The History of the TOE

Is the Physical Theory of Everything possible?

Published by kazikq 05-13-2005

Introduction

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Fr. Kazimierz Kubat SDS

Since the beginning of humanity, one of the biggest temptations of mankind was the desire to understand: "The universe, its functions, its construction, its beginning and destination, but also, our place in it"

Men tried to explain it in different ways, searching for the answer not only in magic, religion, and the stars but also in philosophy and sciences and nowadays even in UFOs. We would like not only to know how the universe continues to develop and what makes up its ultimate large scale structure. We also want to know why the universe exists, its point of origin, our origin and our place in it.

These kinds of research and endeavors that try to explain the Universe as a whole in one short and understandable way may be called Theories of Everything. (TOE). We can find examples of religious TOE in the Bible, in the Sacred Scriptures of India; (Wedda, Ramayana and Mahabharata) but also in Buddhist and Taoist scriptures in China as well as in every other religion and mythology. The religious answers - although holistic and ultimate - are for some people not adequate because they are not precise. They even seem to avoid the clue of the ultimate questions and finally they do not seem to solve the problem.

For others, convinced of the correctness and exactness of them, these kinds of answers are only a challenge and an invitation to further questions, research and investigations. Although personally, I believe that: "In the beginning God created the heavens and the earth. Now the earth was formless and empty" (Gen. 1, 1-2), I would like, if possible -following the idea of Saint Augustine "Fides querrens intellectum"- to see how God did it, how the creation was done, how the earth was formless and empty. I don’t think that this desire is a negation of the faith or a revolution against the power of God, even if it is a kind of "looking up God’s sleeves". Of course, someone could say that I pretend to understand God, but what is wrong with this, as long as I keep in mind that God’s thoughts are not my own and God’s ways are not mine. It is in order, as long as I am aware of my own limits and of the limitations of my reason, and as long as I don’t try to replace the ultimate truths of the faith by the partial -and far from ultimate- truths of my own.

We can find more examples of TOE. For our purposes, we can divide them into three groups:

Religious TOE

Philosophical TOE - trying to explain the Universe as a whole in a philosophical way Physical TOE - attempting to represent the Universe as a whole in the form of one quite simple mathematical equation using observations and mathematical language. Let us see, first of all, how the philosophers have been dealing with the problem.

One of the non-religious (but not anti-religious) attempts at answering the above mentioned questions, is certainly the philosophy of nature which tries to create a comprehensive TOE.

Since the time of the first philosophers (seventh and sixth centuries B.C.), people have been trying to find a simple and rational explanation or justification of the Universe as a whole. The first attempt to answer the question "What is the most fundamental principle of everything?" is certainly the Ionian philosophy of nature. This was proposed at the very beginning of philosophical thinking and also at the very beginning of Western Culture and Civilization. I dare say that this is the first attempt of TOE. Thales of Millet (surveyor, mathematician, astronomer and politician) living in the seventh and sixth centuries B.C., explained that the water, from which everything emanates and towards which everything will return, is the most fundamental building material of the Universe. In the thinking of Thales, the mythological gods of Oceanos and Thetida were, for the first time, replaced by material bodies and forces. The fantastic explanations were replaced by materialistic and rational ideas.

This was the first non-religious and non-mythological attempt to understand the Universe -- to gather totality in one simple and understandable concept. In this way, the first Theory Of Everything (TOE) was postulated.

There were many other philosophers who followed Thales.

For Anaximander (649-546 B.C.), this fundamental principle and the reason of everything (arche) was. the hard and unchangeable building material - the indefinite (apeiron), limitless and boundless but still material base, out of which "all heavens and the worlds held in them, were created."

For the next philosopher of that time, Anaximenes (585-525 B.C.), the most fundamental principle and the cause of the Universe, which gives insight into the understanding of the whole, was the air. It is interesting to note that these three first philosophers, who attempted the first TOE, came from Millet, the Ionian colony of Greece on the coast of Asia Minor.

