The Oneness and the Unified Theory of Fundamental Interactions

The European nuclear research centre CERN is planning to build a new particle accelerator. In a ring-shaped tunnel 500 m below Lake Geneva and with a circumference of 100 km, the physicists want to study the interactions of electrons, positrons or protons at far higher energies than before. The particle accelerator LHC, which exists today, was used to test the standard theory, i.e. the unified theory of the so-called strong, weak and electromagnetic interaction. The result was a view of our nature on a length scale of about 10-15 m, in which on the one hand there was a good agreement between theory and experiment, but on the other hand new questions arose which the theory could not answer and for which the experiments so far could not yet give any indication. One would therefore have to look “more closely”, with even higher resolution, i.e. let the particles collide with each other with even higher energy, so that one can uncover a further substructure in today’s picture of nature through the analysis of the decay products.

The plan for such an accelerator represents a completely new dimension in the search for a unified theory for all fundamental interactions of nature. The search seems to be a project of the more recent history of modern physics, but basically it is a human project that was already started 2,500 years ago, by the “pre-Socratics”, those ancient Greek philosophers who mainly worked in the time before Socrates, more precisely in the years from -600 to -400.

People probably always felt the urge to reduce the complexity of their impressions of the world and thus always tried to make a sense of the world. At first this happened in the form of stories about the work of gods and spirits who ruled the world and people. We know such myths from the Gilgamesh epic or from the works of Homer and Hesiod. Thales of Miletus (ca. -624 to ca. -555) is regarded as the first of the pre-Socratics, as the first philosopher of Greek antiquity at all, who went a completely different way to explain the world. In the stories “about God and the world” reasons appeared now: For statements about the world as a whole, one now used everyday observations. The gods were no longer superhumans who could switch and rule as they wished. One could even think of them quite differently than in human categories, and one actually no longer needed their stories. Now there counted arguments with which one could justify his statements.

Two fundamental Questions

One could also call the pre-Socratics the first physicists, even the first cosmologists, because with their questions they went straight to the “whole”, as today only the theologians hold it in this directness. Nevertheless, they were “physicists” because they invoked nature (ἡ φύσις = physis, gr.: nature) in their justifications and no longer put forward mythical ideas.

Two questions crystallized, which became decisive for the whole history of the mind. The first question arose from the feeling that there must be something “behind” the plurality of things that we discover in our everyday world, something of which this “variety” consists or has arisen. The pre-Socratics called it the “primordial matter” of all things or the “being”. In the world in which we can live and gain experience, however, “being” shows itself as the “plurality”.  Hence there are always two levels of being, the “higher”, where being is a “oneness”, and the “lower”, where people live and encounter the “many”, the plurality. But the “oneness” could also be a “principle” or that which was called “God” in religions.

The question then was: What is the primordial matter, what does it have to do with the matter that we perceive with our senses? Or: What is the basic principle, the underlying.

A second question then inevitably arises: What can I even know about it? Or: How can I gain knowledge about it?

The first question concerns the nature of the world, the second our cognitive faculties. These are questions that still arise today.

In the first question we now see the connection with the physicists’ search for a unified theory of all the fundamental forces of nature. In this theory there should then be only one fundamental force, from which all other forces such as the gravitational force and the forces of the standard theory mentioned at the beginning result under certain circumstances. Obviously, people have made some progress in the question of the “oneness”, although the question is now posed on a completely different level, namely not on a “material” but on an “intellectual” level. One has good hope to find sometime the “one” theory which contains the “many” other theories about the individual fundamental forces.

This hope can indeed be had today because concrete progress has been made on the second question, even in ancient Greece. There mathematics came to its first bloom and it had been learned that mathematical conclusions were “irrefutable”. In the field of mathematics one can therefore gain reliable knowledge. This led to the search for necessary rules of inference outside mathematics. Aristotle (-384 to -322), in a sense an early “post-Socratic”, was probably the first to formulate rules of inference of this kind and thus to establish a doctrine of the laws of thought, a logic.

“Logical” for us today, however, in colloquial language stands for something like this that goes without saying in the context of our world of experience and thought. One sometimes speaks of women’s or men’s logic. We often hear “It’s logical – isn’t it?” when a friend tells us about a decision that he has made and found to be highly reasonable because it obviously corresponded to his goals or principles. However, this has only a limited connection with real logic. We will see this in detail in later blog posts.

Logos

The term “logic” developed in ancient Greece from the word “logos”. This initially meant something like “word” or “speech”.  In the context of speech, however, the scope of meaning expanded to include reasonable speech and that which makes a speech intelligible and convincing: Conclusions which prove to be “necessary”, irrefutable, i.e. which cannot be rejected, if one does not want to be regarded as unreasonable. “logos” thus stood for understanding and reason, and one discovered that one could find rules for such reasonable reasoning.

