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- W2783282831 abstract "Relativistically, time $t$ is an observable just like position $r$. In quantum theory, $t$ is a parameter, in contrast to the observable $r$. This discrepancy suggests that there exists a more elaborate formalization of time, which encapsulates both perspectives. Such a formalization is proposed in this paper. The evolution is described in terms of sequential time $nin mathbf{mathbb{N}}$, which is updated each time an event occurs. Sequential time $n$ is separated from relational time $t$, which describes distances between events in space-time. There is a space-time associated with each $n$, in which $t$ represents the knowledge at time $n$ about temporal relations. The evolution of the wave function is described in terms of the parameter $sigma$ that interpolates between sequential times $n$. For a free object we obtain a Stueckelberg equation $frac{d}{dsigma}Psi(r_{4},sigma)=frac{ic^{2}hbar}{2langle epsilonrangle}BoxPsi(r_{4},sigma)$, where $r_{4}=(r,ict)$. Here $sigma$ describes the time $m$ passed between the start of the experiment at time $n$ and the observation at time $n+m$. The parametrization is assumed to be natural, meaning that $frac{d}{dsigma}langle trangle=1$, where $langle trangle$ is the expected temporal distance between the events that define $n$ and $n+m$. The squared rest energy $epsilon_{0}^{2}$ is proportional to the eigenvalue $tilde{sigma}$ that describes a 'stationary state' $Psi(r_{4},sigma)=psi(r_{4},tilde{sigma})e^{itilde{sigma}sigma}$. The Dirac equation follows as a `square root' of the stationary state equation from the condition that $tilde{sigma}>0$, which follows from the directed nature of $n$. The formalism thus implies that all observable objects have non-zero rest mass, including elementary fermions. The introduction of $n$ releases $t$, so that it can be treated as an observable with uncertainty $Delta t$." @default.
- W2783282831 created "2018-01-26" @default.
- W2783282831 creator A5065668283 @default.
- W2783282831 date "2018-01-10" @default.
- W2783282831 modified "2023-09-27" @default.
- W2783282831 title "Evolution equations from an epistemic treatment of time" @default.
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