by Georgi Stankov, Copyright 2009
Conventional science has not yet discovered a single law of Nature, with which all natural phenomena can be assessed without exception. Such a law should be defined as “universal”. Based on sound, self-evident scientific principles and facts, the current article analyses, from the viewpoint of the methodology of science, the formal theoretical criteria, which a natural law should fulfil in order to acquire the status of a “Universal Law”
In science, some known natural laws, such as Newton’s law of gravitation, are referred to as “universal”, e.g. “universal law of gravitation”. This term implies that this particular law is valid for the whole universe independently of space and time, although these physical dimensions are subjected to relativistic changes as assessed in the theory of relativity (e.g. by Lorentz’ transformations).
The same holds true for all known physical laws in modern physics, including Newton’s three laws of classical mechanics, Kepler’s laws on the rotation of planets, various laws on the behaviour of gases, fluids, and levers, the first law of thermodynamics on the conservation of energy, the second law of thermodynamics on growing entropy, diverse laws of radiation, numerous laws of electrostatics, electrodynamics, electricity, and magnetism, (summarised in Maxwell’s four equations of electromagnetism), laws of wave theory, Einstein’s famous law on the equivalence of mass and energy, Schrödinger’s wave equation of quantum mechanics, and so on. Modern textbooks of physics contain more than a hundred distinct laws, all of them being considered to be of universal character.
According to current physical theory, Nature – in fact, only inorganic, physical matter – seems to obey numerous laws, which are of universal character, e.g. they hold true at any place and time in the universe, and operate simultaneously and in a perfect harmony with each other, so that human mind perceives Nature as an ordered Whole.
Empirical science, conducted as experimental research, seems to confirm the universal validity of these physical laws without exception. For this purpose, all physical laws are presented as mathematical equations. Laws of Nature, expressed without the means of mathematics, are unthinkable in the context of present-day science. Any true, natural law should be empirically verified by precise measurements, before it acquires the status of a universal physical law. All measurements in science are based on mathematics, e.g. as various units of the SI-System, which are defined as numerical relationships within mathematics, and only then derived as mathematical results from experimental measurements. Without the possibility of presenting a natural law as a mathematical equation, there is no possibility of objectively proving its universal validity under experimental conditions.
State-of-the-Art in Science
From the above elaboration we can conclude that the term “Universal Law”, should be applied only to laws that can be presented by means of mathematics and verified without exception in experimental research. This is the only valid “proof of existence” (Existenzbeweis, Dedekind) of an “universal law” in science from a cognitive and epistemological point of view.
Until now, only the known physical laws fulfill the criterion to be universally valid within the physical universe and at the same time to be independent of the fallacies of human thinking at the individual and collective level. For instance, the universal gravitational constant G in Newton’s law of gravitation, is valid at any place in the physical universe. The gravitational acceleration of the earth g, also a basic constant of Newton’s laws of gravitation, applies only to our planet – therefore, this constant is not universal. Physical laws which contain such constants are local laws and not universal.
It is important to observe that science has discovered universal laws only for the physical world, defined as inanimate matter, and has failed to establish such laws for the regulation of organic matter. Bio-science and medicine are still not in the position to formulate similar universal laws for the functioning of biological organisms in general and for the human organism in particular. This is a well-known fact that discredits these disciplines as exact scientific studies.
The various bio-sciences, such as biology, biochemistry, genetics, medicine – with the notable exception of physiology, where the action potentials of cells, such as neurons and muscle cells, are described by the laws of electromagnetism – are entirely descriptive, non-mathematical disciplines. This is basic methodology of science which should be cogent to any specialist.
This conclusion holds true independently of the fact that scientists have introduced numerous mathematical models in various fields of bio-science, with which they experiment in an excessive way. Until now they have failed to show that such models are universally valid.
The general impression among scientists today is that organic matter is not subjected to similar universal laws as observed for physical matter. This observation makes, according to their conviction, for the difference between organic and inorganic matter.
The inability of scientists to establish universal laws in biological matter may be due to the fact that:
a) such laws do not exist or
b) they exist, but are so complicated, that they are beyond the cognitive capacity of mortal human minds.
