Quantum Mechanics

QUANTUM MECHANICS

Introduction.

quantum mechanicsThis article is not intended to create controversy of any kind; after all there is plenty of controversy surrounding this theory already. It is important to state that the sole intention of this article is to present the reader with the (unbiased)basic ideas of a highly complex and controversial theory. I claim also that none of the ideas of this article is mine,but they are all paraphrased from the various, eminent experts in the field of Quantum Mechanics, and whose works are gratefully acknowledged at the end of this article.

Background Information: Quantum Mechanics (QM) is a complexity of mathematical equations and philosophical reasoning that allow scientists to predict the workings of the atomic and molecular realms with great accuracy. While reflecting on the meaning of the word: ‘great accuracy’, and coupled with the numerous, unresolved  paradoxes of the theory, Richard Feynman’s words ring true: “Nobody understands quantum mechanics”.

This, however, does not mean that every principal statement of quantum mechanics is flowed or suspect, because, as the defenders of the theory wish to emphasise for  the public to understand, that  all our digital appliances owe their very existence to the scientists’- and engineers’ ability to predict and control the behaviour of sub-atomic particles. Let it be known also that it does not mean either that major quantum experiments refute any of the accepted theories of the classical physics; but it only means that ‘In many cases theories have been found to have a narrower scope of application than had been thought originally’.

A General Analysis of the Theory

The modus operandi of Quantum Mechanics lies in its interrelated theories of systems, experiments, such as the probabilities of measurements, observability, uncertainty, in-determinism, the theory of sub-atomic particles, ambiguities and paradoxes, (e.g. the Schrodinger’s cat); etc. Someone aptly characterised this scientific method as the problem of the ‘One and Many’, which has taken on a new form of ‘virtual particles in a virtual reality’.

Quantum theory developed principally by Planck, Heisenberg Bohr, Schrodinger and von Neumann. It emerged primarily from empirical research into measurements of the heat radiation spectrum, the photoelectric effect, specific heats of solids, radioactive decay, the hydrogen spectrum, and much more.

The known laws of heat and radiation emitted by a ‘black body’ at high temperatures gave rise to further research into its physical properties. At first, there were complex problems and serious difficulties associated with the preliminary experiments carried out by Lord Rayleigh and Jeans.

The early applications of known laws did not lead to sensible results. Then Max Planck took over in 1895, who tried to turn the problem from radiation to the radiating atom. This resulted in nothing more than the simplified re-interpretation of the empirical facts. Meanwhile, in 1900, Rubens’ accurate measurements combined with Planck’s calculations led to the discovery of Planck’s famous Law of Radiation.

Planck observed that electromagnetic radiation (i.e. energy) was emitted in discreet packets or ‘quanta’. Becquerel, Curie (a double- Nobel laureate) and Rutherford, in 1911 clarified the structure of the atom, though its stability was still not yet clear, until Niels Bohr explained it as well, as the line spectra that emitted by the atoms after the excitation through electric discharge or heat. His theory established the quantum conditions combined with classical mechanics for the motion of the electrons.

Bohr suggested in 1913 the strange quantum laws governing the motions of the electrons in the atom. The attempt to describe atomic events in the traditional terms of physics led to contradictions.The uncertainty principle is one of the basic tenets of Quantum Mechanics posited by Heisenberg; that tells us the minimum degree to which we can ‘separate’ in our experiments the observer from the observed object.

While ideal experiments answered critical questions, physicists stayed clear of controversial and contradictory experiments up until the twentieth century. Such experiment was in 1923 by Compton on the scattering of X-rays. Born, Jordan and Dirac proved that the matrices representing position and momentum of the electron do not commute.

George Gamow one of the pioneers of the Big Bang cosmological theory, used the newly formulated quantum theory to estimate how hot the Sun’s core would need to be for hydrogen fusion to be self-sustaining.

Schrödinger described the atom as a system not of a nucleus and electrons but of a nucleus and matter waves. The most common viewpoints of all these experimental findings and their mathematical theories were finalised in 1927 in the Copenhagen interpretation, and confirmed at the Solvay conference in Brussels as the ‘Standard Interpretation’.

