to General Relativity while there are many other ways to save the same observation more precisely? Because they are the faithful with authority to define. And that’s a dangerous combination.
Mercury’s perihelion is an astronomical issue that can be solved by adding an ad hoc term to Kepler’s rule. And this is what Einstein did.
The fact is that there are trigonometric astronomical methods that save Mercury’s perihelion with smallest residuals that the simplistic ellipse equation cannot match. The general relativistic ellipse equation is a physics textbook trope that will be repeated for ever but it has no practical value.
The more I study methods of physics the more it looks like a legal dogma defended blindly and fanatically by physicists. This is the state of science in the 21st century. State of physics rather, not science.
But of course physicists have the authority to save anything by defining new semantics. Physicists will simply say that the arguments above are historical arguments, and that they do physics, not history and they now have new methods to save the perihelion of mercury.
I, as a physicist, am mainly interested in understanding and explaining how physics works. So what mainly interests me is physics and not the history of physics.
Legal physics says that Mercury’s precession of the perihelion is saved by Einstein’s General Relativity. Any statement to the contrary is wrong by definition. No amount of criticism will ever change physicists’ ownership of the perihelion of mercury.
A perihelion of Mercury problem no longer exists in practice. NASA fits orbits into precise astronomical tables with numerical integration but physicists will perpetuate this mythology to eternity because it has become a bureaucratic habit.