In modern science, there is no unambiguous and precise definition of the words time, space, dimension, numbers, zero, infinity, charge, quantum particle, wave-function etc. The operational definitions have been changed from time to time to take into account newer facts that facilitate justification of the new “theory”. For example, the fundamental concept of the quantum mechanical theory is the concept of “state”, which is supposed to be completely characterized by the wave-function. However, till now it is not certain “what” a wave-function is. Is the wave-function real – a concrete physical object or is it something like a law of motion or an internal property of particles or a relation among spatial points? Or is it merely our current information about the particles? Quantum mechanical wave-functions cannot be represented mathematically in anything smaller than a 10 or 11 dimensional space called configuration space. This is contrary to experience and the existence of higher dimensions is still in the realm of speculation. If we accept the views of modern physicists, then we have to accept that the universe’s history plays itself out not in the three dimensional space of our everyday experience or the four-dimensional space-time of Special Relativity, but rather in this gigantic configuration space, out of which the illusion of three-dimensionality somehow emerges. Thus, what we see and experience is illusory! Maya?
The measurement problem in quantum mechanics is the unresolved problem of how (or if) wave-function collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. If it is postulated that a particle does not have a value before measurement, there has to be conclusive evidence to support this view. The wave-function in quantum mechanics evolves according to the Schrödinger equation into a linear superposition of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was “discovered” to be in when the measurement was made, implying that the measurement “did something” to the process under examination. Whatever that “something” may be does not appear to be explained by the basic theory. Further, quantum systems described by linear wave-functions should be incapable of non-linear behavior. But chaotic quantum systems have been observed. Though chaos appears to be probabilistic, it is actually deterministic. Further, if the collapse causes the quantum state to jump from superposition of states to a fixed state, it must be either an illusion or an approximation to the reality at quantum level. We can rule out illusion as it is contrary to experience. In that case, there is nothing to suggest that events in quantum level are not deterministic. We may very well be able to determine the outcome of a quantum measurement provided we set up an appropriate measuring device!
The operational definitions and the treatment of the term wave-function used by researchers in quantum theory progressed through intermediate stages. Schrödinger viewed the wave-function associated with the electron as the charge density of an object smeared out over an extended (possibly infinite) volume of space. He did not regard the waveform as real nor did he make any comment on the waveform collapse. Max Born interpreted it as the probability distribution in the space of the electron’s position. He differed from Bohr in describing quantum systems as being in a state described by a wave-function which lives longer than any specific experiment. He considered the waveform as an element of reality. According to this view, also known as State Vector Interpretation, measurement implied the collapse of the wave function. Once a measurement is made, the wave-function ceases to be smeared out over an extended volume of space and the range of possibilities collapse to the known value. However, the nature of the waveform collapse is problematic and the equations of Quantum Mechanics do not cover the collapse itself.
The view known as “Consciousness Causes Collapse” regards measuring devices also as quantum systems for consistency. The measuring device changes state when a measurement is made, but its wave-function does not collapse. The collapse of the wave-function can be traced back to its interaction with a conscious observer. Let us take the example of measurement of the position of an electron. The waveform does not collapse when the measuring device initially measures the position of the electron. Human eye can also be considered a quantum system. Thus, the waveform does not collapse when the photon from the electron interacts with the eye. The resulting chemical signals to the brain can also be treated as a quantum system. Hence it is not responsible for the collapse of the wave-form. However, a conscious observer always sees a particular outcome. The wave-form collapse can be traced back to its first interaction with the consciousness of the observer. This begs the question: what is consciousness? At which stage in the above sequence of events did the wave-form collapse? Did the universe behave differently before life evolved? If so, how and what is the proof for that assumption? No answers.
Many-worlds Interpretation tries to overcome the measurement problem in a different way. It regards all possible outcomes of measurement as “really happening”, but holds that somehow we select only one of those realities (or in their words – universes). But this view clashes with the second law of thermodynamics. The direction of the thermodynamic arrow of time is defined by the special initial conditions of the universe which provides a natural solution to the question of why entropy increases in the forward direction of time. But what is the cause of the time asymmetry in the Many-worlds Interpretation? Why do universes split in the forward time direction? It is said that entropy increases after each universe-branching operation – the resultant universes are slightly more disordered. But some interpretations of decoherence contradict this view. This is called macroscopic quantum coherence. If particles can be isolated from the environment, we can view multiple interference superposition terms as a physical reality in this universe. For example, let us consider the case of the electric current being made to flow in opposite directions. If the interference terms had really escaped to a parallel universe, then we should never be able to observe them both as physical reality in this universe. Thus, this view is questionable.
