Quantum limits for measurement of the metric tensor

          @misc{ pirsa_PIRSA:10120053,
            doi = {10.48660/10120053},
            url = {https://pirsa.org/10120053},
            author = {},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Quantum limits for measurement of the metric tensor},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {dec},
            note = {PIRSA:10120053 see, \url{https://pirsa.org}}
          }
          

Abstract

Tony Downes The geometry of space-time can only be determined by making measurements on physical systems. The ultimate accuracy achievable is then determined by quantum mechanics which fundamentally governs these systems. In this talk I will describe uncertainty principles constraining how well we can estimate the components of a metric tensor describing a gravitational field. I shall outline a number of examples which can be easily constructed with a minimum of mathematical complexity. I will also attempt to derive a general bound on the uncertainty in any attempt to determine the metric tensor which is expected to hold in an arbitrary globally hyperbolic space-time. I shall use tools developed within the algebraic approach to quantum field theory on a classical space-time background. I shall not consider limits on estimating space-time metrics that might arise from a quantisation of gravity itself.