The latter hypothesis has given birth to the religious notion of the existence of divine universal laws, by which God or a higher consciousness has created Nature and Life on earth and regulates them in an incessant, invisible manner.
These considerations do not take into account the fact that there is no principle difference between inorganic and organic matter. Biological organisms are, to a large extent, composed of inorganic substances. Organic molecules, such as proteins, fatty acids, and carbohydrates, contain for instance only inorganic elements, for which the above mentioned physical laws apply. Therefore, they should also apply to organic matter, otherwise they will not be universal. This simple and self-evident fact has been grossly neglected in modern scientific theory.
The discrimination between inorganic and organic matter – between physics and bio-science – is therefore artificial and exclusively based on didactic considerations. This artificial separation of scientific disciplines has emerged historically with the progress of scientific knowledge in the various fields of experimental research in the last four centuries since Descartes and Galilei founded modern science (mathematics and physics). This dichotomy has its roots in modern empiricism and contradicts the theoretical insight and the overwhelming experimental evidence that Nature – be it organic or inorganic – operates as an interrelated, harmonious entity.
Formal Scientific Criteria for a “Universal Law”
From this disquisition, we can easily define the fundamental theoretical criteria, which a natural law must fulfill in order to be called “Universal Law”. These are:
1. The Law must hold true for inorganic and organic matter.
2. The Law must be presented in a mathematical way, e.g. as a mathematical equation because all known physical laws are mathematical equations
3. The Law must be empirically verified without exception by all natural phenomena.
4. The Law must integrate all known physical laws, that is to say, they must be derived mathematically from this Universal Law and must be ontologically explained by it. In this case, all known physical laws are mathematical applications of one single Law of Nature.
5. Alternatively, one has to prove that all known fundamental natural constants in physics, which pertain to numerous distinct physical laws are interrelated and can be derived from each other. This will be a powerful mathematical and physical evidence for the unity of Nature under one Universal Law, as all these constants can be experimentally measured by means of mathematical equations.
In this way one can integrate for the first time gravitation with the other three fundamental forces (see below) and ultimately unify physics. Until now conventional physics, which stipulates in the standard model, cannot integrate gravitation with the other three fundamental forces. This is a well-known fact among physicists and this circumstance discredits the whole edifice of this natural science. Physics is unable to explain the unity of Nature. This fact is not well understood by all people nowadays, because it is deliberately neglected or even covered up by all theoreticians.
The unification of physics has been the dream of many prominent physicists such as Einstein, who introduced the notion of the universal field equation, also known as “Weltformel” (world equation) or H. Weyl, who believed physics can be developed to a universal field theory.
This idea has been carried forward in such modern concepts as Great Unified Theories (GUTs), theories of everything or string theories, however, without any feasible success.
If such a law can be discovered, it will lead automatically to the unification of physics and all natural sciences to a “General Theory of Science”.
At present, physics cannot be unified. Gravitation cannot be integrated with the other three fundamental forces in the standard model, and there is no theory of gravitation at all. Newton’s laws of gravitation describe precisely motion and gravitational forces between two interacting mass objects, but they give us no explanation as to how gravitation is exerted as an “action at a distance”, also called “long-range correlation”, or what role photons play in the transmission of gravitational forces, given the fact that gravitation is propagated with the speed of light, which is actually the speed of photons.
If this hypothetical “Universal Law” also holds true for the organisation of human society and for the functioning of human thinking, then we are allowed to speak of a true “Universal Law”. The discovery of such a law will lead to the unification of all sciences to a pan-theory of human knowledge. This universal theory will be, in its verbal form presented as a categorical system (Aristotle), without contradictions, that is to say, it will follow the formalistic principle of inner consistency.
From a mathematical point of view, the new General Theory of Science, based on the Universal Law, will be organised as an axiomatics. The potential axiomatisation of all sciences will be thus based on the “Universal Law” or a definition thereof. This will be the first and only axiom, from which all other laws, definitions, and conclusions will be derived in a logical and consistent way. All these theoretical statements will then be confirmed in an experimental manner.
These are the ideal theoretical and formalistic criteria, which a “Universal Law” must fulfill. The new General Theory of Science based on such an “Universal Law” will be thus entirely mathematical, because the very Law is of mathematical origin – it has to be presented as a mathematical equation.
