I've had a look at your essay, Mikalai - and there are quite a few points I'd like to address. I'll try not to make this too long :)
1) I agree that "It" and "Bit" are on the same level. As my essay at http://fqxi.org/community/forum/topic/1606 puts it, "My entry refers to time being nonlinear (I believe this agrees with Einstein's description of warped time) with "It" and "Bit" both being absolutely vital."
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2) I don't think "quantum systems are ... made of fundamental particle events" for the reason that particles seem to be made of gravitation, which seems to be made of mathematics (this makes gravity fundamental and maths even more fundamental).
Suppose Albert Einstein was correct when he said gravitation plays a role in the constitution of elementary particles (in "Do Gravitational Fields Play An Essential Part In The Structure of the Elementary Particles?" - a 1919 submission to the Prussian Academy of Sciences). And suppose he was also correct when he said gravitation is the warping of space-time. Then it is logical that 1) gravitation would play a role in constitution of elementary particles and also in the constitution of the nuclear forces, and 2) the warping of space-time that produces gravity means space-time itself plays a role in the constitution of elementary particles and the nuclear forces. Gravity, being united with electromagnetism1 and the nuclear forces, is therefore the ultimate physical source of all repelling and attracting. Mass increase at increasing accelerations is inevitable because the object is encountering more spacetime and gravity (the producers of mass; which also confer mass's equivalent [energy] on cosmic rays that travel far enough through space, turning them into ultra-high-energy cosmic rays). But mass increase cannot become infinitely large since space-time, gravity and mass don't exist at Lightspeed 2. The object is converted into energy which means mass and energy must be equivalent and Energy must equal Mass related to the Speed of Light (E=mc^2, in the words of Albert Einstein).
1 BITS or BInary digiTS called 1's and 0's would make the bosons of gravity and electromagnetism which would interact in Wave Packets to produce matter. This contradicts the Standard Model and Higgs field - but to paraphrase what John Wheeler said in 1989's "Proceedings of the Third International Symposium on the Foundations of Quantum Mechanics", we should not accept any pre-definition of the word BIT but we should be truly creative (I think identifying Wheeler's BITS with the binary digits of electronics is not only an obvious step, but creative because most people wouldn't take that step). All matter in the universe then has the potential to behave like a Bose-Einstein condensate (a state of matter composed of bosons cooled close to absolute zero in which atoms fall or condense into the lowest accessible quantum state, at which point quantum effects become apparent on a macroscopic scale). The bosons composing gravity and EM can all have the same properties e.g. position, velocity, magnetism and spin (force-carrying particles, or bosons, defy Pauli's exclusion principle). The matter we know obeys Pauli's exclusion principle. So how is it different from a Bose-Einstein condensate. To exhibit Bose-Einstein condensation, the fermions (particles of matter) must "pair up" (not in the normal manner of sharing electrons) to form compound particles that are bosons. This "pairing-up" may be achieved by using e-infinity to delete distance 3. This leads to a photon (such as from the Sun) experiencing the whole universe - including BECs, gravitons, and other photons - in its existence.
2 The basic standard of time in the universe is the measurement of the motions of photons i.e. of the speed of light. This is comparable to the 1960's adoption on Earth of the measurement of time as the vibration rate of cesium atoms. At lightspeed, time = 0 (it is stopped). Below 300,000 km/sec, acceleration or gravitation causes time dilation (slowing of time as the speed of light is approached). If time's 0, space is also 0 because space and time coexist as space-time whose warping (gravity) is necessarily 0 too. Spacetime/gravity form matter/mass, so the latter pair can't exist at lightspeed and photons are massless (even when not at rest). Mass increase at increasing accelerations is inevitable because the object is encountering more spacetime and gravity (the producers of mass; which also confer mass's equivalent [energy] on cosmic rays that travel far enough through space, turning them into ultra-high-energy cosmic rays). But mass increase cannot become infinitely large since mass doesn't exist at lightspeed. The object is converted into energy which means mass and energy must be equivalent and Energy must equal Mass related to the Speed of Light (E=mc^2, in the words of Albert Einstein).
3 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 (associated with particles) partly depends on the distance between their centres, the distance of separation only goes to zero when those centres occupy the same space-time coordinates (not merely when the particles' or objects' sides are touching i.e. infinity equals the total elimination of distance). The infinite cosmos4 could possess this absence of distance in space and time, via the electronic mechanism of binary digits. To distinguish this definition from "the universe going on and on forever", we can call it "electronic infinity or e ".