The next Greek philosophers tried to give a new kind of explanation and justification of the Universe, but still in the same way. For Heraclites (sixth and fifth centuries B.C.) the most fundamental principle explaining everything was fire, which could change into everything without limits. Moreover, the fire is not only the fundamental principle of everything, but also the cause of the most fundamental fact present in nature- change itself. For Heraclites, the world doesn’t exist but it changes, it flows constantly (pantha rei)-it becomes. The change is not random, haphazard or accidental; it is rational, logical and teleological. In order to understand the Universe, we must first find this logical principle included in it. Reason (logos) is not only a human feature but also a cosmic power, the most immanent nature of the world. Thus, fire is not the unchangeable and fixed element of nature and the world, but rather a symbol of its constant change and flux, which is following the principle of reason governed by logos.

Here we have the beginning of something which will be re-born twenty-five centuries later, in another way; i.e. in physical or cosmological theories of the evolution of the Universe or in unification theories. The logos, governing the world, organizing it and leading it, could be rationally understood and known by men. Man should only read it from nature. Let us not hurry but let us recognize that the temptation to unify the image of the Universe--all the attempts at creating TOE--are nothing new. We can already find its traces at the very beginning of the intellectual adventure of humanity known as philosophy.

The answer to the flux and variability in the world of Heraclites was the ontological monism of Parmenides. Once again, in the name of reason and logic, Parmenides ( sixth and fifth centuries B.C. therefore contemporary with Heraclites) tries to prove that the most fundamental principle of the Universe and its element of unification is the Unity of being, or, Being as such. "Being is, nonbeing doesn’t exist."

Because each change is the passage from something to something else (which is the opposite to the starting point), the change itself can only be recognized as the passage from being towards nonbeing. If the nonbeing doesn’t exist, the passage itself is impossible. Change doesn’t exist. Unlike Heraclites, Parmenides acknowledges that the Universe is unchangeable; moreover, there is only one unchangeable and monolithic being, therefore change itself is fiction. This concept of monolithic being is the most fundamental principle explaining everything in Parmenides’ philosophy. So we have the next TOE.

For Xenophanes (580-480 B.C.) the fundamental element and the principle of the Universe is the earth.

For Empedocles (490-430 B.C.) the four elements mentioned above (water, air, fire and earth) are altogether the fundamental principles of the Universe. The scheme of Empedocles is worth remembering because it will be influencing our further investigations. According to Empedocles thus, "four are the roots of everything, four are the forces of nature or states of matter."

It is not without reason that we speak more precisely concerning these first attempts of TOE. They show that since man tried to think independently and to liberate himself from religious and mythological beliefs, he tried simultaneously to understand the Universe and to create a comprehensive and coherent theory explaining the totality of the surrounding reality. These are not yet physical approaches (physical in the sense of contemporary physics) but nevertheless they are rational and philosophical approaches, and in a certain way, materialistic theories trying to justify the Universe and to explain it, using one short and understandable physical (material, non-spiritual) principle. Behind these attempts, we can notice another kind of temptation, which we can call "looking up God’s sleeve". Understanding the Universe, its composition, its way of working, means to create it, or re-create it, even theoretically, that is, only on paper. So it is not surprising that nowadays theoretical physicists and cosmologists cannot avoid such a temptation.

Plato and Aristotle also created their own philosophical TOE. For Plato, the condition sine qua non of understanding the structure and the construction of the Universe is the dialectical ascension into the world of pure ideas. Achieving this ascension means reaching the highest level of knowledge (gnosis or episteme) and it gives the philosopher the full insight into the nature of the Universe through the reminiscence of the world of pure ideas. This is only possible on one condition, namely if man liberates himself from the chains binding him to material reality, to the temporary world of shadows. The liberated man is able to reach the ideal and perfect world, where perfect and full knowledge is attainable. In this sense, Plato’s TOE is possible only for mystics, in an almost religious revelation. TOE can be created or understood just at the top of the laborious ascension through the steps of knowledge (from doxa through the pisitis and dianoia to the gnosis-episteme.)

Aristotle tries to pull down Plato from heaven to earth and to show that the world is knowable not through the ideal world but in the realistic and philosophical vision of the nature of this material world. Aristotle’s explanation of the Universe, though nowadays archaic, nonetheless still remains a good example of a rational attempt towards the understanding of reality, based on what nature itself reveals to us through sensual knowledge. The world is not a shadow of ideal reality, but it is reality itself, knowable by our senses and explainable by reason, not by reminiscence of what we knew about it in the ideal world. To create TOE, we have to know everything which is accessible to our senses and to generalize, to summarize everything to the most fundamental and general principles. For Aristotle, this is the theory of material being which is temporal, spatial and changeable. Understanding this being and its principles gives us the insight into the nature of the Universe and into the most fundamental principles of existence.

