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[Phys-l] Decoherence in Quantum Cosmology J.J Halliwell.




The issue of the arrow of time in a collapsing universe raised in the
dispute between Price-Zeh and Hawking-Page may relate to the faulty notion of the
existence of a classical space time at the scale of the bounce. Also the
author writes

" In Particular , one could associate increasing entropy, and hence the
thermodynamic arrow of time , with the direction of decreasing coherence. This
means that entropy increases when the universe expands and decreases when
the Universe contracts , in this model."

In the Hawking Hartle model we have

Psi_HH= C*exp[i*S] + C^c*exp[-i*S]

The Hawking Hartle proposal is the only CPT invariant cosmological model
which is a strong point in its favor though it is almost certainly incomplete
if not outright incorrect. Nevertheless, it might make sense to take
seriously the quantum nature of the Universe which this model does.


This model presented in this paper predicts that the reduced density matrix
over the transition from initial to final states in terms of scale factor and
matter fields is given by

Rho(
a,theta,a',theta') =


exp[ i*( S(a) -S(a'))] *
chi^c(a,theta)*chi(a',theta;)*F_11


+ exp[i*( S(a)+S(a')]*
chi^c(a,theta)*chi(a',theta;)*F_21


+ exp[- i*( S(a)+S(a')]*
chi^c(a,theta)*chi(a',theta;)*F_12

+ exp[-i*( S(a)-S(a')]*
chi^c(a,theta)*chi(a',theta;)*F_22


Where chi(a,theta) is the scale factor- matter field dependent wave
function and F-ij is the trace over the long wavelength modes ( the
environment) given by


F_11= F_22^c= INTEGRAL d(theta) Chi(a,theta_L)*chi(a',theta_L)


F_12=F_21^c= INTEGRAL d(theta) Chi(a',theta_L)*chi(a,theta_L)




So ultimately , assuming this proposal makes sense , the observed arrows
of time in the Universe has its origin in the Decoherence process and the
higher entropy of the Universe at current times compared to its initial state may
possibly be explained by the decoherence process.

Bob Zannelli

Upon request I will make this paper available. Unfortunately this list
does not permit attachments.







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