In this case all natural and social sciences can be principally presented as mathematical systems for their particular object of investigation, just as physics today is essentially an applied mathematics for the physical world. Exact sciences are therefore “exact”, because they are presented as mathematical systems.
The Foundation Crisis of Mathematics
(see Wikipedia: Grundlagenkrise der Mathematik)
This methodological approach must solve one fundamental theoretical problem that torments modern theory of science. This problem is well-known as the “Foundation Crisis of mathematics“. Mathematics cannot prove its validity with its own means. As mathematics is the universal tool of presenting Nature in all exact physical disciplines, the Foundation Crisis of mathematics extends to all natural sciences. Social sciences do not claim any universal validity, as they cannot be mathematically expressed. Therefore, the Foundation Crisis of mathematics is the Crisis of Science.
Although this crisis should be basic knowledge to any scientist or theoretician, present-day scientists are completely unaware of its existence. Hence their total agnosticism with respect to the essence of Nature.
This ignorance is difficult to explain, as the foundation dispute in mathematics, known in German as Grundlagenstreit der Mathematik, has dominated the spirits of European mathematicians during the first half of the 20th century. The current ignorance of scientists about this crisis of science stems from the fact that mathematicians have not yet been able to solve the foundation crisis of mathematics and have swept it with a large broom under the carpet of total forgetfulness.
Mathematics is a hermeneutic discipline and has no external object of study. All mathematical concepts are “objects of thought” (Gedankendinge). Their validity cannot be verified in the external world, as this is the case with physical laws. Mathematics can only prove its validity by its own means.
This insight emerged at the end of the 19th century and was formulated for the first time as a theoretical programme by Hilbert in 1900. By this time, most of the mathematicians recognized the necessity of unifying the theory of mathematics through its complete axiomatisation. This was called “Hilbert’s formalism“. Hilbert, himself, made an effort to axiomatize geometry on the basis of few elementary concepts, such as straight line, point, etc., which he introduced in an apriori manner.
The partial axiomatisation of mathematics gained momentum in the first three decades of the 20th century, until the Austrian mathematician Gödel proved in 1931 in his famous theorem that mathematics cannot prove its validity by mathematical, axiomatic means. He showed in an irrevocable manner, that each time, Hilbert’s formalistic principle of inner consistency and lack of contradiction is applied to the system of mathematics – be it geometry or algebra – it inevitably leads to a basic antinomy (paradox). This term was first introduced by Russell, who challenged Cantor’s theory of sets, the basis of modern mathematics. Gödel showed by logical means that any axiomatic approach in mathematics inevitably leads to two opposite, excluding results.
The Continuum Hypothesis
Until now, no one has been able to disprove Gödel’s theorem, which he further elaborated in 1937. With this theorem the foundation crisis of mathematics began and is still ongoing as embodied in the Continuum hypothesis, notwithstanding the fact, that all mathematicians after Gödel prefer to ignore it. On the other hand, mathematics seems to render valid results, when it is applied to the physical world in form of natural laws.
This observation leads to the only possible conclusion.
The Discovery of the “Universal Law”
The solution of the continuum hypothesis and the elimination of the foundation crisis of mathematics can only be achieved in the real physical world and not in the hermeneutic, mental space of mathematical concepts. This is the only possible “proof of existence” that can eliminate the Foundation Crisis of mathematics and abolish the current antinomy between its validity in physics and its inability to prove the same in its own realm.
The new axiomatics that will emerge from this intellectual endeavour will no longer be purely mathematical, but will be physical and mathematical at once. Such an axiomatics can only be based on the discovery of the “Universal Law”, the latter being at once the origin of physics and mathematics. In this case, the “Universal Law” will be the first and only primary axiom, from which all scientific terms, natural laws and various other concepts in science will be axiomatically, i.e. consistently and without any inner contradiction, derived. Such axiomatics is rooted in experience and will be confirmed by all natural phenomena without exception. This axiomatics will be the foundation of the General Theory of Science, which the author developed after he discovered the Universal Law of Nature in 1994.
- Dr. Georgi Stankov, Munich, Germany
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