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I show that, by the same criteria that led to Galilean and Special Relativity and gauge symmetries, there is no way to identify a unique set of observables that give the structure of space or spacetime. In some sense, space is lost in the state space itself. Moreover, the relationship between the observables and the physical properties they represent becomes relative. But we can verify that they are not relative, and the spacetime structure is unique. I show that this implies that not all structures isomorphic with observers can be observers, contradicting Structural Realism and Physicalism. This indicates a strong connection between spacetime and the sentience of the observers, as anticipated by some early contributors to Special and General Relativity.
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Ovidiu Cristinel Stoica (2024) studied this question.
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