Skip to main content
SpringerLink
Log in

Infrared Acceleration Radiation

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

We present an exactly soluble electron trajectory that permits an analysis of the soft (deep infrared) radiation emitted, the existence of which has been experimentally observed during beta decay via lowest order inner bremsstrahlung. Our treatment also predicts the time evolution and temperature of the emission, and possibly the spectrum, by analogy with the closely related phenomenon of the dynamic Casimir effect.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. In the closely related moving mirror model, (see [17]), the usual convention is to move to the left (see Fig. 3). The difference is a sign change in the angular distribution. The energy remains invariant.

  2. Eq. (4) is unique within the Möbius symmetries of bilateral linear fractional transformations. The dual constraints of (A) reproducing the total energy Eq. (3), and (B) maintaining instantaneous collision reference frame asymptotics are highly restrictive. An alternate trajectory replicates (A) but including (B), i.e. requiring it start with initial zero velocity and end with final asymptotic constant final speed, forces the electron to travel in imaginary space or time, or move faster than light, \(\beta > c\).

  3. Since the acceleration is non-zero for all \(t>-\infty \), cf. Fig. 2, the old puzzle of acausal pre-acceleration associated with radiation reaction in classical electrodynamics remains. Zhang [32] points out the possibility for an exact model like Eq. (8) with a classical-quantum correspondence.

  4. See [34, Eqs. 11, 14] for the photon count and the relevant expressions that match Eq. (3).

  5. This accounts for the generalization from 1+1 dimensions to 3+1 dimensions of spacetime [28].

  6. The range can be observed by two detector types: one composed of bismuth germanium oxide (BGO) scintillators and an avalanche photo diode (APD). A low energy spectrum, 0.3 keV to 20 keV, can be measured by the APD and a higher energy spectrum, 10 keV to 1000 keV, can be measured by the BGO.

References

  1. Bloch, F., Nordsieck, A.: Note on the radiation field of the electron. Phys. Rev. 52, 54–59 (1937). https://doi.org/10.1103/PhysRev.52.54

    Article  ADS  MATH  Google Scholar 

  2. Wang Chang, C.S., Falkoff, D.L.: On the continuous gamma-radiation accompanying the beta-decay of nuclei. Phys. Rev. 76, 365–371 (1949). https://doi.org/10.1103/PhysRev.76.365

    Article  ADS  Google Scholar 

  3. Ballagh, H.C., et al.: Observation of muon inner bremsstrahlung in deep inelastic neutrino scattering. Phys. Rev. Lett. 50, 1963–1966 (1983). https://doi.org/10.1103/PhysRevLett.50.1963

    Article  ADS  Google Scholar 

  4. Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999)

    MATH  Google Scholar 

  5. Davies, P.C.W.: Scalar particle production in Schwarzschild and Rindler metrics. J. Phys. A 8, 609–616 (1975). https://doi.org/10.1088/0305-4470/8/4/022

    Article  ADS  Google Scholar 

  6. Fulling, S.A.: Nonuniqueness of canonical field quantization in Riemannian space-time. Phys. Rev. D 7, 2850–2862 (1973). https://doi.org/10.1103/PhysRevD.7.2850

    Article  ADS  Google Scholar 

  7. Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D 14, 870–892 (1976). https://doi.org/10.1103/PhysRevD.14.870

    Article  ADS  Google Scholar 

  8. Moore, G.T.: Quantum theory of the electromagnetic field in a variable-length one-dimensional cavity. J. Math. Phys. 11, 2679–2691 (1970). https://doi.org/10.1063/1.1665432

    Article  ADS  Google Scholar 

  9. DeWitt, B.S.: Quantum field theory in curved space-time. Phys. Rept. 19, 295–357 (1975). https://doi.org/10.1016/0370-1573(75)90051-4

    Article  ADS  Google Scholar 

  10. Fulling, S.A., Davies, P.C.W.: Radiation from a moving mirror in two dimensional space-time: conformal anomaly. Proc. R. Soc. Lond. A 348, 393–414 (1976)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Davies, P.C.W., Fulling, S.A.: Radiation from moving mirrors and from black holes. Proc. R. Soc. Lond. A A356, 237–257 (1977). https://doi.org/10.1098/rspa.1977.0130

    Article  ADS  Google Scholar 

  12. Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975). https://doi.org/10.1007/BF02345020

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Cardoso, V.L., Jose, P.S., Yoshida, S.: Electromagnetic radiation from collisions at almost the speed of light: an extremely relativistic charged particle falling into a Schwarzschild black hole. Phys. Rev. D 68, 084011 (2003). https://doi.org/10.1103/PhysRevD.68.084011

