6. The ZPE and Redshift Quantum Jumps

note: March, 2007 -- this section has been changed in response to the recent Puthoff paper and the information he made available in it: "Casimir vacuum energy and the semiclassical electron."

6.1 The Cause of Quantum Changes in Atomic Masses
6.2 The Magnitude of the Atomic Quantum Change:
6.3 Atomic Mass Quantum Changes:
6.4 Atomic Orbit Quantum Changes:
6.5 Electron Orbits and Related Quantities:


6.1 The Cause of Quantum Changes in Atomic Masses

Reference [25] derived the dimensionless component of the ZPE power in a manner similar to Appendix 5. A new level of power thus became available to all atoms once a threshold was exceeded. Here we examine changes occurring in atomic particles themselves that result in the redshift quantum jump. We note, as we begin, that at the actual moment of the jump, the change in the ZPE strength is infintessimally small. So Planck's constant, h, the permittivity, ε, the electronic charge, e, and the speed of light, c, will all remain unchanged. Examination of (34) then reveals that the only basic quantity left to change in the orbit energy equation is the mass of atomic particles, m, since the Bohr quantum number, n, remains fixed.

The only way of changing the electron mass, m, or the equivalent mass of the other partons making up the atom, is by changing their radii (which changes their volume). This is a real possibility in a ZPE context, and will be discussed shortly. However, in the following discussion about electron radii, it should be remembered that all atomic particles, or partons, will behave similarly. The following analysis confirms that this is the cause of the redshift quantum changes in atoms. Furthermore, it will be shown that the quantum change in the volume of the partons is of a magnitude that accords with Tiffts' redshift data.

To begin we note that the classical electron radius, rc, is related to both e and m, so both quantities need to be examined in this context. They are linked in the following way [120]:

rc  =  e2/(ε mc2)                        (35)

 At this juncture the ZPE does become important because it has been noted that “one defensible interpretation is that the electron really is a point-like entity, smeared out to its quantum dimensions by the ZPF fluctuations” [121]. MacGregor emphasized this “smearing out” of the electronic charge by the ZPF involves vacuum polarization and the Zitterbewegung [122]. If there is a quantum change in the electron volume due to an increase in the energy density of the ZPE, then it might be expected that the “point-like entity” of the electron should “smear out” even more. Boyer's analysis on the stability of a spherical electronic charge immersed in the ZPE agrees. He shows that the Casimir pressure within the point-like sphere of the electron is outwardly directed. As a result, he specifically states that “the quantum zero-point force also expands the sphere” [121]. Thus all charges experience an internal force from the ZPE which tends to expand them. Once the ZPE strength (and hence Casimir expansion force) increases to a quantum threshold, the electron’s radius, (and hence its volume), would be expected to undergo a quantum increase.

6.2 The Magnitude of the Atomic Quantum Change

There is one immediate difficulty through lack of precision in (35) with regard to m and rc. Thus French notes that if m is derived from the energy density of the electron’s magnetic field, a factor of 2/3 is required in (35), while use of the Poynting vector and the electron’s electric field needs a factor of √(8/3) [123]. This conflict elicited the comment “…without some idea concerning the precise distribution of charge within the electron volume, we cannot be sure about numerical factors of order unity. It was therefore decided to define a so-called ‘classical electron radius’ rc …” without any numerical coefficients at all [123]. MacGregor listed six additional options [121].  To overcome this difficulty, we note that a more precise expression for rcis obtained if the Compton radius, Rc = h/mc, is multiplied by the fine structure constant, α = e2/(2εhc) , as noted in reference [124]. From this we get

2Rc  =  e2/(ε mc2)         (36)

Our next move is to substitute for m in (36). The formulation in (34) informs us that the quantity │m =  E (ε2 h2 n2) / (2π2 e4 ). Substituting this in (36) then gives us the Compton radius in terms that are independent of mass, m. All the terms now employed for the expression of the Compton radius remain unchanged at the quantum jump, as outlined above, and can be seen by inspection of the following equation:

Rc  = ( π2 e6 ) /3 h2 n2c2)        (37)

From this we can write that

Rc2 = A                              (38)

where A contains all the other dimensional terms which remain fixed at the quantum change.

