Glimmers of a Pre-geometric Perspective |
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Authors: | Federico Piazza |
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Institution: | 1.Institute of Cosmology and Gravitation,University of Portsmouth,Portsmouth,UK |
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Abstract: | Spacetime measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual
relationships. As a consequence, any operationally meaningful assertion about spacetime is in fact an assertion about the
degrees of freedom of the matter (i.e. non gravitational) fields; those, say for definiteness, of the Standard Model of particle
physics. As for any quantum theory, the dynamics of the matter fields can be described in terms of a unitary evolution of
a state vector in a Hilbert space. By writing the Hilbert space as a generic tensor product of “subsystems” we analyse the
evolution of a state vector on an information theoretical basis and attempt to recover the usual spacetime relations from
the information exchanges between these subsystems. We consider generic interacting second quantized models with a finite
number of fermionic degrees of freedom and characterize on physical grounds the tensor product structure associated with the
class of “localized systems” and therefore with “position”. We find that in the case of free theories no spacetime relation
is operationally definable. On the contrary, by applying the same procedure to the simple interacting model of a one-dimensional
Heisenberg spin chain we recover the tensor product structure usually associated with “position”. Finally, we discuss the
possible role of gravity in this framework. |
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Keywords: | |
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