Earlier, we had presented \cite{heuristic} heuristic arguments to show that a {\em natural unification} of the ideas of the quantum theory and those underlying the general principle of relativity is achievable by way of the measure theory and the theory of dynamical systems. Here, in Part I, we provide the complete physical foundations for this, to be called, the {\em Universal Theory of Relativity}. Newton's theory and the special theory of relativity arise, situationally, in this Universal Relativity. Explanations of quantum indeterminacy are also shown to arise in it. Part II provides its mathematical foundations. One experimental test is also discussed before concluding remarks.
Earlier, we had presented \cite{heuristic} heuristic arguments to show that a {\em natural unification} of the ideas of the quantum theory and those underlying the general principle of relativity is achievable by way of the measure theory and the theory of dynamical systems. Here, in Part I, we provide the complete physical foundations for this, to be called, the {\em Universal Theory of Relativity}. Newton's theory and the special theory of relativity arise, situationally, in this Universal Relativity. Explanations of quantum indeterminacy are also shown to arise in it. Part II provides its mathematical foundations. One experimental test is also discussed before concluding remarks.
The purpose of this article is to outline a framework of concepts and principles to combine quantum mechanics and general relativity so that time and measurement (reduction) are present as integral parts of the basic foundations. First, the problem of time in quantum gravity and the measurement problem in quantum mechanics are briefly reviewed and the popular proposals to tackle these two problems are briefly discussed. Next, on the already known foundations of quantum mechanics, a framework of principles of dynamics is built: 1) Self-Time Evolution - Newtons first law is reinterpreted to define time, 2) Local Measurement by Local Reduction - Quantum diffusion theory is adapted, and 3) Global Evolution by Global Reduction. Ideas on how to apply the framework to study quantum general relativistic physics are discussed. Further, more general and modified forms of some of these principles are also discussed. The theoretical elements in the framework to be made concrete by further theoretical and experimental investigations are listed.
This paper takes a look at the two cornerstones of modern physics--Quantum Mechanics and The Theory of Relativity (Both Special and General). The differences and similarities for the two subjects are presented. More of their differences and similarities will emerge with new developments in physics. One can't rule out the possibility of the two being unified into one one fine day. That will herald another triumphant moment in physics. Introduction In 1905, Albert Einstein at the age of twenty-six formulated single-handedly, among others, the Theory of Special Relativity together with his other seminal papers on photoelectricity, Brownian motions of atoms and molecular dimensions. The year has been universally declared the Miraculous Year [1]. Ten years later, he came up with the theory of General Relativity--a new and revolutionary framework on gravity. Meanwhile in Europe a group of young physicists played pivotal role in the birth of Quantum Mechanics. Many of them went on to win Nobel prizes for their monumental contributions. Einstein also won the coveted prize not for Relativity but ironically for Photoelectric Effect. Irony has been part of physics in its history. Relativity with its weird 'Twin Paradox', constancy of the speed of light and the interchangebility between mass and energy (E=[mc.sup.2]) enthralls the public and scientists alike. It provides a way to measure particle masses [2]. The Quantum Theory has its fair share of weirdness and bewilderment. Both Quantum Mechanics and the Theory of Relativity bring forth new ideas in human thoughts. They are among Joanne Baker's 50 physics ideas [3]. Quantum Mechanics and the Theory of Relativity The quantum world where counterintuition reigns supreme is couched in uncertainty as epitomised by Heisenberg's uncertainty principle. Things do not behave in a deterministic way as enshrined and expected in classical Newtonian physics. The microscopic world of the electrons was dictated by randomness and indeterminacy. Albert Einstein was appalled by such dictates that he famously declared: 'God does not play dice with the universe.' The famous Danish physicist Neils Bohr sprang to his feet by saying: 'Stop telling God what to do with his dice.' The sparring between the two stalwarts in physics is legendary. According to Trefil [4], there are a couple of things that need to be said about the uncertainty principle: it does not imply that we cannot know either the position or the velocity of a particle, and it does not require the presence of a conscious mind. Marcus Chown [5] wraps up by saying 'The bitter irony, not lost on Einstein, was that he was the one who, by postulating the existence of the photon, had inadvertently set loose the genie of randomness of physics. The two theories of relativity by Einstein are not couched in randomness however. According to Smoot [6], both implied a radically new cosmology. Many people are of the opinion that with Einstein's theory of relativity, old classical physics is no more in vogue. According to Angier [7], Albert Einstein did not prove that Isaac Newton was wrong. Instead, he showed that Newton's theories of motion and gravity were incomplete, and that new equations were needed to explain the behavior of objects under extreme circumstances, such as when tiny particles travel at or near the speed of light. …