This interpretation was made feasible only after its unification in 1932 by von Neumann, who codified it for common understanding.

There are various interpretations of the theory; the present-day viewpoint of the theory is based on the so called Copenhagen interpretation, known the Standard Interpretation. According to that, words and concepts familiar to us lose their meaning in the interpretation; hence, it has deep, implications for our view of the entire physical reality.

The salient points of the Standard Interpretation were: All daily phenomena and atomic events will be described in  terms of the classical physics. Experiments with inaccuracies will have their errors of measurement. These inaccuracies will allow us to translate the result of the observation into the mathematical scheme of quantum theory. A probability function is noted, and it represents two things: partly a fact and partly our knowledge of a fact. The error in the experiment does not represent a property of the electron but a deficiency in our knowledge of the electron.Also this deficiency of knowledge expressed in the probability function.

An important principle is that every system is governed by a ‘wave function’, whose behaviour is exactly determined by Schrodinger’ equation until an observer chooses to make a particular measurement. This leads to what is called ‘collapse of the wave function’. Information complementary to what is actually measured is then irretrievably lost.

The theoretical interpretation of an experiment requires three distinct steps:

  1. Translation of experimental result into a probability function.
  2. Follow up of this function in the course of time.
  3. The result of a new measurement is calculated from the probability function.Note that the authors of the theory provide ample illustrations for these three steps, which, for obvious reason, are left strictly for the experts. This quantum theory was developed later on into “quantum mechanics”, henceforth abbreviated in this article as QM.

The main feature of QM is that in the observable physical reality there is a certain lack of determinism, causality and certainty, and it is the case where one is unable to measure, nor observe sub-atomic particles individually in action.These phenomena were ‘confirmed’ by Heisenberg’s rejection of objective reality of the sub-atomic particles.

In a molecule, the uncertainty in an atom’s position is determined by the mass of its nucleus. The orbits of electrons around the nucleus are very much larger, since electrons are lighter, and there is consequently more fuzziness in their positions. Because protons are 1,836 times heavier than electrons, atoms can be quite precisely located relative to their neighbours.

There are philosophical arguments throughout QM, characterised by the following fallacious procedure: In order to prove some a priori argument about certainties or events, by positing a concept in an abstract environment, whereby they prove the existence of the subject of the argument in the physically reality.

Such reasoning appears to be a philosophical sleight of hand, because it violates the basic rule of philosophical reasoning.This rule states that an argument consists of three propositions so connected that when the first two are given as true, the third follows of equal necessity of truth. An other fallacy in such an argument lies in the fact when it ‘jumps’ from the abstract realm of thought, (such as a hypothesis or any idea), called the logical order, to the realm of physical reality, (outside the mind), called the ontological order, leaving a ‘gap’ in the reasoning process. Philosophy calls this method of reasoning the ‘Ontological Argument’.

In other words, one cannot arrive at a conclusion without providing an evidence-based logical ‘connection’ (in the physical reality), between the major term (predicate of the conclusion) and the conclusion. The major term and a minor term ( subjects of the conclusion) are compared, and this ‘comparison’ (the connection) is missing in several of the QM arguments. E.g.: The use of abstract laws of mathematics, through their logic or even their accuracy, is not of itself  sufficient evidence for  an argument for physical reality.

The following episode illustrates this point: In 1931, Paul Dirac proved mathematically that magnetic monopoles are compatible with QM. He even showed how the magnetic charge should be ‘quantized’ (appear in integer multiples of a minimum unit), just as electric charge distributions are always multiples of the electron’s charge. However, there is one thing Dirac did not know, that is after almost a century of searching, magnetic monopoles were nowhere to be found.

Question by a Scientist: “What is the nature of the physical reality where its fundamental particles are uncertain or unreal, and what are the properties of such a virtual reality? How can we rely on our measuring instruments that are made of similarly incomprehensible and unpredictable particles? How scientific conclusions could be deduced with certainty from such uncertain conditions, which applies to everything, from sub-atomic particles to the recent concept of ‘multiverse’.

