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The Possibilist Transactional Interpretation and Relativity

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Abstract

A recent ontological variant of Cramer’s Transactional Interpretation, called “Possibilist Transactional Interpretation” or PTI, is extended to the relativistic domain. The present interpretation clarifies the concept of ‘absorption,’ which plays a crucial role in TI (and in PTI). In particular, in the relativistic domain, coupling amplitudes between fields are interpreted as amplitudes for the generation of confirmation waves (CW) by a potential absorber in response to offer waves (OW), whereas in the nonrelativistic context CW are taken as generated with certainty. It is pointed out that solving the measurement problem requires venturing into the relativistic domain in which emissions and absorptions take place; nonrelativistic quantum mechanics only applies to quanta considered as ‘already in existence’ (i.e., ‘free quanta’), and therefore cannot fully account for the phenomenon of measurement, in which quanta are tied to sources and sinks.

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Notes

  1. E.g., Dirac [16], Hoyle and Narlikar [19], Konopinski [25], Pegg [28], Bennett [4].

  2. Emission is of course defined by the action of the corresponding creation operator on the vacuum state: \(a^{\dag}_{p}|0\rangle = |p\rangle\).

  3. Technically, the Davies theory, which is probably the best currently articulated theoretical model for TI and which is discussed below, is a direct action (DA) theory in which field creation and destruction operators for photons are superfluous; the electromagnetic field is not really an independent entity. Creation and annihilation of photons is then physically equivalent to couplings between the interacting charged currents themselves, and it is the coupling amplitudes that physically govern the generation of offers and confirmations. The important point is that couplings between fields are inherently stochastic and so are the generations of OW and CW.

  4. The term ‘current’ in this context denotes the generalization of a probability distribution for a particle associated, in the relativistic domain, with a quantum field.

  5. This is demonstrated by the Reeh-Schlieder Theorem; cf. Redhead [29].

  6. The Landau and Peierls paper has been reprinted in Wheeler and Zurek [34].

  7. That these expressions are equivalent is proved in [11] and reviewed in [12]. The currents j μ are fermionic currents.

  8. The caveat ‘theoretically’ is introduced because a genuinely free photon can never be observed: any detected photon has a finite lifetime (unless there are ‘primal’ photons which were never emitted) and is therefore not ‘free’ in a rigorous sense. This is elaborated below and in footnote 11.

  9. Feynman [17]. Sakurai [p. 256, 30] also makes this point: As a matter of fact most real photons of physical interest are, strictly speaking, virtual in the sense that they are emitted at some place and absorbed at another place.

  10. “Off-shell” behavior applies in principal for any photon that lacks an infinite lifetime; this is expanded on in Sect. 3.2.

  11. Of course, this is theoretically possible (even if not consistent with current ‘Big Bang’ cosmology), and could be regarded as the initial condition that provides the thermodynamic arrow, as well as an interesting agreement with the first chapter of Genesis. But the existence of such ‘primal photons’ would not rule out the direct emitter-absorber interaction model upon which TI is based. It would just provide an unambiguous direction for the propagation of positive energy.

  12. While this might seem as a drawback at first glance, the standard theory simply disregards the advanced solutions in an ad hoc manner (which, as noted previously, is inconsistent with the unification of space and time required by relativity). In the time-symmetric theory, the appearance of a fully retarded field can be explained by physical boundary conditions.

  13. These plane waves are simplified components of the currents appearing in (1) and (2).

  14. The term ‘generic’ reflects the fact that the denominator here is simply q 2. The different types of propagators involve different prescriptions for the addition of an infinitesimal imaginary quantity, for dealing with the poles corresponding to ‘real’ photons with q 2=0. However, in actual calculations, one often simply uses this expression. The fact that the generic expression yields accurate predictions can be taken as an indication that the theoretical considerations surrounding the choice of propagator do not have empirical content in the context of micro-processes such as scattering.

  15. To be precise, all orders up to a natural limit short of the continuum; see footnote 17.

  16. I refer here to the distinguishing features of fractals: (1) a progressively finer structure continuing to arbitrarily small scales and (2) self-similarity in the ‘branching’ of those finer processes from the ‘parent’ process.

  17. Adopting a realist view of the perturbative process might be seen as subject to criticism based on theoretical divergences of QFT; i.e., it is often claimed that the virtual particle processes corresponding to terms in the perturbative expansion are ‘fictitious.’ But such divergences arise from taking the mathematical limit of zero distances for virtual particle propagation. This limit, which surpasses the Planck length, is likely an unwarranted mathematical idealization. In any case, it should be recalled that spacetime indices really characterize points on the quantum field rather than points in spacetime [3, p. 48]; according to PTI, spacetime emerges only at the level of actualized transactions. Apart from these ontological considerations, progress has been made in discretized field approaches to renormalization such as that pioneered by Kenneth Wilson (lattice gauge theory, cf. Wilson [35–37]). Another argument against the above criticism of a realist view of QFT’s perturbative expansion is that formally similar divergences appear in solid state theory, for example in the Kondo effect [24], but these are not taken as evidence that the underlying physical model should be considered ‘fictitious.’