    Article  ADS  Google Scholar 

  14. Zangwill, A.: Modern Electrodynamics. Cambridge Univ. Press, Cambridge (2013)

    MATH  Google Scholar 

  15. Cardoso, V., et al.: Gravitational radiation in D-dimensional space-times. Phys. Rev. D 67, 064026 (2003). https://doi.org/10.1103/PhysRevD.67.064026

    Article  ADS  Google Scholar 

  16. Strominger, A.: Les Houches lectures on black holes. In: NATO Advanced Study Institute: Les Houches Summer School, Session 62: Fluctuating Geometries in Statistical Mechanics and Field Theory (1994)

  17. Good, M.R.R.: Reflecting at the Speed of Light. World Scientific, Singapore (2017)

    Book  Google Scholar 

  18. Carlitz, R.D., Willey, R.S.: Lifetime of a black hole. Phys. Rev. D 36, 2336–2341 (1987). https://doi.org/10.1103/PhysRevD.36.2336

    Article  ADS  MathSciNet  Google Scholar 

  19. Bianchi, E., Smerlak, M.: Entanglement entropy and negative energy in two dimensions. Phys. Rev. D 90, 041904 (2014). https://doi.org/10.1103/PhysRevD.90.041904

    Article  ADS  Google Scholar 

  20. Barcelo, C., Liberati, S., Sonego, S., Visser, M.: Minimal conditions for the existence of a Hawking-like flux. Phys. Rev. D 83, 041501 (2011). https://doi.org/10.1103/PhysRevD.83.041501

    Article  ADS  Google Scholar 

  21. Carlitz, R.D., Willey, R.S.: Reflections on moving mirrors. Phys. Rev. D 36, 2327–2335 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  22. Ford, L.H., Vilenkin, A.: Quantum radiation by moving mirrors. Phys. Rev. D 25, 2569 (1982). https://doi.org/10.1103/PhysRevD.25.2569

    Article  ADS  Google Scholar 

  23. Nikishov, A.I., Ritus, V.I.: Emission of scalar photons by an accelerated mirror in (1+1) space and its relation to the radiation from an electrical charge in classical electrodynamics. J. Exp. Theor. Phys. 81, 615–624 (1995)

    ADS  Google Scholar 

  24. Ritus, V.I.: Symmetries and causes of the coincidence of the radiation spectra of mirrors and charges in (1+1) and (3+1) spaces. J. Exp. Theor. Phys. 87, 25–34 (1998). https://doi.org/10.1134/1.558646

    Article  ADS  Google Scholar 

  25. Ritus, V.I.: Vacuum-vacuum amplitudes in the theory of quantum radiation by mirrors in 1+1-space and charges in 3+1-space. Int. J. Mod. Phys. A 17, 1033–1040 (2002). https://doi.org/10.1142/S0217751X02010467

    Article  ADS  MathSciNet  Google Scholar 

  26. Ritus, V.I.: The Symmetry, inferable from Bogoliubov transformation, between the processes induced by the mirror in two-dimensional and the charge in four-dimensional space-time. J. Exp. Theor. Phys. 97, 10–23 (2003). https://doi.org/10.1134/1.1600792

    Article  ADS  Google Scholar 

  27. Ritus, V.I.: Finite value of the bare charge and the relation of the fine structure constant ratio for physical and bare charges to zero-point oscillations of the electromagnetic field in the vacuum. Usp. Fiz. Nauk 192, 507–526 (2022). https://doi.org/10.3367/UFNe.2022.02.039167

    Article  Google Scholar 

  28. Zhakenuly, A., Temirkhan, M., Good, M.R.R., Chen, P.: Quantum power distribution of relativistic acceleration radiation: classical electrodynamic analogies with perfectly reflecting moving mirrors. Symmetry 13, 653 (2021). https://doi.org/10.3390/sym13040653

    Article  ADS  Google Scholar 

  29. Ievlev, E., Good, M.R.R.: Thermal larmor radiation. Preprint at http://arxiv.org/abs/2303.03676 (2023)

  30. Good, M.R.R., Temirkhan, M., Oikonomou, T.: Stationary worldline power distributions. Int. J. Theor. Phys. 58, 2942–2968 (2019). https://doi.org/10.1007/s10773-019-04176-7

    Article  MathSciNet  MATH  Google Scholar 

  31. Bekenstein, J.D., Mayo, A.E.: Black holes are one-dimensional. Gen. Rel. Grav. 33, 2095–2099 (2001). https://doi.org/10.1023/A:1015278813573