‘All the above quantum-uncertainties remind us the skeptics, whose philosophy applies between two extremes of reasoning:the doubting of general grounds of a belief and the rejection of any reason that would justify belief in anything. If we gave up this belief, the existence of common-sense judgement and even science itself would have to be abandoned.’ (R. Stoeger.)

‘QM, with its inter-related theories of phenomena, fights simultaneously on many fronts, whose abstract results are genuinely difficult to understand. The objects of their fight concern primarily the classical physics, namely Einstein’s relativity theories, the causal order of events, Pauli’s exclusion principle, action at a distance, and classical philosophy; etc. As it attempts to describe a world behind the appearance of entities and events, that new reality is so esoteric as to be literary unimaginable. As if QM would have arrived at the border line with metaphysics.’ (Scruton.)

Heisenberg commented that every tool carries with it the spirit by which it has been created. If this is true, then we ought to be rightly question the ‘New Physics’. Instead of clarifying the definitions of words and phrases, QM introduces at every turn a new concept, which complicates only further its philosophical system. (This sounds familiar like ‘Post-modernism.’) Einstein questioned the whole theory on the basis that in a classical world our observations do not create reality; they only uncover it. Therefore he thought that QM is basically an incomplete, inconsistent and a flowed theory.

QM caused a greater philosophical upheaval than did Einstein’s relativity theories. The problem arises not from what the QM does or predicts, but from its intrinsically philosophical consequences. Notwithstanding the above philosophical implications, the theoretical failure to find a plausible alternative to QM suggests that QM may be describing the way things are, because any small change to it would lead to logical absurdities.

In conclusion, there is one major advance made by Paul Dirac, who in 1928 produced through his equation the compatibility of the basic principles of Q.M. with those of the Theory of Special Relativity.

Item No. 1. The Uncertainty Principle.

QM uses the theory of probabilities for the results of measurements, conditional of course, on the hypothesis that a measurement is made. Any process at all is a measurement if it satisfies certain purely physical conditions of qualitative properties, and without any reference to a conscious observer. The answer to what could happen when no measurement is made: Anything is possible. This does not mean anything logically conceivable. The follow-up explanation is far too complicated as it involves the knowledge of the resources of quantum logic.

Bohr proposed that the energy of electrons bound within an atom is restricted to certain discrete values, multiples of a fixed and fundamental energy quantum. The electrons cannot change their energies continuously and so do not steadily slide into the nucleus. In order to lower their energies they have to change their value by a whole quantum. Such quantum particles are e.g. electrons, protons, neutrons and photons, whose positions and angular momenta can be measured in action only individually, but without precise values of both events when happening simultaneously.

The principle concepts of the mathematical system of quantum mechanics were based on Heisenberg’s “uncertainty principle”, which evolved later on by others into the theory of “quantum universe”. Heisenberg’s uncertainty principle implies an inevitable fuzziness in the location of any particle, though the uncertainty is less for heavier particles.All physical entities and events that are observable by humans are subject to unpredictable “fluctuations”, hence their values can never be precisely defined.

The theory adds that the uncertainty between the values of position and momentum are so vanishingly small that it is unobservable in our daily life, nevertheless it is real. This Heisenberg re-phrases elsewhere in his work as: Although quantum effects in meter pointers and photographic grains are negligibly small, they are there nevertheless in principle.

Heisenberg points out further, that this inability to measure two simultaneous values is not due to lack of suitable instruments, but it is because a sub-atomic particle simply does not have precise values of its two properties simultaneously. The implication of this phenomenon is that the simultaneity of the two values is unobservable because of their uncertainty. The imperceptibility of electrons is thought to be mainly due to the super-fast reaction by these elementary particles on our sensory-nervous system. (It appears the principle of the theory is getting bogged down in  details.)

Item No.2. In-determinism.

In-determinism caused by the uncertain path of electrons circling the nucleus along a conventionally assumed distinct orbit. It is impossible to ascribe a precise trajectory linking the starting- point orbit with the arrival-point orbit of an electron. We cannot determine the location and the speed of motion of a particle at the same time with complete precision of a measurement.

