Is the Physical Theory of Everything possible? p. II

Second part

Fr. Kazimierz Kubat SDS

Let us jump 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 each physical body can be totally characterized by its motion or momentum, it means that if we were able to know the momentum of all the physical bodies at a certain time, we would be able to calculate the whole past and future of the Universe and this could be possible only with the help of the most general laws of mechanics. This is finally the idea of Maxwell's demon, which is able not only to know the momentum of all the physical bodies but also to calculate for all of them the “life trajectory”. Such a demon has certainly a full TOE. He knows everything about everything anytime. This is the very TOE. This philosophy governs in the XVII, XVIII and XIX centuries. Each event in the Universe is only one amongst all calculable mechanical states of the system. The mechanicism of Descartes is absolutely precise, deterministic and equivalent. There is no place for any kind of accident, everything is predictable and calculable. Everything in the Universe can be reduced to the pure mechanical motion, and this motion can be described by the differential calculus of mechanics. It was precisely Descartes who introduced in the 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 gave 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 issue of the deepest conviction of Descartes that geometry (Euclidean) is the most ideal and the clearest science and at the same time it is the ideal and the model or paradigm of all the 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 the totally mathematisable and absolutely deterministic physics which cannot be developed to infinity. The physics must terminate ones, or close itself at the moment we will know everything that can be known. For this reason perhaps, and the end of the XIXth century, the physicists were convinced that the physics is a science at “the end”. They were persuaded that there is nothing more for physics than to state precisely the further places after the comma in the figure . 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.

1 „Newton’s first law of motion states that if the vector sum of the forces acting on an object is zero, then the object will remain at rest or remain moving at constant velocity.”

2 „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

3 „Newton’s third law of motion states that an object experiences a force because it is interacting with some other object. The force that 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 equal reaction . This equation is only the other form of Cartesian law of the 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 the 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 is describing the trajectory of the celestial bodies and … the falling down of an apple. The TOE would like to really 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 in the daily life scale, the Newtonian theory of gravitation to describe events in the macro scale (cosmology) and the theory of electromagnetism of Maxwell to describe the events in micro scale. It is good to stress that the four equations of J. C. Maxwell (1831 – 1879.) were the next element of 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, since Maxwell, became one theory of electromagnetism.

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

– Gauss’s law

– no magnetic charge

– Ampère's law

– Faraday's law

The unification of two fields (or forces): electrical and magnetic in 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, which is very interesting. A few quite simple mathematical equations describe larger and larger areas of reality. So a very philosophical question arises: “Why does the physical world follow our mathematics?” Other questions follow:

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

– is it so that we are discovering 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 so that precisely the mathematics 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 that in fact the Universe is built out of numbers. We just have to listen to the harmonious “celestial's spheres music” in order to know the enigma of the Universe and to describe it, to calculate it or even to create it yet only on the 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 because the most fundamental building material of the Universe is not the 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 a “Chaos,” that it is knowable and that inside it we can find a 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 is calculating 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 things 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 coming 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 included in it billions years ago. Everything that happens and will happen – even in a million years ahead, is only the issue 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 the idea, but… if the TOE is possible, (and everything is showing 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 are difficult to predict. Human freedom is disappearing, but also 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 marionettes.

The second set of ideas or philosophical consequences coming out of the XVIII and XIX centuries researches of TOE are the philosophical theories or researches done in the XVIII and XIX centuries, 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 by thinking.” 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 a 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.

So at the end of the XIXth century, we have on the one side the clearer possibility of physical and 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 XIXth 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 interfere in the theorem of Gödel announcing that a very true TOE is impossible.