Physical Theories: An Overview

Now that I have described how modern physics was founded by Galileo Galilei as a new science, I will follow the path of physics in the following and show how the legacy of the pre-Socratics and ancient mathematicians has borne fruit. After a decline of the ancient culture one could, after about 2000 years, revive it and reach new heights of knowledge. The fact that it took so long may has many reasons – if one can speak of reasons at all in history. However, I do not wish to take part in such considerations.

First, I want to give an overview of the theories that have been developed and established in physics over the course of time. The fact that they always had to prove themselves in competition with other theories than the “better ones” in each case was explained, for example, in (Honerkamp, 2017, p. 111ff). In the next chapters I will show what role the questions raised by the pre-Socratics have played in the development of these theories. In particular, I will discuss the development of the theories and their relationships to each other. Especially I will pursue the path along which there have always been mergers or unifications of theories. Thus, today we are only talking about two great theories and are out to recognize these two as parts of a single “theory for everything”. This would answer the most noble question of the pre-Socratics, the question of a “One”, albeit in a completely different way than one could imagine at that time.

The development and establishment of a physical theory always involved the explanation of phenomena of a certain type. We have already seen that the phenomenon of “motion” was the first theme that interested people in antiquity and again in the Renaissance. It is the most original and probably also the most general phenomenon that we know. 

We encounter the phenomenon of “light” in a similarly direct way.  So, it is no wonder that at the beginning of modern physics not only the phenomenon of motion was dealt with, but also experiments with light were carried out, as we know them from Isaac Newton, for example. A century later, people began to study other, seemingly quite different phenomena, electrical or magnetic. Finally, at the turn of the 20th century, they discovered sorts of radiation which obviously differed greatly from light rays, and among these new rays there were also different types.

The space of phenomena

In short, the history of physical theories is a history of discoveries in a “space of phenomena” where there have always been certain objects in play. In this space, one can identify large areas in which there are phenomena that seem to be so similar to each other that one might be tempted to invoke the same reason for their explanation. Thus, over time, the idea of fundamental forces acting between planets and the sun, electrons and other found or discovered objects emerged. Over time, four such interactions were distinguished: Gravitational, electromagnetic, strong and weak interaction. This distinction is still very helpful for an overview of the set of the theories developed in the 400 years since Galileo.

There are, however, two other categories in respect of which one should distinguish the theories. It is not only the interaction or the force that can be decisive for a phenomenon. This can also be the range on a length scale. Thus, phenomena can be distinguished according to the scale of length on which the phenomenon appears, whether in the world of the smallest dimensions, the largest dimensions or the middle dimensions.

Finally, an aspect will become important that has to do with our cognitive abilities, namely the question of whether we must describe the phenomenon as a complex one, namely as one in which it is not sufficient for an understanding to consider only a few objects with few important properties. Many or very many objects can represent a system that has new properties that are not inherent to the individual objects themselves, but only “emerge” through the interaction of the objects. Water, for example, has the property of being liquid. However, this does not apply to its components, the H2O molecules.

With these two characteristics, spatial size and complexity, we can already consider aspects that allow us to have an overview in the form of a landscape of phenomena. If one enters the characteristic length of some objects, which play a role in physical theories, into a coordinate system, in which this size is plotted against the complexity of the objects, then one obtains e.g. Fig.4.2.

Fig.4.2: Rough classification of certain objects according to size and complexity. Objects like planets can appear at different places, depending on how much of their properties you want to consider (R stands for order of magnitude, N for number of degrees of freedom or complexity resp.).

On this figure we can show how far we have explored the space of natural phenomena today with our physical theories. It also makes it clear that in addition to the physics of fundamental interactions, there is also a very large area of complex systems for which areas of physics such as thermodynamics or statistical mechanics, solid state physics, etc. are responsible. This should be kept in mind, even if we do not deal with it here and we mainly consider the wide range of spatial scales in the area of “simple” systems – from 10-15 to 1020 m.

The world of the middle dimensions in the range of about 10-4 to 1010 m is most accessible to us intellectually, because we ourselves, as participants of this world, can have direct experiences with it. Thus, the phenomena of this world are also the subject of the earliest physical theories; they are also called classical theories. The exploration of the space of phenomena thus started in the world of the middle dimension.

