This month has been an incredible drain on my time. I never have time to reply to the people who have written to me. I have a few minutes now to post this reply to the second person who sent me a response, and I'll work my way down my page as time permits. Hopefully, I'll be able to reply to every unanswered message before the contest ends.
Hi Joe, I can certainly understand why many people view the idea of the universe being a computer simulation as far-out and totally unrealistic. The most powerful supercomputer in the world that's devoted to astronomy (ATERUI in Japan) can model a supernova. But that's a far cry from actually building a supernova - much less the entire universe! But let's cast aside our doubts for a moment, and assume that such a feat will oneday be possible.
Suppose humans of the distant future become capable of building a simulation of the universe. That would explain why our observations and experiments work so well. And it would explain why, as Einstein said, the most incomprehensible thing about the universe is that it is comprehensible. Building such a simulation would, of course, depend on our observations and experimental results. My essay suggests the following hypothetical foundation for building the simulation -
The ultimate origin of the laws of science/nature could be the on-off states of the Virtual Particles filling space-time. These "particles" are actually energy pulses, and their motions could be seemingly random if they obey Chaos theory's principle of "hidden order existing in apparent disorder". The on-off pulses can be viewed as producing the binary digits of 1 and 0, i.e. base-2 maths, arranged in the shape of 2D (two-dimensional) Mobius Strips, explaining space-time curvature. These strips then follow the rules of maths and combine into four-dimensional Klein bottles long before reaching the scale of subatomic particles which have 1 time and 3 space dimensions. One theory scientists have for the universe's shape says it is a doughnut. From that, I conclude the type of Klein bottle that Mobius Strips combine into is the four-dimensional figure-8 Klein bottle (because this somewhat resembles the doughnut).
The universe - including all the galaxies and planets, even the Milky Way and Earth - could be made infinite and eternal by making the universe a computer simulation that includes so-called Imaginary Time. Boundaries don't exist in imaginary time [Hawking S (1988) "A Brief History of Time", p.139. Bantam Press]. There'd be no start or end to space, no beginning or finish to time, and no boundary between the simulation and this "real" universe. Imaginary time is presently purely a mathematical convenience. But maybe it could become real physics in the same way that Albert Einstein postulated that Max Planck's initially purely-mathematical quanta were real physical particles (what we now call photons). From there, Einstein developed his explanation for the photoelectric effect. Also, a simulation can be refreshed/reloaded like a computer screen. So despite the entropy of the 2nd law of thermodynamics, things can only get better.
On page 168 of his book "A Brief History of Time", Stephen Hawking says: "If a complete unified theory was discovered, it would only be a matter of time before it was digested and simplified - and taught in schools, at least in outline. We should then all be able to have some understanding of the laws that govern the universe and are responsible for our existence."
A complete unified theory that includes everything in the universe, i.e. in space and in its eternal partner of time, means all information is available to YOU and ME through pure reason, intuition or revelation from advanced natural intelligence.
The mathematical laws in the simulation (the universe's information) establish Hawking's unified theory and Einstein's "double-sided" length contraction. Regarding the question of length contraction in Special Relativity, Einstein wrote in 1911:
"It doesn't 'really' exist, in so far as it doesn't exist for a co-moving observer;^ though it 'really' exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer." (Einstein, Albert [1911]. "Zum Ehrenfestschen Paradoxon. Eine Bemerkung zu V. Variﾄ餌ks Aufsatz". Physikalische Zeitschrift 12: 509-510)
^ The co-moving observer for whom contraction doesn't really exist would be a scientist moving along with the object at a significant fraction of the speed of light. Contraction "could be demonstrated in principle by physical means by a non-comoving observer" (by experiments performed by scientists).
This example of length contraction applies to all observations/experiments and, since we can't physically co-move at the speed of light (not at present, anyway), it means we're content with one side of empiricism (the experiments performed by non-comoving scientists). Other methods of acquiring knowledge - like reason and intuition involving the unified theory - could complement that empiricism by revealing the "other side" of Einstein's co-movement.
When it's necessary to refresh or reload the simulation, this combining of empirical methods with complementary other methods of acquiring knowledge enables us to do it properly. This refreshing of part of the infinite universe would produce what we call an observable universe, and what we interpret as a Big Bang. Refreshment of part of the universe might also be used to prevent a star turning into a red giant.
Perhaps I'm mistaken, but these paragraphs seem to describe what you call "one unified visible infinite surface".
