## 1. Introducing the Zero Point Energy

1.1 Concepts of the Vacuum
1.2 Problems With the Cosmological Constant
1.3 The Alternative Approach That Physics Offers
1.4 The ZPE and the Cosmological Constant
1.5 Gravity and the Zero Point Energy
1.6 The ZPE and General Relativity

1.1 Concepts of the Vacuum

The vacuum is popularly considered to be a void, an emptiness, or just ‘nothingness.’ This is the definition of a bare vacuum [1]. Today, science has a different description of what is now called the physical vacuum [1]. In order to explain this, take a perfectly sealable flask and remove all solids, liquids and gases, and then cool it to zero degrees Kelvin so that there is no temperature radiation in the flask. It might be expected that this vacuum is now totally empty. However, it is found that there is still an intrinsic energy in this vacuum called the Zero Point Energy (ZPE). The existence of the ZPE was first indicated by Planck’s so-called ‘second theory’ in 1911 [2]. In that paper, his equations revealed that what is now Planck’s constant, h, was a measure of the strength of the ZPE.  The ZPE can be considered as being an all-pervasive sea of electromagnetic waves of all wavelengths up to the Planck length cut-off [3]. The actual existence of the ZPE is demonstrated by the Casimir effect, Van der Waal’s forces, the necessity for pressure to solidify liquid helium, a random noise in microwave receivers and electronic systems that limits amplification, and other physical effects [4]

### 1.2 Problems With the Cosmological Constant

In order to assess the behaviour of the ZPE over time, we must first come to some conclusions about the processes involved in its origin. Quantum electrodynamics (QED) and General Relativity (GR) consider the ZPE to be a manifestation of, and have its origin in, the cosmological constant, Λ. However this approach runs into some problems which need to be examined before we can proceed.

Since the properties of the physical vacuum can be described by the action of Λ in GR, it might be thought that the ZPE is due to the direct action of this quantity. But Kochanek noted that the observational “constraints are consistent with an open, low density model [of the universe] and no cosmological constant” [5]. Barrow and Magueijo also point out “If Λ > 0, then cosmology faces a very serious fine-tuning problem…There is no theoretical motivation for a value of Λ of currently observable magnitude…” [6]. In addition, the problem of trying to incorporate Λ into ZPE theory has proved very difficult for QED. Thus, Zeldovich pointed out that the proposed values for Λ from vacuum and particle theory can disagree with observation by a factor of up to 1046 as observation suggests Λ ≈10–54 cm–2or lower [7]. Abbott reached the same conclusion from different reasoning [8]. Similarly, Greene has noted that “…the cosmological constant can be interpreted as a kind of overall energy stored in the vacuum of space, and hence its value should be theoretically calculable and experimentally measurable. But, to date, such calculations and measurements lead to a colossal mismatch… Observations show that the cosmological constant is either zero (as Einstein ultimately suggested) or quite small; calculations [based on QED theory]… tend to generate a nonzero cosmological constant whose value is some 120 orders of magnitude larger than experiment allows!” [9]. These difficulties seem to indicate that the cause of the problem may be in the QED and GR approach. If this is so, an alternative approach may be worthy of examination.

### 1.3 The Alternative Approach That Physics Offers

An alternative physical formalism does exist, namely stochastic electrodynamics (SED).  It began with Planck in 1911 [2], Einstein and Stern in 1913 [10], and Nernst in 1916 [11]. De Broglie reinvigorated it in 1962 [12], followed by a landmark paper in 1966 by Nelson [13]. SED formalism has claimed some remarkable successes, beyond Planck’s initial explanation of the black-body spectrum. They include a Newtonian derivation of the Schroedinger equation using the ZPE and simple mathematics [13]. Again, SED plus classical physics has shown that the Heisenberg uncertainty relationship is due to the fluctuations caused by the Zero Point Fields (ZPF) on the positions of charged point particles [14]. A third example took these same ZPE induced particle oscillations and demonstrated that, when the particle was in motion, a beat frequency equal to the Compton frequency was superimposed on the oscillations, thereby accounting for the wavelike character of atomic particles [15, 16].

A clarified understanding of mass and gravity has also developed using SED concepts, some of which are explored later. The one question that this development inevitably raises is the status of General Relativity. It turns out that all the major predictions of GR can be reproduced fairly simply using a ZPE methodology, but in a manner originally suggested by Eddington in 1920 [17] and later by Einstein. Their comments are discussed and amplified later in this paper using an approach similar to de Felice [18] and Setterfield [19].

### 1.4 The ZPE and the Cosmological Constant

With this background, it can be stated that SED offers an approach to the cosmological constant problem that makes predictions more in keeping with observation. Thus Haisch and Rueda, using SED formalism, noted that “the ZPF [zero point fields] cannot be the manifestation of a cosmological constant, Λ, or vice versa.” Indeed, “The ZPF is NOT a candidate source for a cosmological constant. The ZPF…can have nothing to do with Λ and is not, of itself, a source of gravitation…Gravitation is not caused by the mere presence of the ZPF, [but] rather by secondary motions of charged particles driven by the ZPF. In this view it is impossible for the ZPF to give rise to a cosmological constant” [20]. So, on the SED approach, the ZPE in and of itself does not exhibit the forces that GR and QED associate with gravity and the cosmological constant. Perhaps a word of explanation is needed about this.

