e-book

Consistent Quantum Theory

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Quantum theory is one of the most difficult subjects in the physics curriculum. In part this is because of unfamiliar mathematics: partial differential equations, Fourier transforms, complex vector spaces with inner products. But there is also the problem of relating mathematical objects, such as wave functions, to the physical reality they are supposed to represent. In some sense this second problem is more serious than the first, for even the founding fathers of quantum theory had a great deal of difficulty understanding the subject in physical terms. The usual approach found in textbooks is to relate mathematics and physics through the concept of a measurement and an associated wave function collapse. However, this does not seem very satisfactory as the foundation for a fundamental physical theory. Most professional physicists are somewhat uncomfortable with using the concept of measurement in this way, while those who have looked into the matter in greater detail, as part of their research into the foundations of quantum mechanics, are well aware that employing measurement as one of the building blocks of the subject raises at least as many, and perhaps more conceptual difficulties than it solves.

It is in fact not necessary to interpret quantum mechanics in terms of measurements. The primary mathematical constructs of the theory, that is to say wave functions (or, to be more precise, subspaces of the Hilbert space) can be given a direct physical interpretation whether or not any process of measurement is involved. Doing this in a consistent way yields not only all the insights provided in the traditional approach through the concept of measurement, but much more besides, for it makes it possible to think in a sensible way about quantum systems which are not being measured, such as unstable particles decaying in the center of the earth, or in intergalactic space. Achieving a consistent interpretation is not easy, because one is constantly tempted to import the concepts of classical physics, which fit very well with the mathematics of classical mechanics, into the quantum domain where they sometimes work, but are often in conflict with the very different mathematical structure of Hilbert space that underlies quantum theory. The result of using classical concepts where they do not belong is to generate contradictions and paradoxes of the sort which, especially in more popular expositions of the subject, make quantum physics seem magical. Magic may be good for entertainment, but the resulting confusion is not very helpful to students trying to understand the subject for the first time, or to more mature scientists who want to apply quantum principles to a new domain where there is not yet a well-established set of principles for carrying out and interpreting calculations, or to philosophers interested in the implications of quantum theory for broader questions about human knowledge and the nature of the world.

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Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

Cambridge : Cambridge University Press., 2003

Deskripsi Fisik

x, 408 Hlm.

Bahasa

English

ISBN/ISSN

9780521539296

Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

MATEMATIKA

Info Detail Spesifik

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Pernyataan Tanggungjawab

agus

Versi lain/terkait

Lampiran Berkas

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