Transactional Interpretation accepts the statistical nature of waveform, but breaks it into an “offer” wave and an “acceptance” wave, both of which are treated as real. Probabilities are assigned to the likelihood of interaction of the offer waves with other particles. If a particle interacts with the offer wave, then it “returns” a confirmation wave to complete the transaction. Once the transaction is complete, energy, momentum, etc., are transferred in quanta as per the normal probabilistic quantum mechanics. Since Nature always takes the shortest and the simplest path, the transaction is expected to be completed at the first opportunity. But once that happens, classical probability and not quantum probability will apply. Further, it cannot explain how virtual particles interact. Thus, some people defer the waveform collapse to some unknown time. Since the confirmation wave in this theory is smeared all over space, it cannot explain when the transaction begins or is completed and how the confirmation wave determines which offer wave it matches up to.
Quantum decoherence, which was proposed in the context of the many-worlds interpretation, but has also become an important part of some modern updates of the Copenhagen interpretation based on consistent histories, allows physicists to identify the fuzzy boundary between the quantum micro-world and the world where the classical intuition is applicable. But it does not describe the actual process of the wave-function collapse. It only explains the conversion of the quantum probabilities (that are able to interfere) to the ordinary classical probabilities. Some people have tried to reformulate quantum mechanics as probability or logic theories. In some theories, the requirements for probability values to be real numbers have been relaxed. The resulting non-real probabilities correspond to quantum waveform. But till now a fully developed theory is missing.
Hidden Variables Theories treat Quantum mechanics as incomplete. Until a more sophisticated theory underlying Quantum mechanics is discovered, it is not possible to make any definitive statement. It views quantum objects as having properties with well-defined values that exist separately from any measuring devices. According to this view, chance plays no roll at all and everything is fully deterministic. Every material object invariably does occupy some particular region of space. This theory takes the form of a single set of basic physical laws that apply in exactly the same way to every physical object that exists. The waveform may be a purely statistical creation or it may have some physical role. The Causal Interpretation of Bohm and its latter development, the Ontological Interpretation, emphasize “beables” rather than the “observables” in contradistinction to the predominantly epistemological approach of the standard model. This interpretation is causal, but non-local and non-relativistic, while being capable of being extended beyond the domain of the current quantum theory in several ways.
There are divergent views on the nature of reality and the role of science in dealing with reality. Measuring a quantum object was supposed to force it to collapse from a waveform into one position. According to quantum mechanical dogma, this collapse makes objects “real”. But new verifications of “collapse reversal” suggest that we can no longer assume that measurements alone create reality. It is possible to take a “weak” measurement of a quantum particle continuously partially collapsing the quantum state, and then “unmeasure” it altering certain properties of the particle and perform the same weak measurement again. In one such experiment reported in Nature News, the particle was found to have returned to its original quantum state just as if no measurement had ever been taken. This implies that, we cannot assume that measurements create reality because; it is possible to erase the effects of a measurement and start again.
Newton gave his laws of motion in the second chapter, entitled “Axioms, or Laws of motion” of his book Principles of Natural Philosophy published in 1687 in Latin language. The second law says that the change of motion is proportional to the motive force impressed. Newton relates the force to the change of momentum (not to the acceleration as most textbooks do). Momentum is accepted as one of two quantities that, taken together, yield the complete information about a dynamic system at any instant. The other quantity is position, which is said to determine the strength and direction of the force. Since then the earlier ideas have changed considerably. The pairing of momentum and position is no longer viewed in the Euclidean space of three dimensions. Instead, it is viewed in phase space, which is said to have six dimensions, three for position and three for momentum. But here the term dimension has actually been used for direction, which is not a scientific description.
In fact most of the terms used by modern scientists have not been precisely defined – they have only an operational definition, which is not only incomplete, but also does not stand scientific scrutiny, though it is often declared as “reasonable”. This has been done not by chance, but by design, as modern science is replete with such instances. For example, we quote from the paper of Einstein and his colleagues Boris Podolsky and Nathan Rosen, which is known as the EPR argument (Phys. Rev. 47, 777 (1935):
“A comprehensive definition of reality is, however, unnecessary for our purpose. We shall be satisfied with the following criterion, which, we regard as reasonable. If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity. It seems to us that this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one such way, whenever the conditions set down in it occur. Regarded not as necessary, but merely as a sufficient, condition of reality, this criterion is in agreement with classical as well as quantum-mechanical ideas of reality.”