Why Einstein was correct, when he was, in his "Relativity" theorizing, was often because hidden facets of mathematics and of the definitions used in physics allowed the ideas to be usable, even if his reasonings were fallacious. In other words, often, he was lucky.
Einstein's Special Relativity, which title for it I am told he disliked, accurately describes how information is changed as the relative velocity of a transmitter/receiver pair approaches the velocity of the carrier wave. When the carrier wave velocity is taken to be the limiting relative velocity of any two independently moving objects, the Special Relativity view leads to nonsensical conclusions.
"SR" accurately predicts that "Mass" will increase when a moving object reaches the "speed of light." However, the prediction is that the mass will go to "Infinity." There are some problems with that. Infinity." in practice, simply means that our measurement device, or our logic, fails at this point. There are two other factors, of which Einstein seems to have been unaware, which come into play here to allow his model to accurately predict a change in the situation at the speed of light.
First, even mathematics does not allow empty space. There is always an implied "dot field" or "dot matrix," so it can be expected that what ever is considered to be moving would be moving within "something."
The other factor is also mathematical. When the process of "Integration " is carried out on the momentum equation, mass times velocity equals momentum, (m x v = P) , this process can be carried out with either the mass or the velocity considered as the variable. If velocity varies, we get the usual kinetic energy equation, KE=(mv^2)/2. However, if mass be considered as the variable, with velocity constant, we obtain another energy equation, (vm^2)/2. This latter does not appear in the literature and has apparently been ignored. These two equations may be interpreted as indicating that "velocity" can change to a limit, if it hits a limit, and the "accelerating situation" continues, then, "mass" will change.
Neither the "dot-matrix" aspect of mathematics, nor the alternative energy formulation, seems to appear in any of Einstein"s work, nor anywhere else in the readily available literature. If both the dot-matrix and the alternative energy expression that appear in the mathematics are reflected in reality, we see that any moving entity within the matrix will, itself, be a part of the matrix and the mass will be a measure of the balance of the interior of the moving entity and the remainder of the matrix. As long as the translational velocity of the moving object is small with respect to the average speed of motion in the matrix, there will be little effect of the "second" energy equation. Velocity will change and the amount of disturbance dissipated by the matrix, i.e., the "Energy" will be measured quite accurately by the "Kinetic Energy" formula. There is a change in the situation when the translational velocity of the moving object starts to equal or to exceed the average of the matrix. ( In the "Universe" In which we exist, this average is known as "c," a "constant of nature" which is the "speed of light in a vacuum.") At this point there will be a significant change in the balance between the rest of the matrix and the part of the matrix within the surface of the moving entity, this surface will become changed in size and shape. The motion disturbance is no longer primarily dissipated into the matrix at large, but becomes localized at the surface of the involved entity. The balance changes, the "mass" increases. Special Relativity turns out to have been at least partially correct. The situation changes at the speed of light.
A third factor hidden in the interface between mathematics and reality apparently allows Einsteinian Space-time modelling to give quite accurate predictions. This is in the definition of "Time." In the "Space-Time World" of conventional thinking, "Time" is a reality which somehow came into being at the beginning of "Existence." Actually, time is a convenient method of keeping track of motion in sequence by a measured interval. The hidden factor that apparently makes "Space-Time" modelling work is that "Time" is always referenced to some reproducible cycle in nature. Therefore, "Time" has hidden within it not only the idea of motion, but also the idea of cyclic motion. A unit of time, a second, for instance, can therefore represent a cyclic motion, or motion in a circle, and the expression "sec^2," could stand for the motion content in the volume of a sphere! This insight leads to some interesting interpretations of some of the equations of physics, which, unfortunately, are beyond the scope of the main thrust of this paper.
The "hidden factor in Time." however, makes Space-Time Modelling and Motion in a Matrix Modelling reach much the same conclusions and, at this point, they seem to be essentially equivalent approaches. The Motion in a Matrix users being, perhaps, more cognizant of why their ideas have validity. This "circle/sphere" aspect of time hints at the idea of a spherical oscillator as a basic entity. This latter idea, has become the basis of a variant of Motion in a Matrix Modelling which could be called the "Oscillator Substance Model."
The "Oscillator Substance" model, although developed independently, echoes Max Planck's ideas of dots controlled by oscillators and is the discovery of a chemist who was once trained as an electronic technician., who has, within the last year, put together insights from both fields to suggest that there is a very simple model of everything which perhaps would have been close to the "Unified Field Theory" which Einstein spent his life trying to develop but could not. We will come back to this later. First, however, since, we are focused on where Einstein was right, or wrong, we should note the errors that probably doomed Einstein's quest for a "Unified Field" from the start.
It is highly probable that the "First Fatal Error" in Einstein's Unified Field attempt was that he "Threw out the field." That is, he assumed a void, a nothingness, for the "Field" to operate in. The "Second Fatal Error" is one that modern theorists continue to make. They try to set up a unified field theory from the "Four Fundamental Forces." The problem is that the "Four Fundamental Forces" all violate the Law of Forces, "For each and every force there is an equal and opposite force." This law of forces, if examined carefully, can be interpreted to clearly indicate that any "Force" is simply a readjustment of pressures within a "substance." The "Four Fundamental Forces" are either, in two cases (Gravitation and Electro-Magnetism) descriptions of observed phenomena, which are the result of other factors, These kind of "Forces" are known as "Fictional Forces," the best known, and best explained of which is "Centrifugal Force." The other two "Fundamental Forces," the "Strong and Weak Nuclear Forces" appear to be simply imaginative explanations which arise as justification for the idea that neutrons exist, as such, in atomic nuclei. A much simpler explanation appears if one considers atomic nuclei to be electron-proton aggregates in which a neutron has, at the best, potential existence. Einstein's frustration was apparently caused by his operating on sets of erroneous ideas.
In the next couple of paragraphs will appear a statement, which Einstein could have published, a logical outgrowth of Planck's ideas, Which might have kept us from almost a century of what this writer considers "semi-mystical nonsense" in scientific theory.
"Let us assume as a working hypothesis that there exists a 'dot matrix' of separable oscillators. These. in turn are collected to form a 'substance' at its 'triple-point,' of larger separable oscillator entities capable of correlating motion and of separation into the electron-anti-electron set and distortion into neutrona." Amplifications of the ideas in this statement, and corollaries, can give explanations for electrons, protons, the expanding universe, "The Big Bang" and almost any other phenomenon to which it has been applied. It is this working hypothesis which has led to the explanations of "Mass" and "Energy" which have been used throughout this paper.
Why was Einstein right? When he was, it was almost as much luck as brilliance. The hidden implications of the mathematics which matched reality made the theorizing seem to fit even when the basic ideas erred. Had he gone in a different direction, following up the ideas of Max Planck, he might have reached the same basic conclusions as the "Oscillator Substance Model" which has arrived nearly a century late, and will probably be ignored.
Post Script: Although this writer finds the Oscillator Substance approach so natural and useful as to feel that it should be common knowledge, the discovery of this possible "Explanation of Everything" is only a few months old. The ideas may wait some years longer for confirmation or disproof as what information published about it, thus far, is almost exclusively on Helium.com. and the discoverer has no professional standing as a member of any research institution or group. It is sad that a young, patent clerk could not have reached these ideas in the early 1900's rather than a very elderly janitor being the discoverer a century later....
Now, if a certain "String Theorist" were to have happened to have come up with this... Oh, well, we can't have a perfect world!
Einstein was very correct to try to explain the workings of reality, it's sad that he made a few key mistakes.