At the beginning of the 20th century, phenomena of the world’s smallest dimensions were discovered. One had to state that the concepts of the world of the middle dimensions are no longer suitable here. A completely different concept, a “quantum”, replaced the concept of a material object and gave physics on this scale the name “quantum physics”. At the same time a modern cosmology and astrophysics began to emerge. Today we hear of particularly spectacular discoveries in this field of the largest dimensions.

Classical physics, quantum physics and cosmology: this is a classification that can also be described as physics of medium, smallest and largest dimensions. Cosmology today has not yet required its own conceptual apparatus, as quantum physics does, which is why it is also added to classical physics, if one wants to emphasize the methodological aspect.

With a distinction regarding the spatial size alone one has of course not yet exhausted the space of phenomena. There are other quantities which, measured by the conditions of our world of daily experiences, can be small or large. Particularly prominent in this context is speed; but the strength of fundamental forces, in particular of gravity, will also be significant for the nature of physical theories. The landscape sketched in Fig.4.2 must therefore only be imagined as a slice from the whole space of phenomena.

The exploration of this space of phenomena resembles the exploration of our earth in the time of the great discoveries in the 16th century. One spoke thereby of the discovery of the “world”, although it were only new ranges of the planet earth, which one discovered at that time gradually. Today one knows almost every corner of the earth and “reaches for the stars”. 

Thus, one also knows all laws of nature in the world of the middle dimensions, but only on the fundamental level. The more complex the systems are in these dimensions, the less familiar they are to us today. But the more we limit ourselves to the fundamental side, the further we have advanced into the world of the smallest and also the largest dimensions.

Even if it were possible in several years or decades to establish a theory for all fundamental interactions, physics would not be at its end. In the direction of complex systems there are still many questions waiting for an answer. The transition to chemistry, biology and cognitive science will be fluent. Also, in the exploration of life and consciousness one will not be able to ignore physical conditions.

The theories of classical physics

Classical physics is dominated by three large phenomenon areas: the phenomenon of motion and the two areas in which we encounter the fundamental forces of gravity and electromagnetism, respectively.

Phenomena from these areas have been known since ancient times. “Nothing is older than motion,” we may quote Galileo once again. For the pre-Socratics, motion or non-motion always played a role, Aristotle distinguished different types of motion and formulated a first kind of theory of motion. Even in the Middle Ages there were always natural philosophers who wanted to trace the nature of motion.

Gravity was also an everyday phenomenon. With Aristotle it was a quality that made all bodies of the sublunar world strive for the centre of the world. Also, the sphericity of the earth was later explained by such a “natural striving”.

We read less about magnetic and electrical forces in early sources, but magnetic and electrical phenomena were already known in ancient times. If you rubbed an amber, it would attract dust or shreds of wool. Iron was attracted by a magnetis stone and it was discovered that splinters of such stones always rotate in a north-south direction.

The physical theories, which today explain all basic phenomena from these three phenomenon areas, are

– for motion: Newton’s and Einstein’s theory of motion,

– for gravitation: Newton’s and Einstein’s theory of gravitation,

– for electrical and magnetic phenomena: Maxwell’s theory of electromagnetism.

Normally, Newton’s theory of motion and gravitation is subsumed under the name classical mechanics. Newton’s theory of gravity essentially consists of a law for the forces between two material bodies. Newton was able to use this law to explain the motion of the planets within the framework of his theory of gravity.

Einstein’s theory of motion is the special theory of relativity, Einstein’s theory of gravity is the general theory of relativity. Both represent extensions of the corresponding Newtonian theories to a larger range of phenomena: for motions to “higher” velocities, for gravitation to “higher” velocities and to “stronger” gravitational forces. It will still be necessary to make precise what the terms “higher” or “larger” mean in each case.

Maxwell’s theory of electromagnetism serves to explain all electrical and all magnetic phenomena as well as those phenomena in which electrical and magnetic effects are mutually dependent. It is the result of a unification of two earlier theories, one for electricity and one for magnetism.

