ADDENDUM--
It's been said that writing is learning. Hemingway re-wrote one of his endings 47 times and according to this idea, he was simply learning what he wanted to say. For me writing this essay has been learning about the Born infomorphism and the associated proper time for the individual particle. Then after writing the essay, writing comments has been learning about N particles. Specifically I have been learning about this question:
If there's a Born infomorphism for N particles, what physically specifies the worldline of the associated proper time?
In the Schrödinger equation for N particles, there is just one time for the system of N particles and not multiple proper times, one for each particle. Then-- is this one time in the Schrödinger equation the proper time for the system of N particles-- is it the proper time for the system of N particles, which holds the Born infomorphism for the system? For support I look to Richard Feynman:
In Space-Time Approach to Non-Relativistic Quantum Mechanics, Richard Feynman wrote, "The formulation is mathematically equivalent to the more usual formulations. There are, therefore, no fundamentally new results...The total contribution from all paths reaching x, t from the past is the wave function Ψ(x,t). This is shown to satisfy Schroedinger's equation."
Rather than finding something like "1+2 = 3 is the same as 2+1=3," Feynman seems to have discovered, here, an "information channel" from the entangled system of N particles to the their quantum fields as represented by a Feynman diagram of the N particles. But Feynman didn't use mathematics to describe the information channel he'd discovered-- instead he used natural language, as above.
In this essay, I used some mathematics to describe an information channel. To show that an information channel exists, I first have to show that an infomorphism exists. Which means showing there are two functions or arrows pointing in opposite directions, with heads connected to tails by each pointing to a respective situation, each situation supporting infons or elements of information from which the respective function or arrow originates-- altogether meaning that the information supported in the one situation is connected by these arrows to the information supported in the other situation. The arrows take you back and forth in a closed circuit to the same information, with two equivalent translations. (Please see the diagram attached to this comment.)
So from the proper time of the system of N entangled particles specified by the Schrödinger equation, there is an arrow to the SET (I must emphasize) of possible coordinate time frames in spacetime, where for each coordinate time frame, the usual defining equation of proper time holds.
To get the above function describing an infomorphism, an arrow must go from the proper time of the entangled system to the SET of possible coordinate time frames.
Because in the other direction, there is the arrow from spacetime to the wave function of the entangled system.
Because (recalling what I learned in the essay) the entangled wave function includes not only possibilities in space but also possibilities in spin (etc.).
Space is just a "part" of these possibilities.
In "part of" relations, there is a function mapping each part to the system of which it is a part.
Which determines the direction of the arrow between the two kinds situations in the infomorphism.
To get a function going in the opposite direction, as required to identify an informorphism, there must also be a function from the proper time of the entangled system of N particles to the SET of possible coordinate time frames in spacetime.
Then to obtain Bohr's correspondence principle, which ultimately enabled Newton to have calculated using centers of mass (which don't exist in relativity), the worldline associated with proper time of the entangled system must be attached to the Fokker-Pryce center of inertia. About which, Pryce wrote, "Of these only one is independent of the frame in which it is defined. It suffers from the disadvantage that its components do not commute (in classical mechanics, do not have zero Poisson brackets), and are therefore unsuitable as generalized co-ordinates in mechanics."
Which "unsuitability" seems compatible with the idea of space emerging or depending upon entangled possibilities-- and not the other way around.Attachment #1: 1_infomorphism.png