The Dancing Wu Li Masters (49 page)

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In practice, some of the lines representing transitions between higher energy states do not appear in absorption spectra.

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Accurately speaking, different experimental equipment is required to photograph each series of the hydrogen spectrum. Therefore, most single photographs of the hydrogen spectrum show only about 10 lines. Theoretically, there are an infinite number of lines in each atomic spectrum. In fact, theoretically, there are an infinite number of lines in each series of each spectrum because the lines in the higher frequency range of each series become so closely spaced that, in effect, they form a continuum.

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The dark-adapted eye can detect a single photon. Otherwise, only the
effects
of subatomic phenomena are available to our senses (a track on a photographic plate, a pointer movement on a meter, etc.).

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At the time of Newton’s discoveries, the power of the church already had been challenged by Martin Luther. Newton himself was a pious person. The specific argument of the church was not with empirical method, but with the theological conclusions that were being developed from Newton’s ideas, conclusions which involved the concept of God as creator and the central position of man in creation.

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Strictly speaking, mass, according to Einstein’s special theory of relativity,
is
energy and energy
is
mass. Where there is one, there is the other.

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This was the 5th Solvay Congress at which Bohr and Einstein conducted their now famous debates. The term “Copenhagen Interpretation” reflects the dominant influence of Niels Bohr (from Copenhagen) and his school of thought.

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The Copenhagen Interpretation says that quantum theory is about correlations in our experiences. It is about what will be observed under specified conditions.

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The philosophy of pragmatism was created by the American psychologist William James. Recently, the pragmatic aspects of the Copenhagen Interpretation of Quantum Mechanics have been emphasized by Henry Pierce Stapp, a theoretical physicist at the Lawrence Berkeley Laboratory in Berkeley, California. The Copenhagen Interpretation, in addition to the pragmatic part, has the claim that quantum theory is in some sense complete; that no theory can explain subatomic phenomena in any more detail.
     An essential feature of the Copenhagen Interpretation is Bohr’s principle of complementarity (to be discussed later). Some historians practically equate the Copenhagen Interpretation and complementarity. Complementarity is subsumed in a general way in Stapp’s pragmatic interpretation of quantum mechanics, but the special emphasis on complementarity is characteristic of the Copenhagen Interpretation.

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“…the hypothesis of quanta has led to the idea that there are changes in Nature which do not occur continuously but in an explosive manner.”—Max Planck, “Neue Bahnender physikalischen Erkenntnis,” 1913, trans., F. d’Albe,
Phil. Mag.
vol. 28, 1914.

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h=6.63 × 10
²⁷
erg-sec

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Bohr speculated that electronic orbits are arranged by nature at unvarying specific distances from the nucleus of the atom and that, when they absorb energy, the electrons in the atom jump outward from the orbit closest to the nucleus (the “ground state” of the atom) and eventually return to the innermost orbit, in the process emitting energy packets equal to the energy packets that they absorbed in jumping outward. Bohr proposed that when only a little energy is available (low heat), only small energy packets are absorbed by the electrons, and they do not jump out very far. When they return to their lowest energy level, they emit small energy packets, like those of red light. When more energy is available (high heat), larger energy packets are available, the electrons make bigger jumps outward and, on returning, they emit larger energy packets, like those of blue and violet light. Therefore, over low heat, metal glows red, and over high heat, it glows blue-white.

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Each of Einstein’s major 1905 papers dealt with a fundamental physical constant: h, Planck’s constant (the photon hypothesis); k, Boltzmann’s constant (the analysis of Brownian movement); and c, the velocity of light (the special theory of relativity).

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If we assume a particle aspect in the double-slit experiment we will violate the uncertainty relation unless we also assume nonlocality.

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An explanation other than “knowing” might be synchronicity, Jung’s acausal connecting principle.

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According to the complementarity argument, which is at the heart of the Copenhagen Interpretation, the latitude in the choice of possible wave functions exactly corresponds to (or at least includes) the latitude in the set of possible experimental arrangements, so that every possible experimental situation or arrangement is covered by quantum theory.

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Each set of experimental specifications A or B, that can be transcribed into a corresponding theoretical description & A or & B, corresponds to an observable. In the mathematical theory the observable is & A or & B; in the world of our experience the observable is the possible occurrence (coming into our experience) of the satisfied specifications.

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The particle is represented by a wave function which has
almost
all of the characteristics (when properly squared, to get a probability function) of a probability density function. However, it lacks the crucial feature of a probability density function, namely the property of being positive.

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From the pragmatic point of view, nothing can be said about the world “out there” except via our concepts. However, even within the world of our concepts particles do not seem to have an independent existence. They are represented in theory only by wave functions and the meaning of the wave function lies only in correlations of other (macroscopic) things.
      Macroscopic objects, like a “table” or a “chair,” have certain direct experiential meanings, that is, we organize our sensory experiences directly in terms of them. These experiences are such that we can believe that these objects have a persisting existence and well-defined location in space-time that is logically independent of other things. Nonetheless, the concept of independent existence evaporates when we go down to the level of particles. This limitation of the concept of independent entity at the level of particles emphasizes, according to the pragmatic view, that even tables and chairs are, for us, tools for correlating experience.

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What we can predict is the probability corresponding to any specification that can be mapped into a density function. Accurately speaking, we do not calculate probabilities at points, but rather transition probabilities between two states (initial preparation, final detection), each of which is represented by a continuous function of x and p (position and momentum).

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The state of a system containing
n
particles is represented at each time by a wave function in a 3
n
dimensional space. If we make an observation on each of the
n
particles the wave function is reduced to a special form—to a product of
n
wave functions each of which is in a three-dimensional space. Thus the number of dimensions in the wave function is determined by the number of particles in the system.

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To see the conciseness of mathematical expression, consider that the entire process described in the Theory of Measurement, from photon (system, S) to detectors (measuring device, M) to technician (observer, O) can be represented mathematically by one “sentence”: