POSSIBLE TYPES OF STATISTICAL INFORMATION ABOUT A SYSTEM 3
The Schrödinger equation was devised to find the probability of finding the particle in the narrow region between x and x+dx, which is denoted by P(x) dx. The function P(x) is the probability distribution function or probability density, which is found from the wave function ψ(x) in the equation P(x) = [ψ(x)]2. The wave function is determined by solving the Schrödinger’s differential equation: d2ψ/dx2 + 8π2m/h2 [E-V(x)]ψ = 0, where E is the total energy of the system and V(x) is the potential energy of the system. By using a suitable energy operator term, the equation is written as Hψ = Eψ. The equation is also written as iħ ∂/∂tψ› = Hψ›, where the left hand side represents iħ times the rate of change with time of a state vector. The right hand side equates this with the effect of an operator, the Hamiltonian, which is the observable corresponding to the energy of the system under consideration. The symbol ψ indicates that it is a generalization of Schrödinger’s wave-function. The equation appears to be an equation in one dimension, but in reality it is a second order equation signifying a two dimensional field, as the original equation and the energy operator contain a term x2. A third order equation implies volume. Three areas cannot be added to create volume. Thus, the Schrödinger equation described above is an equation not in one, but in two dimensions. The method of the generalization of the said Schrödinger equation to the three spatial dimensions does not stand mathematical scrutiny.
Three areas cannot be added to create volume. Any simple mathematical model will prove this. Hence, the Schrödinger equation could not be solved for other than hydrogen atoms. For many electron atoms, the so called solutions simply consider them as many one-electron atoms, ignoring the electrostatic energy of repulsion between the electrons and treating them as point charges frozen to some instantaneous position. Even then, the problem remains to be solved. The first ionization potential of helium is theorized to be 20.42 eV, against the experimental value of 24.58 eV. Further, the atomic spectra show that for every series of lines (Lyman, Balmer, etc) found for hydrogen, there is a corresponding series found at shorter wavelengths for helium, as predicted by theory. But in the spectrum of helium, there are two series of lines observed for every single series of lines observed for hydrogen. Not only does helium possess the normal Balmer series, but also it has a second “Balmer” series starting at λ = 3889 Å. This shows that, for the helium atom, the whole series repeats at shorter wavelengths.
For the lithium atom, it is even worse, as the total energy of repulsion between the electrons is more complex. Here, it is assumed that as in the case of hydrogen and helium, the most stable energy of lithium atom will be obtained when all three electrons are placed in the 1s atomic orbital giving the electronic configuration of 1s3, even though it is contradicted by experimental observation. Following the same basis as for helium, the first ionization potential of lithium is theorized to be 20.4 eV, against the experimental value of 202.5 eV to remove all three electrons and only 5.4 eV to remove one electron from lithium. Experimentally, it requires less energy to ionize lithium than it does to ionize hydrogen, but the theory predicts ionization energy one and half times larger. More serious than this is the fact that, the theory should never predict the system to be more stable than it actually is. The method should always predict energy less negative than is actually observed. If this is not found to be the case, then it means that an incorrect assumption has been made or that some physical principle has been ignored.
Further, it contradicts the principle of periodicity, as the calculation places each succeeding electron in the 1s orbital as it increases nuclear charge by unity. It must be remembered that, with every increase in n, all the preceding values of l are repeated, and a new l value is introduced. The reasons why more than two electrons could not be placed in the 1s orbit has not been explained. Thus, the mathematical formulations are contrary to the physical conditions based on observation. To overcome this problem, scientists take the help of operators. An operator is something which turns one vector into another. Often scientists describe robbery as an operator that transforms a state of wealth to a state of penury for the robbed and vice versa for the robber. Another example of an operator often given is the operation that rotates a frame clockwise or anticlockwise changing motion in northern direction to that in eastern or western directions. The act of passing light through a polarizer is called an operator as it changes the physical state of the photons polarization. Thus, the use of a polarizer is described as measurement of polarization, since the transmitted beam has to have its polarization in the direction perpendicular to it. We will come back to operators later.
The probability does not refer to (as is commonly believed) whether the particle will be observed at any specific position at a specific time or not. Similarly the description of different probability of finding the particle at any point of space is misleading. A particle will be observed only at a particular position at a particular time and no where else. Since a mobile particle does not have a fixed position, the probability actually refers to the state in which the particle is likely to be observed. This is because all the forces acting on it and their dynamics, which influence the state of the particle, may not be known to us. Hence we cannot predict with certainty whether the particle will be found here or elsewhere. After measurement, the particle is said to acquire a time invariant “fixed state” by “wave-function collapse”. This is referred to as the result of measurement, which is an arbitrarily frozen time invariant non-real (since in reality, it continues to change) state. This is because; the actual state with all influences on the particle has been measured at “here-now”, which is a perpetually changing state. Since all mechanical devices are subject to time variance in their operational capacities, they have to be “operated” by a “conscious agent” – directly or indirectly – because, as will be shown later, only consciousness is time invariant. This transition from a time variant initial state to a time invariant hypothetical “fixed state” through “now” or “here-now” is the dividing line between quantum physics and the classical physics, as well as conscious actions and mechanical actions. To prove the above statement, we have examined what is “information” in latter pages, because only conscious agents can cognize information and use it to achieve the desired objects. However, before that we will briefly discuss the chaos prevailing in this area among the scientists.
