Fig. 3: Degrees of freedom of nth particle.
From: Quantum clocks observe classical and quantum time dilation
The temporal degrees of freedom \(({x}_{{\mathrm{n}}}^{0},{P}_{{\mathrm{n}}}^{0})\) and center-of-mass degrees of freedom \(({x}_{{\mathrm{n}}}^{{\mathrm{i}}},{P}_{{\mathrm{n}}}^{{\mathrm{i}}})\) of the nth relativistic particle are depicted. This particle carries an internal degree of freedom \(({q}_{{\mathrm{n}}},{P}_{{{\mathrm{q}}}_{{\mathrm{n}}}})\) that is used to construct a clock which measures the nth particle’s proper time.
