Abstract
Before our journey comes to an end, we propose to look at one more trace of the zero-point field on matter. In previous chapters, most important aspects of the behavior of quantum systems have been shown to carry the signature of this field. However, one feature that has been left aside so far is the de BroglieDe Broglie, L. wave, just the creature that gave life to the quantum description of matter. De Broglie’s wavelength is reconstructed from the perspective of the present theory and shown to be associated with a wave of electromagnetic nature. This physical notion of theDe Broglie’s wave de Broglie wave is applied to the simplest example of all, the infinite square well, in an effort to refine our image of the motion of particles taking place in this system. Further, the ‘matter diffraction’ by a double slit is explained by arguing that what is really diffracted is the background field, its diverted rays ‘guiding’ the particles to form the well-known diffraction pattern on the far-away screen. Finally, on the other extreme of the scale, a cosmological model is put forward for the zero-point field. It is shown that this permanent component of the background radiation can be considered the result of a regenerative process, sustained by the radiation of all the charges in the Universe; this model explains thus a well-known ‘strange’ relation between the large numbers.
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Notes
- 1.
- 2.
Detailed, first-hand expositions of de Broglie’s theory can be found in de Broglie (1926, 1956, 1963). Modern presentations by one of its advocates made in Selleri (1990). A most elaborate development of a variant of de Broglie’s theory for the relativistic electron is the geometrical mechanics Geometrical mechanics developed by Synge (1954)Synge, J. L.. An informed historical discussion of de Broglie’s work up to the 1927 Solvay conference is given in Bacciagaluppi and Valentini (2009). MacKinnon (1976)MacKinnon, E. presents a detailed analysis and improvement of de Broglie’s derivation in his thesis. Another detailed discussion of de Broglie’s phase waves is presented in Espinosa (1982).
- 3.
In Surdin (1979)Surdin, M. it is proposed to consider that de Broglie’s wave is of electromagnetic nature, in some undefined way associated with the electromagnetic zpf.
- 4.
A crude way to reach the same conclusion is the following. From the Heisenberg inequality one obtains \(\sigma _{x}^{2}\ge (\hbar ^{2}/4\sigma _{p}^{2}),\) whence the minimum dispersion in the position variable determines an Effective radiuseffective radius \(a\sim (\sigma _{x})_{\text {min}}.\) Such minimum value is achieved for the largest \(\sigma _{p}^{2},\) which in the nonrelativistic regime can be limited by \(m_{0}^{2}c^{2}.\) This results in \(a\sim (\hbar /m_{0}c).\)
- 5.
A detailed discussion can be seen in de la Peña et al. (1982), and The Dice, Sects. 3.4 and 7.3.3. In this latter it is shown that the selfcorrelation of the position coordinate of a harmonic oscillator Oscillatorcontains a permanent oscillatory contribution of a frequency determined by the cutoff Cutoff(Eq. 7.101), and with a value that is not too far from the Compton frequency.
- 6.
Or rather, into the ontology of quantum mechanics. We see in the wave function of quantum mechanics an abstract object that lives in a mathemathical configuration space. By contrast, the de Broglie wave associated with the zpf modulations should be understood as a real wave in three-dimensional space. They are therefore two objects of an entirely different nature.
- 7.
The term wavelet refers to localized nonspreading solutions of massless wave equations that move like massive quantum particles. Wavelets are seen as a bridge between classical point particles and the waves of qm; the mass of the particle is determined by the internal frequency of the wavelet, much as the ‘internal clock’ in the Broglie’s theory.
- 8.
The results obtained with this numerical experiment are similar to those obtained by Couder, Y. Couder and Fort (2006)Fort, E. in their macroscopic Young-type experiment, showing clearly that the bouncing droplet goes through either one of the two slits but the associated wave passes through both slits, and the interferenceInterference of the resulting waves is responsible for the trajectory of the walker.
- 9.
Recently we have become aware of a similar proposal by Mavrychev (1967)Mavrychev, Yu. S. Yu, S., in which the author reaches a comparable result.
- 10.
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de la Peña, L., Cetto, A.M., Valdés Hernández, A. (2015). The Zero-Point Field Waves (and) Matter. In: The Emerging Quantum. Springer, Cham. https://doi.org/10.1007/978-3-319-07893-9_9
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