### 1.5 Gravity and the Zero Point Energy

The initial work on the ZPE, gravity and mass was done in 1968 by the Russian physicist Andrei Sakharov. In 1989 Puthoff developed it further. Later, Haisch and Rueda formulated it into a quantifiable theory of gravitation. They noted that all point charges in the universe, such as electrons and quarks, undergo jostling through interaction with the ZPF. As Dirac pointed out, these fluctuations, which Schroedinger called the Zitterbewegung, are relativistic because the charges move at velocities near that of light. Haisch, Rueda & Puthoff elaborate:

“Now a basic result from classical electrodynamics is that a fluctuating charge emits an electromagnetic radiation field. The result is that all charges in the universe will emit secondary electromagnetic fields in response to their interactions with the primary field, the ZPF. The secondary electromagnetic fields turn out to have a remarkable property. Between any two [charged] particles they give rise to an attractive force… whether the charges are positive or negative. The result is that [this weak attractive force] may be identified with gravity. …Since the gravitational force is caused by the trembling motion [Zitterbewegung], there is no need to speak any longer of a gravitational mass as the source of gravitation. The source of gravitation is the driven motion of a charge, not the attractive power of the thing physicists are used to thinking of as mass” [21].

The calculations of those physicists verify these concepts. The understanding of mass that particle interaction with the ZPE provides is amplified below. But the key point for our purpose here is that, on the SED approach, the mere existence of the ZPE does not of itself result in gravitational or cosmological constant forces. The problems caused by these forces being directly associated with the ZPE in GR and QED are thus obviated by this approach.

### 1.6 The ZPE and General Relativity

While these developments raise the question of the relevance of GR, the SED treatment of gravitation presents alternative approaches to GR. The important concept is that, in locations where mass exists, additional secondary electromagnetic fields augment the already existing ZPE. With these augmenting fields in mind, the background for an SED approach was given by Sir Arthur Eddington who stated that: “Light moves more slowly in a material medium than in a vacuum, the velocity being inversely proportional to the refractive index of the medium… We can thus imitate the gravitational effect on light precisely, if we imagine the space round the sun filled with a refracting medium which gives the appropriate velocity of light. To give the velocity c(1-2µ/r) the refractive index must be 1/(1-2µ/r).. …[Geometrical optics shows] the total deflection of a ray passing at a distance r from the centre of the sun is then a deflection of the same ray [in accord with] Einstein’s theory” [17].

Since then, others have discussed this proposal. De Felice mentioned nine authors who have looked at this similarity and points out that Einstein himself also suggested the idea that gravitation is equivalent to an optical medium [18]. The optical medium in SED physics is, of course, the ZPE itself, while the spatial changes in the density of the medium are due to the secondary fields of oscillating particles. Using this type of approach, University of Connecticut physicist Howard Hayden noted that the same results as GR can be derived exactly by this method “with a few lines of high school algebra” [full statement available at: http://www.ldolphin.org/vanFlandern/  as of 20th May 2006]. It can also be shown that other predictions of GR can be equally simply obtained, including the perihelion advance of the planet Mercury, in a manner similar to Setterfield [19] and other works referenced therein.

Section 1 References

[1]  Timothy H. Boyer, “The Classical Vacuum”, Scientific American,  August (1985) 70-78.
[2]  M. Planck, Verhandlungen der Deutschen Physikalischen Gesellschaft 13 (1911) 138.
[3]  California Institute for Physics and Astrophysics (CIPA), An Introduction to Zero-Point Energy, p.3.  Available  (March 7, 2006) online at: http://www.calphysics.org/zpe.html
[4]  B.Setterfield, ‘Exploring the Vacuum’, Journal of Theoretics, (January 2003) available online (March 7, 2006) at http://www.journaloftheoretics.com/Links/Papers/Setterfield.pdf
[5]  C.S. Kochanek, Ap. J. 466 (1996) 638.
[6]   J. D. Barrow and J. Magueijo, Ap. J. 532 (2000) L87.
[7]  Ya. B. Zeldovich, Sov. Phys. Uspekhi 11:3 (1968) 381.
[8]   L. Abbott, Scientific American 258:5 (1988) 106.
[9]   B. Greene, “The Elegant Universe,” W. W. Norton & Company Inc., New York (1999)  225.
[10]  A. Einstein and O. Stern, Ann. Physik 40 (1913)  551.
[11]  W. Nernst, Verhandlungen der Deutschen Physikalischen Gesellschaft (1916)  83.
[12]  L. de Broglie, “New Perspectives in Physics, Basic Books Publishing Co. New York (1962).
[13]  E. Nelson, Phys. Rev. 150 (1966), 1079; also “Dynamical Theories of Brownian Motion,” Princeton University Press, (1967).
[14]  T.H. Boyer, Phys. Rev. D. 11 (1975)  790.
[15]  H.E. Puthoff, New Scientist, 28 July (1990)  36.
[16]  B. Haisch, A. Rueda and H.E. Puthoff, Speculations in Science and Technology, 20 (1997)  99.
[17]  A. S. Eddington, Space, Time and Gravitation, (Cambridge University Press 1920, reprint 1987)  109.
[18]  F. de Felice, ‘On the gravitational field acting as an optical medium’, Gen. Rel. & Grav. 2:4 (1971)  347-357.
[19]  B. Setterfield, ‘General Relativity & the Zero Point Energy,’ Journal of Theoretics, October, 2003 available (March 7, 2006) online at http://www.journaloftheoretics.com/Links/Papers/BS-GR.pdf.

[20]  B. Haisch and A. Rueda, Ap. J. October 20 (1997), pre-print.
[21]  B. Haisch, A. Rueda and H.E. Puthoff, The Sciences, (Nov/Dec 1994) 26-31.

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