Existence of observers

Daniel John Murray

Stanley Gudder

Until recently observables have been nothing more than self-adjoint operators.However, due to axiomatic formulations of quantum mechanics, observables have now been placed in a more abstract setting.With the advent of this abstract concept comes the natural questions concerning uniqueness and existence.The uniqueness problem considered here seeks to answer the question: if two bounded observables have the same expectations in every state, are the observables equal?We say that an observable z is the sum of two bounded observables x and y if the expectation of z is the sum of the expectations of x and y for every state.The existence problem would pose the question: does the sum of two bounded observables exist?The author has found only partial answers to these questions.It is shown that the uniqueness property holds for simultaneous observables and certain classes of nonsimultaneous or complementary observables.The existence property holds for simultaneous observables, and a counterexample is given to show that this property does not hold in general.The last section of this paper considers systems in which the existence and uniqueness properties are known to hold.

Kureshi, Sufiyan

We develop a mathematical and philosophical framework in which conscious obser- vation is the fundamental act that brings reality into existence. Before observation, nothing exists in an actualized sense: not space, time, laws, or structures. Reality is purely a manifold of potential universes, each containing possible laws and possible observers. When a conscious observer emerges, the act of observation actualizes the unique minimal universe consistent with its existence. This is not a selection among alternatives but an ontological crystallization that transforms possibility into actuality, retroactively defining the universe’s laws, constants, structure, and history. Within this actualized universe, unobserved properties remain probabilistic un- til collapsed by observation. We formalize sensory collapse, observer priority, multi- observer shared reality, emergent time, retroactive history, and the closed feedback loop between observers and their universe. This framework unifies consciousness, existence, physics, and cosmology into a single observer-centric formalism.

Hector Dehesa

Maxine Pitter Lunn

An elementary proof of the results of Wightman concerning the existence and non-existence of position observables for relativistic systems is presented. The method uses an explicitly described unitary transformation to relate the representations of the Euclidean group obtained by restricting the m not=0 representations of the Poincare group to representions having position observables. The position observables are displayed explicitly as differential operators in the cases in which they exist.

Otto E. Rössler