  18. Technically, by comparison with the standard time-asymmetric theory, the product of the original offer wave component amplitude, \(\frac{1}{2}a\), and its complex conjugate, \(\frac{1}{2}a*|\), yields an overall factor of \(\frac{1}{4}\), but this amounts to a universal factor which has no empirical content since it would apply to all processes and therefore would be unobservable.

  19. The symmetry breaking aspect of transaction actualization is introduced in [23] and further explored in a forthcoming work.

  20. For the present argument, I disregard the issue of renormalization, in which an arbitrary cutoff is implemented in order to avoid self-energy divergences resulting from this apparently infinite regression. But see foonote 17 for why the latter is probably a mathematical idealization not applicable to physical reality.

  21. The photon, being virtual, cannot attain full absorber status; the other way to see this is that conservation of energy does not allow a single photon to absorb a single electron.

  22. Since those expressions will in general be sums, there will be cross terms mixing the couplings, but this simply illustrates the higher level of interference in the relativistic case.

  23. The discussion has addressed coupling amplitudes as amplitudes for confirmations, but a vertex also involves the possible generation of an OW. One can think of the virtual particle as the manifestation of both the ‘failed’ OW and CW.

  24. To be more precise in terms of TI, the existence of a large number of absorbers (the slitted screen) which allow only specific OW components to proceed through the experiment.

  25. The electromagnetic field and the electromagnetic vector potential are related by

    $$\vec{E}(x,t) = - \frac{1}{c}\frac{\partial \vec{A}}{\partial t} - \nabla A_{t}. $$

  26. In practice, when the initial and final states are spacetime points, they are ‘dummy variables’; i.e., variables of integration. In quantum field theory it is not meaningful to talk about a quantum being created and destroyed at specific spacetime points.

  27. See, for example, [6].

  28. Figures 4 and 5 are reproduced from the dissertation of Breitenbach and are in the public domain at http://upload.wikimedia.org/wikipedia/commons/1/1a/Coherent_state_wavepacket.jpg.

  29. For those concerned about whether the universe may not be a ‘light tight box’ as required by traditional ‘direct action’ (DA) theories, thus not providing for full future absorption of the OW, it should be noted that confirmations may also be provided by a perfectly reflecting past boundary condition, as proposed in [8]. This is a type of ‘absorberless’ confirmation in which the advanced wave from the emitter is reflected at t=0 and thereby cancels the remnant advanced wave from the emitter and builds the emitter’s retarded OW up to full strength, resulting in an actualized transfer of energy into the infinite future.

  30. By ‘collapse of superpositons’, I refer to the superposition of a single object. For example, we can see evidence of superposition in the two-slit experiment, in which both the OW and CW have access to both slits, but any individual mark corresponding to a particular ‘hit’ is itself in a determinate position (i.e., not in a superposition of positions).

References

  1. Aharonov, Y., Albert, D.: Can we make sense out of the measurement process in relativistic quantum mechanics? Phys. Rev. D, Part. Fields 24, 359–370 (1981)

    Article  ADS  Google Scholar 

  2. Arndt, M., Zeilinger, A.: Buckeyballs and the dual-slit experiment. In: Al-Khalili, J. (ed.) Quantum: A Guide for the Perplexed. Weidenfeld & Nicolson, London (2003)

    Google Scholar 

  3. Auyang, S.: How is Quantum Field Theory Possible? New York, Oxford (1995)

    Google Scholar 

  4. Bennett, C.L.: Precausal quantum mechanics. Phys. Rev. A 36, 4139–4148 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  5. Beretstetskii, V.B., Lifschitz, E.M., Petaevskii, L.P.: Quantum electrodynamics. In: Landau, L.P., Lifshitz, E.M. Course of Theoretical Physics, vol. 4. Elsevier, Amsterdam (1971)

    Google Scholar 

  6. Breitenbach, G., Schiller, S., Mlynek, J.: Measurement of the quantum states of squeezed light. Nature 387, 471 (1997)

    Article  ADS  Google Scholar 

  7. Cramer, J.G.: Generalized absorber theory and the Einstein-Podolsky-Rosen paradox. Phys. Rev. D 22, 362–376 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  8. Cramer, J.G.: The arrow of electromagnetic time and the generalized absorber theory. Found. Phys. 13, 887–902 (1983)

    Article  ADS  Google Scholar 

  9. Cramer, J.G.: The transactional interpretation of quantum mechanics. Rev. Mod. Phys. 58, 647–688 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  10. Davies, P.C.W.: A quantum theory of Wheeler-Feynman electrodynamics. Proc. Camb. Philol. Soc. 68, 751 (1970)

