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I think the view that we live in "An Acataleptic Universe" (an ancient Skeptical view that no more than probable knowledge is available to human beings) is a mistake. In the light of the quantum mechanical understanding that there is no certainty, only probability, this is an understandable mistake, but an error nevertheless. What is needed is comprehension of quantum mechanics. Einstein did not actually say it was wrong - he agreed that it's correct as far as it goes. But he thought it was very, very incomplete ... and didn't go far enough. You and I may philosophically (or acataleptically) differ, but I'm sure we agree that modern science's understanding of quantum mechanics cannot be called complete. However, that doesn't mean it will never be complete.
"Hidden variables" is an interpretation of quantum mechanics which is based on belief that the theory is incomplete (Albert Einstein is the most famous proponent of hidden variables) and it says there is an underlying reality with additional information of the quantum world. I suggest this underlying reality is binary digits generated in 5th-dimensional hyperspace.
I think this information underlying reality can borrow a few ideas from string theory's ideas of everything being ultimately composed of tiny, one-dimensional strings that vibrate as clockwise, standing, and counterclockwise currents in a four-dimensional looped superstring. We can visualize tiny, one dimensional binary digits of 1 and 0 (base 2 mathematics) forming currents in a 2-dimensional program called a Mobius loop - or in 2 Mobius loops, clockwise currents in one loop combining with counterclockwise currents in the other to form a standing current. Combination of the 2 loops' currents requires connection of the two into a four-dimensional Klein bottle* by the infinitely long irrational and transcendental numbers. Such an infinite connection translates - via bosons being ultimately composed of 1's and 0's depicting pi, e, √2 etc.; and fermions being given mass by Einstein's 1919 proposal of gravitational and electromagnetic bosons interacting in what quantum mechanics calls "wave packets" - into an infinite number of Figure-8 Klein bottles composing the infinite universe (according to the known definition of "infinite"). (Each Klein bottle, whose gaps are deleted by the flexibility of binary digits to form a continuous space-time where surrounding subuniverses fit together perfectly, is a "subuniverse" - and we live in a finite, 13.7 billion year old, subuniverse.)
* This Klein bottle could possibly be a figure-8 Klein bottle because its similarities to a doughnut's shape suggests an idea of mathematics' "Poincare conjecture". The conjecture has implications for the universe's shape and says you cannot transform a doughnut shape into a sphere without ripping it. One interpretation follows: This can be viewed as subuniverses shaped like Figure-8 Klein Bottles gaining rips called wormholes when extended into the spherical spacetime that goes on forever (forming one infinite superuniverse which is often called the multiverse when subuniverses - which share the same set of physics' laws - are incorrectly called parallel universes which are wrongly claimed to each possess different laws). Picture spacetime existing on the surface of this doughnut which has rips in it. These rips provide shortcuts between points in space and time - and belong in a 5th-dimensional hyperspace. The boundary where subuniverses meet could be called a Cosmic String (they'd be analogous to cracks that form when water freezes into ice i.e. cosmic strings would form as subuniverses cool from their respective Big Bangs).
"Empty" space (according to Einstein, gravitation is the warping of this) seems to be made up of what is sometimes referred to as virtual particles by physicists since the concept of virtual particles is closely related to the idea of quantum fluctuations (a quantum fluctuation is the temporary change in the amount of energy at a point in space). The production of space by BITS (BInary digiTS) necessarily means there is a change in the amount of energy at a certain point, and the word "temporary" refers to what we know as motion or time (in a bit-universe, motion would actually be a succession of "frames"). Vacuum energy is the zero-point energy (lowest possible energy that a system may have) of all the fields (e.g. gravitational / electromagnetic / nuclear) in space, and is an underlying background energy that exists in space even when the space is devoid of matter. Binary digits might be substituted for the terms zero-point energy (since BITS are the ground state or lowest possible energy level) and vacuum energy (because BITS are the underlying background energy of empty space).
I call hidden variables (or virtual particles) binary digits generated in a 5th-dimensional hyperspace which makes them - as explained in the next sentence - a non-local variety, in agreement with the limits imposed by Bell's theorem. (Bell's Theorem is a mathematical proof discovered by John Bell in 1964 that says any hidden variables theory whose predictions agree with quantum mechanics must be non-local i.e. it must allow an influence to pass between two systems or particles instantaneously, so that a cause at one place can produce an immediate effect at some distant location [not only in space, but also in time].) Comparing space-time to an infinite computer screen and the 5th dimension to its relatively small - in this case, so tiny as to be nonexistent in spacetime (at least to observation) - Central Processing Unit, the calculations in the "small" CPU would create and influence everything in infinite space and infinite time. This permits a distant event to instantly affect another (exemplified by the quantum entanglement of particles separated by light years) or permit effects to influence causes (exemplified by the retrocausality or backward causality promoted by Yakir Aharonov and others (see "Five Decades of Physics" by John G. Cramer, Professor of Physics, University of Washington - http://www.physics.ohio-state.edu/~lisa/CramerSymposium/talks/Cramer.pdf). This means quantum processes, in which effects and causes/distant events are not separated, wouldn't be confined to tiny subatomic scales but would also occur on the largest cosmic scales.
My shortened entry in FQXi's current contest (the complete version is at vixra.org and researchgate.net) does refer to the Big Bang, actually to Big Bangs, but the article is not suggesting these came from nothing. It refers to a nonlinear concept of time where inhabitants of this universe learn about the cosmos then apply that knowledge to produce the Big Bang which did not form the universe but only our infinitesimal local part of it (our subuniverse). Applying the knowledge gained over thousands of years to our local Big Bang requires time travel to 13.7 billion years ago. The method of doing this (via a 5th-dimensional hyperspace) was written in detail in my original entry - but was unfortunately one of the things deleted to meet FQXi's length restrictions.
The inverse-square law states that the force between two particles becomes infinite if the distance of separation between them goes to zero. Remembering that gravitation partly depends on the distance between the centres of objects, the distance of separation between objects only goes to zero when those centres occupy the same space-time coordinates (not merely when the objects' sides are touching i.e. infinity equals the total elimination of distance - the infinite cosmos could possess this absence of distance in space and time, via the electronic mechanism of binary digits).
Certainly, zero-separation makes no sense at all if the universe is confined to the laws of physics we're familiar with. It seems to only be possible if, as FQXi's member Professor Max Tegmark states, we live in a mathematical universe. That is, if the sentence "Information has nothing to do with reality" is an incomplete description of reality.
This known definition (of an infinite universe going on and on forever) is something observation and experiment might confirm. The definition of infinity as "elimination of distance" would depend on the 1's and 0's of the binary digits. Without this "companion" definition, time travel (whether into the future or past) would be impossible if it's an instant effect. With it, intergalactic space travel can become possible. And the companion can explain (by the elimination of distance) quantum entanglement in space, as well as time's retrocausality in which the future affects the past.
Pardon me for getting carried away and writing too much, Phil. But I'm quite a perfectionist - if I write anything at all, I end up writing a lot because I have this need to explain every detail thoroughly. Right this minute, I'm worrying that I might have forgotten something :(