“…the electron has more of the attributes of a classical particle than does the light quantum although neither, of course, has all the attributes of a classical particle, since they both show interference effects. In the chapter on the uncertainty principle we shall verify that, in an actual process of measurement of the position of a light quantum, it is impossible to localize its position within a region Δx, which is smaller than the wavelength of the photon.
In the light of these results, how do we interpret an experiment in which a light quantum strikes an atom of diameter of the order of 10-8 cm, whereas the light wavelength is much larger, of the order of 10−5 cm? Can we not say that the quantum was found within a region much smaller than its wavelength? The answer is that the quantum can be localized in this way only at the moment that it disappears by absorption. The concept of a particle is, therefore, of no help in interpreting the result of any other experiment; with an electron, however, we can say that immediately after it has been found at a given spot another observation will disclose the same electron at the same point. In this way, the concept of a particle unifies many different experimental results, whereas the idea that a light quantum exists at the point where it is absorbed explains only this one result. As we shall see, whenever the light quantum is observed under conditions in which it is not absorbed, it cannot be localized to a region smaller than λ.”
Excerpt From
Quantum Theory
David Bohm
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“We were led to the value ½ ħ for the spin of the electron by an argument depending simply on general principles of quantum theory and relativity. One could apply the same argument to other kinds of elementary particle and one would be led to the same conclusion, that the spin angular momentum is half a quantum. This would be satisfactory for the proton and the neutron, but there are some kinds of elementary particle (e.g. the photon and certain kinds of meson) whose spins are known experimentally to be different from ½ ħ, so we have a discrepancy between our theory and experiment.
The answer is to be found in a hidden assumption in our work. Our argument is valid only provided the position of the particle is an observable. If this assumption holds, the particle must have a spin angular momentum of half a quantum. For those particles that have a different spin the assumption must be false and any dynamical variables x1, x2, x3 that may be introduced to describe the position of the particle cannot be observables in accordance with our general theory. For such particles there is no true Schrödinger representation. One might be able to introduce a quasi wave function involving the dynamical variables x1, x2, x3, but it would not have the correct physical interpretation of a wave function—that the square of its modulus gives the probability density. For such particles there is still a momentum representation, which is sufficient for practical purposes.”
Excerpt From
The Principles of Quantum Mechanics
P. A. M. Dirac
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