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The Planck Vacuum Volume 1 PROGRESS IN PHYSICS January, 2009 The Planck Vacuum William C. Daywitt National Institute for Standards and Technology (retired), Boulder, Colorado, USA E-mail: [email protected] This paper argues that there is a polarizable vacuum state (the Planck vacuum) that is the source of the quantum vacuum; the free particles; the gravitational, fine structure, and Planck constants; the gravitational field and the spacetime of General Relativity; the Maxwell equations and the Lorentz transformation; and the particle Compton relations and the quantum theory. 1 Introduction source of these pre-existing theories. The simple calculations in the paper lead to the above constants and from there to This is an unusual paper that needs to be put into perspec- the many suggestions, assumptions, speculations, and hand- tive to be understood because the definitions contained herein waving that necessarily characterize the PV theory at this evoke preconceived ideas that get in the way of the reader. For early stage of development. It is expected, however, that the example, the words “bare charge” mean something very spe- theory will eventually lead to a “sea change” in the way we cific to the quantum-field-theory specialist that evoke notions view fundamental physics. So let’s begin. of renormalization and Feynman diagrams. The definition of these words given here, however, mean something quite dif- The two observations: “investigations point towards a com- ferent; so this preface is intended to provide a setting that will pelling idea, that all nature is ultimately controlled by the ac- make the paper easier to understand. tivities of a single superforce”, and “[a living vacuum] holds About ten years ago the author derived the gravitational the key to a full understanding of the forces of nature”; come 2 2 2 (G = e=m), Planck (~ = e=c), and also fine structure from Paul Davies’ popular 1984 book [1] entitled Superforce: 2 2 ( = e =e) constants in a somewhat confused and mixed- The Search for a Grand Unified Theory of Nature . This liv- up manner. Although their derivation at that time left some- ing vacuum consists of a “seething ferment of virtual parti- thing to be desired, the simple elegance and connectedness of cles”, and is “alive with throbbing energy and vitality”. Con- these three fundamental equations has provided the motiva- cerning the vacuum, another reference [2] puts it this way; tion behind the search for their explanation. Thus it was the “we are concerned here with virtual particles which are cre- “leading” of these three constants that resulted in the paper ated alone (e.g., photons) or in pairs (e+e), and with the that is about to be read. The intent at the beginning of the vacuum — i.e., with space in which there are no real par- investigations was not some urge to discover a grand theory ticles”. This modern vacuum state, as opposed to the clas- that unifies diverse areas of physics, although the search for sical void, is commonly referred to as the quantum vacuum the physics behind the constants appears to be doing just that. (QV) [3]. The virtual particles of this vacuum are jumping The Planck vacuum (PV) state is envisioned as an infinite, in and out of existence within the constraints of the Heisen- invisible (not directly observable), omnipresent, uniform, and berg uncertainty principle (Et ~); i.e., they appear for homogeneous negative energy state somewhat analogous to short periods of time (t) depending upon their temporal en- the Dirac “sea” in quantum mechanics. The quantum vac- ergy content (E), and then disappear. The QV, then, is an uum, on the other hand, consists of virtual particles that ap- ever-changing collection of virtual particles which disappear pear and disappear at random in free space, the space where after their short lifetimes t, to be replaced by new virtual free particles and the rest of the universe are observed. The particles which suffer the same fate, ad infinitum. source of this quantum vacuum is assumed to be the PV, Among other things, the following text will argue that the where the fields of the quantum vacuum are analogous to non- source of the QV is the Planck vacuum (PV) [4] which is an propagating induction fields with the PV as their source. The omnipresent degenerate gas of negative-energy Planck parti- PV is also assumed to be the source of the free particles. cles (PP) characterized by the triad (e, m, r), where e, The charge of the Planck particle is called the bare charge, m, and r (=2) are the PP charge, mass, and Compton and it is this bare charge that is the true, unscreened, charge of radius respectively. The