QM posits that if the measurement is made that is an interference, and the result is probabilistic, because the system is no longer isolated. Comment: The general view of the world we live in is that it is in-deterministic. Therefore, the result of any measurement is to some extent a matter of chance. But does this not rule out necessarily that the chance result came about deterministically.

Heisenberg used to remark bluntly that reality is in the observations and not in the particle. For his defense, he emphasised that the in-deterministic nature of QM is founded on the same mathematical laws that confirmed for us the deterministic nature of physical reality. The Standard interpretation, however, is more careful in its denial of physical reality.

Schrodinger discovered why sub-atomic phenomena display simultaneously the properties of waves and particles, and he formulated it mathematically in the so called wave function. The key difference between the classical and quantum phenomena is that, although both were developed on deterministic equations, in the quantum phenomena the quantity is not observable.

Bohr was worried about the interpretations of QM and the fact that it gives only probabilistic predictions of the behaviour of the world. Einstein, on the other hand, disliked all together the lack of determinism in the system and doubted if it ever would be part of the ultimate theory of ‘Everything’.

Weinberg points out that even in QM there is still a sense in which the behaviour of any physical system is completely determined by its initial conditions and the laws of nature. This determinism of course does not apply to human activities or life itself under any conditions.

QM is a statistical theory; it can make predictions to events in a group of identical systems, but not in individual systems. The chance element in QM is intrinsic with the system itself, while the unpredictability in other statistical systems, like entropy, is implied to unknown factors extrinsic to the system.

Item No. 3. The Nature of Particles.

Many scientists wonder about the question of whether QM is necessarily true. It had phenomenal success in explaining the properties of particles and atoms and molecules, so we know that it is a very good approximation to the truth.

It is often found in descriptions of QM that single quantum particle systems moving along a well-defined path through space, but without a determined trajectory. This phenomenon is used as analogy to describe the orbit of an electron causing a smearing effect by its position and momentum combined.

There is ample reference to quantum systems as opposed to a single particle, but without defining what a quantum system would comprise. It is of course a different situation from nature’s own arrangement, when e.g. firing single particles, such as electrons, at a target and they scatter in different directions.

Einstein felt uneasy about a quantum experiment that showed two separated systems of particles, where each carried through interaction the imprint of the other, (although proven mathematically). This result was apparently contrary to the Einsteinian tenet that forbids any instantaneous interaction between any single particles.

Heisenberg invokes Bohr’s principle of complementarity to shore up the QM’s uncertain duality of particles. Heisenberg illustrated the wave-particle ambiguity of an electron, where either of the two properties can be manifested, but neither of which has any meaning in the absence of observational experiment. He warned about an unsystematic use of language, which could lead into difficulties; the physicist has to withdraw into the mathematical scheme (i.e. the abstract realm) and its unambiguous correlation with experimental facts.

Comment by a Scientist: Single particles without interactions are called “bare particles”; we know; however, they are purely hypothetical creations; they simply do not exist.

Furthermore, no single particle can be defined without referring to all other particles, whose definitions in turn depend on the first particles, etc. ad infinitum. If particles did not interact with each other, things would be incredibly simple in nature, because then the behaviour of all particles could easily be calculated.

Finally, real particles through interaction usually get tangled up together and referred to as “re-normalised”. A physical particle (re-normalised particle) involves a bare particle and a huge tangle of virtual particles, which are inextricably nested inside each other in a recursive mess, which state defies description.

Item No.4. Quantum Cosmology.

As if the micro-cosmic philosophical complexity would not have been complex enough, now several of the modern-day physicists, self-styled unexpectedly as ‘quantum cosmologists’, proposing to extend a similar complexity of QM-uncertainty to the entire Universe. The Universe is much too large now for QM to make much difference, but according to the Big Bang theory, there was a time in the past when the particles were so close together that quantum effects must have been important. No one today knows even the rules for applying QM in this context.

