In doing technical calculations, we perform transformations and superpositions that lead to large sets of quantum states which we now regard as templates, or candidate models for processes that can always be superimposed at a later stage to describe the phenomena we observe.
Lattice of ratios wave scaling harmonic time constraints as such the circle, largest obtained angle, is beautiful invariance.
A template state can be used to serve as a model of some actually observed phenomenon. It can be any quantum superposition of ontological states. The inner product expressions then represent the probabilities that ontological state is actually realized.
According to the Copenhagen rule #ii, the probability that the template state is found to be equal to the state , is given. However, already at the beginning, we stated that the inner product should not be interpreted this way. Even if their inner product vanishes, template states and may both have a non vanishing coefficient with the same ontological state. This does not mean that we depart from Copenhagen rule #ii, but that the true wave function cannot be just a generic template state; it is always an ontological state.
Use the Born interpretation of the inner product if one of the two templates is regarded as a candidate ontological state. This is legitimate, as we know that the ontological states are complicated superpositions of our templates. There are unobserved degrees of freedom, and how these are entangled with this state is then immaterial. Thus, one of our template states then can be assumed to represent a probability distribution of the ontological states of the universe, the other is a model of an ontological state.
Thus all reduces itself at first to subsistence, and in that respect man is attached to everything in his environment. He depends on everything and he becomes what everything he depends upon forces him to be. Climate, soil, air, water, productions of the earth and sea, form his temperament, his character, determine his tastes, his passions, his work, his actions of all kinds. [The natural explanation is not good for the atoms of culture but for the total social fact:] If that is not exactly true of individuals, it is undeniably true of peoples…. Thus before one broaches the history of our species, one must begin by examining its habitation and all its varieties.
We see that the inner product rule can be used in two ways; one is to describe the probability distribution of the initial states of a system under consideration, and one is to describe the probability that a given classical state is reached at the end of a quantum process. If the Born rule is used to describe the initial probabilities, the same rule can be used to calculate the probabilities for the final states.
The time symbol is a parameter in classical mechanics, statistical mechanics, quantum mechanics, in hydrodynamics, electromagnetism. As these theories describe the evolution of physical phenomena over time, time is in the background, so to speak. It is not an object of investigation in itself. By contrast, in cosmology, the time symbol can be a variable: it can vary with the scale factor or with temperature. The general situation in physics is that the physical theories do not have anything to say about time proper. They just use it as an element of the general framework in which the descriptions of phenomena hold. The symbol t has a life of its own in the equations, so to speak. It is independent of the physical laws in the sense that it does not enter into the equations otherwise than in “going further”, or “stepping further”, that is, in going from one instant to the next. Newton devoted a few pages of the Principia to a discourse about space and time. In his view, a physical theory like his own had to say something about space and time: he conceived space and time as proper objects of physical theorizing and his discourse about them as a necessary component of his theory. Within modern theories, fragmented as they are, it is striking that the theories which represent time by a parameter are deliberately at odds with the theories that say something about time. It is as if these theories did not take seriously what relativity (special and general) has to say about the nature of time. It is notoriously difficult to translate these mathematical relationships into conceptual relationships. There is a sort of blind spot here: the concept of time in classical mechanics, say, is clearly different from the concept of time in relativity, and the difference cannot be reduced to any approximation relation.