Abstract
This chapter derives and discusses quantisation of the relativistic “clock” Hamiltonian, providing dynamics of low energy quantum systems with internal degrees of freedom in a fixed background.
Section 3.2 contains material from Quantum formulation of the Einstein Equivalence Principle, M. Zych and Č. Brukner, arXiv:1502.00971 (2015).
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Notes
- 1.
The mass energy equivalence—the change of the mass of the particle by \(\delta E/c^2\) when its internal energy changes by \(\delta E\)—is currently verified up the precision of \(10^{-7}\) [4].
- 2.
Recall that unitary representation of \(g_\alpha \in \mathcal G\) (a transformation parametrised by \(\alpha \)) generated by an operator G reads \(U=e^{{ \textstyle -i\alpha G/\hbar }}\).
- 3.
Equivalence of the two pictures in classical physics was rooted in the fact that a constant generator does not induce any transformation. This is in full agreement with the quantum case, since the diagonal elements of a density operator of a quantum system can be seen as classical states.
- 4.
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Zych, M. (2017). Quantum Clocks in General Relativity. In: Quantum Systems under Gravitational Time Dilation. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-53192-2_3
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