Weinberg points out that quantum cosmology is right now a matter of active controversy among theorists; the conceptual and mathematical problems are very difficult, and we do not seem to be moving toward any definite conclusion. This touches on the recent attentions payed to chaos, the quintessence of in-determinism in the macro-cosmos; the point to emphasise is that the scientific excitement is not so much about the discovery of chaos, but that certain kinds of chaos exhibits some nearly universal properties that can be analysed mathematically.

QM speculates further that the Universe is also a quantum system of interest. Of course, there is no mention of what that means specifically, except that they endorse the full range of philosophical quantum alternatives as existing physical realities. Again there is no mention of what detail these quantum alternatives entail. To their credit, however, they do not accept the Copenhagen interpretation.

Heisenberg was asked the question: What actually happens inside a piece of measuring apparatus when a measurement of a quantum particle is made? He replied: The Copenhagen interpretation is that one merely treats the apparatus classically; but if instead it is treated (more realistically) as a collection (albeit) of quantum particles, the result is deeply worrying. The same vagueness and in-determinism that afflict the quantum particle now invade the entire system. He kept emphasising that sooner or later, the quantum effects (whatever they are), specifically the interference of possibilities, dissipate into the macro-cosmic environment.

A quantum measurement involves an assumption of an infinite numbers of “universes” (multiverse), as co-existing realities. There is a remarkable possibility that the constants of Nature may be predictable but their values will be affected quantum statistically by the space-time fabric of the Universe.

General Comments:

The mystery in our Universe is that it is so certain and reliably deterministic mainly through its laws and constants, such are e.g. the speed of gravitational force and electromagnetism.The reader is invited to contemplate on a possible universe without certainty of its laws and constants. Would there be any scientific certainty, as we know it today, if for instance, there would be no inverse-square law to control the speeds of gravitational force and the electromagnetic radiation? Could the stars and galaxies traverse distances on a cosmic scale, and in a precisely defined direction? And what if the speed of light would be variable?

The ‘Ockham’s razor’: Don’t multiply entities more than is absolutely necessary’, did not mean much to scientists, who introduced into QM the ‘many worlds’ concept, (the multiverse). This approach was taken as a counter-proposal to the so called ‘Intelligent Design’, and envisaged the entire multiverse, with our Universe in it, as a single quantum system.This explains several basic features of the Universe, such as why it is so large and why it is expanding. However, the theory is un-testable; therefore it does not seem properly scientific, but it appears more the “stuff of science fiction”, said  Sir Martin Rees. During the final phases of discussions, there were heated arguments among the principal players of quantum theory over the definitive proposition to break completely with classical physics. And they ultimately formulated the philosophical bases of quantum-mechanical world of both microcosm and macrocosm, where not only determinism but also causality is lost.

After having completed his studies in QM, Gleiser, the cosmologist, who published some sixty papers on related topics, asked the question: How could Heisenberg, Pauli and Schroder all be wrong after being right about so many things?

Weinberg thought the final agreement among quantum scientists was inevitable, and yet, it discouraged him to such an extent that he wrote: The more the Universe seems comprehensible, the more it seems pointless. After much prodding by his friend, Vaucouleurs about his ‘mis-statement’ (what he later on regretted), he added that he was nostalgic for a world in which ‘The heaven declared the glory of God’. Heisenberg repeated the question to himself again and again: ‘Can nature possibly be as absurd as it seemed to us in these quantum experiments’?

Acknowledgements

The reader is informed that all previous texts were paraphrased from the following sources:-

  • Quantum Mechanics. By: Bas C. van Fraassen.
  • Quantum. By: Manjit Kumar.
  • Gödel, Escher, Bach. By: D.R. Hofstadter.
  • Dreams of a Final Theory. By: S. Weinberg.
  • Physics and Philosophy. By: W. Heisenberg.
  • Imperfect Creation. By: M. Gleiser.
  • Between Inner Space and Outer Space. By: J.D. Barrow.
  • Our Cosmic Habitat. By: M. Rees.
  • Before the Beginning. By: M. Rees.The Self-Disclosure….

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