Of course, this development could only exist in a community in which much had to be said and discussed in public. This was the case in the early democracies of ancient Greece. Rhetorical arts and dialectical skills offered a great advantage in court and in political assemblies, and so-called sophists taught these arts. At some point one had to realize that argumentations could be incontestable, others not; yet others had to be seen as attempts at persuasion or as truly misleading.

Thus “logos” initially stood for logically respected thinking and the doctrine for this thinking became “logic”.

But the term “logos” itself made a career as well, with the second question mentioned above, to what extent we as humans can have access to the “higher level”. Of course, the “logos” had to play a role, understood as reason or cognitive ability. What role exactly this should play differs from the various philosophical schools that had emerged in the course of history. But the “logos” became the cause of a cognitive capacity, could even become a being of its own, a mediator between the two levels and later also played an important role in Christianity. But that is another story.

On this occasion it should only be mentioned that the role of the “logos” as mediator between two levels is also today found in the concept of “logistics”, a field of knowledge in which it is about the transport of goods, people and information. And it is no coincidence that a large German logistics company is called “Hermes”, after the messenger of the gods who, in Greek mythology, passed on the decisions of Zeus, the father of the gods.

Looking back and with this term “logos” in our luggage, we can say that with the pre-Socratics the logos came into a world in which until then myth had explained the world to mankind. This new line of thought was to become stronger and stronger in the course of the intellectual history, and on many further questions it also competed with the myth. This led to a division of philosophy into two fundamentally different schools of thought: logos versus myth. The logos only gained ground in thrusts, with long periods of strong predominance of myth in between. Today – in the globalized world as well as within individual cultures – we are dealing with a variety of intellectual situations in which the relationship between logos and myth is very different, and it is not clear which relationship could be particularly beneficial for humanity.

I will not report here on the struggle between myth and logos for supremacy in people’s minds, however exciting it may be. We will focus here on logic, which in another way is also very exciting and will lead us to the most modern developments in physics, artificial intelligence and cognitive science.

Logic

Therefore, “logic” is a knowledge of how to use reason, an answer to the question of what rigour in thinking actually means. Aristotle and representatives of the Stoa took the first steps to answer this question. They discovered in the first place that there are rules of inference in argumentation and that they can be very different in terms of convincing power. In particular, they discussed how to construct irrefutable rules of inference.

For over 2,000 years it was believed that there was no need to add anything to these logical doctrine until the philosophers and mathematicians Frege, Whitehead and Russel developed a mathematical logic at the end of the 19th century which was more general and meaningful, and which seemed to have been made just for digitalisation. Not to forget, however, Gottfried Wilhelm Leibniz, who in the 17th century had already foreseen important aspects of modern logic such as the necessity of a formal language and the meaning of a calculus at the level of this language.

With modern mathematical logic, logic has become a science in its own right.  Today is pursued at faculties of mathematics or computer science. It has, in a sense, emigrated from philosophy, as mathematics did already in ancient Greece.

Logic and Mathematics

Logic had actually been in people’s minds even before the pre-Socratics, in the form of a rudimentary form of mathematics. In the early communities there was already trade and administration, so one had to be able to count, measure, add, multiply and divide, and one will have already known that this kind of thinking leads to indisputable results. In my book ” Denken in Strukturen und seine Geschichte – Von der Kraft des mathematischen Beweises” (“Thinking in Structures and its History – The Power of Mathematical Proof”) I reported, among other things, on such first mathematical approaches in early Egypt and Mesopotamia and also on how this mathematics also reached Greek culture through trade.

The Greeks then brought mathematics to its first bloom. The preoccupation with mathematics and above all the discovery of mathematical proof may have inspired Aristotle to develop logic. Only much later should one understand the connection between logic and mathematics.

Mathematics and Physics in modern Times

During the Renaissance, when the scholars of Europe got to know and receive the culture and science of the ancient Greeks, the logos entered a phase of accelerated growth. Galileo Galilei discovered a “new science” in which mathematics, including logic, was the language of communication. He demonstrated the power of this new science in a phenomenon that is highly unimpressive for us today, the fall of a sphere. Two generations later, Isaac Newton developed a general theory of motion within the framework of this new science and also showed how motions in the sky and on earth can be calculated and reliably predicted under the influence of gravity. Modern physics had emerged.

In the following centuries new fundamental forces of physics were to be discovered and theories based on Newton’s theory were to be established for their effects. The idea of a unified theory always stood in the foreground, and indeed it was often possible to find a common, superordinate theory for two theories. Today we believe we know all the fundamental forces and are on the verge of a final step towards unification. The goal is a single theory for all fundamental forces. Then the programm of the pre-Socratics would have come to a conclusion in a way, however in a way that is quite different from what one could have imagined at the time.

I will deal with this important topic of our intellectual history in more detail in future blog posts.