Aristotle develops his metaphysical theory of ontological constitution of being, but he is also the first to show the way to modern physics, accentuating the phenomena of motion and the necessity of its study. It is true that in his metaphysical theory of motion he is talking rather about the qualitative aspects of motion, but the quantitative aspects of his theory (although false) are the foundation of classical mechanics. From his physical theory of motion, there is only a small step to be taken towards modern physics although for this step science and philosophy will have to wait for centuries. Nevertheless, Aristotle should be recognized among those who have attempted to understand the Universe as a whole in a rational way and to build up a philosophical TOE. As for Plato, the knowledge of idea was the main point to understand reality; so for Aristotle, the knowledge of material reality opens the way for us to understand the totality.

So, in ancient philosophy we already have examples of the construction of the TOE, which will be developed (in further history) into two different kinds of theories. On the one side we will have a continuation of the research into the philosophical explanation as a whole, while on the other (starting from Fifteenth and Sixteenth Centuries) the autonomization of the physical attempts of constructing the TOE based on the natural sciences, especially physics. In the process of development of the tools of physics, the philosophical attempts will be put on the periphery of human knowledge because of their insufficiency or inaccuracy. The qualitative aspects of philosophical ideas will gradually be replaced by the qualitative aspects derived from physics. In this way, natural sciences, with physics and cosmology at the top, become primary. Nevertheless, we cannot neglect the value of those philosophical attempts present in antiquity. They forged ideas and concepts. They tried to present the rational understanding of the Universe as a whole, which was attainable for humanity at that time.

It is thus comprehensible that man would like to understand the Universe and its structure, and his place in it in each era. It is understandable that he would like to understand origins; the origin and the destiny of the Universe as well as his own. So man would desire to understand the Universe creating the Theory of Everything, literally "everything." Is there something intrinsically evil in this attempt? Are such attempts not an expression of the fundamental human desire to discover his non-accidental and non-transient nature? To understand, to know, means to govern, to take his own future in his hands and to be a non random result of a blind game of the forces of nature. Of course, such a desire can lead us to boldness, arrogance, atheism and rejection of God who will be replaced by arrogant reason. Indeed, in the history of philosophy, we encounter such events.

On the other hand, those desires and researches can lead to humility and to the deepening of faith, to the acceptance of the truth that the final explanation and justification of everything can be found in God. This is the place where the religious truths that are "ex-definitione" TOE, can meet the rational or even the scientific attempts of TOE. I am certainly not in favor of a concordant idea of mixing scientific knowledge with philosophy or religion. But, from another point of view it is also not acceptable to bring natural sciences and religion into contradiction. Saint Augustine did not err speaking of the necessity of understanding in order to deepen the faith "intellige ut credas". He also, underlines the necessity of faith in order to better understand "crede ut intelligas". Thus faith is not a contradiction of rational understanding and vice versa. Personally, I am deeply convinced that TOE’s are the basis on which science and faith can meet each other with mutual respect and show together the deepest meaning of the existence of the world and ourselves.

In the second part of this article, I would like to show how TOE’s were further developed in the history of philosophy, and particularly how they became the domain of natural sciences.

