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Another very good test some readers may want to look up, which we do not have space to describe here, is the Casimir effect, where forces between metal plates in empty space are modified by the presence of virtual particles.Thus virtual particles are indeed real and have observable effects that physicists have devised ways of measuring. Their properties and consequences are well established and well understood consequences of quantum mechanics.

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Quite obviously, a theoretical determination of the numerical value of α would signify great progress in our understanding of fundamental interactions. Many physicists have tried to find it, but without significant success to this day. Richard Feynman, the theory wizard of Caltech in Pasadena, once suggested that every one of his theory colleagues should write on the blackboard in his office: 137 -- how shamefully little we understand!

HF
Harald Fritzsch

Elementary Particles: Building Blocks of Matter

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Realizing its fundamental importance in understanding spectral lines, in atomic physics and in the theory of how light and electrons interact, quantum electrodynamics, Pauli and Heisenberg were determined to derive it from quantum theory rather than introducing it from the start. They believed that if they could find a version of quantum electrodynamics capable of producing the fine structure constant, it would not contain the infinities that marred their theories.

AM
Arthur I. Miller

Deciphering the Cosmic Number: The Strange Friendship of Wolfgang Pauli and Carl Jung

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In his first philosophical lecture on modern physics that Pauli gave in November 1934 to the Zurich Philosophical Society he said that only a formulation of quantum theory would be satisfactory which expresses the relation between the value of [the fine structure constant] and charge conservation in the same complementary was as that between the space-time description and energy-momentum conservation.

CE
Charles P. Enz

No Time to Be Brief: A Scientific Biography of Wolfgang Pauli

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Here the attention of the research workers is primarily directed to the problem of reconciling the claims of the special relativity theory with those of the quantum theory. The extraordinary advances made in this field by Dirac ... leave open the question whether it will be possible to satisfy the claims of the two theories without at the same time determining the Sommerfeld fine-structure constant.

WH
Werner Heisenberg

Physics and Philosophy: The Revolution in Modern Science

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Heisenberg's uncertainty relation measures the amount by which the complementary descriptions of the electron, or other fundamental entities, overlap. Position is very much a particle property - particles can be located precisely. Waves, on the other hand, have no precise location, but they do have momentum. The more you know about the wave aspect of reality, the less you know about the particle, and vice versa. Experiments designed to detect particles always detect particles; experiments designed to detect waves always detect waves. No experiment shows the electron behaving like a wave and a particle at the same time.

JG
John Gribbin

In Search of Schrödinger's Cat: Quantum Physics and Reality