Gravity and electromagnetic forces act over long distances. Otherwise, we wouldn’t have felt it all the time. They are therefore called long-range, in contrast to the short-range forces that were only discovered in the world of the smallest dimensions. They hold the world “together at its innermost” and their reach does not go beyond that. Of course, the long-range forces can affect even at short distances, electromagnetic forces are even quite important for understanding structure of atoms. However, gravitational forces at the level of atoms have not yet been registered. The masses of the building blocks of the atoms are obviously much too small.

The theories of quantum physics

The establishment of Maxwell’s theory, in particular by the discovery of electromagnetic waves in 1886, increasingly drew physicists to the question of how an electric current and how electromagnetic radiation can be generated in matter. In the end, the question of the structure of matter stood in the center of attention.

From a pre-Socratic Leukipp and his follower Democritus one knew the concept of an atom, a smallest indivisible particle (άτομος gr. indivisible). The chemists used this idea in the 19th century with great profit for the explanation of the laws in the reactions of different chemical elements. But there were also vehement opponents, because one had not yet “really seen” an atom and the idea of indivisibility only raised new questions.

But other questions also came to mind. In the “golden years of physics” from 1895 to 1898 further rays were discovered, such as X-rays, cathode rays, α-, β- or γ-rays. Finally, there were the heat rays, a phenomenon that had been known for some time: All bodies become red, light red and finally white-yellow with constant heating; and one feels that heat emanates from them.

The origin and nature of these rays had to be understood. It was a very fruitful time for physics, and during this time the idea of atoms should establish itself as building blocks of matter, but only as a milestone on the way to ever smaller building blocks. One could then obtain an explanation for all these rays and thereby gain a consistent picture of the structure of matter and the atom.

In an attempt to develop this picture into a consistent theory success was only achieved after daring to describe the discovered relationships between the experimental results with a completely different mathematical conceptual apparatus.

A test case for each approach of a theory for the structure of an atom was the calculation of the possible energy states of a hydrogen atom. The success or failure of a mathematical calculation thus now decided on the success of a theory in this world of the smallest dimensions. The building blocks of an atom such as electrons, protons or neutrons could then no longer be regarded as particles in the sense of classical physics and the living world. They were soon called “quanta”, like the energy packages Max Planck had talked about in a lecture on 14 December 1900 when he gave an explanation of thermal radiation. By the way, the date of this lecture is regarded today as the birthday of quantum physics.

The quantum theories responsible for all the fundamental phenomena of the world’s smallest dimensions are first of all

– quantum mechanics, to a certain extent the replacement for classical mechanics

– quantum electrodynamics, the continuation of electrodynamics on the atomic level.

An explanation of the origin and nature of α- and β-rays could only be achieved by introducing two completely new types of forces, the “strong” force, which is responsible for the binding of the building blocks of the atomic nucleus, and the “weak” force, which can cause the transformation of a neutron into a proton, but also serves to describe the decays of other later discovered “particles”. Thus

– theories of weak and of strong interaction

were created. These two theories were constructed according to the model of quantum electrodynamics. This soon led to the desire to describe these three interactions within a unified theory. As an intermediate step the

– theory of electroweak interaction,

a unification of the electromagnetic and weak interaction was found, and finally

– the unified theory of electrical, weak and strong interaction, the so-called standard model.

Today, this model is regarded as the basic quantum theory. Quantum mechanics now plays the role of a theory for a limited range of phenomena in which relativistic effects do not have to be taken into account and in which there is no decay and no generation of particles.

Figure 4.3 shows the development of the individual theories over the course of time.

Fig.4.3: Timetable for the emergence of physical theories of fundamental interactions