Let us leap many centuries ahead, to the time of Descartes (1596-1650), who was the first to try to "mathematizise" the most fundamental principle of the Universe. His first equation of mechanics gives basis to a large discussion and research in the area of physics. If it’s true that each physical body can be totally characterized by its motion or momentum, then if we were able to know the momentum of all physical bodies at a certain time, we would be able to calculate the whole past and future of the Universe. This could be possible only with the help of the most general laws of mechanics. This is ultimately the idea of Maxwell’s Demon, which is able, not only to know the momentum of all physical bodies but also to calculate for all of them their "life trajectory". Such a demon has certainly a full TOE. He knows everything about everything anytime. This is truly TOE. This philosophy reigns in the XVII, XVIII and XIX centuries. Each event in the Universe is only one amongst all calculable mechanical states of the system. The mechanism of Descartes is absolutely precise, deterministic and univocal. There is no place for any kind of accident, everything is predictable and calculable. Everything in the Universe can be reduced to pure mechanical motion, and this motion can be described by differential calculus of mechanics. It was Descartes who introduced into philosophy the concept of "Deus ex machina", God, the Perfect Watchmaker who created the Universe as a very precise watch mechanism and who intervenes only in case this mechanism needs adjustment. Somebody who is able to know the functioning of this mechanism will be able to know the TOE. Moreover, Descartes developed further implications of his mechanics. He proposed to build up all the sciences in a mechanical way "more mechanico" and even further, "more geometrico." This idea is the result of the deepest conviction of Descartes, that Euclidean geometry is the most ideal and the clearest science, and -at the same time- it is the ideal science and even the model or paradigm of all sciences. Even mechanics or rather its differential calculus should be reduced to the level of geometry (as he himself proved). So, the most fundamental building material of the Universe is not matter nor energy, but geometry. All sciences should be built up in a geometrical way. In this way geometry becomes the ultimate TOE.

Moreover, the mechanicism of Descartes leads to totally mathematical and absolutely deterministic physics which cannot be infinitively developed. Physics must lead to an absolute conclusion, or conclude at the moment when we will know everything that can be known. For this reason perhaps, at the end of the XIXth century, physicists were convinced that physics is a science at its final stage. They were persuaded that there is nothing more to do for physics than to calculate more and more accurately the further places after the decimal point in the constant p. In this way, physics becomes the ultimate science, i.e. TOE.

The Cartesian mechanistic philosophy was supported by the Newtonian theory of gravitation. Isaac Newton (1642-1727) confirms the Cartesian idea in his three laws of motion.

Newton’s first law of motion states that "if the vector’s sum of the forces acting on an object is zero, then the object will remain at rest or remain moving at constant velocity." Newton’s second law relates net force and acceleration. A net force on an object will accelerate it -- that is, change its velocity. The acceleration will be proportional to the magnitude of the force and in the same direction as the force. The proportionality constant is the mass, m, of the object. or in the differential form

Newton’s third law of motion states that "an object experiences a force because it is interacting with some other object. The force which object 1 exerts on object 2 must be of the same magnitude but in the opposite direction as the force, that object 2 exerts on object 1. Action equals reaction".This equation is only an another form of the Cartesian law of conservation of momentum i.e. the first law of mechanics of Descartes If, to these three principles of mechanics, we add the genial equation of the gravitational field ruling the totality of the Universe, we have a very simple and convincing TOE. Knowing the masses of all bodies present in the Universe we know the forces attracting them and so we are able to know all past and future configurations of these bodies. The same equation describes the trajectory of all celestial bodies and .. the falling down of an apple. The TOE would really like to describe everything, independently of the place and conditions in which the events take place.

Thus, it seems that at the end of the XIXth century we have a very clear situation in physics. We have Cartesian -- Newtonian mechanics describing events on the everyday human scale, the Newtonian theory of gravitation to describe events on the macro scale (cosmology) and the theory of electromagnetism of Maxwell to describe the events on micro scale. It is good to stress that the four equations of J. C. Maxwell (1831 -- 1879) were the next element in the process of the unification of the Universe’s image. Maxwell unified two independent theories (the theory of electricity and the theory of magnetism), which were described in two different ways and two different theories, thanks to Maxwell, they became one theory of electromagnetism.

These four equations of Maxwell’s electromagnetism are known by children in secondary school.

- Gauss’s law

- no magnetic charge

- Ampère’s law

- Faraday’s law

The unification of these two fields (or forces): electrical and magnetic into one coherent system of differential calculus unifies the image of the Universe and it is certainly a further step on the way towards TOE. In this way, the image of the Universe becomes clear and the Universe itself becomes mathematizable. This fact by itself is already very interesting. A few (quite simple) mathematical equations describe larger and larger areas of reality. So, a truly philosophical question arises: "Why does the physical world follow our mathematics?" Other questions follow:

is it that we invent mathematics and if so, why does the reality follow our invented mathematics? or,

is it that we discover mathematics in the real world and if so, the mathematics is the most fundamental fiber and building material?

