Philosophical interpretation of classical physics

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Classical Newtonian physics has, formally, been replaced by quantum mechanics on the small scale and relativity on the large scale. Because most humans continue to think in terms of the kind of events we perceive in the human scale of daily life, it became necessary to provide a new philosophical interpretation of classical physics. Classical mechanics worked extremely well within its domain of observation but made inaccurate predictions at very small scale – atomic scale systems – and when objects moved very fast or were very massive. Viewed through the lens of quantum mechanics or relativity, we can now see that classical physics, imported from the world of our everyday experience, includes notions for which there is no actual evidence. For example, one commonly held idea is that there exists one absolute time shared by all observers. Another is the idea that electrons are discrete entities like miniature planets that circle the nucleus in definite orbits .

Quantum mechanics branch of physics dealing with phenomena at scales of the order of the Planck constant

Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

Theory of relativity physical theory

The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity. Special relativity applies to elementary particles and their interactions, describing all their physical phenomena except gravity. General relativity explains the law of gravitation and its relation to other forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.

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The correspondence principle says that classical accounts are approximations to quantum mechanics that are for all practical purposes equivalent to quantum mechanics when dealing with macro-scale events.

In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics reproduces classical physics in the limit of large quantum numbers. In other words, it says that for large orbits and for large energies, quantum calculations must agree with classical calculations.

Various problems occur if classical mechanics is used to describe quantum systems, such as the ultraviolet catastrophe in black-body radiation, the Gibbs paradox, and the lack of a zero point for entropy.

Ultraviolet catastrophe disproven prediction in physics

The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation in all frequency ranges, emitting more energy as the frequency increases. By calculating the total amount of radiated energy, it can be shown that a blackbody is likely to release an arbitrarily high amount of energy. This would cause all matter to instantaneously radiate all of its energy until it is near absolute zero - indicating that a new model for the behaviour of blackbodies was needed.

Black-body radiation thermal electromagnetic radiation

Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body. It has a specific spectrum and intensity that depends only on the body's temperature, which is assumed for the sake of calculations and theory to be uniform and constant.

In statistical mechanics, a semi-classical derivation of the entropy that does not take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive. This leads to a paradox known as the Gibbs paradox, after Josiah Willard Gibbs who proposed this thought experiment in 1874‒1875. The paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics. A related paradox is the "mixing paradox". If one takes the perspective that the definition of entropy must be changed so as to ignore particle permutation, the paradox is averted.

Since classical physics corresponds more closely to ordinary language than modern physics does, this subject is also a part of the philosophical interpretation of ordinary language, which has other aspects, as well.

Philosophy of language, in the analytical tradition, explored logic, the nature of meaning, and accounts of the mind.

The measurement process

In classical mechanics it is assumed that given properties – speed or mass of a particle; temperature of a gas, etc. – can in principle be measured to any degree of accuracy desired.

Study of the problem of measurement in quantum mechanics has shown that measurement of any object involves interactions between the measuring apparatus and that object that inevitably affect it in some way; at the scale of particles this effect is necessarily large. On the everyday macroscopic scale the effect can be made small.

The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus. The question of how the operational process measurement affects the ontological state of the observed system is unresolved, and called the measurement problem.

Furthermore, the classical idealization of a property simply being "measured" ignores the fact that measurement of a property – temperature of a gas by thermometer, say – involves a pre-existing account of the behavior of the measuring device. When effort was devoted to working out the operational definitions involved in precisely determining position and momentum of micro-scale entities, physicists were required perforce to provide such an account for measuring devices to be used at that scale. The key thought experiment in this regard is known as Heisenberg's microscope.

Operational definition

An operational definition is the articulation of operationalization used in defining the terms of a process needed to determine the nature of an item or phenomenon and its properties such as duration, quantity, extension in space, chemical composition, etc. Since the degree of operationalization can vary itself, it can result in a more or less operational definition. The procedures included in definitions should be repeatable by anyone or at least by peers.

Heisenberg's microscope exists only as a thought experiment, one that was proposed by Werner Heisenberg, criticized by his mentor Niels Bohr, and subsequently served as the nucleus of some commonly held ideas, and misunderstandings, about Quantum Mechanics. In particular, it provided an argument for the uncertainty principle on the basis of the principles of classical optics. Recent theoretical and experimental developments have argued that Heisenberg's intuitive explanation of his mathematical result is misleading. While the act of measurement does lead to uncertainty, the loss of precision is less than that predicted by Heisenberg's argument when measured at the level of an individual state. The formal mathematical result remains valid, however, and the original intuitive argument has also been vindicated mathematically when the notion of disturbance is expanded to be independent of any specific state.

The problem for the individual is how to properly characterize a part of reality of which one has no direct sense experience. Our inquiries into the quantum domain find most pertinent whatever it is that happens in between the events by means of which we obtain our only information. Our accounts of the quantum domain are based on interactions of macro domain instruments and sense organs with physical events, and those interactions give us some but not all of the information we seek. We then seek to derive further information from series of those experiments in an indirect way.

One interpretation of this conundrum is given by Werner Heisenberg in his 1958 book, Physics and Philosophy,p. 144f:

We can say that physics is a part of science and as such aims at a description and understanding of nature. Any kind of understanding, scientific or not, depends on our language, on the communication of ideas. Every description of phenomena, of experiments and their results, rests upon language as the only means of communication. The words of this language represent the concepts of daily life, which in the scientific language of physics may be refined to the concepts of classical physics. These concepts are the only tools for an unambiguous communication about events, about the setting up of experiments, and about their results. If therefore the atomic physicist is asked to give a description of what really happens in his experiments, the words "description" and "really" and "happens" can only refer to the concepts of daily life or of classical physics. As soon as the physicist gave up this basis he would lose the means of unambiguous communication and could not continue in his science. Therefore, any statement about what has "actually happened" is a statement in terms of the classical concepts and -- because of thermodynamics and of the uncertainty relations -- by its very nature incomplete with respect to the details of the atomic events involved. The demand to "describe what happens" in the quantum-theoretical process between two successive observations is a contradiction in adjecto, since the word "describe" refers to the use of the classical concepts, while these concepts cannot be applied in the space between the observations; they can only be applied at the points of observation.

Primacy of observation in quantum mechanics and special relativity

Both quantum mechanics and special relativity begin their divergence from classical mechanics by insisting on the primacy of observations and a refusal to admit unobservable entities. Thus special relativity rejects the absolute simultaneity assumed by classical mechanics; and quantum mechanics does not permit one to speak of properties of the system (exact position, say) other than those that can be connected to macro scale observations. Position and momentum are not things waiting for us to discover; rather, they are the results that are obtained by performing certain procedures.

Notes

  1. ^ Messiah, Albert, Quantum Mechanics, volume I, pp. 45–50.

See also

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