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Zhang, S.: Pre-acceleration from Landau–Lifshitz series. PTEP 2013, 123A01 (2013). https://doi.org/10.1093/ptep/ptt099

    Article  MATH  Google Scholar 

  33. Feynman, R.P.: Feynman Lectures on Gravitation. CRC Press, Cambridge (1996)

    Google Scholar 

  34. Tomaras, T.N., Toumbas, N.: Ir dynamics and entanglement entropy. Phys. Rev. D 101, 065006 (2020). https://doi.org/10.1103/PhysRevD.101.065006

    Article  ADS  MathSciNet  Google Scholar 

  35. Wilczek, F.: Quantum purity at a small price: easing a black hole paradox. In: International Symposium on Black holes, Membranes, Wormholes and Superstrings, pp. 1–21. Preprint at http://arxiv.org/abs/hep-th/9302096 (1993)

  36. Walker, W.R., Davies, P.C.W.: An exactly soluble moving-mirror problem. J. Phys. A Math. Gen. 15, L477–L480 (1982). https://doi.org/10.1088/0305-4470/15/9/008

    Article  ADS  Google Scholar 

  37. Good, M.R.R., Linder, E.V., Wilczek, F.: Moving mirror model for quasithermal radiation fields. Phys. Rev. D 101, 025012 (2020). https://doi.org/10.1103/PhysRevD.101.025012

    Article  ADS  MathSciNet  Google Scholar 

  38. Good, M.R.R., Yelshibekov, K., Ong, Y.C.: On horizonless temperature with an accelerating mirror. JHEP 03, 013 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Good, M.R.R., Singha, C., Zarikas, V.: Extreme electron acceleration with fixed radiation energy. Entropy 24, 1570 (2022). https://doi.org/10.3390/e24111570

    Article  ADS  MathSciNet  Google Scholar 

  40. Ievlev, E., Good, M.R.R., Linder, E.V.: Thermal radiation from an electron with Schwarzschild–Planck acceleration. Preprint at http://arxiv.org/abs/2304.04412 (2023)

  41. Good, M.R.R., Ong, Y.C.: Electron as a tiny mirror: radiation from a worldline with asymptotic inertia. Physics 5, 131–139 (2023). https://doi.org/10.3390/physics5010010

    Article  ADS  Google Scholar 

  42. Nico, J.S., et al.: Observation of the radioactive decay mode of the free neutron. Nature 444, 1059 (2006). https://doi.org/10.1038/nature05390

    Article  ADS  Google Scholar 

  43. Bales, M.J., et al.: Precision measurement of the radiative \(\beta \) decay of the free neutron. Phys. Rev. Lett. 116, 242501 (2016). https://doi.org/10.1103/PhysRevLett.116.242501

    Article  ADS  Google Scholar 

  44. Fulling, S.A.: Review of some recent work on acceleration radiation. J. Mod. Opt. 52, 2207–2213 (2005). https://doi.org/10.1080/09500340500303637

    Article  ADS  Google Scholar 

  45. Good, M.R.R., Linder, E.V.: Quantum power: a Lorentz invariant approach to Hawking radiation. Eur. Phys. J. C 82, 204 (2022). https://doi.org/10.1140/epjc/s10052-022-10167-6

    Article  ADS  Google Scholar 

  46. Myrzakul, A., Xiong, C., Good, M.R.R.: CGHS black hole analog moving mirror and its relativistic quantum information as radiation reaction. Entropy 23, 1664 (2021). https://doi.org/10.3390/e23121664

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors thank Stephen Fulling for useful discussion. Funding comes in part from the FY2021-SGP-1-STMM Faculty Development Competitive Research Grant No. 021220FD3951 at Nazarbayev University. Appreciation is given to the organizers, speakers, and participants of the QFTCS Workshop: May 23-27, 2022, at which preliminary results were first presented and helpful feedback are included therein.

Author information

Authors and Affiliations

  1. Department of Physics & Energetic Cosmos Laboratory, Nazarbayev University, Kabanbay Batyr Ave 53, Astana, 010000, Kazakhstan

    Michael R. R. Good

  2. Department of Physics and Beyond: Center for Fundamental Concepts in Science, Arizona State University, Tempe, AZ, 85287, USA

    Paul C. W. Davies

Authors
  1. Michael R. R. Good
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul C. W. Davies
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael R. R. Good.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Good, M.R.R., Davies, P.C.W. Infrared Acceleration Radiation. Found Phys 53, 53 (2023). https://doi.org/10.1007/s10701-023-00694-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10701-023-00694-x

Keywords

Search

Navigation