Now H.E. Puthoff has recently obtained an expression for the vacuum energy, W, inside the sphere of a parton of radius a. This vacuum energy tending to expand the sphere is given by

W = h Ω4a3 / (12π2c3     (39)

where h is Planck’s constant. The term Ω is the upper limit frequency cutoff, which is proportional to lightspeed, c, as outlined above. This means that [hΩ4/c3] will remain invariant with ZPE changes. Equation (39) here is Puthoff’s equation (5) with the limits removed [see http://www.arxiv.org/ftp/physics/papers/0610/0610042.pdf ]. If we now replace the parton radius term, a, in (39) with A from (38), we can then express the vacuum energy in terms of the Compton radius so that (39) becomes:

W = [(h Ω4) / (c3)] [( Rc / π2)3] [1 / (12π2)] = 
[Q] [Rc3 / (12π8)] = W*/ 113862                     (40)

Again we note that the terms making up Q and W* in (40) remain fixed at the quantum change. Now in (40), the vacuum energy, W, inside the parton tending to expand its volume, is shown to be made up of two components so that W = W*d. Here, W* is the component that retains the dimensions and fundamental properties of W. Furthermore, the combination of dimensional parameters that make up W* results in a quantity which does not change. By contrast, d is the dimensionless portion of W which is equal to the fraction 1/113862. In this way, the quantity d has come to contain all the numerical factors, like π2, which convert one dimensional quantity to another. These numerical factors are needed in their entirety, not just in part. Therefore, at the quantum change, since W* is fixed, any change in the volume of the parton can only occur in whole multiples, n, of the quantity d. We can therefore write

nd =  n / 113862  =  n (8.78256 x 10-6)            (41)

Thus, as the vacuum energy increases within the parton, its volume only increases once the energy has increased by a factor of W*nd, where n = 1, 2, 3, etc.  Thus, as we look back in time through a quantum jump to increasingly distant objects we have

W1*d  =  W2*d  (1 + nd)  so that   W1  =  W2 (1 + nd)  and  V = V2 (1 + nd)      (42)

The last step in (42) follows since equation (40) indicates that W is directly related to the cube of the Compton radius. Therefore we can substitute the parton volume, V, as in (42). This also means that, since W is directly related to vacuum energy density U, we can write from equation (26A) that

U1 / U2  =  W1 / W2  =  V1 / V2  =  (1 + nd)  =  (1 + z)  =  (1 + n Δz)        (43)

From equations (43) and (41) it can also be stated that the quantity

nd  =  n Δz  =  n /113862  =  n (8.78256 x 10-6)       (44)

If (44) is expressed as a velocity we have   

cΔz  =  c (8.78256 x 10-6)  =  2.633 km/s       (45)

This again comes very close to Tifft’s 2.667 km/s, being within 1.3% of his observational data. Therefore, both the power transferred from the ZPE to the atom, and the expansion of the parton volume by the ZPE, allow the size of Tifft’s quantization to be closely reproduced.

6.3 Atomic Mass Quantum Changes

With this change in parton volume comes a change in parton mass. Examination of (43) indicates that, at the quantum change with time moving forward, the volume of the electron or parton is increased. This means that the mass of the atomic particle has decreased. This conclusion is a result of the fact that partons are “jiggled” by waves of the ZPE. Waves that are significantly smaller than the parton produce little translational movement of the parton [72]. A larger parton has a lower resonant frequency and so is “jiggled” by ZPE waves of longer wavelength. But the waves of the ZPE have a frequency cubed distribution which means that there are far fewer waves of long wavelengths than there are of short wavelengths. As a consequence, with a larger parton volume, there are fewer ZPE waves of the longer wavelengths needed to get the parton to resonate or “jiggle”. Thus a parton with a larger volume has a lower kinetic energy imparted to it by the ZPE waves and hence a lower mass.

