# Contribution to Inertial Mass by Reaction of the Vacuum to Accelerated Motion

- 124 Downloads
- 16 Citations

## Abstract

We present an approach to understanding the origin of inertia involving the electromagnetic component of the quantum vacuum and propose this as a step toward an alternative to Mach's principle. Preliminary analysis of the momentum flux of the classical electromagnetic zero-point radiation impinging on accelerated objects as viewed by an inertial observer suggests that the resistance to acceleration attributed to inertia may be at least in part a force of opposition originating in the vacuum. This analysis avoids the ad hoc modeling of particle-field interaction dynamics used previously by Haisch, Rueda, and Puthoff (Phys. Rev. A 49, 678, (1994)) to derive a similar result. This present approach is not dependent upon what happens at the particle point, but on how an external observer assesses the kinematical characteristics of the zero-point radiation impinging on the accelerated object. A relativistic form of the equation of motion results from the present analysis. Its manifestly covariant form yields a simple result that may be interpreted as a contribution to inertial mass. We note that our approach is related by the principle of equivalence to Sakharov's conjecture (Sov. Phys. Dokl. 12, 1040, (1968)) of a connection between Einstein action and the vacuum. The argument presented may thus be construed as a descendant of Sakharov's conjecture by which we attempt to attribute a mass-giving property to the electromagnetic component—and possibly other components—of the vacuum. In this view the physical momentum of an object is related to the radiative momentum flux of the vacuum instantaneously contained in the characteristic proper volume of the object. The interaction process between the accelerated object and the vacuum (akin to absorption or scattering of electromagnetic radiation) appears to generate a physical resistance (reaction force) to acceleration suggestive of what has been historically known as inertia.

## Preview

Unable to display preview. Download preview PDF.

