Sunday, February 9, 2014

Ghost-rascal conjecture and the Ultimate Reality

Byron Jennings (a physicist at TRIUMF, Canada) wrote an article “Reality and the Interpretations of Quantum Mechanics” which in my view is the most important issue of physics today. I thus wrote a comment on it (at, ).  The following is a deeper elaboration of that comment.

The basic of atheism is of against the concepts of ‘supernatural (being)’ and the ‘design’ of the universe. Of course, the Christian cosmology is total nonsense in terms of the modern physics. But, what is the difference between {un-naturalness, tuning} and {supernatural, design}? This neo-atheism is now falling into a trap of no return in its own making. Yet, thus far, the issue of the ‘ultimate nature of reality’ is still elusive in all disciplines.

In Buddhism, it searches the ‘Ultimate’ with a methodology, the ‘negation’ (emptying out the non-eternal). In Science, it searches the ‘Ultimate’ also with a methodology, the ‘falsifiability’. Now, Buddhism has taken its ‘methodology’ as the ‘Ultimate’ (a total confusion), and physicists have also mistaken the ‘falsifiability’ as the Gospel.  For a given destination, it could have many different pathways. Furthermore, the two pathways of above cannot reach the destination by definition, as the true ‘Ultimate’ (if any) must not
a.       be emptied out,
b.      be falsified.

In a sense, the ‘Ultimate’ is already defined above, but it is operational useless. Thus, I will try to give it an operational definition. The ‘Ultimate’ (if any) must consist of two parts.
A.      It must be ‘eternal’, that is, it is time-independent; not created in-time and cannot be destroyed at the end of time.
B.      It must give rise to ‘this’ universe; an itemized list of realities, such as,
1.       gives rise to nature constants {Alpha, e (electric charge), c (light speed), ħ (Planck constant), etc.},
2.       gives rise to the particle zoo of the Standard Model,
3.       gives rise to quantum principle,
4.       gives rise to unified force equation (including gravity),
5.       gives rise to dark mass and dark energy, the Planck data,
6.       gives rise to life,
7.       gives rise to arithmetic,
8.       gives rise to baryongenesis,
9.       gives rise to cosmological constant (Λ),
10.   gives rise to the Quantum-Spin,
11.   gives rise to … everything in ‘this’ universe.

Then, is the ‘Ultimate’ a reality? How to verify a theory to be the ‘Ultimate’ theory? Both questions can be answered, as the definition of ‘Ultimate’ is now super clear. A failure of any one of the ‘gives rise to …’, it cannot be the Ultimate theory.

In the book ("Linguistics Manifesto", ISBN 978-3-8383-9722-1), its central issue is one statement (or thesis), as follow,
     “Every chaotic system can always be described with an ordered system (from a Formal system to Godel to Life system)”.
That is, any chaotic system is a ‘shadow’ of an ordered system. Note: a biological system is a Life system, but the Life system is much bigger than a bio-system by definition in that book.

This statement is truly time-independent. Yet, its direct consequence is that any chaotic system (such as the quantum system) can arise from a simple ordered formal system. The argument of this statement in the book is very complicated, thus I will only give a simple example here to show the point. A system of two persons (I and a ghost) and one game (flipping an American quarter 10 times as a game).

By playing alone (me only), the probability of the outcome patterns (one head/9 tails; …, 9 heads/one tail, etc.) should all be the same after played a large number (such as 10^500) of times. Now, a ghost (not visible by me) comes in and tries to mess up my play either randomly or with a planed-system (of sabotages); yet, he is unable to change the outcome when the played number of times is as large as the 10^500 (a very large but finite number). On a first glance, this seems not logic. Yet, when we change ‘a game’ from flipping coin 10 times to 20 times, it becomes obvious that the Ghost’s task becomes much harder. When we change that number from 10 to one million, the Ghost will probably give up on this sabotage task. Of course, without providing a mathematical proof, I call this the “Ghost-rascal conjecture”: that is,

Ghost-rascal conjecture --- For a coin flipping game (head vs tail), T is the number times flip as one ‘game’, N is the number times that that ‘game’ is played. If T >= 10 and N >= 10^500, then no amount of sabotage from a Ghost can change the outcome of this game.

With this “Ghost-rascal conjecture”, the words of ‘eternal’ and ‘immutable’ are no longer the terms of philosophy and theology only, as this conjecture is a concrete game which can be played even by a first grader. Yet, if it cannot meet the second part of the definition of ‘Ultimate nature of Reality’ above (a long list of ‘gives rise to …’), then it becomes an absolutely useless nonsense. Thus, if this game cannot make any contact to ‘this’ physical universe, it will be just a meaningless game for physics although it can still be a fun game in math.