charge e is the bare (true) electronic the electron and the rest of the charged elementary particles. charge common to all charged elementary particles and is The polarizability of the PV is shown to be responsible for related to the observed electronic charge e through the fine 2 2 the fact that the observed electronic charge e has a smaller structure constant = e =e which is one manifestation of magnitude than the bare charge e. the PV polarizability. The PP mass and Compton radius are The PV theory is not derived from some pre-existing the- equal to the Planck mass and length [5] respectively. The ory, e.g. the quantum field theory — it is assumed to be the zero-point (ZP) random motion of the PP charges e about 20 William C. Daywitt. The Planck Vacuum January, 2009 PROGRESS IN PHYSICS Volume 1 their equilibrium positions within the PV, and the PV dynam- forces between two like, charged elementary particles are ics, are the source of both the QV and the free particles. The used in this section to derive the fine structure constant, the PV is held together by van der Waals forces. In addition to ultimate Coulomb force, the ultimate gravitational force, the the fine structure constant, the PV is the source of the gravi- gravitational constant, and the ultimate PV-curvature force. 2 2 2 tational (G = e=m) and Planck (~ = e=c) constants. The Using a new expression (4) for the gravitational force, and non-propagating virtual fields of the QV are assumed to be the results from the above; the Compton relation of the PP, real fields appearing in free space which are analogous to in- and the free-space permittivities (the dielectric constant and duction fields with the PV as their source. magnetic permeability) are derived. These derivations utilize A charged elementary particle is characterized by the triad three normalization constants to isolate the ultimate forces. (e, m, rc), where m and rc are the particle’s mass and The three constants correspond to charge normalization (e), Compton radius. The field intrinsic to the particle is the mass normalization (m), and length normalization (r). 3 bare Coulomb field er=r , where r is the radius vector These constants start out as normalization constants, but end from the particle to the field point. All other fields, clas- up defining a new fundamental particle (the PP) and a funda- sical or quantum, associated with the particle and its mo- mental vacuum state (the PV). tion arise from this fundamental field and its interaction with The static Coulomb force between two like, charged par- the PV. ticles can be expressed in the following two forms: Section 2 traces the concept of the PV from the first obser- e2 r 2 vation of the initial paragraph after the preface to the deriva- F = = F 0 ; el r2 r (1) tion of the fine structure, gravitational, and Planck constants; 2 2 to the Compton relation of the PP; and to the free-space per- where r is the distance between particles, e =e, and 0 2 2 mittivities. A rough heuristic argument shows the binding F e=r. If e is assumed to be the maximum parti- force of the vacuum to be van-der-Waals in nature. cle charge (the electronic charge unscreened by a polarizable The ultimate PV-curvature force is derived in Section 2 vacuum state), and r is assumed to be some minimum length 0 from Newton’s gravitational equation. This ultimate force is (r < r for all r); then F is the ultimate Coulomb force. shown in Section 3 to be tied to the Riemannian spacetime of The static gravitational force of Newton acting between General Relativity (GR) which, therefore, is related to the real two particles of mass m separated by a distance r can be ex- physical curvature of the PV. As a consequence, GR describes pressed in the following forms: the spacetime curvature of the PV. 2 2 2 m G m r Using the Coulomb field of the bare charge, the polar- F = = F ; gr r2 m2 r (2) izability of the PV, and an internal feedback mechanism in- trinsic to the PV; Section 4 derives the relativistic electric where G denotes Newton’s gravitational constant, and 2 2 and magnetic fields associated with the charge, and infers the F mG=r. If m is the maximum elementary particle Lorentz transformation and constancy of the speed of light mass, and r is the minimum length, then F is the ultimate from the results. gravitational force as m=r is the maximum mass-to-length The electromagnetic vacuum (EV) consists of the virtual ratio. photons mentioned in the first paragraph which lead collec- Adhering to the idea of a single superforce implies that 0 tively to the ZP electromagnetic field with which Section 5 the force magnitudes F and F must be equal.
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