PRL 106, 110404 (2011)

PHYSICAL REVIEW LETTERS week ending 18 MARCH 2011

*Entanglement between the Future and the Past in the Quantum Vacuum*

S. Jay Olson* and Timothy C. Ralph

Centre for Quantum Computing Technology, Department of Physics, University of Queensland, St Lucia, Queensland 4072, Australia

(Received 5 March 2010; published 17 March 2011)

We note that massless fields within the future and past light cone may be quantized as independent systems. The vacuum is shown to be a nonseparable state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. This leads to a notion of timelike entanglement. We describe an inertial detector which exhibits a thermal response to the vacuum when switched on at t 1⁄4 0, due to this property. The feasibility of detecting this effect is discussed, with natural experimental parameters appearing at the scale of 100 GHz. ...

Conclusions.—In contrast to earlier work which attempted

to define ‘‘entanglement in time’’ as a new and

different quantity [13], the definition of entanglement we

have used is the standard one—the nonseparability of a

pure state (in this case the vacuum). The implications of

timelike entanglment have not been explored in depth. The

thermal effect we describe here is only the first such

consequence. We speculate, however, that most consequences

of ordinary entanglement have a directly analogous

interpretation in timelike entanglement. For example,

the no-signaling theorem [14] may be interpreted to forbid

the use of timelike entanglement as a means of communication

with the past. Nevertheless, projecting onto states in

F should collapse the state in P.

It was noted above that the entangled modes we have

described in F-P are the same mode solutions as the

entangled Rindler modes in R-L. In other words,

F-P entanglement is not merely analogous to R-L

entanglement—it is precisely the same entanglement,

viewed in a different region of space-time. Recently, theoretical

work has focused on manipulating or extracting

vacuum entanglement by interacting with the R-L entangled

modes [15–20]—this illustrates ‘‘exotic effects’’

which are in principle allowed by relativistic quantum field

theory. We speculate that due to the dimensional improvement

and the lack of need for acceleration, some of these

effects may in fact become experimentally accessible,

when converted to equivalent interactions in F-P.

S. Jay Olson* and Timothy C. Ralph

Centre for Quantum Computing Technology, Department of Physics, University of Queensland, St Lucia, Queensland 4072, Australia

(Received 5 March 2010; published 17 March 2011)

We note that massless fields within the future and past light cone may be quantized as independent systems. The vacuum is shown to be a nonseparable state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. This leads to a notion of timelike entanglement. We describe an inertial detector which exhibits a thermal response to the vacuum when switched on at t 1⁄4 0, due to this property. The feasibility of detecting this effect is discussed, with natural experimental parameters appearing at the scale of 100 GHz. ...

Conclusions.—In contrast to earlier work which attempted

to define ‘‘entanglement in time’’ as a new and

different quantity [13], the definition of entanglement we

have used is the standard one—the nonseparability of a

pure state (in this case the vacuum). The implications of

timelike entanglment have not been explored in depth. The

thermal effect we describe here is only the first such

consequence. We speculate, however, that most consequences

of ordinary entanglement have a directly analogous

interpretation in timelike entanglement. For example,

the no-signaling theorem [14] may be interpreted to forbid

the use of timelike entanglement as a means of communication

with the past. Nevertheless, projecting onto states in

F should collapse the state in P.

It was noted above that the entangled modes we have

described in F-P are the same mode solutions as the

entangled Rindler modes in R-L. In other words,

F-P entanglement is not merely analogous to R-L

entanglement—it is precisely the same entanglement,

viewed in a different region of space-time. Recently, theoretical

work has focused on manipulating or extracting

vacuum entanglement by interacting with the R-L entangled

modes [15–20]—this illustrates ‘‘exotic effects’’

which are in principle allowed by relativistic quantum field

theory. We speculate that due to the dimensional improvement

and the lack of need for acceleration, some of these

effects may in fact become experimentally accessible,

when converted to equivalent interactions in F-P.

With non-orthogonal distinguishable Glauber states in the ground state of the brain as in Vitiello and Freeman - we may explain both memory and Bem's "feeling the future" as in my SLAC talk.