The notions of time in the theories of Newton and Einstein are reviewed so that the difficulty which impedes the unification of quantum mechanics (QM) and general relativity (GR) is clarified. It is seen that GR by itself contains an intrinsic difficulty relating to the definition of local clocks, as well as that GR still requires a kind of absolute that can serve as an objective reference standard. We present a new understanding of time, which gives a consistent definition of a local time associated with each local system in a quantum mechanical way, so that it serves the requirements of both GR as well as QM. As a consequence, QM and GR are reconciled while preserving the current mathematical formulations of both theories.
Can our extremely complicated world be explained, starting from simple conditions and laws? Such questions easily become metaphysical, but at the same time they have historically served science well by promoting new and fruitful ideas. Of particular interest in this paper is the unification of general relativity and quantum mechanics. It is suggested that a way to find a common basis for these theories could be to view them both as stochastic theories which, among all possible macroscopic developments, promote the simplest ones. But with the difference that general relativity uses real probabilities, whereas quantum mechanics uses complex weights. In a certain sense this approach goes back to the Principle of Least Action, although the perspective on this principle in the present paper is different from the one which is commonly used in contemporary physics. It is also suggested that a more general principle, which applies to both theories and which is beyond both stationarity and minimizing, could give us a better starting point for the unification.
IntroductionPhysics has always had several different domains of application in on-going development, and physicists have always striven for unification among its different domains.Unification is usually achieved through development of so-called 'covering theories'.In the nineteenth century, the stunning example was Maxwell's Electrodynamics (MED), which unified electricity and magnetism as one domain of theory.Another major domain of theory then present was Newton's Mechanics (NM), which in the eighteenth century had really launched modern physics as a mathematical discipline.At the turn of the twentieth century, NM and MED were well in place, and were fulfilling many technologically important requirements.But there seemed to be an incompatibility between them.The problem concerned their invariance with respect to choice of reference frame: NM exhibited invariance if the allowed reference frames were all connected through Galilean transformations, whereas MED exhibited invariance if the allowed reference frames were all connected through Lorentz transformations.It looked as though one of these two theories must be more nearly correct than the other, but it was not clear which one was the better one.That problem seemed resolved with the advent of Einstein's Special Relativity Theory (SRT).SRT was believed to capture the true meaning of MED concerning the behavior of light signals, and SRT was certainly an endorsement of Lorentz transformation, so SRT was believed to offer the one possible revision of NM that could make mechanics fully consistent with MED.But meanwhile, new phenomena were being discovered at the micro scale of physics, and they often seemed inexplicable with any known theory, whether NM, SRT, or MED.These were phenomena suggesting quantization of light, quantized atomic states, atomic, molecular and crystal structures, radioactivity, etc.So at almost the same time as one problem seemed to be resolved, other problems were emerging.Since the earlier situation between NM and MED had demanded that Physics allow two seemingly discordant theories to co-exist until some good argument could replace one of them, the situation then presented by the new phenomena being discovered naturally invited the development of another potentially discordant theory: Quantum Mechanics (QM).The discovery of the photoelectric effect, and the introduction of the idea of the photon, initiated QM.Almost immediately, QM was developed to handle the Hydrogen atom, and the ground state thereof, the stability of which was thought to be impossible with MED.www.intechopen.