Definition of mass, the gateway to the final unification in physics

Now, LHC is probing the spacetime inside of protons and is investigating the mass-rising mechanism, as these researchers are the final steps for a final physics. Yet, I have shown that there is an anchor-lock (Alpha, the Electron Fine Structure Constant) in Nature, and it locks the absolute definitions for the space, time and mass. Thus, the physics which gives rise to this Alpha (that is, the physics which provides the theoretical calculation for the Alpha) should be the final physics.

However, Richard Feynman (a Nobelist on Physics) said, 'There is a most profound and beautiful question associated with the observed coupling constant, e - the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!'

The Inverse-Alpha = 1/Alpha = 137.03597… is a dimensionless pure number, and it can be reached by many numerological formulas. However, if we can show that each term and each number used in the equation which calculates the Alpha has physics meaning, then that equation is about physics, not a simple numerological formula. And, I have shown the following equations online since 1997.

Beta = 1/alpha = 64 ( 1 + first order mixing + sum of the higher order mixing)

         = 64 (1 + 1/Cos A(2) + .00065737 + …)

         =  137.0359 …

 A(2) is the Weinberg angle, A(2) = 28.743 degrees

 The sum of the higher order mixing = 2(1/48)[(1/64) + (1/2)(1/64)^2 + ...+(1/n)(1/64)^n +...]

       = .00065737 + … 

  

There is no question of any kind about the equation of Beta which gives a dimensionless “number” exactly identical to the known value of the Inverse-Alpha. Yet, is the equation of Beta simply a numerological formula? The answer is, of course, hinging on its terms and numbers used in the formula. That is, are the terms and numbers in the formula [64, A(2) and the formula for the sum of the higher order mixing] simply numerological choices or the bases for an underlying physics?

As the A(2) is the Weinberg angle, it is a very important physics parameter in the Standard Model. Yet, is the chosen value (28.743 degrees) a numerological choice? Can this value be calculated with the “same physics” which gives rise to Alpha? After these questions are answered, we will know for sure that we have a physics equation for Alpha or simply a numerological formula for it.

As this Weinberg angle is the key parameter for calculating the mass of weak bosons, I will start this analysis from the meaning and the definition of “mass”.

In physics, mass was “first” defined only with an operational definition, that is, with measurement, either for accelerating mass or gravitational mass. The epistemology for this is the “interplay of theory and test”, and it can be called as T-physics.

After the introduction of Special Relativity (SR), a semi-paradoxical mass-energy relationship was discovered.  Professor Matt Strassler gave a great explanation about mass with his article “Mass and Energy” (available at http://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/mass-and-energy/ ). In that article, two issues about mass are clearly explained.

1. A semi-paradoxical attribute about mass --- the mass of an object has a universal value for all observers while the measurement of mass of that object is following exactly with the law of SR.

2. By understanding this semi-paradoxical attribute about mass, there is a clear procedure to distinguish the signals of the Higgs decay into diphotons from its background noises.

However, the definition of mass in Matt’s explanation is still wholly in terms of “operational” although the law of SR is used.

In fact, after we have learned enough from the T-physics, we can organize that knowledge as an axiomatic system, the knowledge physics (K-physics in short). Of course, the epistemology here can be different, by using the rules of the axiom system. Thus, the mass or energy can be defined with some axiomatic sentences (or equations). Among the fundamental parameters (time, space, mass, energy, electric charge, etc.) of this K-physics, the electric charge is obviously a derived parameter as it can be written as a function of h-bar and c (light speed). There are also two axiomatic sentences for energy.

      a. Einstein, E = mc^2

      b. Planck, E = h-bar v(frequency)

If we combine the two axiomatic sentences above, the mass can also be expressed as a function of h-bar and c. That is, the mass and the electric charge differ only in degree, not in kind. Thus, if we can truly understand the definition of mass in this way, it might lead us to a true Super Unification.

In Physics, there are three different types of energy, the motion energy (in terms of momentum), the rest energy (mass) and the relational energy. If there is a Super Unification in the Nature physics, those three types of energy must be unified first. Thus, in addition to Einstein’s E = mc^2 which transforms “mass” into energy, the energy (a massless particle) must be able to become (acquire) “massive”.  That is, there must be a mass-rising mechanism.

In the macro-world, the mass is simply the aggregate of a pile of elementary particles. Thus, by understanding the mass-rising mechanism for elementary particles, we will know exactly what the “mass” is. There are, at least, two mass-rising mechanisms in the discussion, the Higgs-mechanism, and the See-Saw mechanism. Basically, if the associated symmetry for a particle is not broken, that particle is massless (no rest mass). Thus, those mechanisms are symmetry breaking procedures. And, the Higgs boson supposes to be the actor in the Higgs-mechanism. Is there a Standard Model Higgs in the Nature physics? This question could be answered in just a few more months with LHC’s upcoming “test” data.

However, with the K-physics (the axiom system of human physics), it can be easily deduced that if there is Super Unification in the Nature physics, then there should be one and only one mass-rising mechanism, not two or many. Thus, both Higgs-mechanism and the See-Saw mechanism are at best the shadows of the real one.

While those two mass-rising mechanisms are still under testing, there are some concrete parameters which did give the precise calculation for the mass of weak bosons, the Cabibbo angle (θ_c  about 13 degrees) and the Weinberg angle (θ_W  from 28 to 30 degrees). The values of these two angles are free parameters in the Standard Model, that is, they were forced into the model with the demand of fitting the data and had no theoretical base for them. Thus, if these two angles can be calculated theoretically, then the “physics” which provides those calculations should be able to give “mass” a theoretical definition.  

I already provided the calculations for both Cabibbo and Weinberg angles in my previous post (Theoretical calculation of Cabibbo and Weinberg angles, http://prebabel.blogspot.com/2011/10/theoretical-calculation-of-cabibbo-and.html ).


Again, I must show that those equations are not numerological formulas but are the consequences of the same physics which gives rise to the Alpha.  And, I will do this in my next posts.


As soon as this is done, the true mass-rising mechanism will be understood, even without the answers from the LHC data.  The LHC data will have no choice but will verify the validity of this mass-rising mechanism derived from this K-physics calculation. Then, the questions of “dark matter” and of “why are the universe accelerating during its expansion?”  will be answered.