The Largest Prime Number Conjecture

Yesterday (11/11/11) was a special day in terms of the calendar numerology. In China, many young people called this day as the “bachelor day of the century”, as every number in the calendar is “1”, single as a bachelor. And, this won’t happen again until 100 years from now. In fact, the entire world celebrated this day in one way or the other.

Obviously, this calendar numerology has no scientific significance. Anyone who thinks it otherwise is, indeed, a solatic (meaning a lunatic in the daylight, a term invented by Matt Strassler, a theorist on physics). Of course, the calendar numerology does have some culture and psychological significances.

However, the simple numerology does have some great importance in modern science. Thus, on this special day, I would like to use a special number game (using only the number 0 and 1) to show this point.

The prime number game --- if X is the largest “known” prime number with m digits (such as, one billion digits),

then    Y1 = (10^n) + 1, and  n = m + 1.

          Y2 = (1111…1110) + 1, there are n digits in the bracketed number, and

                         n = m + 1 if m is an even number,

                         n = m + 2 if m is an odd number.
                      

           Then, n is checked with two steps.

  step 1. if  {3, 5, 7, 11 or 13} is a divisor of n, then n = n + 2

  step 2. if the square root of n [n^(1/2)],  [n^(1/3)], [n^(1/5)], [n^(1/7)], [n^(1/11)], or  [n^(1/13)]

                 i. is equal to an integer, then n = n + 2 and go back to step 1.

                 ii. is not equal to an integer, then n is chosen. 

           Thus, Y2 must have odd number digits and all its digits are “1”.

As this is only a game for this special (11/11/11) day, I will not try to prove a “Largest Prime Number” theorem but make it as a conjecture.

Largest Prime Number Conjecture:
 a. if X is the largest “known” prime number with m digits (such as, one billion digits), then one of the two numbers (Y1 or Y2) is a larger prime than X.

 b. if the Y2 above is not a prime, then let n = n + 2 and repeat the n-check steps to get a new Y2. There is always a Y2 which is a prime and Y2 > X.

Technicolor, simply wrong

In the recent LHC data, the supersymmetry and superstring theories are basically ruled out. Thus, the Technicolor has gained some attention among physicists.

  

Technicolor in terms of Rishon Model  (RM) was internally inconsistent and was ruled out 30 years ago theoretically. In my view, technicolor is simply wrong.

The rishon model (RM) is the result of a reverse-engineering of trying to explain the quark color by postulating preons (sub-particle of quarks) which carry Technicolor (the hypercolor). And, the preons are postulated "point-like" particles, conceived to be subcomponents of quarks and leptons. That is, the RM has no underlying physics as its foundation.

Yet, Prequarks in Prequark Chromodynamics (PM) are often mistaken to be similar to the preons. Although quarks and leptons are composed of prequarks, prequarks are not particles at all but are attributes of the spacetime sheet. There are at least four major differences between Preon (Rishons) model.

One, The Preon model (done by Abdus Salam) which was expanded as Rishons model (mainly done by Haim Harari). This Rishons model is very similar to my Prequark model. It has sub-quarks (T, V): {T (Tohu which means "unformed" in Hebrew Genesis)  and V ( Vohu which means "void" in Hebrew Genesis)}. But, Harari did not know what T is (just being unformed). On the other hand, the A (Angultron) is an innate angle, a base to calculate Weinberg angle and Alpha.

Two, the choosing of (T, V) as the bottom was ad hoc, a result of reverse-engineering. On the contrary, there is a very strong theoretical reason for where the BOTTOM is for G-theory.

In G-theory, the universe is ALL about computation, computable or non-computable. For computable, there is a TWO-code theorem. For non-computable, there are 4-color and 7-color theorems.

That is, the BOTTOM must be with two-codes. Any lower level under the two code will become TAUTOLOGY, just repeating itself.

Anything more than two codes (such as 6 quarks + 6 leptons) cannot be the BOTTOM.

Three, rishons (T or V) carry hypercolor to reproduce the quark color, but this set up renders the model non-renormalizable, quickly going into a big mess. So, it was abandoned on day one. On the other hand, prequarks (V or A) carry no color, and the quark color arises from the “prequark SEATs”. In short, Rishons model cannot work out a {neutron decay process} different from the SM process.

This is one of the key differences between prequark and (Rishons and SM).

Four, Preon/Rishons model does not have Gene-colors.

This new physics goes way beyond the gadget physics, and thus I presented it with a new methodology, the Fictitious Universe (FU) Physics.  In FU physics, all physics (principles or laws) are derived, not discovered. Then, these FU laws are compared to the discovered physics laws, as a fingerprints marching or a beauty contest. I have shown many fingerprints marching in my last post (http://prebabel.blogspot.com/2011/11/physics-laws-must-give-rise-to.html ) without revealing the underlying physics. Now, I will give a brief outline about this new physics which has only two simple points.

