Sunday, February 06, 2005

Proton and Neutron Mass from GUITAR

Once we have discovered the natural unit set, which is also the scale of natural discreteness of spacetime. Now let's try to figure out the mass of proton and mass of neutron.

Actually, the mass of proton and mass of neutron, expressed in terms of kilogram, are in factor mass ratio of these particles against that standard one kilogram alloy metal chuck, whose mass is really not very precise known due to the limitation of technology. I would rather talk about the mass ratio between these particles against the mass of electron. That mass ratio is more precisely known.

From particle collider experiments, we know there must be a 3 fold microstructure within the proton. Gell-man used that 3-fold structure discovery to construct a model of quarks of 3 different flavors, to describe that 3-fold structure. Which is OK. But for now let's forget about quarks, and think about what that 3-fold structure tells us.

It is a structure unknowable to us, you can never disasseble that structure, and exam an individual quark. But we may be able to figure out how many distinguishable different ways that 3-fold structure can be constructued. That would tell us the entropy. With that we can calculate the mass.

I am not going to reveal all the details, But I find that given if the structure is constructed using a building element of 3 different flavors, there is exactly one way of forming one solid piece, and exact one way when all three pieces are separated from each other. And there are 3 ways one separate from the group of the other two. That's (1, 3, 1). When I futher study how many different ways within each scenary they can interact with each other, there are (1, 5!,7!) ways respectively.

So the total number of intrisic states are:

Wi = (1,3,1) * (1,5!7!) = (1x1 + 3*5! + 1*7!) = 1 + (3*5!) + 7!

Isn't that elegant? Now don't forget that externally, for proton, it has a spin up and spin down state. That's two different states. The total number of states would then be two multiplied by the intrisic number of states above:
W = Wspin * Wi = 2x(1+3*5!+7!)
The entropy then would be
S = ln(Wi)
The simplest structure has two states, 0, 1, and the entropy is ln(2).

So that's it. We have obtained the proton mass! Since proton is considered a point particle so far and NO geometric factor is involved, it's entropy from interla states corresponds to its mass linearly:

Mp = S/ln(2) = ln(W)/ln(2) = ln(2*(1+3*5!+7!))/ln(2)
Mp = ln(10802)/ln(2) = 13.39901083

That is the proton mass! Although we have used some simplicifications so far. It agrees with experimental value excellently!

How come? Remember we are using the natural units so far. In the matural unit set, the electron mass is:
Me = alpha * M0 = alpha = 1/137.03599911 = 7.297352568x10^-3

Let's see the mass ratio between proton and electron:
Mp/Me = 13.39901083/7.297352568x10^-3
Mp/Me = 1836.146836

My calculation matches excellently with the accepted value of 1836.15, See

The discrepancy is 3x10^-6, i.e., three parts out of a million. The actual value is slightly higher than my calculation. I believe this is due to the fact that protons may decay, slightly raise the mass, although the mass raise is so small, that the delay must be outrageously slow to be detectable at all.

My speculation is confirmed in the case of neutron, whose delay time is known. And I obtained a glorious success in obtaining the neutron mass, which agrees with experimental value completely, and so confirms my speculation that limited delay life really do increase the mass slightly.

Neutron can be considered as simply a proton combined with an electron. So it's mass could have been simply the theoretical proton mass calculated above, plus the electron mass. The presumed electric interaction energy between the positively charged proton and negatively changed electron, shall not be counted, because externally, electric field resulting from such interaction is none-observable. So it does not exist as long as it is not observable.

However, the electron mass within a neutron is not the regular electron mass we know. It has a limited lifespan staying within the neutron (it can decay and be emitted out), so the delay mean lifetime increases the mass by a factor of beta^2, with beta related to the delay lifetime, compared to the "age of the universe".

We have:

Mn - Mp = Me * beta^2,


beta = ln (Tu/sqrt(PI)) / ln((sqrt(2)/PI) * Tau/sqrt(PI))

where Tu is the age of the universe, and Tau is the neutron decay mean lifetime.

Keep in mind we are using the natural unit set, discussed in my previous message on this BLOG. In which the unit of time:
T0 = time for light to go across the length of one classical electron radius
T0 = 9.399637148(94)x10^-24 second

And Tu, in natural unit set, is simply:
Tu = PI*N,
with N = PI*exp(2/(3*alpha)),
alpha = fine structure constant = 1/137.03599911(46)

The neutron delay mean lifetime can be found here:

The most precise result found in the paper is 885.4 +- 0.4 seconds. The author averages all accurate and inaccurate results and obtained 885.7 +- 0.8 seconds, which is also what the internationally accepted value of 885.7 +- 0.8 seconds. I think it is wrong to dilute the accuracy by averaging in inaccurate results. So I simply use the most accurate one, 885.4 +- 0.4 seconds.
If any one wants to use 885.7+-0.8 seconds, OK, and the end conclusion is still the same.

Based on the above Tu and Tau, any one with a good calculator can calculate beta, and then the correction of neutron mass from proton mass from beta^2:

Beta = 93.07442757(31) / 58.43688(50)
Beta = 1.592734(14)
Beta^2 = 2.536802(46)


Mn/Me = (Mp/Me) + beta^2
Mn/Me = 1836.1468368(60) + 2.536802(46)

Mn/Me = 1838.683638(46)

Or in another way, Mn/Me is between
1838.683592 to 1838.683684

The large argin of error is due to the inaccuracy of known neutron delay lifetime, 885.4 +- 0.4 seconds.

Compare my result with the accepted value:
Mn/Me = 1838.6836598(13)

My result agrees with the accepted value completely within margin of error, with 10 effective decimal places!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!