Socrates, Plato and Aristotle

If I wanted to write a treatise on the pre-Socratics, I would now have to deal in this blog post with the so-called pluralists and atomists such as Anaxagoras, Empedocles, Leukipp and Democritus. But I do not want to give an outline of the philosophy of the pre-Socratics here. This has happened often enough elsewhere, and certainly after a much more detailed study of the literature of the past millennia than I can show. I am essentially interested in the thoughts of the pre-Socratics, in which one can discover the precursors of the way of thinking of modern physics, mathematics and logic.
There it is without doubt the three basic ideas which have been expressed so aptly and so early in the history of ideas by the school of Miletus, by the Pythagoreans and by Xenophanes: In nature there is such a thing as a causal connection, the regularities in nature can be formulated in the language of mathematics, and knowledge can be attained by “finding the better by searching”. But there can be no ultimate knowledge.
The first tentative steps of the pre-Socratics towards basic concepts such as ” motion ” are also remarkable. The long history of the clarification of this concept over the millennia clearly shows how much effort it takes to gradually move from the darkness of the first reflections to a clear idea with which one can argue reliably.
If I now follow the development of the “logos” in the history of philosophy, I will be even more selective. I will concentrate on the highlights, i.e. the works where substantial progress has been made. Of course, one often recognizes these only by looking back from today’s standpoint. The focus will be on such developments in logic, mathematics and physics that have become significant for the present state of the art in terms of both methods and the formation of concepts.
So, if one begins to look at the development in the time after the pre-Socratics, one must first speak of the three greats of Greek philosophy: Socrates (-469 to -399), Plato (-428 to -348) and Aristotle (-384 to -322). As already mentioned in the first blog post, Socrates introduced a new topic into philosophy: Ethics. But it was not only this new topic that led to a new era in philosophy. Anaxagoras from Kleizomenai ( Ionia ) had moved to Athens in the year -462 and had made the thoughts of the Milesians and other pre-Socratics known there.
Where more people can come together, it is also more likely that people with the same interests will meet and talk about them. In addition to teacher-pupil relationships, communities can now also emerge in which discussions can take place on an equal footing. Dialectics came into fashion. Already Zenon of Elea had been her great friend, Aristotle had later even praised him as their inventor (Mansfeld & Primavesi, 2011, pp. 361, No.4). Attic democracy flourished, it was an early type of democracy in which the “people of state” ruled, where the people of state consisted of the full male citizens of the city of Athens who had reached the age of 30. These full citizens could also turn to matters which were not directly necessary to daily life; for such work there were enough slaves, women or immigrants. Especially in political meetings and in court, eloquence and the art of dialectics were in demand, i.e. to find the right reasons for opinions and to spread those that could be applauded by listeners. Sophists taught for money to master this art, even to be able to skilfully involve the opponent in a contradiction in discussions.
About Socrates we know some about Diogenes Laertius (Laertius, 2015, pp. 67-90), in particular he is supposed to have said: ” I know nothing except that I know nothing” (DL 83). And “the good is nothing small, but start with small things” (DL 83). But we don’t know any of his writings. Plato, however, puts a lot into his mouth in his works. These works always represent dialogues that Socrates conducts with a wide variety of dialogue partners and in which it is always a matter of clarifying a concept or a question.


After the death of Socrates, Plato, in his years of teaching and travel, first stayed with a follower of the philosophy of Parmenides, “travelled to Cyrene to the mathematician Theodoros and from there to Italy to the Pythagoreans Philolaos and Eurytos; from there to Egypt to the prophets” (Laertius, 2015, p. 141). Thus he collected various impressions and combined them to a grandiose mythical thought building, which is still effective today and continues to inspire many people.
He must have been a great storyteller. In his works he described in the form of a dialogue the effort to find concepts and answers to the question of correct behaviour or a good life. Who first chose this literary form is controversial. “It is said that Zenon, the Eleate, was the first to write dialogues, but Aristotle names as such […] Alexamos from Styra […]. I, on the other hand, think that Plato, through his strict treatment and training […], has secured himself the right to first place […]”. Dialogue is “a question-and-answer execution of a philosophical or political theme”, but dialectics “is the art of persuasion, through which we prove something void or right on the basis of the question-and-answer procedure of the undermentioners” (all quotations: (Laertius, 2015, p. 159)).
Diogenes Laertius says of Plato’s works: “TIMAIOS belongs to the field of physics, to the logic belongs POLITIKOS, KRATYLOS, PARMENIDES and SOPHISTES” (Laertius, 2015, p. 160).
When he, as in TIMAIOS, came to talk about the ideas of the pre-Socratics about the cosmos, he did so in mythical form or tied to Pythagoras and saw the world built up from geometric forms. At that time, logic was still predominantly understood to mean the work on terms, i.e. the uncovering of the relationships between related terms, e.g. their classification as superordinate or subordinate terms. A clearer definition was expected from such a division of terms, called “dihairesis”. One could already see, however, that a definition often required definitions of the determinants, thus leading to an infinite regress.
Aristotle grew up in the Academy with this method. Thus, in his logic, which he was soon to develop, the concepts were also at the centre. This thus became a so-called term logic. Modern logic, on the other hand, is a propositional logic. In the next blog post I will work out the difference exactly.
Plato mainly used induction, i.e. the conclusion from special to general, for a demonstration of evidence, “which through some true cases opens up the same truth for other cases in an appropriate way”, as Laertius (Laertius, 2015, p. 161) says. For a long time this conclusion was considered “appropriate”, only David Hume stressed that this conclusion is not mandatory, thus not always “appropriate”. In modern logic there is no place for this conclusion either.
Plato’s central theme, however, was the human soul and how it can express itself in language, ethics, art and politics. He adorns existing myths, redesigns them or invents completely new stories.

