Is a Quantum Theory of Resonances Really Time Asymmetric?

The title “Time Asymmetric Quantum Theory: the Theory of Resonances” (without questionmark) of the CFIF workshop (23.–26.7.2003, Lisbon, Portugal) implies that the theoretical description of resonances is uniquely described by the formalism of A. Bohm et al. [1, 2] reflecting the title of the workshop. Our presentation in this workshop tries to introduce an apparently inequivalent, alternative feasible relativistic formalism provided by the author [3, 4, 5, 6, 7, 8, 9] under the name “(Anti)Causal Quantum Theory” ((A)CQT) which is compared to the former. 1. The “Time Asymmetric Quantum Theory” of A. Bohm et al. One longstanding debate on Quantum Theory (QT) finds its origin in a logical discrepancy between the description of stationary and time-dependent quantum problems. To put it in the words of A. Bohm et al. [1]: “. . . Quantum Theory in Hilbert space is time symmetric. This is not so bad for the description of spectra and structure of quantum physical systems, whose states are (or are considered as) stationary. But this is particularly detrimental for the description of decay processes and resonance scattering, which are intrinsically irreversible processes. There is no consistent theoretical description for decaying states and resonances in Hilbert space quantum mechanics 1 . . .” In order to overcome this problem A. Bohm et al. suggest to change one axiom of Quantum Mechanics (QM).2 We note Note on the contrary P.T. Matthews & A. Salam [10, 12] or N. Nakanishi [13]! To use their words [1]: “. . . Whereas the standard Hilbert space axiom does not distinguish mathematically be-