Now the parton’s resonant frequency ω = kc where k depends inversely upon parton size [71, 72]. At the quantum jump, the size of the parton changes, so the value of k and the parton’s resonant frequency, ω, change inversely in response. Because it is the whole volume of the parton which is reacting to the battering waves of the ZPE, let us conclude that k is inversely dependent upon parton volume, V, so that, in turn, ω will be proportional to 1/V.

Now the mass, m, of the parton is given in (12) which includes the Abraham-Lorentz damping constant, Γ. This damping constant also contains a term m* which is the intrinsic mass of the parton that is interacting with the ZPE. This term can also be considered as an intrinsic energy if it is coupled with the speed of light terms as in (14). The final result is obtained in (16A). However the same result also is obained if m* is considered to be the same as m since both quantities are ZPE dependent. When this is done from (13), we get the result that  [m2 = e2hω2 / (24π3εc5)]. Now in this formulation, all the terms remain unchanged at the quantum jump except ω2. Therefore we have the conclusion that, at the quantum jump, m2 is proportional to ω2 so m is proportional to ω and hence to 1/V. Including this result with (43) and (44) gives us the information that, specifically at the quantum jump, looking further out into space and back in time

U1 / U2  =  W1 / W2  =  V1 / V2  = m2 / m1 = 1.00000878256      (46)

Note that, in contrast to this, during the interval between jumps, all sub-atomic particle masses increase smoothly and particle volumes remain fixed because energy is conserved. But at the jump itself, with time increasing, the ZPE has increased to its threshold value, which results in a discrete increase in parton volume in (43), and hence a discrete decrease in m in (46). The graph describing m is therefore a saw-tooth function rising with time, with a drop at the quantum jump. So (16) and (16A) show atomic masses follow the smooth curve of (58) below with a small saw-tooth ripple from (46).

6.4 Atomic Orbit Quantum Changes

With a change in m at the quantum jump will come changes in some atomic orbit parameters. At the moment of the jump, there is an infinitesimally small change in the energy density U of the ZPE. Essentially no change in the value of μ, ε, e, h, or c will occur at the jump either, as they all vary smoothly. Let us apply this informiation to equation (34) for orbit energy, E. Exaimination of (34) reveals that, at the moment of the quantum change, when electron masses change by the discrete amount given in (46), orbit energy, E, changes by the same discrete amount. In this case, since m gets smaller, E also gets smaller. But, because of the minus sign, E becomes less negative as time moves forward, and so orbit energies undergo a quantum increase indicated by (46). This quantum increase is very close to the redshift quantum change picked up in the data by Tifft.

A further matter requires our attention. The quantum condition for the Bohr atom describes the orbital angular momentum at the quantum jump for orbit n as being

 mvr = nh/(2π) = constant                            (47A)

since both h and n are unchanged at the jump. But if m changes in (46) the m term on the left hand side of (47A) must change. The second equation describing the Bohr atom establishes that

mv2r = e2/ε = constant                              (47B)

since e2/ε remains unchanged. Equations (47A) and (47B) then suggest that orbit radius, r, varies. This is confirmed by the following procedure. If we square (47A) and divide it into (47B) we get

 1/(mr) = 4π2e2/(εh2n2) =  constant                     (48)

This result follows since h remains unchanged at the jump as does e2/ε. So, at the jump

 mr = constant                                     (49)

Therefore, at the jump, the electron’s orbit velocity is unchanged. We thus conclude that

r ~ 1/m                                           (50)

If m1and r1 are recent values, then at the first quantum jump back in time (50) indicates that

m2/m1 = r1/r2 = 1.00000878256                        (51)

where the evaluation comes from (44) and (46). So a discrete change in particle masses plus an inverse change in orbit radii gives the basic redshift quantization. Orbit changes now need discussion.