As stated above, the bigger the T is, the smaller the N is needed. If we choose T >= 100, this immutable power is much stronger, but it becomes a too big a game for a grade school kid to play, although it is not too big for a computer programmer. When T = 1, the conjecture could fail unless the ‘N’ goes to infinite. When T = 2, the Ghost’s hand can still be very powerful, and the conjecture needs a very large ‘N’. When T >= 3, the power of immutable becomes strong, and my-hand becomes dominant.  In fact, when T >= 3, the conjecture can be easily empirically proved. But, the key point here is not only to play a game of immutability but to meet the long list of ‘gives rise to …”.  Thus, I will show a game with T = 3 and get three games, as below.

Game 1: (tail, head, head)
Game 2: (head, tail, head)
Game 3:  - (tail, tail, head)

Can these three games make contact with this physical universe? When we make this game a bit spicier, we can truly surprise ourselves. Let’s add three more spices (hot, color, and twister) for this game.

One, hot-juice: the head carries 1/3 of electric charge, the tail with zero (0).

Two, color: the first flip (or spin) is red, yellow the second and the blue the third. Then, every game carries a color-tag which is the color of the ‘single’, such as the Game 1 is red; Game 2 is yellow; Game 3 is blue.

Three, twister: flipped by the left hand (sabotaged by the Ghost) is marked with a negative sign. Flipped by the right-hand carries a positive sign for the game.

With these additional spices, this game can actually describe all the Standard Model particles (excluding the bosons) symbolically.  That is, this game has made one ‘gives rise to …’ of the above list.

Then, when we make the three-game (1, 2, 3) as a compound game, it actually is the symbolical description of ‘proton’. Yet, for a color-blind person who is unable to see (the color), to feel (the hot juice) or to know (the twisting), he sees that the three games above are as below.
Game 1: (# * *)
Game 2: (* # *)
Game 3: (# # *)

This new compound game is, in fact, a glider of Conway’s Life game which can be the base for building a Turing computer. That is, there is a chance for this game to ‘give rise to life’.

Then, for this Ghost-rascal game, the probability of each game-pattern should all be the same at a number N (z). Then, we can define a special function Λ ,

Function Λ =  P (top, the largest probability of a game-pattern) – P (bottom, the smallest probability of a game-pattern) at any given N

By the definition of the conjecture, the probability of each game-pattern should all be the same at a number N (z), that is Λ (z)= 0 (exactly) at N (z). For a number N (i) < N (z),  Λ (i) > 0. When this N (i) is very large, this Λ  (i) should be almost to be zero. And now, zero (0) is precisely defined operationally in a finite {N (z) is very large but finite} ‘physical’ game, in addition to be only as a math concept. Furthermore, a Λ function must be a part of ‘this’ universe.

In summary, this game has the following attributes.
            i.  It is time-independent, not created in time and will not be destroyed at the end of time.
ii. It is immutable; no amount of sabotage can change the outcome of this game. Furthermore, it is a ‘concrete’ thing, not a philosophical or theological ‘speculation’.
iii.  It can devour all types of order (systematic sabotage). That is, it can, in fact, puke up all types of order too.
iv.  The left-hand game (sabotaged by the Ghost, marked with a negative sign) is the ‘source’ of ‘orderliness’, not a true symmetrical partner of the right-hand game. That is, there is a right-hand-genesis which is similar to the baryongenesis (see ).

Now, we have a definition for the ‘Ultimate Nature of Reality’ and have a concrete thing which meets that definition. I also showed a few examples about the ‘gives rise to …”, but it must meet ‘all’ of them in the above list. In order to that, I must introduce the ‘gives rise to Quantum-Spin’ first (see ). The Quantum-Spin arises via a Perfect Symmetry (the Real/Imaginary Time symmetry). By adding this new symmetry on the Ghost-rascal conjecture, it will give rise to three structure numbers (64, 48, 24) which give rise to Cabibbo, Weinberg angles, and Alpha. The explanation of this is available via the links below.

1.       Gives rise to the cosmological constant (Λ),
2.       gives rise to Cabibbo and Weinberg angles (see ),
5.       gives rise to Planck data (for dark energy, see ).
6.       gives rise to the particle zoo of the Standard Model (see ),
7.       gives rise to Baryongenesis (see link above),
8.       gives rise to quantum principle (see ),
9.       gives rise to unified force equation (see ),
10.   gives rise to life (see ),
11.   gives rise to arithmetic (see ),
12.   gives rise the Quantum-Spin (see link above).

13.   Why is there something rather than nothing? ( )