Radiation from violently accelerated bodies

Physical Review D

Volumn 64, Issue 10, 2001, Pages

  Gerlach, Ulrich H ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; ARTICLE; ASTRONOMY; COSMOS; INTERFEROMETER; LINEAR ACCELERATOR; MEASUREMENT; RADIATION SCATTERING;

EID: 0035890877     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. A. Einstein, Jahrbuch der Radioaktivitaet und Electronik 4, Sec. V, p. 411;
2. English translation in The Collected Papers of Albert Einstein, Vol. 2, The Swiss Years: 1900-1909, translated by Anna Beck (Peter Havas, Consultant) (Princeton University Press, Princeton, NJ, 1989), p. 252.
3. Instead of meter sticks with equally spaced markings, it is better to have equally spaced detectors and probes. This means that instead of measuring a particle in relation to the meterstick markings, measure it by the "click" this particle produces in the corresponding detector. Furthermore, by having the clocks keep track of the relative phase between adjacent detection probes, one can measure the wavelength of an electromagnetic wave train passing through the lattice work of equally spaced probes.
4. The other breakthrough was, of course, his focus on the "principle of the uniqueness of free fall" ("Eotvos property"), which he identified as a manifestation of his "equivalence hypothesis" according to which a body's acceleration in a static gravitational field is merely a kinematical effect due to an accelerated reference frame relative to which the body is observed.
5. U.H. Gerlach, Phys. Rev. D 59, 104009 (1999);
6. see also U.H. Gerlach, in Proceedings of the 8th Marcel Grossmann Meeting, edited by T. Piran (World Scientific, Singapore, 1999), pp. 952-954.
7. See, for example, L.L. Landau and E.M. Lifshits, The Classical Theory of Fields (Addison-Wesley, Reading, MA, 1962), Sec. 71.
8. See, for example, C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation (Freeman, San Francisco, 1973), Sec. 1.2, including Fig. 1.4.
9. There are additional difficulties which are spelled out in [6], Sec. 6.3, p. 168.
10. The concept of a recording clock was first made explicit by E.F. Taylor and J.A. Wheeler, Spacetime Physics (Freeman, San Francisco, 1966), Sec. 2.4
11. and in Spacetime Physics, 2nd ed. (Freeman, San Francisco, 1992), Secs. 2.6 and 2.7. Unlike theirs, each of our recording clocks resembles the one found in a GPS satellite: each one also includes a transmitter.
12. See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, Elmsford, NY, 1980), p. 312.
13. Notation: (i) Throughout Sec. III and from Sec. V onward primed coordinates, such as (τ′,ξ′,r′,θ′) or (t′,z′,r′,θ′), refer to the source (transmitter) in Rindler sector I and/or II, while unprimed coordinates, such as (ξ,τ,r,θ) or (t,z,r,θ), refer to the observer (receiver) in Rindler sector F. Also note that in listing these coordinates, e.g., (τ′,ξ′) or (ξ,τ), the timelike coordinate is first, followed by the spacelike coordinate(s).
14. Remark by E. Wigner on p. 285 in the discussion following papers by S.S. Chern and T. Regge, in Some Strangeness in Proportion, edited by Harry Wolf (Addison-Wesley, Reading, MA, 1980).
15. E. Schrödinger, Expanding Universes (Cambridge University Press, New York, 1956), p. 20.
16. The sourceless field equations in Rindler sector I have been, considered by P. Candelas and D. Deutsch, Proc. R. Soc. London, Ser. A 354, 79 (1977),
17. and by A. Higuchi, G.E.A. Matsas, and D. Sudarsky, Phys. Rev. D 46, 3450 (1992).
18. F.J. Alexander and U.H. Gerlach, Phys. Rev. D 44, 3887 (1991), exhibit the inhomogeneous TE and TM wave equations in terms of gauge-invariant mode expansions.
19. A discussion of Hertz's electric and Right's magnetic "superpotential" vectors is given in a tutorial article "Classical Electrodynamics" by M. Phillips, in Encyclopedia of Physics, Volume IV, edited by S. Flugge (Springer-Verlag, Berlin, 1962), p. 74. This tutorial also refers to Whittaker's result.
20. Simply express G as a double Fourier integral. Using Cauchy's integral formula, evaluate the first Fourier (frequency) integral first. Do this by having the integration path go slightly above the two poles on the real frequency axis. The result is the sum of two contributions. This yields the sum of two Fourier integral expressions for the zero order Hankel function of the first and second kind, respectively. Their sum is the zero order Bessel function.
21. A. Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1949), Sec. 21, p. 108.
22. 2 X (proper current) for the proper magnetic dipole moment.
23. m which expresses a phase increase because in II τ increases towards the past.
24. T. Padmanabhan, Phys. Rev. Lett. 64, 2471 (1990).