A PHILOSOPHY OF THE FOUR-DIMENSIONAL SPACE-TIME
The Worldview of Relative Simultaneity (MURAYAMA Akira)
CHAPTER I
Relativity and Four-dimensional spacetime
[The Latter half] ---- Philosophical Examination ----8. Problems in the Quantum Theory
(1) The Establishment Process of Quantum Mechanics
This section outlines how quantum mechanics was established. From the late nineteenth to the early twentieth century, the "continuity myth" collapsed in the physical world. What emerged was that an infinitely and evenly separable model used in calculus could not be applied to existing substances and energy. Substances involve basic units, such as atoms and molecules. Studies on black body radiation demonstrated that even energy showed discrete values. Furthermore, studies on the photoelectric and Compton effects and the discovery of electronic diffraction phenomenon demonstrated that micro-substances generally involved wave and particle natures were incompatible with macroscopic conceptual models.
In the early twentieth century, studies on atomic internal structures were advanced and the atomic model in which electrons move discontinuously was invented on the basis of wave equation. In addition, observations of microscopic objects presented the Heisenberg uncertainty principle. This principle argues that in particular combinations, such as positions and momentum or time and energy, when you excessively focus on the precision of one factor, you have to de-emphasize the accuracy of the other factor.
There were several conceivable ways to describe microscopic phenomena, but the Schrödinger wave function was adopted as the most common model. The double-slit experiment on electronic interference typically represented the wave nature of micro-particles. It is widely known that waves cause diffraction phenomenon when they go through latticed walls with shorter grid interval than their lengths, which leads to interference reactions, and check patterns are observed. When electrons were projected upon the micro-double-slits, check patterns were also observed.
Waves in a macro world are caused by the aggregation of many particles. In accordance with this reasoning, it was unthinkable that waves would occur only by a single electron. To examine this hypothesis, a test was conducted to project electrons upon the double slits one by one. Then, check patterns were obtained by superimposing points at which each electron was observed. This mysterious result suggests that if only a single electron caused interference reactions with many other imaginary electrons that exist only as possibility to be projected under the same condition. However, when it was examined which slit the electron went through, the check patterns did not appear.
Max Born (1882-1970) gave the Schrödinger wave equation a certain probability-based interpretation. As long as electrons are not observed, they propagate as the state of a group of complex numbers. These groups can be superposed and realize wave nature. A positive real number can be obtained by multiplying those values of complex-number of the state by complex conjugate values. This represents the probability of electrons being observed as established existences. Micro-particles like electrons are neither just ordinary particles nor waves in which a certain medium oscillates. They are imaginary pictures around which the contrasting density of the state (probability distribution density) corresponding to their existing probability vaguely expands. Strictly speaking, to approach this state, you need to consider an infinite dimensional abstract Hilbert space that is compatible with its infinite degree of freedom of the object. This is beyond the scope of human imagination. As noted above, with regard to individual phenomena, quantum mechanics could just predict only their probability. However, for the space-time distribution of probability, quantum mechanics was completely established as a theoretical system for predicting it on the basis of determinism, for example, by solving differential equations under particular conditions.
It is only probability now that connects the theory of quantum mechanics with its actual observed facts. It is the probability distribution of position and time states for individual particles that the theory can make exact predictions. However, now this theoretical development can account for many mysteries in conventional dynamics, which have been confirmed in the micro world, such as why only discrete energy values were obtained. In addition, the inevitability of physical laws established in a conventional macro world has been interpreted as an almost 100 percent probability (high probability), which is achieved by regarding innumerable cases that can be distinguished from a micro perspective as being in the same state that cannot be distinguished from the macro perspective.
Subsequently, quantum mechanics was modified by Paul Dirac (1902-1984) and other physicists to make it consistent with the special theory of relativity, and basic theories were almost completed as the quantum theory of fields. In accordance with this reasoning, the existence of antimatters with the same mass and spins but reverse charges was predicted. The representative instance is positive electron, which is antimatter of electron. Afterward, particle physics verified the existence of antimatters through experiments.
Throughout the twentieth century quantum mechanics had an enormous impact on various areas of natural science beyond physics including chemistry and biology and remarkably contributed to a wide variety of applied fields. Quantum mechanics supports electronics and many other endeavors in modern civilization.