The essence of creation is accumulation and reduction of the number of particles in each system in various combinations. Thus, Nature has to be mathematical. But then physics should obey the laws of mathematics, just as mathematics should comply with the laws of physics. We have shown elsewhere that all of mathematics cannot be physics. We may have a mathematical equation without a corresponding physical explanation. Accumulation or reduction can be linear or non-linear. If they are linear, the mathematics is addition and subtraction. If they are non-linear, the mathematics is multiplication and division. Yet, this principle is violated in a large number of equations. For an example, the Schrödinger’s equation in one dimension has been discussed earlier. Then there are unphysical combinations. For example, certain combinations of protons and neutrons are prohibited physically, though there is no restriction on devising one such mathematical formula. There is no equation for the observer. Thus, sole dependence on mathematics for discussing physics is neither desirable nor warranted.
We accept “proof” – mathematical or otherwise – to validate the reality of any physical phenomena. We depend on proof to validate a theory as long as it corresponds to reality. The modern system of proof takes five stages: observation/experiment, developing hypothesis, testing the hypothesis, acceptance or rejection or modification of hypothesis based on the additional information and lastly, reconstruction of the hypothesis if it was not accepted. We also adopt a five stage approach to proof. First we observe/experiment and hypothesize. Then we look for corroborative evidence. In the third stage we try to prove that the opposite of the hypothesis is wrong. In the fourth stage we try to prove whether the hypothesis is universally valid or has any limitations. In the last stage we try to prove that any theory other than this is wrong.
Mathematics is one of the tools of “proof” because of its logical constancy. It is a universal law that the tools are selected based on the nature of operations and not vice-versa. The tools can only restrict the choice of operations. Hence mathematics by itself does not provide proof, but the proof may use mathematics as a tool. We also depend on symmetry, as it is a fundamental property of Nature. In our theory, different infinities co-exist and do not interact with each other. Thus, we agree that the evolutionary process of the Universe could be explained mathematically, as basically it is a process of non-linear accumulation and corresponding reduction of particles and energies in different combinations. But we differ on the interpretation of the equation. For us, the left hand side of the equation represents the cause and the right hand side the effect, which is reversible only in the same order. If the magnitudes of the parameters of one side are changed, the effect on the other side also correspondingly changes. But such changes must be according to natural laws and not arbitrary changes. For example, we agree that e/m = c2 or m/e = 1/c2, which we derive from fundamental principles. But we do not agree that e = mc2. This is because we treat mass and energy as inseparable conjugates with variable magnitude and not interchangeable, as each has characteristics not found in the other. Thus, they are not fit to be used in an equation as cause and effect. Simultaneously, we agree with c2 as energy flow is perceived in fields, which are represented by second order quantities.
If we accept the equation e = mc2, according to modern principles, it will lead to m = e/c2. In that case, we will land in many self contradicting situations. For example, if photon has zero rest mass, then m0 = 0/c2 (at rest, external energy that moves a particle has to be zero. Internal energy is not relevant, as a stable system has zero net energy). This implies that m0c2 = 0, or e = 0, which makes c2 = 0/0, which is meaningless. But if we accept e/m = c2 and both sides of the equation as cause and effect, then there is no such contradiction. As we have proved in our book “Vaidic Theory of Numbers”, all operations involving zero except multiplication are meaningless. Hence if either e or m becomes zero, the equation becomes meaningless and in all other cases, it matches the modern values. Here we may point out that the statement that the rest mass of matter is determined by its total energy content is not susceptible of a simple test since there is no independent measure of the later quantity. This proves our view that mass and energy are inseparable conjugates.
The domain that astronomers call “the universe” – the space, extending more than 10 billion light years around us and containing billions of galaxies, each with billions of stars, billions of planets (and maybe billions of biospheres) – could be an infinitesimal part of the totality. There is a definite horizon to direct observations: a spherical shell around us, such that no light from beyond it has had time to reach us since the big bang. However, there is nothing physical about this horizon. If we were in the middle of an ocean, it is conceivable that the water ends just beyond your horizon – except that we know it doesn’t. Likewise, there are reasons to suspect that our universe – the aftermath of our big bang – extends hugely further than we can see.
