Professor Singh,
Thank you for sending me to this paper! I will read it many times. It clarifies for me that while I have been playing with "toy models" (at best, like the toy model of an airplane in a wind tunnel), you are working on the real thing (a test pilot flying the full size plane).
In addition to my essay in this contest, much of the following is in this text (as well as in a previous essay for the FQXI mathematics contest linked within this text):
https://leebloomquist.wordpress.com/
("An overall approach to the observer")
-- A model of time that is not classical: In my world of toys I use nonstandard analysis and the co-algebra of streams to glue together a model of time that goes in one direction only.
-- The incompleteness of quantum mechanics: I start with Schrodinger's study of the Greeks to arrive at an equation where the particle is not an object, but a process: "particle = (physicalExtension, particle)". Incompleteness means that the Schrodinger equation does not model the existence of the particle, only the possibilities for the elements of its stream. "Particle = (physicalExtension, particle)" models the existence of the particle.
-- The collapse of the wave function: This is in my essay for the current contest. I follow Samson Abramsky's "Big Toy Models...". Using Wigner's theorem he obtains a "three valued Chu space," which I then use to show the collapse of the wave function.
-- An underlying Universe: Although I don't show it anywhere, a stream representing Bohm's holomovement can be "zippered together" with the stream "particle = (physicalExtension, particle)".
-- Derivation of the Born rule: In the world of learning algorithms, when the wave function is installed in the nonStandardFuture of the monad of properTime, and the associated probabilities in the nonStandardPast, there exists the signature of a learning algorithm. What is it learning? The laws of physics. Who is teaching it? The underlying Universe.
-- The connection to relativity: Using an informorphism to make this explicit, because ordinary space-time emerges from an underlying Universe, properTime of the particle (as above) maps to a set of possible coordinate times.
Now the question becomes like that in software engineering: There are formal languages for specifying and analyzing software which are quite different from the languages used to write the actual software. For example, to specify and analyze software, one can use Petri nets, streams, and/or Chu spaces. But to write the software, one would use, say, C++.
But is any software written like this?
Very little. It's rare to find a software engineering organization where coders in C++ follow the models or listen to the analyses given to them by other engineers writing specifications and analyses in, say, Petri nets. Probably the only application where you do see this kind of cooperation between specification and coding is where human life is at stake.
By analogy we now have questions like these:
Professor Singh, could any of these toy models possibly be useful to you?
Are there any difficulties for your languages that might be easier in these specification and analysis languages?
Very Best Regards,
Lee