Modern science fails to answer the question “why” on many occasions. In fact it avoids such inconvenient questions. Here we may quote an interesting anecdote from the lives of two prominent persons. Once, Arthur Eddington was explaining the theory of the expanding universe to Bertrand Russell. Eddington told Russell that the expansion was so rapid and powerful that even a most powerful dictator would not be able to control the entire universe. He explained that even if the orders were sent with the speed of light, they would not reach the farthest parts of the universe. Bertrand Russell asked, “If that is so, how does God supervise what is going on in those parts?” Eddington looked keenly at Russell and replied, “That, dear Bertrand does not lie in the province of the physicists.” This begs the question: What is physics? We cannot take the stand that the role of physics is not to explain, but to describe reality. Description is also an explanation. Otherwise, why and to whom do you describe? If the validity of a physical statement is judged by its correspondence to reality, we cannot hide behind the veil of reductionism, but explain scientifically the theory behind the seemingly “acts of God”.
There is a general belief that we can understand all physical phenomenon if we can relate it to the interactions of atoms and molecules. After all, the Universe is made up of these particles only. Their interactions – in different combinations – create everything in the Universe. This is called a reductionist approach because it is claimed that everything else can be reduced to this supposedly more fundamental level. But this approach runs into problem with thermodynamics and its arrow of time. In the microscopic world, no such arrow of time is apparent, irrespective of whether it is being described by Newtonian mechanics, relativistic or quantum mechanics. One consequence of this description is that there can be no state of microscopic equilibrium. Time-symmetric laws do not single out a special end-state where all potential for change is reduced to zero, since all instants in time are treated as equivalent.
The apparent time reversibility of motion within the atomic and molecular regimes, in direct contradiction to the irreversibility of thermodynamic processes constitutes the celebrated irreversibility paradox put forward by in 1876 by Loschmidt among others (L. Boltzmann: Lectures on Gas Theory – University of California Press, 1964, page 9). The paradox suggests that the two great edifices – thermodynamics and mechanics – are at best incomplete. It represents a very clear problem in need of an explanation which should not be swept under carpet. As Lord Kelvin says: If the motion of every particle of matter in the Universe were precisely reversed at any instant, the course of Nature would be simply reversed for ever after. The bursting bubble of foam at the foot of a waterfall would reunite and descend into water. The thermal motions would reconcentrate energy and throw the mass up the fall in drops reforming in a close column of ascending water. Living creatures would grow backwards – from old age to infancy till they are unborn again – with conscious knowledge of the future but no memory of the past. We will solve this paradox in later pages.
The modern view on reductionism is faulty. Reductionism is based on the concept of differentiation. When an object is perceived as a composite that can be reduced to different components having perceptibly different properties which can be differentiated from one another and from the composite as a whole, the process of such differentiation is called reductionism. Some objects may generate similar perception of some properties or the opposite of some properties from a group of substances. In such cases the objects with similar properties are grouped together and the objects with opposite properties are grouped together. The only universally perceived aspect that is common to all objects is physical existence in space and time, as the radiation emitted by or the field set up by all objects create a perturbation in our sense organs always in identical ways. Since intermediate particles exhibit some properties similar with other particles and are similarly perceived with other such objects and not differentiated from others, reductionism applies only to the fundamental particles. This principle is violated in most modern classifications.
To give one example, x-rays and γ-rays exhibit exclusive characteristics that are not shared by other rays of the electromagnetic spectrum or between themselves – such as the place of their origin. Yet, they are clubbed under one category. If wave nature of propagation is the criterion for such categorisation, then sound waves that travel through a medium such as air or other gases in addition to liquids and solids of all kinds should also have been added to the classification. Then there are mechanical waves, such as the waves that travel though a vibrating string or other mechanical object or surface, waves that travel through a fluid or along the surface of a fluid, such as water waves. If electromagnetic properties are the criteria for such categorisation, then it is not scientific, as these rays do not interact with electromagnetic fields. If they have been clubbed together on the ground that theoretically they do not require any medium for their propagation, then firstly there is no true vacuum and secondly, they are known to travel through various mediums such as glass. There are many such examples of wrong classification due to reductionism and developmental history.
The cults of incomprehensibility and reductionism have led to another deficiency. Both cosmology and elementary particle physics share the same theory of the plasma and radiation. They have independent existence that is seemingly eternal and may be cyclic. Their combinations lead to the sub-atomic particles that belong to the micro world of quantum physics. The atoms are a class by itself, whose different combinations lead to the perceivable particles and bodies that belong to the macro world of the so-called classical physics. The two worlds merge in the stars, which contain plasma of the micro world and the planetary system of the macro world. Thus, the study of the evolution of stars can reveal the transition from the micro world to the macro world. For example, the internal structures of planet Jupiter and protons are identical and like protons, Jupiter-like stars are abundant in the stars. Yet, in stead of unification of all branches of science, Cosmology and nuclear physics have been fragmented into several “specialized” branches.