1. The law of creation --- the term “Law of Creation” is a no-no word in science, especially in the gadget physics. In fact, the “First” spontaneous symmetry breaking (FSSB) is the result of the law of creation, which consists of two parts.

a. The “Original” symmetry

b. The symmetry breaking process.

This “Law of Creation” was described in detail in the book “Super Unified Theory” (ISBN 0-916713-02-4, Copyright # TX 1-323-231, Library of Congress Catalog Card Number 84-90325) and is available online. Thus, I will only discuss it very briefly here.

The result of this symmetry breaking (creation) is the spacetime sheet. The breaking process is to transform the symmetry “dimension” (X) to the spacetime “dimension” (n). In Super Unified Theory (SUT), the above process is called the “dimension concretization” or dimension expression, and the n = 11 in SUT.

2. The attributes of spacetime  --- “time” comes into being after the above creation, and it has the following attributes in SUT.

a. “Time” is a quanta, that is, delta T > 0. Delta T can never be equal to zero.

b. “Time” is a 4-dimensional vector, delta T = (t, -t, it, -it). That is, every quanta of time must be identified with 4 labels. “it and –it” are the imaginary time.

c. “Space” is the expression of the “moving” time, that is, delta S = N* C* delta T. N is a time-moving matrix. C is the light speed.

The entire Fictitious Universe arose from these three attributes of time. All derived laws and prequarks (described in the previous posts) are direct consequences of them. I will reiterate some other important direct consequences below.

i. The universe must expand with Acceleration, as the creation process continues (see http://prebabel.blogspot.com/2011/10/nobel-prize-2011-accelerating-expansion.html ). Of course, when the mass of the universe reaches a critical point, the expansion will become decelerating.

ii. Every fermion’s (including neutrino’s) rest mass arises from the “flip-flop” between the “real” and the “imaginary” time mechanism.  That is, the Higgs mechanism is only the shadow of this RI-flip-flap mechanism. So, Higgs boson of any kind is not needed (see http://prebabel.blogspot.com/2011/10/higgs-boson-bad-idea-part-nine.html ).

iii. As the rest mass of neutrino arises from this RI-flip-flap mechanism, neutrinos must oscillate (see http://prebabel.blogspot.com/2011/10/neutrino-oscillation-mystery-no-more.html ). And, there must not have the fourth type of neutrino of any kind.

Physics laws must give rise to biological lives directly

The scope of “Fictitious Universe (FU) physics” must encompass the entire known physics (derived by the gadgets, such as Tevatron or LHC) and “all” known realities, such as,

a. the rise of biological lives from the laws of physics, not just obeying physics laws by lives, and

b. the rise of intelligence in terms of physics laws.

This concept of going beyond the gadget physics was described in the article “Higgs Boson, a bad idea, part seven” at (http://prebabel.blogspot.com/2011/08/higgs-boson-bad-idea-part-seven.html ).  Thus far, I have shown many fingerprints marching between this FU physics and the gadget physics. The FU physics did reproduce the following known physics.

1. The particle zoo of Standard Model, see http://prebabel.blogspot.com/2011/11/m-theory-toe-if-and-only-if-it-adds-two.html       

2. Uncertainty principle, see http://prebabel.blogspot.com/2011/10/super-unification-in-fictitious.html

3. Theoretical calculation of Cabibbo and Weinberg angles, see http://prebabel.blogspot.com/2011/10/theoretical-calculation-of-cabibbo-and.html

4. Theoretical calculation of Alpha (Electron Fine structure constant), see http://prebabel.blogspot.com/2011/10/v-behaviorurldefaultvmlo.html

With these fingerprints marching, there are enough and enough proofs to show that the gadget physics is only a subset of the FU physics (Super Unified Theory). However, if the FU physics cannot encompass “all known realities”, then it is useless.

Every biological life processes information, that is, it needs a bio-computer. In the 1970s, John Horton Conway invented “Life Game” and discovered that the “glider” of the life game can be the base to construct a Turing computer.

In Prequark Chromodynamics, both proton and neutron are gliders with the prequark representations. See the table below.  

Comparison of proton, glider and neutron
Proton as quarks	Proton as Prequarks		Glider		Neutron as Prequarks	Neutron as quarks
up (red)	(V, A, A)		( , * *)		- (A, V, V)	down (red)
up (yellow)	(A, V, A)		(* , *)		- (V, A, V)	down (yellow)
down (blue)	- (V, V, A)		( , , *)		(A, A, V)	up (blue)

That is, with the Prequark Chromodynamics, a Turing computer is embedded in the basic building blocks of life. Thus, the laws of FU physics do provide the essential parts of biological lives. The detail of this is described in the article “The Rise of Biological Life”, available at http://www.prequark.org/Biolife.htm .

M-theory, a TOE if and only if it adds two points

M-theory (Mother of all theories) is a new name for the old Superstring theory which claims to be a TOE (theory of everything), as it can be a way of describing every force and matter regardless of how large or small or weak or strong it is.

