Is the Physical Theory of Everything possible? Second part
I'll be exploring in my articles the history of the Theory of Everything from the philosophical point of view.View all articles by Kazimierz Kubat
See the first part of the article
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.