The Platonic Academy

For the development of the “logos” all this does not give much. It is interesting in this context, however, that he also promoted training in analytical subjects, probably motivated by the impression that Pythagorean mathematicians made on him. He was not only a great narrator, but also a good organizer and designer. He founded a school where young people were taught philosophy and science. For this he acquired, probably in -387, a plot of land near a grove called Akademeia, because it had been dedicated to the Heros Akademos. In addition to metaphysics, ethics, dialectics and the doctrine of the soul, physics and especially mathematics were studied there, which soon became part of the basic education of every student of a philosopher. The academy remained, with interruptions, over many centuries, it was closed only around 530.
The Platonic Academy became a model: since Augustine (354 to 430) and Martianus Capella, a Roman encyclopedist from the 5th or 6th century, a canon of seven subjects had become established for the schools of late antiquity. This was divided into a trivium (grammar, rhetoric and dialectic or logic) and a quadrivium (arithmetic, geometry, astronomy, music theory). These subjects were called the seven liberal arts because they were “worthy of a free man,” and “free” was a man when he was free from the necessity of earning a living.
In the Middle Ages this study of the liberal arts was regarded as preparation for scientific studies in theology, jurisprudence and medicine. In the universities, the liberal arts were soon taught within the framework of a separate faculty, the Facultas Artium. The “Liberal Arts”, which we know from the USA e.g. as “undergraduate studies” and which are introduced nowadays also e.g. in Germany, try to continue this tradition. However, dialectics is more in the foreground here than any of the mathematical disciplines.


Aristotle, a pupil of Plato’s, had particularly fertile ground for his rigorous training at the Platonic Academy. Born into an educated and wealthy family in Stageira (Chaldidike) in the year -384, he was sent to Plato’s Academy in Athens in the year -367 at the age of 17. The mathematician Eudoxos von Knidos (ca. -395 to ca. -350) played an important role there.
Aristotle, on the one hand, loved to argue and discuss with dissenters. On the other hand, he showed – as with people who have not passed a mathematical education without consequences – a tendency to work systematically and to collect the doctrines of former philosophers such as Pythagoras or Democritus (Schupp, I 256).
Aristotle became such a great systematist, attentive to the methodical in a thought process and vigilant for connections. He was the first of this kind, and he was also to establish a completely new kind of philosophy, which is no longer a poiesis, a “production” of doctrines in a poetic manner. Instead, the focus is on analysis and methods, reasons are required and the results are checked for conclusiveness.
It is probably plausible that one feels the urge for such things when one has a large corpus of doctrines before one’s mind’s eye and at some point wonders why the respective philosophers can so firmly hold their views. But you also have to live in a stimulating environment and, above all, have the talent to make such a new start. So Aristotle soon went his own way in the academy. According to Diogenes Laertius, Plato is said to have said: “Aristotle beat me like young fillings do against their own mother” (Laertius, 2015, p. 225).
In the list of Aristotle’s writings, Laertius lists 146 titles and speaks of a total of 445 270 lines. According to him, the work on logic is “very clearly marked as a tool for all sub-areas.” These writings were later combined into a collection of six books entitled “Organon” (gr. ὄργανον = tool).