The above paragraphs show that gravity is fundamental. How is mathematics "more fundamental"? Let's 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 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 as a four-dimensional Klein bottle. This connection can be made with 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 bosons interacting in matter particles' "wave packets" - into an infinite number of Figure-8 Klein bottles 5. Slight imperfections in the way the Mobius loops fit together determine the precise nature of the binary-digit currents (the producers of gravitational waves, electromagnetic waves, the nuclear strong force and the nuclear weak force) and thus of exact mass, charge, quantum spin, and adherence to Pauli's exclusion principle. Referring to a Bose-Einstein condensate, the slightest change in the binary-digit flow (Mobius loop orientation) would alter the way gravitation and electromagnetism interact, and the BEC could become a gas.
4 As Bob Berman's article "Infinite Universe" ("Astronomy" - Nov. 2012) wrote, "The evidence keeps flooding in. It now truly appears that the universe is infinite" and "Many separate areas of investigation - like baryon acoustic oscillations (sound waves propagating through the denser early universe), the way type 1a supernovae
compare with redshift, the Hubble constant, studies of cosmic large-scale
structure, and the flat topology of space - all point the same way."
Support for the infinite universe - (after examining recent measurements by the Wilkinson Microwave Anisotropy Probe, NASA declared "We now know that the universe is flat with only a 0.4% margin of error." - http://map.gsfc.nasa.gov/universe/uni_shape.html;
and according to "The Early Universe and the Cosmic Microwave Background:
Theory and Observations" by Norma G. Sànchez, Yuri N. Parijskij (published by
Springer, 31/12/2003), the shape of the Universe found to best fit observational data is the infinite flat model).
5 Each one is a "subuniverse" composing the physically infinite and eternal space-time of the universe (our own subuniverse is 13.7 billion years old). We don't have to worry about accelerating cosmic expansion - the result of more space, forces, energy and matter being continually produced by binary digits - leaving our galaxy alone in space. As "dark energy" causes known galaxies to depart from view, more energy and matter can replace them (since the universe obeys fractal geometry, gravity is the source of repelling and attracting not only on a quantum scale but on a cosmic scale, too i.e. it accounts for dark energy - it accounts for dark matter and Kepler's laws of planetary motion, too [but that's a long explanation best left in http://vixra.org/abs/1303.0218]). The Law of Conservation says neither matter nor energy can be created or destroyed (though the quantity of each can change), so a better phrase might be "binary digits recycle spacetime" (when matter changes into energy or energy becomes matter, we commonly say matter or energy has been created). As well, other expanding subuniverses can collide with ours and their galaxies enter our space to keep our galaxy company. Combination of the 2 loops' currents requires connection of the two as a four-dimensional Klein bottle whose construction from binary digits would make it malleable and flexible, deleting any gap and molding its border to perfectly fit surrounding subuniverses (form a continuous universe). This Klein bottle could possibly be a figure-8 Klein bottle because its similarities to a doughnut's shape describes an idea suggested by 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).
* Iin a universe structured according to the rules of fractal geometry, 5th dimensional hyperspace would occupy every fermion and boson, alongside space-time which is ultimately composed of 1's and 0's like particles. When forced to summarize the general theory of relativity in one sentence, Einstein said: time and space and gravitation have no separate existence from matter.
3) Bell's theorem, hidden variables, and How Binary Digits Produce Wave-Particle Duality
"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 5-Dimensional hyperspace. These allow time travel by making it possible to warp space 6 (wormholes being one example of doing this).
6 Maybe hidden variables called binary digits could permit time travel into the future by warping positive space-time. And maybe they'd allow time travel into the past by warping a 5D hyperspace that is translated 180 degrees to space-time, and could be labelled as negative or inverted. (The space-time we live in is described by ordinary [or "real"] numbers which, when multiplied by themselves, result in positive numbers e.g. 2x2=4, and -2x-2 also equals 4. Inverted "positive" space-time becomes negative hyperspace which is described by so-called imaginary numbers that give
negative results when multiplied by themselves e.g. i multiplied by itself
gives -1. [Supporting info from Stephen Hawking's "A Brief History of Time"
- Bantam Press 1988, p.134]) The past can never be changed from what
occurred, and the future can never be altered from what it will be. Both are
programmed by the 1's and 0's.
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 eternal time. In other words, bosons would be ultimately composed of 1's and 0's depicting pi, e, √2 etc.; and fermions would gain mass by bosons interacting in "wave packets" (everything is unified by the fundamental gravity and even more fundamental maths). 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.ohiostate.
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.
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Well, as you can see, I'm not good at keeping my writing short ... which gave me big problems meeting FQXi's length limits.