Here we are reminded of an anecdote related to Lord Chaitanya. While in his southern sojourn, a debate was arranged between him and a great scholar of yore. The scholar went off explaining many complex doctrines while Lord Chaitanya sat quietly and listened with rapt attention without any response. Finally the scholar told Lord Chaitanya that he was not responding at all to his discourse. Was it too complex for him? The Scholar was sure from the look on Lord Chaitanya’s face that he did not understand anything. To this, Lord Chaitanya replied; “I fully understand what you are talking about. But I was wondering why you are making the simple things look so complicated?” Then he explained the same theories in plain language after which the scholar fell at his feet.
There has been very few attempts to list out the essence of all branches and develop “one” science. Each branch has its huge data bank with its specialized technical terms glorifying some person at the cost of a scientific nomenclature thereby enhancing incomprehensibility. Even if we read the descriptions of all six proverbial blind men repeatedly, one who has not seen an elephant cannot visualize it. This leaves the students with little opportunity to get a macro view of all theories and evaluate their inter-relationship. The educational system with its examination method of emphasizing the aspects of “memorization and reproduction at a specific instant” compounds the problem. Thus, the students have to accept many statements and theories as “given” without questioning it even on the face of ambiguities. Further, we have never come across any book on science, which does not glorify the discoveries in superlative terms, while leaving out the uncomfortable and ambiguous aspects, often with an assurance that they are correct and should be accepted as such. This creates an impression on the minds of young students to accept the theories unquestioningly making them superstitious. Thus, whenever some deficiencies have been noticed in any theory, there is an attempt at patch work within the broad parameters of the same theories. There have been few attempts to review the theories ab initio. Thus, the scientists cannot relate the tempest at a distant land to the flapping of the wings of the butterfly elsewhere.
Till now scientists do not know “what” are electrons, photons, and other subatomic objects that have made the amazing technological revolution possible? Even the modern description of the nucleus and the nucleons leave many aspects unexplained. Photo-electric effect, for which Einstein got his Noble Prize, deals with electrons and photons. But it does not clarify “what” are these particles. The scientists, who framed the current theories, were not gifted with the benefit of the presently available data. Thus, without undermining their efforts, it is necessary to ab initio re-formulate the theories based on the presently available data. Only this way we can develop a theory whose correspondence resembles to reality. Here is an attempt in this regard from a different perspective. Like the child revealing the secret of the Emperor’s clothes, we, a novice in this field, are attempting to point the lamp in the direction of the Sun.
Thousands of papers are read every year in various forums on as yet undiscovered particles. This reminds us of the saying which means: after taking bath in the water of the mirage, wearing the flower of the sky in the head, holding the bow made of the horns of a rabbit, here goes the son of the barren woman! Modern scientists are precisely making similar statements. This is a sheer waste of not only valuable time but also public money worth trillions for the pleasure of a few. In addition, this amounts to misguiding general public for generations. This is unacceptable because a scientific theory must stand up to experimental scrutiny within a reasonable time period. Till it is proved or disproved, it cannot be accepted, though not rejected either. We cannot continue for three quarters and more of a century to develop “theories” based on such unproven postulates in the hope that we may succeed someday – may be after a couple of centuries! We cannot continue research on the properties of the “flowers of the sky” on the ground that someday it may be discovered.
Experiments with the subatomic phenomena show effects that have not been reconciled with our normal view of an objective world. Yet, they cannot be treated separately. This implies the existence of two different states – classical and quantum – with different dynamics, but linked to each other in some fundamentally similar manner. Since the validity of a physical statement is judged by its correspondence to reality, there is a big question mark on the direction in which theoretical physics is moving. Technology has acquired a pre-eminent position in the global epistemic order. However, Engineers and Technologists, who progress by trial and error methods, have projected themselves as experimental scientists. Their search for new technology has been touted as the progress of science, questioning whose legitimacy is projected as deserving a sacrament. Thus, everything that exposes the hollowness or deficiencies of science is consigned to defenestration. The time has come to seriously consider the role, the ends and the methods of scientific research. If we are to believe that the sole objective of the scientists is to make their impressions mutually consistent, then we lose all motivation in theoretical physics. These impressions are not of a kind that occurs in our daily life. They are extremely special, are produced at great cost, time and effort. Hence it is doubtful whether the mere pleasure their harmony gives to a selected few can justify the huge public spending on such “scientific research”.
A report published in the Notices of the American Mathematical Society, October 2005 issue shows that the Theory of Dynamical Systems that is used for calculating the trajectories of space flights and the Theory of Transition States for chemical reactions share the same mathematics. This is the proof of a universally true statement that both microcosm and the macrocosm replicate each other. The only problem is to find the exact correlations. For example, as we have repeated pointed out, the internal structure of a proton and that of planet Jupiter are identical. We will frequently use this and other similarities between the microcosm and the macrocosm (from astrophysics) in this presentation to prove the above statement. Also we will frequently refer to the definitions of technical terms as defined precisely in our book “Vaidic Theory of Numbers”.