Anyway, this logic and mathematizability of the Universe are very surprising. Is it not precisely mathematics that is the key to the TOE or even TOE itself?

If the affirmative answer to the second question is true, it means that the ancient Pythagorean philosophers (VIth century B. C.) were right, and in fact the Universe is built out of numbers. We just have to listen to the harmonious "music ofcelestial spheres" in order to know the enigma of the Universe and to describe it, to calculate it or even to create it yet only on paper in the form of mathematical equations. In this way, it seems that the Ionian philosophers of nature weren’t right, assuming that the "arche" of the Universe is present in material principles or elements. The most fundamental building material of the Universe is not a material element (water, air, earth or fire) but the non material mathematics and all these material elements are also built up out of non material mathematics. Moreover, in this world, nothing can exist that is not mathematizable or that cannot be described by mathematics. We can even say that anything that is illogical or not mathematizable is impossible. Perhaps this is the reason why Leibniz (1646-1714) insisted in his "Theodicea" that our "existing Universe is the best of all possible because God as the most perfect and wisest being cannot choose anything less than the best because it would be against the logic."

However we answer these questions, we have to acknowledge at least that the Universe is a "Cosmos" and not "Chaos," that means, it is knowable and that inside it we can find logical (mathematical) order and harmony. The Universe is certainly neither the result of a random and blind accident nor a set of facts or events which are not interconnected. Everything in the Universe is a pattern and if so, it is possible to know the facts and the events, but also the connections between them, to classify them, to generalize and to develop the most general theory of this set of events, i.e. TOE. It is only necessary to check a sufficient number of representative facts and to find a generalization for them or the largest mathematical description including all those facts. The example of such an "automat" which calculates all the possible cases and configurations of the Universe is the above mentioned "Demon of Maxwell." Having all the data concerning all the physical bodies and knowing the laws of nature governing these bodies, it is possible to predict with an infinite accuracy the past and the future of the Universe, i.e. to describe all and everything.

The description of all philosophical implications of this reasoning is going far beyond the frame of this article but nevertheless it would be interesting to point out at least two of them. The first one is the idea that the Universe which emerges out of this reasoning is not only logical and rationally knowable, but it is also absolutely deterministic. Nothing in this world is accidental, and everything we see today was already virtually included in it many billions of years ago. Everything that happens and will happen -- even a million years ahead, is only the result of the simple mathematical calculation of the initial state. Such an image is at the same time very pessimistic, because our feeling of freedom revolts against this idea, but... if the TOE is possible, (and everything shows that it is), so our freedom is only a ghost and an illusion. I am not doing what I would like to do, but only what I have to do or what I must do, according to the physical, mathematical and geometrical structure of the Universe. This is the first philosophical implication of the research of TOE. All philosophical and even moral implications of this statement are difficult to predict. Human freedom disappears, and so does human responsibility. Somebody is a murderer or a criminal, but he is not responsible for his acts because he "has to be" a murderer, because it was pre-established at the very beginning of the Universe in its geometrical structure. Nobody can change it because it would be against the most fundamental (mathematical or geometrical) nature of the world. So, all of us are puppets.

The second set of ideas or philosophical consequences coming out of the searches for a TOE in the XVIII and XIX centuries are the philosophical theories of TOE, e.g. the absolute idealism of G. W. F. Hegel (1770 -- 1831). The German philosopher created a philosophical TOE. According to this theory, the totality of the reality can be included in "a dialectically developing thought which is thinking itself." In this philosophical theory, everything is interconnected and mutually dependent. This thought or spirit is developing itself in three dialectical phases (mutually interconnected): a subjective one, an objective and an absolute one. The subjective spirit (area of logic), Hegelian dialectical thesis, is exteriorizing itself (alienating) in the material nature, which is the Hegelian antithesis, and the area of natural sciences (physics, chemistry, biology etc.) in order to "recognize" itself in the absolute spirit (the area of social and humanistic sciences, religion and philosophy.) This triadic structure of the evolution includes everything in itself. The spirit is the thought which is thinking itself and this spirit is also "thinking" the material Universe. Everything we see, everything surrounding us, ourselves included, is nothing else than the thought of the thinking spirit, a stage or phases in the dialectical evolution of spirit. The key to the understanding and knowledge of everything is a dialectic triad: thesis, antithesis, synthesis and an acknowledgment that myself, I am only this very thought which is thinking itself, that I am thinking myself and everything in the surrounding world. The totality of Hegelian philosophy and what follows, the totality of the Universe (thought, spirit) can be presented in the following table:

LOGOS -- subjective thought logic Thesis
 NATURE -- philosophy of nature -- objective thought - Antithesis
 ABSOLUTE SPIRIT -- philosophy of the human spirit -- absolute thought -- Synthesis

Thesis -- subjectivity
 Theory of being
 Mechanics -- Theory of time
 Subjective spirit -- anthropology, phenomenology, psychology

Antithesis --objectivity
 Theory of substance
 Physics -- Theory of space
 Objective spirit -- law, individual and social ethics

Synthesis -- absolute
 Theory of concept
 Biology -- Theory of space-time
 Absolute spirit -- arts, religions, philosophies

In this, (Hegelian, dialectical schedule) everything is really included, the Universe with its richness and variety, all the sciences and beings, all acts and human activities, all that existed, exists and will exist. Man is only "the bit of matter experiencing time and space". The top and achievement of everything -in this scheme- is obviously the Hegelian philosophy where the spirit (philosopher) realizes that he himself is only an element of this gigantesque Thought "which is thinking itself and thinking everything existing in the Universe." The Logos -- thesis is objectivizing itself in Nature -- antithesis. to --eventually - synthesize or recognize itself in the Absolute Spirit.

The Hegelian schedule can also be presented in a circular form, because the evolution of the Absolute Spirit is never ending and much more, it is not even a process dispatched in space and time, because even space and time are the products of this spirit. Precisely this Thought (Spirit) is creating time and space by objectivization in nature, to be able to exist as the material beings of nature. The spirit -- the Thought is constantly thinking itself and is constantly objectivizing itself in the antithesis "creating" (thinking) nature to be able to recognize itself constantly in the Absolute Spirit.

Thesis- Logos

Synthesis- Spirit

Antithesis - Nature

No matter which way we interpret Hegelian philosophy, it is sure that it is pretending to be a philosophical TOE. It seems that there is not only one such philosophical synthesis like this. Besides, there is nothing to be astonished about because as we said in the first part, philosophy is "ex definitione"; predestined to create the synthesis and TOE. It is enough to remember the philosophical pantheistic systems of Plotinus (203 - 270) or B. Spinoza (1632 - 1677) or even the Monadology of Leibniz.

mathematical totalistic description of the Universe and on the other side, gigantesque philosophical syntheses like the absolute idealism of Hegel, the pantheism of B. Spinoza or Marxist materialism. Physics becomes a leading science and it seems to be the ultimate and terminating science. Philosophy is not staying far behind, creating philosophical syntheses and trying to challenge physics and its achievements. Obviously there are still biology, psychology and sociology, but many of the physicists of that time neglect them or consider them as a little bit more complicated physics. Following this idea, it would be possible that in the near future all those sciences would be swallowed by physics.

Moreover the Darwinian theory of the evolution of the species seems to be the first step to the rationalization or the mathematization of biology. Marxism from its side proposes the rationalization of the sociology and using the Hegelian dialectic system, tries to explain not only the evolution of sociological structures, but also to prove that everything (biological and psychological life included) is coming out of the non living matter.

The optimism of physics at the end of the XIX century seems to be justified and TOE seems to be within hand’s reach. The world is not only knowable but repeatable, i.e. it could be re-created. It is possible to explain it ultimately and put it in mathematical structure; in another way we are very close to "looking up God’s sleeve" and we are not too far from knowing all the tricks He used in creating the Universe if He at all created it. "If" because it seems rather that nothing like creation happened and that the Universe created itself and it is internally justifying its own existence or that it exists eternally. In this case we don’t need to look for the beginning.

In the third part, we will see how the temptations of TOE took possession of contemporary theoretical physics and cosmology, and how mathematics, logic and especially the theorem of G&oulm;del interfere in, announcing that the final and ultimate TOE is --probably-- impossible.

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