As long as humans have been trying to understand the laws of objective reality, they have been proposing theories. In contrast to the well-known quantum theory, the most fundamental theory of matter currently available, Laplace's demon and Einstein's Weltformel are related more widely at least by standing out against the indeterminacy as stipulated by today’s quantum theory. Randomness as such does not exclude a deterministic relationship between cause and effect, since every random event has its own cause. The purpose of this publication is to provide a satisfactory description of the microstructure of space-time by mathematising the deterministic relationship between cause and effect at quantum level in the form of a mathematical formula of the causal relationship k.
As long as humans have been trying to understand the laws of objective reality, they have been proposing theories. In contrast to the well-known quantum theory, the most fundamental theory of matter currently available, Laplace's demon and Einstein's Weltformel are related more widely at least by standing out against the indeterminacy as stipulated by today’s quantum theory. Randomness as such does not exclude a deterministic relationship between cause and effect, since every random event has its own cause. The purpose of this publication is to provide a satisfactory description of the microstructure of space-time by mathematising the deterministic relationship between cause and effect at quantum level in the form of a mathematical formula of the causal relationship k.
Abstract—The deterministic relationship between cause and effect is deeply connected with our understanding of the physical sciences and their explanatory ambitions. Though progress is being made, the lack of theoretical predictions and experiments in quantum gravity makes it difficult to use empirical evidence to justify a theory of causality at quantum level in normal circumstances, i. e. by predicting the value of a well-confirmed experimental result. For a variety of reasons, the problem of the deterministic relationship between cause and effect is related to basic problems of physics as such. Despite the common belief, it is a remarkable fact that a theory of causality should be consistent with a theory of everything and is because of this linked to problems of a theory of everything. Thus far, solving the problem of causality will help us to solve the problems of the theory of everything (at quantum level).
The deterministic relationship between cause and effect is deeply connected with our understanding of the physical sciences and their explanatory ambitions.Though progress is being made, the lack of theoretical predictions and experiments in quantum gravity makes it difficult to use empirical evidence to justify a theory of causality at quantum level in normal circumstances, i. e. by predicting the value of a well-confirmed experimental result.For a variety of reasons, the problem of the deterministic relationship between cause and effect is related to basic problems of physics as such.Despite the common belief, it is a remarkable fact that a theory of causality should be consistent with a theory of everything and is because of this linked to problems of a theory of everything.Thus far, solving the problem of causality will help us to solve the problems of the theory of everything (at quantum level).
In general, a physical theory is based on some fundamental principles concerning space, time, matter, and the laws prescribing how matter is distributed in space and how it evolves in time, and even how spacetime itself changes in response to the changes of matter. The spectrum of the known theories is very diverse, since they are based on different assumptions. Some theories assume that space and time are totally independent, some that they are warped in a continuum named "spacetime", and some even that there are more dimensions than the usual 3+1. Most theories consider that space and time are continuous, but many recent theories consider them to be discrete. Most dynamical laws of fundamental Physics are deterministic, but apparently Quantum Mechanics shows that they may have an indeterministic component. Despite these distinctions between various theories, our intuition and experience tells us that they have a lot in common. In this paper I will try to capture the common features in a single mathematical structure. This is not a Theory of Everything, but only a mathematical structure which is common to most physical theories known so far. We will see that these theories can be obtained as particular cases of this structure, which I will call "world". In particular, the worlds described by the Classical Mechanics, the Theory of Relativity and the Quantum Mechanics are examples of worlds according to this definition, but also some theories attempting to unify gravity and QM, like String Theory. The purpose of this distillation is to provide a mathematical common background to both physical and metaphysical discussions about the various theories of the World.
In a recent number of Blackfriars (July, 1949) Dr A. W. Gledhill has discussed very competently some aspects of the statistical method as used in modern physics. He has tried to show there ‘that modern physical theory does not contradict the principle of causality’. Having made a study of this subject over quite a number of years, the writer, while agreeing with some of Dr Gledhill’s conclusions, feels nevertheless that there are a few points which have not been covered as adequately as the importance of the subject for modern philosophy seems to warrant. In order to understand the controversy about the validity or non-validity of the principle of causality, which has been initiated by Heisenberg’s uncertainty principle, it is necessary to realise, first of all, that when a physicist speaks about causality, he usually does not mean the same thing as a scholastic philosopher. In scholastic philosophy one distinguishes different kinds of causes, such as the material, the efficient, the final, as well as the formal and exemplary causes. The classical physicist, on the other hand, since the time of Galileo, admits only efficient causes. Let us therefore give a brief sketch of the development of this concept of scientific causality and show the reasons for this limitation. The purpose of a scientific theory is the prediction of events among the natural objects which form the field of enquiry of the particular science concerned. Evidently, the more certain the prediction, the better the theory on which it is based.
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Every vertex of the magic cube of physics discussed so far introduced a major element in the development of physics and the whole of science. Mechanics introduced the basic concept of equations of motion, or time-evolution of a physical system given certain initial condition and the associated idea of determinism, even with its generalization in the form of chaos, the dependence of the outcomes of the temporal evolution on the initial conditions. These concepts taken for many particles, or elements of a physical system, led to the probabilistic description of many particle systems, in the realm of statistical physics and thermodynamics, whereby the averages over time of various observable quantities were related to the ensemble averages, that involve classical, so-called Kolmogorov, probability measures, at least for certain “equilibrium” situations. The second law of thermodynamics introduced the concept of entropy and its probabilistic increase, the first truly emergent, probabilistic law in physics (temperature and pressure, being other emergent quantities, apart from entropy, the measure of disorder of a statistical system). In the context of Newtonian gravity, one gets, at least in retrospect the geometric description of gravity in non-relativistic, Galilean spacetime. Galilean relativity, based on the asymmetric mixing of space and time, with the absolute, universal time, true for all observers, gets generalized in special theory of relativity to observer dependent space and observer dependent time, viewed as “slices” of a new concept of spacetime, with the new concept of causal structure, that distinguish timelike, null and spacelike events. This in turn is made into a full dynamical geometric structure of spacetime with a relativistic description of gravity stemming from curvature of spacetime, and a dynamical causal structure, tied to gravity. In our next story, the story of quantum theory, we will encounter fundamental, intrinsic probabilities, that can interfere, unlike the classical probabilities of statistical thermodynamics, and which are consistent with equations of motion of individual elements, and not, as in statistical thermodynamics, with temporal averages over the time evolution of many elements. This is the big new lesson of quantum theory, that transcends the lessons of classical spacetime physics.