Abstract
We are near the end of our journey—though the theory is still far from the finish line, as is only the case with any scientific theory. The time has come, therefore, to recapitulate; recapture the most relevant points of the material presented in previous chapters, summarize some of the answers afforded by present stochastic electrodynamics to the questions posed at the beginning, and put on the table some of the many questions that remain to be explored. The chapter starts therefore with a summary of the most relevant results presented in the body of the book, stressing the genetic power of the zero-point field, on the basis of which the quantum scheme of matter in contact with the radiation field is constructed. Some particular features of quantum mechanics are discussed from this synoptic perspective. A condensed, itemized repertory of the answers offered by present stochastic electrodynamics to the conceptual problems of quantum theory is then provided, followed by a short critical review of the fussy definitions and conceptions of the modern photon. The chapter concludes with some comments on the limitations of the theory here discussed and possibilities for future developments and extensions.
Nothing in Nature is random.... A thing appears random only through the incompleteness of our knowledge.
Spinoza (2005)
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Notes
- 1.
Something similar happens with the photoelectric effect.Photoelectric effect This just was the example that Einstein 1905 used to argue in favor of the quantun of radiation. But it is a matter of fact that the cause of this effect can be attributed to the quantization of matter (see e.g. Schiff 1955,Schiff, L. I. Chap. X; Lamb and Scully 1969 Scully, M. O.; Mandel 1976).
- 2.
We have in mind true probabilities. Negative ‘probabilities’ are consubstantial to the technique of the so-called weak measurementsMeasurement, i.e., non-projective measurements (Aharonov et al. 1988).
- 3.
There are other cases in theoretical physics where approximations transform an otherwise causal theory into one that violates causalityCausality. Perhaps one of the best known examples is the Abraham-Lorentz equationAbraham-Lorentz!equation of motion. This equation is dCommutator!derivederived from a perfectly causal combination of Maxwell’s theory and classical mechanics. The end result, the Abraham-Lorentz equation, can however give rise to noncausal phenomena as preacceleration,Preacceleration the anticipated response to a future force [see e.g. Eq. (4.42)]. Again in this case, the root of such noncausal behavior is to be found in the approximations leading from the original causal full description to the final simplified (and noncausal)Evolution!noncausal one. Approximate physical theories are not bound to satisfy the same rigorous requirements that fundamental theories are supposed to fulfil; this is particularly true in what refers to consistency with first principles.
- 4.
The contributions to the cited supplement to Optics & Photonic News are collected in Roychoudhuri and Roy (2003). The book Roychoudhuri et al. (2008)Creath, K. Roychoudhuri, Ch. and the proceedings of subsequent SPIE meetings under the same title "The Nature of Light: What are Photons?"contains an ample collection of papers on the nature of the photon, showing the broad diversity of views and deep contradictions still existing on this matter.
- 5.
Newton and Wigner showed that it is not possible to define any position operator for a massless free particle with a nonzero spin, in sharp contrast to the case of massive particles, which can be localized. This is clearly in contradiction to the almost familiar notion of ‘position of a photon’, as one basic ingredient of the intended theoretical description.
- 6.
Einstein’s photon of (1909) is defined by \(E=cp=\hbar \omega .\) It was in 1916 that he added a well-defined direction to the photon, transforming it into a ‘needle of radiation’.Photon!needle of radiation On the other hand, Wigner’s photon is its helicity, which is a Lorentz-invariantSpectrum, Lorentz-invariant concept coming from a subgroup of the Lorentz group for massless particles.
- 7.
The coexistence of both aspects in quantum behavior has meanwhile become an experimentally verified fact; see Aldemade et al. (1966)Van der Veer, J. H. C., Kattke and Ziel (1970)Van der Ziel, A. Kattke, G. W.. For more recent work on ComplementaritycomplementarityEnglert, B.-G. see e.g. Jaeger et al. (1995)Jaeger, G., Englert (1996),Bergou, J. A. Engert and Bergou (2000), Liu et al. (2009) and Liu, N.-L. Flores, E. V. De Tata Flores and de Tata (2010).
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de la Peña, L., Cetto, A.M., Valdés Hernández, A. (2015). Quantum Mechanics: Some Answers. In: The Emerging Quantum. Springer, Cham. https://doi.org/10.1007/978-3-319-07893-9_10
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