6.5 Electron Orbits and Related Quantities

An atom is no longer considered to be a hard, incompressible sphere but a positively charged nucleus surrounded by a cloud of negative electrons. Increasing the number of electrons increases their mutual repulsion so their orbits expand. The reverse is also true since fewer electrons mean less repulsion, and orbits shrink. So electron cloud sizes vary. A metallic cation, or atom with an electron(s) removed, has less electron repulsion and electron orbits shrink to some extent [125]. Anions, or atoms with an additional electron(s), have increased repulsion so electron clouds expand [125]. So an atom may be pictured as an incompressible nucleus surrounded by an electron cloud that compresses or expands depending on existing conditions. Crystals are considered to be nuclei fixed at their final crystalline inter-nuclear separation, and electrons poured into this force field without crystal sizes changing [126].

Three definitions of an atomic radius come from this [127].  If atoms just touch, yet are “unsquashed” without being bonded, then the Van der Waal’s radius results. For chlorine, this is 0.180 nanometers. But, when chlorine atoms are covalently bonded, as in a chlorine gas, its covalent radius is 0.099 nanometers. The chloride anion, as in sodium chloride, has an ionic radius of 0.181 nanometers. Thus, the minute quantum increases in orbit radii from (51) should be absorbed by a different degree of cloud “squashing” without any additional effects.

As far as the bonding energy between atoms to form molecules is concerned, several points should be noted. It is true that completed electron shells will be fractionally larger because of slightly larger orbit radii, r. It is also true that the quantity e2/ε remains fixed. This means that the bond energy will be proportional to 1/r. However, to offset that, the mass of the particles in both the atomic nuclei and the orbiting electrons is also proportional to 1/r from equation (50). This means that the fractionally lower electrostatic bond energy of attraction is acting to pull together atomic particles whose mass is also fractionally lower in the same proportion, and so are more easily attracted. This means that the bond energy per atomic particle mass remains fixed, and so no change in bonding should occur.



[25]  B. Setterfield, D. Dzimano, ‘The Redshift and the Zero Point Energy’ Journal of Theoretics, (Dec. 2003).  Available online at http://www.journaloftheoretics.com/Links/Papers/Setter.pdf

[71]  H. E. Puthoff, Phys. Rev. A, 39:5 (1989) 2333-2342. See also D. Bohm, The Special Theory of Relativity, Benjamin-Cummings, Reading, MA, (1965) Chapt. 19.
[72]  B. Haisch, A. Rueda and H. E. Puthoff, Phys. Rev. A, 49:2 (1994)  p.678.

[119] A.P. French, op.cit., pp. 108, 109.(see ref. #73)
[120] Ibid, p.67.
[121] M. MacGregor, “The Enigmatic Electron,” Dordrecht: Kluwer, (1992) 5-6.
[122] Ibid, p. 28.
[123] A.P. French, op. cit., pp. 63-67.
[124] K.W. Ford, “Classical and Modern Physics,” Vol. 3, Wylie, (1974) 1152, A10.
[125] G.R. Delpierre and B.T. Sewell, “Periodicity of Atomic Properties”, GRD Training Corporation Physchem Co.(2002), available until Dec. 2005 at: http://www.physchem.co.za/Atomic/Periodicity.htm.
[126] W.J. Moore, “Physical Chemistry,” third edition,  Longmans, (1961) 396.
[127] CCEA A level Chemistry (2004) at: http://www.alevelchemistry.co.uk/Module_1/HTML_Pages/Atomic_Size_HTML.htm (as of March 7, 2006).  Also see http://chemguide.co.uk/atoms/properties/atradius.html (2004)(available online until December 2005) And http://web.mit.edu/3.091/www/pt/pert1.html (2005)(as of March 7, 2006).

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