    Article  ADS  Google Scholar 

  11. Davies, P.C.W.: Extension of Wheeler-Feynman quantum theory to the relativistic domain. I. Scattering processes. J. Phys. A, Gen. Phys. 6, 836 (1971)

    Article  ADS  Google Scholar 

  12. Davies, P.C.W.: Extension of Wheeler-Feynman quantum theory to the relativistic domain. II. Emission processes. J. Phys. A, Gen. Phys. 5, 1025–1036 (1972)

    Article  ADS  Google Scholar 

  13. De Broglie, L.: C. R. Acad. Sci. 177, 507–510 (1923)

    Google Scholar 

  14. De Broglie, L.: On the theory of quanta. Ph.D. dissertation (1924)

  15. Dirac, P.A.M.: The quantum theory of the emission and absorption of radiation. Proc. Roy. Soc. Lon. A 114, 243–265 (1927)

    Article  ADS  MATH  Google Scholar 

  16. Dirac, P.A.M.: Proc. R. Soc. A 167, 148–168 (1938)

    Article  ADS  Google Scholar 

  17. Feynman, R.P.: Theory of Fundamental Processes p. 95. Benjamin, Elmsford (1961)

    Google Scholar 

  18. Hellwig, K.E., Kraus, K.: Formal description of measurements in local quantum field theory. Phys. Rev. D 1, 566–571 (1970)

    Article  ADS  Google Scholar 

  19. Hoyle, F., Narlikar, J.V.: Ann. Phys. 54, 207–239 (1969)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Kastner, R.E.: The quantum liar experiment in Cramer’s transactional interpretation. Stud. Hist. Philos. Mod. Phys. 41, 86–92 (2010). Preprint available at. http://arxiv.org/abs/0906.1626

    Article  MathSciNet  MATH  Google Scholar 

  21. Kastner, R.E.: De Broglie waves as the “bridge of becoming” between quantum theory and relativity. Found. Sci. (2011a, forthcoming). doi:10.1007/s10699-011-9273-4

    Google Scholar 

  22. Kastner, R.E.: On delayed choice and contingent absorber experiments. ISRN Math. Phys. (2011b). Article ID 617291. doi:10.5402/2012/617291

    Google Scholar 

  23. Kastner, R.E.: The broken symmetry of time. In: Quantum Retrocausation: Theory and Experiment AIP Conf. Proc. vol. 1408, pp. 7–21 (2011c). doi:10.1063/1.3663714

    Google Scholar 

  24. Kondo, J.: Resistance minimum in dilute magnetic alloys. Prog. Theor. Phys. 32, 37 (1964). Free access

    Article  ADS  Google Scholar 

  25. Konopinski, E.J.: Electromagnetic Fields and Relativistic Particles, Chapt. 14, McGraw-Hill, New York (1980)

    Google Scholar 

  26. Landau, L.D., Peierls, R.: Z. Phys. 69, 56 (1931)

    Article  ADS  Google Scholar 

  27. Marchildon, L.: On relativistic element of reality. Found. Phys. 38, 804–817 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Pegg, D.T.: Rep. Prog. Phys. 38, 1339 (1975)

    Article  ADS  Google Scholar 

  29. Redhead, M.: More ado about nothing. Found. Phys. 25, 123–137 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Sakurai, J.J.: Advanced Quantum Mechanics, 4th edn. Addison-Wesley, Reading (1973)

    Google Scholar 

  31. Shimony, A.: Bell’s theorem. Stanford Encyclopedia of Philosophy (2009). http://plato.stanford.edu/entries/bell-theorem/#7

  32. Wheeler, J.A., Feynman, R.P.: Interaction with the absorber as the mechanism of radiation. Rev. Mod. Phys. 17, 157–161 (1945)

    Article  ADS  Google Scholar 

  33. Wheeler, J.A., Feynman, R.P.: Classical electrodynamics in terms of direct interparticle action. Rev. Mod. Phys. 21, 425–433 (1949)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Wheeler, J.A., Zurek, W.H.: Quantum Theory and Measurement. Princeton Series in Physics. Princeton University Press, Princeton (1983)

    Google Scholar 

  35. Wilson, K.G.: Feynman graph expansion for critical exponents. Phys. Rev. Lett. 28, 548 (1971). 1971

    Article  ADS  Google Scholar 

  36. Wilson, K.G.: Phys. Rev. D 10, 2445 (1974)

    Article  ADS  Google Scholar 

  37. Wilson, K.G.: The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773–840 (1975)

    Article  ADS  Google Scholar 

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Acknowledgements

I am grateful to two anonymous reviewers for their helpful comments in improving the presentation of this paper.

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    Ruth E. Kastner

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Kastner, R.E. The Possibilist Transactional Interpretation and Relativity. Found Phys 42, 1094–1113 (2012). https://doi.org/10.1007/s10701-012-9658-4

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