Dear Sir,
What is meant by the equality sign? Both in physics, mathematics and metaphysics, this means we are comparing two related aspects of some objects, when by changing any parameter on the left hand side the behavior of the right hand side matches observation. If you assign the "person" to the left hand side, he being unique, A=A. If you assign the "name" to the left hand side, it being unique among names, again A=A. Where is the confusion? Your definition of metaphysics is correct, but that does not affect the outcome. There are no paradoxes in mathematics. All paradoxes are wrong description of facts, as is explained below in refuting equivalence principle:
The cornerstone of GR is the principle of equivalence. It has been generally accepted without much questioning. Equivalence is not a first principle of physics, as is often stated, but merely an ad hoc metaphysical concept designed to induce the uninitiated to imagine that gravity has magical non-local powers of infinite reach. The appeal to believe in such a miraculous form of gravity is very strong. Virtually everyone, and especially physicists, accept Equivalence as an article of faith even though it has never been positively verified by either experimental or observational physics. All of the many experiments and observations show that the equivalence of gravity and inertia simply does not exist. If we analyze the concept scientifically, we find a situation akin to the Russell's paradox of Set theory, which raises an interesting question: If S is the set of all sets which do not have themselves as a member, is S a member of itself? The general principle (discussed in our book Vaidic Theory of Numbers) is that: there cannot be many without one, meaning there cannot be a set without individual elements (example: a library - collection of books - cannot exist without individual books). In one there cannot be many, implying, there cannot be a set of one element or a set of one element is superfluous (example: a book is not a library) - they would be individual members unrelated to each other as is a necessary condition of a set. Thus, in the ultimate analysis, a collection of objects is either a set with its elements, or individual objects that are not the elements of a set.
Let us examine set theory and consider the property p(x): x does not belong to x, which means the defining property p(x) of any element x is such that it does not belong to x. Nothing appears unusual about such a property. Many sets have this property. A library [p(x)] is a collection of books. But a book is not a library [x does not belong to x]. Now, suppose this property defines the set R = {x : x does not belong to x}. It must be possible to determine if R belongs to R or R does not belong to R. However if R belongs to R, then the defining properties of R implies that R does not belong to R, which contradicts the supposition that R belongs to R. Similarly, the supposition R does not belong to R confers on R the right to be an element of R, again leading to a contradiction. The only possible conclusion is that, the property "x does not belong to x" cannot define a set. This idea is also known as the Axiom of Separation in Zermelo-Frankel set theory, which postulates that; "Objects can only be composed of other objects" or "Objects shall not contain themselves".
In order to avoid this paradox, it has to be ensured that a set is not a member of itself. It is convenient to choose a "largest" set in any given context called the universal set and confine the study to the elements of such universal set only. This set may vary in different contexts, but in a given set up, the universal set should be so specified that no occasion arises ever to digress from it. Otherwise, there is every danger of colliding with paradoxes such as the Russell's paradox. Or as it is put in the everyday language: "A man of Serville is shaved by the Barber of Serville if and only if the man does not shave himself?"
There is a similar problem in the theory of General Relativity and the principle of equivalence. Inside a spacecraft in deep space, objects behave like suspended particles in a fluid or like the asteroids in the asteroid belt. Usually, they are relatively stationary in the medium unless some other force acts upon them. This is because of the relative distribution of mass inside the spacecraft and its dimensional volume that determines the average density at each point inside the spacecraft. Further the average density of the local medium of space is factored into in this calculation. The light ray from outside can be related to the space craft only if we consider the bigger frame of reference containing both the space emitting light and the spacecraft. If the passengers could observe the scene outside the space-craft, they will notice this difference and know that the space craft is moving. In that case, the reasons for the apparent curvature will be known. If we consider outside space as a separate frame of reference unrelated to the space craft, the ray emitted by it cannot be considered inside the space craft. The emission of the ray will be restricted to those emanating from within the spacecraft. In that case, the ray will move straight inside the space craft. In either case, the description of Mr. Einstein is faulty. Thus, both SR and GR including the principles of equivalence are wrong descriptions of reality. Hence all mathematical derivatives built upon these wrong descriptions are also wrong. We will explain all so-called experimental verifications of the SR and GR by alternative mechanisms or other verifiable explanations.
Relativity is an operational concept, but not an existential concept. The equations apply to data and not to particles. When we approach a mountain from a distance, its volume appears to increase. What this means is that the visual perception of volume (scaling up of the angle of incoming radiation) changes at a particular rate. But locally, there is no such impact on the mountain. It exists as it was. The same principle applies to the perception of objects with high velocities. The changing volume is perceived at different times depending upon our relative velocity. If we move fast, it appears earlier. If we move slowly, it appears later. Our differential perception is related to changing angles of radiation and not the changing states of the object. It does not apply to locality. Einstein has also admitted this. But the Standard model treats these as absolute changes that not only change the perceptions, but change the particle also!
Regards,
basudeba