But, 20 years ago, Sheldon Glashow said, "They [superstring physicists] have the feeling that they require, as Ed Witten says, the construction of five new fields of mathematics before they have any reason to become confident that they have a theory. In fact, they do not have a theory. They have a complex of ideas which do not evidently form any kind of theory and they cannot even say whether their structure describes the successful accomplishments that have been obtained in the laboratory, and in theoretical physics."

Now, 20 years later, Rudolf Haag (wrote in 2010), “String theory is hailed as the most promising among present endeavors. But it is an overstatement to call it a theory. It has not settled down to a well-defined formalism nor has it explained any existing puzzle nor can I see that it can make contact with any observable phenomenon in the foreseeable future.”

The bottom line is that the M-theory cannot make contact with any observable phenomenon in particle physics. However great a TOE the M-theory is, it cannot reproduce the particle zoo which is well understood now.

However, the quark in the Prequark Chromodynamics is a superstring, composed of prequarks. By adding Prequark Chromodynamics, the M-theory makes contact with the known physics right the way. The following is a brief description of the Prequark Chromodynamics.

There are three quark colors. In Prequark theory, these three colors can be represented as three seats (in spacetime). For each seat, it can be either empty (Vacutron) or occupied (Angultron). Thus, only four different kinds of particles can be formed:

1. A particle with all seats occupied by Angultrons carries one unit of electric charge, and it is named positron.
2. A particle with two seats occupied by Angultrons carries 2/3 units of electric charge, and it is named UP quark.
3. A particle with one seat occupied by an anti-Angultron carries -1/3 units of electric charge, and it is named Down quark.
4. A particle with no seat occupied by Angultron carries zero units of electric charge, and it is named neutrino.

Furthermore, for a given quark (as an open string), there are three ways to arrange the seating, and each way is distinguishable from others. Physicists have chosen three color labels to identify these differences. So, two quarks (Up and Down) evolve into six distinguishable quarks.

Again, in Quantum Chromodynamics, there are three generations of quarks. These three generations are identified with three numbers, 1, 2 and 3. Thus, the prequark representations for those elementary particles are listed in table I and table II. 

Table I: Prequark Representation for Leptons
Generation	Particle name	Prequark Representation	Colors	Electric Charge
1st	Electron	-(A, A, A1)	colorless	one (1)
1st	Neutrino	(V, V, V1)	colorless	0
2nd	Muon	-(A, A, A2)	colorless	one (1)
2nd	Muon neutrino	(V, V, V2)	colorless	0
3rd	Tau	-(A, A, A3)	colorless	one (1)
3rd	Tau neutrino	(V, V, V3)	colorless	0

Table II: Prequark Representation for Quarks
Generation	Particle name	Red	Yellow	Blue	Electric Charge
1st	Up quark	(V, A, A1)	(A, V, A1)	(A, A, V1)	2/3
1st	Down quark	-(A, V, V1)	-(V, A, V1)	-(V, V, A1)	-1/3
2nd	Charm quark	(V. A. A2)	(A, V, A2)	(A, A, V2)	2/3
2nd	Strange quark	-(A, V, V2)	-(V, A, V2)	-(V, V, A2)	-1/3
3rd	Top quark	(V, A, A3)	(A, V, A3)	(A, A, V3)	2/3
3rd	Bottom quark	-(A, V, V3)	-(V, A, V3)	-(V, V, A3)	-1/3

Three notions shall be mentioned here.

First, the quark color corresponds to a special seating arrangement. I have chosen the first seat to be red, yellow for the second seat, blue for the third. The quark color is identified by the seat's color which is occupied by a minority prequark. For example, V is the minority prequark in (V, A, A1), and it sits on the red seat; so (V, A, A1) has a red color. (V, A, V1) is yellow because the minority prequark A sits on the yellow seat. The prequarks (A or V) themselves are colorless.

Second, quark colors obey the complementary rules: a) R + Y + B = White (colorless), b) R + Y = anti-B, etc.

Third, the generation of a quark or a lepton is represented by a number, 1, 2 or 3. For convenience, the generation numbers are attached to the third seat. The prequarks and seats themselves have no generation.

The “generation” is a color charge in the Prequark Chromodynamics, and it obeys the color complementary rules. Thus, in Prequark Chromodynamics, the fourth generation of quarks is prohibited.

Note: Angultron could be much more massive than quarks. So, it is called prequark (before quarks), not subquark.

The major difference between the Prequark Chromodynamics (PC) and the M-theory is that PC knows the detailed internal structure of the quark superstring while M-theory does not.

In his book “Not Even Wrong”, Peter Woit shows “that what many physicists call superstring ‘theory’ is not a theory at all. It makes no predictions, even wrong ones, and this very lack of falsifiability is what has allowed the subject to survive and flourish. Not Even Wrong explains why the mathematical conditions for progress in physics are entirely absent from superstring theory today and shows that judgments about scientific statements, which should be based on the logical consistency of argument and experimental evidence, are instead based on the eminence of those claiming to know the truth.”

Yet, I have shown that by adding Prequark Chromodynamics  (one of the two points), a superstring theory can make contact with the known physics.