An idea called eternal inflation suggested by some cosmologists envisages big bangs popping off, endlessly, in an ever-expanding substratum. Or there could be other space-times alongside ours – all embedded in a higher-dimensional space. Ours could be but one universe in a multiverse. Other branches of mathematics then may become relevant. This has encouraged the use of exotic mathematics such as the transfinite numbers. It may require a rigorous language to describe the number of possible states that a universe could possess and to compare the probability of different configurations. It may just be too hard for human brains to grasp. A fish may be barely aware of the medium in which it lives and swims; certainly it has no intellectual powers to comprehend that water consists of interlinked atoms of hydrogen and oxygen. The microstructure of empty space could, likewise, be far too complex for unaided human brains to grasp. Can we guarantee that with the present mathematics we can overcome all obstacles and explain all complexities of Nature? Should we not resort to the so-called exotic mathematics? But let us see where it lands us.
The manipulative mathematical nature of the descriptions of quantum physics has created difficulties in its interpretation. For example, the mathematical formalism used to describe the time evolution of a non-relativistic system proposes two somewhat different kinds of transformations:
· Reversible transformations described by unitary operators on the state space. These transformations are determined by solutions to the Schrödinger equation.
· Non-reversible and unpredictable transformations described by mathematically more complicated transformations. Examples of these transformations are those that are undergone by a system as a result of measurement.
The truth content of a mathematical statement is judged from its logical consistency. We agree that mathematics is a way of representing and explaining the Universe in a symbolic way because evolution is logically consistent. This is because everything is made up of the same “stuff”. Only the quantities (number or magnitude) and their ordered placement or configuration create the variation. Since numbers are a property by which we differentiate between similar objects and all natural phenomena are essentially accumulation and reduction of the fundamental “stuff” in different permissible combinations, physics has to be mathematical. But then mathematics must conform to Natural laws: not un-physical manipulations or the brute force approach of arbitrarily reducing some parameters to zero to get a result that goes in the name of mathematics. We suspect that the over-dependence on mathematics is not due to the fact that it is unexceptionable, but due to some other reason described below.
In his book “The Myth of the Framework”, Karl R Popper, acknowledged as the major influence in modern philosophy and political thought, has said: “Many years ago, I used to warn my students against the wide-spread idea that one goes to college in order to learn how to talk and write “impressively” and incomprehensibly. At that time many students came to college with this ridiculous aim in mind, especially in Germany …………. They unconsciously learn that highly obscure and difficult language is the intellectual value par excellence……………Thus arose the cult of incomprehensibility, of “impressive” and high sounding language. This was intensified by the impenetrable and impressive formalism of mathematics…………….” It is unfortunate that even now many Professors, not to speak of their students, are still devotees of the above cult.
The modern Scientists justify the cult of incomprehensibility in the garb of research methodology – how “big science” is really done. “Big science” presents a big opportunity for methodologists. With their constant meetings and exchanges of e-mail, collaboration scientists routinely put their reasoning on public display (not the general public, but only those who subscribe to similar views), long before they write up their results for publication in a journal. In reality, it is done to test the reaction of others as often bitter debate takes place on such ideas. Further, when particle physicists try to find a particular set of events among the trillions of collisions that occur in a particle accelerator, they focus their search by ignoring data outside a certain range. Clearly, there is a danger in admitting a non-conformist to such raw material, since a lack of acceptance of their reasoning and conventions can easily lead to very different conclusions, which may contradict their theories. Thus, they offer their own theory of “error-statistical evidence” such as in the statement, “The distinction between the epistemic and causal relevance of epistemic states of experimenters may also help to clarify the debate over the meaning of the likelihood principle”. Frequently they refer to ceteris paribus (other things being equal), without specifying which other things are equal (and then face a challenge to justify their statement).
The cult of incomprehensibility has been used even the most famous scientists with devastating effect. Even the obvious mistakes in their papers have been blindly accepted by the scientific community and remained un-noticed for hundreds of years. Here we quote from an article written by W.H. Furry of Department of Physics, Harvard University, published in March 1, 1936 issue of Physical Review, Volume 49. The paper “Note on the Quantum-Mechanical Theory of Measurement” was written in response to the famous EPR Argument and its counter by Bohr. The quote relates to the differentiation between “pure state” and “mixture state”.