### REFERENCES

- 1.
- 2.W. H. McCrea,
*Nature***230**, 95 (1971). See also an attempt at an alternative approach by R. C. Jennison and A. J. Drinkwater,*J*.*Phys*.*A***10**, 167 (1977).Google Scholar - 3.D. W. Sciama,
*Mon*.*Not*.*Roy*.*Astron*.*Soc*.**113**, 34 (1953). See also G. Cocconi, and E. Salpeter,*Nuovo Cimento***10**, 646 (1958).Google Scholar - 4.S. Weinberg,
*Gravitation and Cosmology*:*Principles and Applications of the General Theory of Relativity*(Wiley, New York, 1972), pp. 86–88.Google Scholar - 5.W. Rindler,
*Phys*.*L ett*.*A***187**, 236 (1994). There was a reply to this paper by H. Bondi and J. Samuel,*Phys*.*L ett*.*A***228**, 121 (1997).Google Scholar - 6.For further detailed discussion of Mach's Principle see J. Barbour, “Einstein and Mach'sPrinciple” in Studies in the History of General Relativity, J. Eisenstadt and A. J. Knox, eds.( Birkhauser, Boston, 1988) , pp. 125-153.Google Scholar
- 7.B. Haisch, A. Rueda, and H. E. Puthoff,
*Phys*.*Rev*.*A***49**, 678 (1994). We also refer to this paper for review points and references on the subject of inertia.Google Scholar - 8.The corresponding required inertial coupling would take place along a spacelike hyper-surface in a manner consistent with the dictates of general relativity. See C. W. Misner, K. S. Thorne, and T. A. Wheeler,
*Gravitation*(Freeman, San Francisco, 1971), pp. 543–549, for a more traditional discussion on Mach's principle within general relativity with several references. See, however, Refs. 1, 4, 5, and 6 above.Google Scholar - 9.A. D. Sakharov,
*Sov*.*Phys*.*Dokl*.**12**, 1040 (1968);*Theor*.*Math*.*Phys*.**23**, 435 (1975). See also C. W. Misner, K. S. Thorne, and J. A. Wheeler,*Gravitation*(Freeman, San Francisco, 1973), pp. 417-428. This approach has been interpreted within SED by means of a tentative preliminary nonrelativistic treatment that models the ZPF-induced ultrarelativistic zitterbewegung: H. E. Puthoff,*Phys*.*Rev*.*A***39**, 2333 (1989); see also S. Carlip,*Phys*.*Rev*.*A***47**, 3452 (1993) and H. E. Puthoff,*Phys*.*Rev*.*A***47**, 3454 (1993). A revision on the status of this last issue has been carried out by K. Danley, Thesis, California State University, Long Beach, 1994. It shows that there remain unsettled questions in the derivation of Newtonian gravitation. However, our inertia work reported here and in Ref. 7 as well as the equivalence principle suggest to us that the ZPF approach to gravitation remains promising once a more detailed relativistic particle model is implemented.Google Scholar - 10.D. C. Cole and A. Rueda (1998), in preparation, and D. C. Cole (1998), in preparation, in which an effort is being made to analyze in a more accurate way the developments of Ref. 7, in particular by not approximating away to zero some terms, like the contribution of the electric part of the Lorentz force, that may arguably be significant. These involved calculations are still in progress at the time of writing of the present paper.Google Scholar
- 11.T. H. Boyer,
*Phys*.*Rev*.*D***29**, 1089 (1984); for clarity of presentation the notation proposed in this article is followed here.Google Scholar - 12.W. Rindler,
*Introduction to Special Relativity*(Clarendon, Oxford, 1991), pp. 91–93. The most relevant part is Sec. 35, pp. 90-93. Hyperbolic motion is found in Sec. 14, pp. 33-36. Further details on hyperbolic motion are given in F. Rohrlich,*Classical Charged Particles*(Addison Wesley, Reading, Massachusetts, 1965), pp. 117 ff and 168 ff. These are important references throughout this paper.Google Scholar - 13.A. Rueda,
*Phys*.*Rev*.*A***23**, 2020 (1981); see, e.g., Eqs. (2) and (9). See also D. C. Cole,*Found*.*Phys*.**20**, 225 (1990), for a more explicit discussion of the need of a normalization factor.Google Scholar - 15.See, e.g., E. J. Konopinski,
*Electromagnetic Fields and Relativistic Particles*(McGraw-Hill, New York, 1981), or J. D. Jackson,*Classical Electrodynamics*(Wiley, New York, 1975).Google Scholar - 16.The Lorentz invariance of the spectral energy density of the classical electromagnetic ZPF was independently found by T. W. Marshall,
*Proc*.*Cambridge Philos*.*Soc*.**61**, 537 (1965) and T. H. Boyer,*Phys*.*Rev*.**182**, 1374 (1969); see also E. Santos,*Nuovo Cimento L ett*.**4**, 497 (1972). From a quantum point of view every Lorentz-invariant theory is expected to yield a Lorentz-invariant vacuum. The ZPF of QED should be expected to be Lorentz-invariant; see, e.g., T. D. Lee, “Is the physical vacuum a medium” in*A Festschrift for Maurice Goldhaber*, G. Feinberg, A. W. Sunyar, and J. Wenesser, eds.,*Trans*.*N*.*Y*.*Acad*.*Sci*.,*Ser*.*II***40**(1980). For nice discussions on the Lorentz invariance of the ZPF and other comments and references to related work in SED, see L. de la Peña, “Stochastic electrodynamics: its development, present situation and perspective,” in*Stochastic Processes Applied to Physics and Other Related Fields*, B. Gomez*et al*., eds. (World Scientific, Singapore, 1983), p. 428 ff.; also L. de la Pena and A. M. Cetto,*T he Quantum Dice*(Kluwer, Dordrecht, 1996), p. 113 ff.Google Scholar - 18.See, e.g., J. M. Jauch and F. Rohrlich,
*The Theory of Photons and Electrons*(Springer, Berlin, 1980), p. 298.Google Scholar - 19.J. Schwinger, L. L. De Rand, and K. A. Milton,
*Ann*.*Phys*. (*N*.*Y*.)**15**, 1 (1978), and references therein to previous work on Schwinger's source theory.Google Scholar - 20.A. O. Barut, J. P. Dowling, and J. F. van Huele,
*Phys*.*Rev*.*A***38**, 4408 (1988). A. O. Barut and J. P. Dowling,*Phys*.*Rev*.*A***41**, 2277 (1990). J. P. Dowling in*New Frontiers in Quantum Electrodynamics and Quantum Optics*, A. O. Barut, ed. (Plenum, New York, 1990), and references therein to further work of Barut and collaborators on QED based on the self-fields approach.Google Scholar - 21.See, however, M. Ibison and B. Haisch,
*Phys*.*Rev*.*A***54**, 2757 (1996) for resolution of an important discrepancy between SED and QED.Google Scholar - 22.
- 23.T. H. Boyer,
*Phys*.*Rev*.*D***21**, 2137 (1980). The time removal procedure for SED used here is implicity found in this paper.Google Scholar - 24.
- 27.For
*P*^{µ}to be a four-vector, the four-divergence of the electromagnetic energy momentum stress tensor should vanish, ¶*∂*_{µ}\(\Theta ^{\mu \nu } \)= 0. As the only interaction considered in this work is the electromagnetic and as explicitly we omit any other components of the vacuum besides the electromagnetic, there is no question that the stress tensor \(\Theta ^{\mu \nu } \) is purely electromagnetic. In more complex models where there are other interactions it would be the four-divergence of the sum of the electromagnetic and the other field stress tensor (Poincaréstress) that should vanish, i.e., ¶*∂*_{µ}\({\text{(}}\Theta ^{\mu \nu } + \Theta _{other}^{\mu \nu } )\) = 0. In such a case it becomes a matter of choice if individually ¶*∂*_{µ}\(\Theta ^{\mu \nu } \) and ¶*∂*_{µ}\(\Theta _{other}^{\mu \nu } \) each separately vanishes or not, and their divergences are then just the opposites of each other. A nice discussion of this point is found in I. Campos and J. L. Jiménez,*Phys*.*Rev*.*D***33**, 607 (1986). See also I. Campos and J. L. Jiménez,*Eur*.*J*.*Phys*.**13**, 177 (1992). T. H. Boyer,*Phys*.*Rev*.*D***25**, 3246 (1982);*Phys*.*Rev*.*D***25**, 3251 (1982). So when there are other fields (interactions), the electromagnetic four-vector character of*P*^{µ}is not that compelling, but in the present purely electromagnetic case such four-vector character necessarily holds since ¶*∂*_{µ}\(\Theta ^{\mu \nu } \) = 0. In the pure electromagnetic case which for simplicity of treatment we assume here, the 4*/*3 factor becomes unity. If, on the other hand, we were to assume other fields (e.g., those participating in the*ŋ*(*ω*) response of the particle), then the obliteration of the 4*/*3 factor becomes more a matter of theoretical preference.Google Scholar