Time from quantum entanglement: An experimental illustration

Abstract

In the last years several theoretical papers discussed if time can be an emergent propertiy deriving from quantum correlations. Here, to provide an insight into how this phenomenon can occur, we present an experiment that illustrates Page and Wootters' mechanism of "static" time, and Gambini et al. subsequent refinements. A static, entangled state between a clock system and the rest of the universe is perceived as evolving by internal observers that test the correlations between the two subsystems. We implement this mechanism using an entangled state of the polarization of two photons, one of which is used as a clock to gauge the evolution of the second: an "internal" observer that becomes correlated with the clock photon sees the other system evolve, while an "external" observer that only observes global properties of the two photons can prove it is static."Quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio." [1] The "problem of time" [2][3][4][5][6] in essence stems from the fact that a canonical quantization of general relativity yields the Wheeler-De Witt equation [7,8] predicting a static state of the universe, contrary to obvious everyday evidence. A solution was proposed by Page and Wootters [9, 10]: thanks to quantum entanglement, a static system may describe an evolving "universe" from the point of view of the internal observers. Energy-entanglement between a "clock" system and the rest of the universe can yield a stationary state for an (hypothetical) external observer that is able to test the entanglement vs. abstract coordinate time. The same state will be, instead, evolving for internal observers that test the correlations between the clock and the rest [9][10][11][12][13][14]. Thus, time would be an emergent property of subsystems of the universe deriving from their entangled nature: an extremely elegant but controversial idea [2,15]. Here we want to demystify it by showing experimentally that it can be naturally embedded into (small) subsystems of the universe, where Page and Wootters' mechanism (and Gambini et al. subsequent refinements [12,16]) can be easily studied. We show how a static, entangled state of two photons can be seen as evolving by an observer that uses one of the two photons as a clock to gauge the time-evolution of the other photon. However, an external observer can show that the global entangled state does not evolve.Even though it revolutionizes our ideas on time, Page and Wootters' (PaW) mechanism is quite simple [9-11]: they provide a static entangled state |Ψ whose subsystems evolve according to the Schrödinger equation for an observer that uses one of the subsystems as a clock system C to gauge the time evolution of the rest R. While the division into subsystems is largely arbitrary, the PaW model assumes the possibility of neglecting interaction among them writing the Hamiltonian of the global system as H = H c ⊗ 1 1 r + 1 1 c ⊗ H r , where H c , H r are the local terms associated with C and R, respectively and Uc(t) = e −iHct/ are the ...

Quantum time

“…The PaW mechanism was criticized in [6,12] and a proposal that overcomes these criticisms [21,22] used Rovelli's evolving constants of motion [3,23] parametrized by an arbitrary parameter that is then averaged over to yield the correct propagators. Although the end result matches the quantum predictions [24], the averaging used there amounts to a statistical averaging which is typically reserved to unknown physical degrees of freedom rather than to parameters with no physical significance. (A different way of averaging over time was also presented in [25] to account for some fundamental decoherence mechanism.…”

“…Clearly the particular form of H T employed above is an idealization where the clock is isomorphic to a particle on a line [10]. Other choices [24,29] are a straightforward modification of the above theory. This approach is consistent with a relational point of view, where the only physically relevant quantities are events defined as coincidences in spacetime [34] …”

“…It consists in enlarging the Hilbert space H S of the system under consideration to H ≔ H T ⊗ H S with H T the space of an ancillary system T (we shall call it the "clock" system) that we assume to be isomorphic to the Hilbert space of a particle on a line (other choices are possible [24,29]). The latter is equipped with canonical coordinatesT andΩ with ½T;Ω ¼ i, which represent position and momentum and (under the following restrictions) can be interpreted as the time and energy indicator of the evolving system.…”

Yet another time about time … Part I: An essay on the phenomenology of physical time

“…In 2013 Moreva and collaborators delivered first tests of Page and Wootters' "emergent time entanglement" theory (Moreva et al, 2013). The experiment was about the creation of a toy universe consisting of only a pair of entangled photons with an observer able to measure their state in one of two modes: endo and exo.…”

The Cosmological Constant Problem and Quantum Spacetime Reference Frame

“…In this sense, the probability of |P i is affected by the probability distribution of |R j . The state |P i of the to-be-studied system has no individual absolute meaning, it makes sense only relative to the state |R j of the measuring device as a reference [11,12], namely, the state is relational [13,14]. The entangled state is purely a quantum state, having no classical correspondence.…”