The Organon

The titles of the six books in the Organon Collection are as follows:
1. the categories,
2. on the interpretation (peri hermeneias),
3. the doctrine of the logical conclusion (analytika protera, first analysis),
4. the study of evidence (analytika hystera, second analysis),
5. the topics and
6. the Sophist Refutations
The books 3,4 and 5 are particularly important for the development of logical thinking, i.e. the doctrines of the logical conclusion and the proof as well as the topics. Here the so-called Aristotelian logic is developed. This is therefore the fruit of a time in which dialectics occupied a high position in society. Even in discussions about more fundamental questions such as those about a good life or “reasonable” morals, it was soon more a question of the power of the arguments than of authoritarian settlements, and finally it could not fail to be thought about directly which forms of argumentation possess such power that they are incontestable, i.e. must be accepted by every sensible person.
The new era of philosophy, with its emphasis on dialectics, has therefore by no means allowed the idea of the logos to recede into the background or hindered its dissemination. On the contrary, dialectics was precisely the field in which this idea could prove to be a particularly useful and valuable tool for thinking. The idea took shape in Aristotelian logic, which was to become a model for a science that today plays a significant role within the framework of artificial intelligence. In the next blog post I will deal explicitly with Aristotelian logic.

Aristotle and the System of Sciences

Aristotle’s talent for analytical thinking and systematic work, as well as his passion for collecting the doctrines of earlier philosophers, showed other fruits. He establishes a systematics of all sciences known at that time. It divides the sciences into practical and ethical sciences, into poetic (manufacturing) sciences such as medicine or craftsmanship, and finally into theoretical sciences. In the latter he distinguished mathematics, natural science and “first philosophy”, to which he added theology, ontology and logic. Theology at that time consisted essentially in a study of the unchangeable “divine” stars.
This division of Aristotle is, so to speak, the first “cashing down” of knowledge of a time and subsumes everything that creates knowledge under science. Probably he also counted the theoretical sciences of mathematics and natural science among philosophy, albeit not among the “first”. About 500 years later Diogenes writes of Laertius:
As for the parts of philosophy, there are three: physics, ethics, and dialectics.(Laertius, 2015, p. 10),
whereby dialectic here also stands for the doctrine of thought principles, i.e. for logic and more generally for epistemology. Ethics had thus immigrated into philosophy and mathematics had been eliminated. There could no longer be a thinker like Pythagoras, who practiced mathematics but also represented a certain world view with religious fervour. Important ancient mathematicians, such as Euclid of Alexandria or Archimedes of Syracuse, do not appear in the work of Diogenes Laertius on the lives and opinions of famous philosophers – except for Eudoxos of Knidos, who was a member of Plato’s Academy for a time.
But physics, too, was to emigrate from philosophy, albeit only about 2,000 years later, when Galileo Galilei overcame the Aristotelian theory of motion. By demonstrating how to describe regularities in nature in the language of mathematics, he discovered a “new science”. Natural science became a modern physics. The consequences of this discovery will be discussed in detail.
Finally, at the end of the 19th century, logic in the form of mathematical logic emigrated from philosophy. It is now a branch of mathematics and computer science. Nowadays it is even observed how epistemology is becoming an area of cognitive science that not only deals with our ability to think, but also with all conscious and unconscious processes in our brain such as perceiving, learning or remembering.
Cosmology, the theme of the pre-Socratics and the first theme of philosophy ever, is today an area of modern physics. A history of cosmology from the pre-Socratics to Hawking would be highly interesting: the “question of the whole” has arisen in mythical thinking and in this form is still present in all religions, and the pre-Socratics already began to look for physical reasons for their ideas. But only for about 100 years has there been a physical cosmology in which the logos rule strictly. This cosmology is a reconstruction of the history of the universe with consistent consideration of physical theories. The development of the cosmos could only be convincingly told after the phenomena of nature had been understood on the grounds of reliable theories. Because this knowledge was just the necessary guidelines for a history of the universe, which no longer wants to be a mythical but a logical one.

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