May I thank you for writing such a super concise summary as you just wrote, Dr. Dick!
Quote: "Since the only original mathematical relation I present is the fact that a sum over Dirac's delta functions of differences can be used together with invented data to constrain any given data to the values desired: i.e., that the rule F=0 is capable of expressing any rules on the knowable data desired, that must be the essence of the theorem.
The rest of the paper is essentially about possible application of the theorem. "
If you trace the position of a car in a deceleration/acceleration traffic jam; take a particular position and pair that with a second arbitrarily chosen position of that car in a superposed traffic jam at right angles;
take this pair and match it with yet another arbitrarily chosen carposition in yet another trafficjam superposed at right angles to the "sum" position of the first pairing; take this new sum (a new pair that contains the previous pair on one side) (note the "containment" aspect)(note "sum of histories" aspect) (like Feynman path integral?) and chose a new carposition to pair it to from a new superposed trafficjam; and soon.....
gives a model of your sum over delta functions?
To constrain the data given, by a rule: what does this mean?: It means placing limits on the possible sequences; it means requiring that the traffic jams be superposed in a particular order.
(And the rule might specify actual car positions in the traffic jams?)
A "rule" looks like a concept analogous to what we call "time". And "space". As "limiting the ordering to a particular sequence gives you "distance structure" and "interaction structure" (time).
Thus you conclude that "past and future" are "a way of looking at information". But I would add: If YOU are the "local RULE"; past and future are your local perspective? What about mutual Pastfuture perspective?
"Invented data to constrain any given data to the values desired":
"Values desired" being? To the desired sequence? The desired ordering of the summation? The sequence in the summation? I guess you mean constrain the; in my analogy; the positions of the cars to particular positions within their respective traffic jams.
Yeah; it seems like if you included enough INVENTED traffic jams at intermediate superpositions; it might conceivably be possible to get ANY combination of car positions IN ANY ORDER?
That is rather amazing; no wonder you were astonished when Shrodinger's equation fell out!
I'm not sure if it works: very easy to test it.
Just draw a straight line of dots, each represents a carposition.
For simplicity (though the spacing could be arbitrary I suspect; so could use sets of numbers, or matrices to do this) make the dots "decelerate" (bunch increasingly together) then "accelerate" (have increasing spacing). This is like a traffic jam on the highway.
Draw another such line of dots at right angles to the first; crossing the first at some point on the first line. Plot the position that represents a dot simultaneously moving through both traffic jams. "Simultaneity" might be here thus called "matching two patterns and retaining that match while changes occur in the surroundings".
You will get a curved line. Now imagine rotating that line till it appears straight (this alters the density or bunching of the dots) (suspect explanation of "quantum spin" to be found here)(Since you have to spin and twist the curved line to straighten it; Roger Penrose's spinors and twistors in complex space (complex= 2D so a pattern/pattern match'space'?) might be found here.
My guess is that the "adding of arrows" and "turn and shrink" of arrows that Richard Feynman describes in his book on QED can be found here.
It seems that Maxwell's equations might be found here.
Now the test:
Can one, by adding an arbitrary number of intervening traffic jams; generate a "sum of histories" that is; a sequence of traffic jams (mnay of which might be invented) to deliver a PARTICULAR ORDER OF SUMMATION OF GIVEN TRAFFIC JAMS AND PRECISE CAR POSITIONS WITHIN THOSE TRAFFIC JAMS?
Have to try that; looks possible.
If so; congratulations Dr. Dick.
Regards,
Alan
