“It is easy to explain something to a layman. It is easier to explain the same thing to an expert. But even the most knowledgeable person cannot explain something to one who has limited half-baked knowledge.” ————- (Hitopadesha).
“To my mind there must be, at the bottom of it all, not an equation, but an utterly simple idea. And to me that idea, when we finally discover it, will be so compelling, so inevitable, that we will say to one another: ‘Oh, How wonderful! How could it have been otherwise.” ———–(John Wheeler).
“All these fifty years of conscious brooding have brought me no nearer to the answer to the question, ‘What are light quanta?’ Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken”. ————— Einstein, 1954
Twentieth century was a marvel in technological advancement. But except for the first quarter, the advancement of theoretical physics has nothing much to be written about. The principle of mass-energy equivalence, which is treated as the corner-stone principle of all nuclear interactions, binding energies of atoms and nucleons, etc., enters physics only as a corollary of the transformation equations between frames of references in relative motion. Quantum Mechanics (QM) cannot justify this equivalence principle on its own, even though it is the theory concerned about the energy exchanges and interactions of fundamental particles. Quantum Field Theory (QFT) is the extension of QM (dealing with particles) over to fields. In spite of the reported advancements in QFT, there is very little back up experimental proof to validate many of its postulates including Higgs mechanism, bare mass/charge, infinite charge etc. It seems almost impossible to think of QFT without thinking of particles which are accelerated and scattered in colliders. But interestingly, the particle interpretation has the best arguments against QFT. Till recently, the Big Bang hypothesis held the center stage in cosmology. Now Loop Quantum Cosmology (LQC) with its postulates of the “Big Bounce” is taking over. Yet there are two distinctly divergent streams of thought on this subject also. The confusion surrounding interpretation of quantum physics is further compounded by the modern proponents, who often search historical documents of discarded theories and come up with new meanings to back up their own theories. For example, the cosmological constant, first proposed and subsequently rejected as the greatest blunder of his life by Einstein; has made a come back in cosmology. Bohr’s complementarity principle, originally central to his vision of quantum particles, has been reduced to a corollary and is often identified with the frameworks in Consistent Histories.
There are a large number of different approaches or formulations to the foundations of Quantum Mechanics. There is the Heisenberg’s Matrix Formulation, Schrödinger’s Wave-function Formulation, Feynman’s Path Integral Formulation, Second Quantization Formulation, Wigner’s Phase Space Formulation, Density Matrix Formulation, Schwinger’s Variational Formulation, de Broglie-Bohm’s Pilot Wave Formulation, Hamilton-Jacobi Formulation etc. There are several Quantum Mechanical pictures based on placement of time-dependence. There is the Schrödinger Picture: time-dependent Wave-functions, the Heisenberg Picture: time-dependent operators and the Interaction Picture: time-dependence split. The different approaches are in fact, modifications of the theory. Each one introduces some prominent new theoretical aspect with new equations, which needs to be interpreted or explained. Thus, there are many different interpretations of Quantum Mechanics, which are very difficult to characterize. Prominent among them are; the Realistic Interpretation: wave-function describes reality, the Positivistic Interpretation: wave-function contains only the information about reality, the famous Copenhagen Interpretation: which is the orthodox Interpretation. Then there is Bohm’s Causal Interpretation, Everett’s Many World’s Interpretation, Mermin’s Ithaca Interpretation, etc. With so many contradictory views, quantum physics is not a coherent theory, but truly weird.
General relativity breaks down when gravity is very strong: for example when describing the big bang or the heart of a black hole. And the standard model has to be stretched to the breaking point to account for the masses of the universe’s fundamental particles. The two main theories; quantum theory and relativity, are also incompatible, having entirely different notions: such as for the concept of time. The incompatibility of quantum theory and relativity has made it difficult to unite the two in a single “Theory of everything”. There are almost infinite numbers of the “Theory of Everything” or the “Grand Unified Theory”. But none of them are free from contradictions. There is a vertical split between those pursuing the superstrings route and others, who follow the little Higgs route.
String theory, which was developed with a view to harmonize General Relativity with Quantum theory, is said to be a high order theory where other models, such as supergravity and quantum gravity appear as approximations. Unlike super-gravity, string theory is said to be a consistent and well-defined theory of quantum gravity, and therefore calculating the value of the cosmological constant from it should, at least in principle, be possible. On the other hand, the number of vacuum states associated with it seems to be quite large, and none of these features three large spatial dimensions, broken super-symmetry, and a small cosmological constant. The features of string theory which are at least potentially testable – such as the existence of super-symmetry and cosmic strings – are not specific to string theory. In addition, the features that are specific to string theory – the existence of strings – either do not lead to precise predictions or lead to predictions that are impossible to test with current levels of technology.
There are many unexplained questions relating to the strings. For example, given the measurement problem of quantum mechanics, what happens when a string is measured? Does the uncertainty principle apply to the whole string? Or does it apply only to some section of the string being measured? Does string theory modify the uncertainty principle? If we measure its position, do we get only the average position of the string? If the position of a string is measured with arbitrarily high accuracy, what happens to the momentum of the string? Does the momentum become undefined as opposed to simply unknown? What about the location of an end-point? If the measurement returns an end-point, then which end-point? Does the measurement return the position of some point along the string? (The string is said to be a Two dimensional object extended in space. Hence its position cannot be described by a finite set of numbers and thus, cannot be described by a finite set of measurements.) How do the Bell’s inequalities apply to string theory? We must get answers to these questions first before we probe more and spend (waste!) more money in such research. These questions should not be put under the carpet as inconvenient or on the ground that some day we will find the answers. That someday has been a very long period indeed!
The energy “uncertainty” introduced in quantum theory combines with the mass-energy equivalence of special relativity to allow the creation of particle/anti-particle pairs by quantum fluctuations when the theories are merged. As a result there is no self-consistent theory which generalizes the simple, one-particle Schrödinger equation into a relativistic quantum wave equation. Quantum Electro-Dynamics began not with a single relativistic particle, but with a relativistic classical field theory, such as Maxwell’s theory of electromagnetism. This classical field theory was then “quantized” in the usual way and the resulting quantum field theory is claimed to be a combination of quantum mechanics and relativity. However, this theory is inherently a many-body theory with the quanta of the normal modes of the classical field having all the properties of physical particles. The resulting many-particle theory can be relatively easily handled if the particles are heavy on the energy scale of interest or if the underlying field theory is essentially linear. Such is the case for atomic physics where the electron-volt energy scale for atomic binding is about a million times smaller than the energy required to create an electron positron pair and where the Maxwell theory of the photon field is essentially linear.