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## Summary:

- Perhaps the Born rule can be understood by considering quantum transitions going both forward and backward in time simultaneously.

## Main Question or Discussion Point

**Summary:**Perhaps the Born rule can be understood by considering quantum transitions going both forward and backward in time simultaneously.

The probability that an initial quantum state ##|\psi_i\rangle## becomes the final quantum state ##|\psi_f\rangle## is given by

\begin{eqnarray*}

P(i \rightarrow f) &=& |\langle\psi_f|\psi_i\rangle|^2 \tag{1}\\

&=& \langle\psi_f|\psi_i\rangle^*\langle\psi_f|\psi_i\rangle \\

&=& \langle\psi_i|\psi_f\rangle\langle\psi_f|\psi_i\rangle.

\end{eqnarray*}

Equation (1) seems to show that the probability for the transition (##i\rightarrow f##) can be interpreted as the system both moving forward in time (##i\rightarrow f##) with amplitude ##\langle\psi_f|\psi_i\rangle## and backward in time (##f\rightarrow i##) with amplitude ##\langle\psi_i|\psi_f\rangle## simultaneously.

Does this reasoning help to explain the Born rule? (Is it like the Transactional Interpretation of QM?)

I guess we must experience the macroscopic direction of time (##i\rightarrow f##) in accord with increasing entropy in an expanding universe whereas microscopically QM works both forwards and backwards in time.