Physical Mathematics

In this article we introduce a new approach for obtaining Lorentz transformations. It is based on tracking light that is emitted from an object that reaches two stationary observers who are in motion relative to one other. This new approach, based on known physical principles and not on an axiom, makes the Lorentz transformations more understandable. In addition, it reveals the meaning of the constancy of the speed of light as well as the meaning of the results of the Special Theory of Relativity. The new approach also reveals that Lorentz transformations for an object found at a general point (x',y') at the coordinate system, cannot be achieved as a superposition of the transformations of the coordinates (x',0) and (0,y'). In this case we need to take into account the time delay between cases. Light aberration, the Doppler effect, time dilation and length contraction are considered within the new approach of obtaining Lorentz transformations.

What does the term “Infinity” mean? There are mathematical, physical and metaphysical definitions of the concept of limitlessness. This study will focus on the scripting of the three philosophical foundations of mathematicsformalism, intuitionism and logicism-in set theory.

Examples will also be provided of the concept of infinity for these three schools of thought. However, none of them cannot prove whether there is an infinite set or the existence of infinity. It forms the foundational crisis of mathematics. Further elaboration on these schools of philosophy leads to the ideas of actual, potential and absolute boundlessness. These correspond to three basic definitions of infinity. These will correspond to Roger Penrose’s Three World Philosophy and hence implies a quantum mind. By employing those special “rational proof” and set theory in this thesis, one may even build a real thinking computer. Indeed, by using Basic Metaphor Infinity, cognitive mechanisms such as conceptual metaphors and aspects, one can appreciate the transfinite cardinals’ beauty fully. This implies the portraiture for endless is anthropomorphic. In other words, because there is a connection between art and mathematics through infinity, one can enjoy the elegance of boundlessness. In the essence, this is what mathematics is: the science of researching the limitless. To conclude, the thinking machine’s behind in this paper is very beautiful.

The fluid space-times carrying a W1 -curvature tensor are studied. It is proved that the energy momentum tensor of the space-time is of Codazzi type if and only if the W1 -curvature tensor is divergence free. We also show that the pseudo Ricci symmetric space-time with divergence free W1 -curvature tensor is a GRW space-time. A necessary and sufficient condition for a perfect fluid space-time to be a GRW space-time is given.