# Constants of Nature (and SM Parameters)

1. Nov 6, 2013

### kye

I'm reading Peter Woit book "Not Even Wrong" and have been contemplating on the constants of nature or the parameters. I have some questions.

1. Which of the Constants of Nature do you think can be calculated by principles? Should they in principle be calculable?

2. Should a Unified Theory supposed to address (and calculate) how the constants of nature came? What exact constants of nature String Theories and Loop Quantum Gravity hope to solve?

3. But supposed it is not just possible to get the values. How could the values of the constants of nature be what they are (let's avoid the Anthropic Principle argument for now)?

4. Which of them have already been derived and what papers have derived them?

5. If there is no physical process wherein for example an electron can store it's charge values, masses and coupling, why is that 2 electrons 100 light years away have the same values? Where is the information exactly stored?

2. Nov 6, 2013

3. Nov 6, 2013

### Myslius

Today there are 335 fundamental physical constants defined by NIST (National Institute of Standards and Technology) http://physics.nist.gov/cuu/Constants/Table/allascii.txt

We had a degree of freedom to choose units, that's why meter/second aren't equal to 1, we have a constant c to represent the ratio between meters and seconds. We can do dimensionless analysis of fundamental constants with a little bit of math. For example, constants displayed below are actually equal to each other (after removing dimensionality):
http://s14.postimg.org/wi16bi9wx/Constants.png [Broken]

134 fundamental physical constants are duplicates (due to dimensionality). But still, we have 201 different constants left.

Some of the constants have very basic relationships, for example "electron gyromag. ratio" and "electron gyromag. ratio over 2 pi". Some are clearly a result of probability, for example "standard atmosphere". This list doesn't include many other constants, for example fundamental particle masses or decay times. We end up with about 150 unique constants that can have "some" physical meaning.

Doing dimensionless analysis shows some weird relationships, for example solving tau particle's mass we get:
(tau mass) = ((muon-electron mass ratio) / (Planck temperature)) / (kelvin-hartree relationship)^2
(tau mass) = (deuteron-neutron mag. mom. ratio) * (helion g factor) * (atomic mass constant)
(tau mass) = (alpha particle-proton mass ratio) / (neutron Compton wavelength over 2 pi) - (atomic unit of charge)
All relationships above are in agreement of uncertainties (0.09%)

There are many papers with weird relations, for example http://arxiv.org/pdf/1005.0238v1.pdf You can find dozens of such papers by searching.
All such conclusions are highly unreliable. I think we have insufficient data for Unified Theory, specially with all those high uncertainties.

Last edited by a moderator: May 6, 2017
4. Nov 8, 2013

### kye

How is Permeability and permissivity values of free space calculated from newton gravitational constant G, planck constant and the speed of light?

UltrafastFED, I read your site, but I need others to exactly share how permeability and permissivity is derived from newton gravitational constant G, planck constant and the speed of light because I don't know how.

5. Nov 8, 2013

### UltrafastPED

Why do you think that it's possible? I've never run across it ...

6. Nov 8, 2013

### kye

I read archive here that spacetime is just geometry. Space is not fundamental, so how can there be permeability and permissivity of space? So anyone knows how they are derived, again from newton gravitational constant G, planck constant and the speed of light?

7. Nov 8, 2013

### kye

Ok. I found the thread "What is Space"

Marcus wrote:

"Regarding epsilon-naught and mu-naught, they can surely be calculated from more fundamental stuff!

For instnace, as I recall, from the elementry charge e, the charge on the electron, and other basics like hbar and c.

The coulomb constant is (1/137) hbar c/e2"

So Marcus, how is Permeability and permissivity values of free space calculated from newton gravitational constant G, planck constant and the speed of light? What is the consensus about this by others?

8. Nov 8, 2013

### atyy

In the view that spacetime is geometry, spacetime is fundamental if geometry is fundamental.

To get the permeability and permitivity of empty space, let us take the flat spacetime case first, and set up inertial coordinates, so that Maxwell's equations take the form of Eq 417-420 in http://farside.ph.utexas.edu/teaching/em/lectures/node46.html . In these equations the permeability is $\mu_{o}$, and the permittivity is $\epsilon_{o}$. From these equations we can get a wave equation for light with speed $c = \frac{1}{\sqrt{\mu_{o}\epsilon_{o}}}$. The derivation is Eq 430-453 of http://farside.ph.utexas.edu/teaching/em/lectures/node48.html. Thus if the values of $c$ and $\mu_{o}$ are defined, then the value of $\epsilon_{o}$ is also defined. See Section II on p4 of http://physics.nist.gov/cuu/Constants/RevModPhys_80_000633acc.pdf for more information.

These generalize to curved spacetime by the Principle of Equivalence.

Last edited: Nov 8, 2013
9. Nov 10, 2013

### lpetrich

Many of those constants can be calculated from the Standard Model of elementary particle physics. Like masses of hadrons, binding energy of nuclei, and magnetic moments.

The Standard Model has 19 free parameters, and making neutrinos massive adds another 7 or 9 free parameters.

So it's the Standard Model that one has to look at.

(numerology snipped)

10. Nov 10, 2013

### lpetrich

That's what I mean by numerology. If one has lots of numbers and does lots of manipulations, one can get arbitrarily close to *any* number.

Furthermore, it's a mistake to use the constants' low-energy values as one's reference values in such calculations. One has to calculate their effective values at Grand Unified Theory energy scales. Even over the Standard Model's energy scales, the constants vary noticeably. The fine structure constant, about 1/137.036 at low energies, becomes about 1/128 at W-particle energies. Its QCD counterpart varies much more, from around 1 at around 1 GeV to about 1/8.4 at Z-particle energies.

11. Nov 10, 2013

### Myslius

Numerology - The branch of knowledge that deals with the occult significance of numbers.
You shouldn't be using this word. Many laws were deduced by looking at experimental data, searching for patterns.
Keppler did.
Hubble did.
etc.
That's part of the physics. If one has numbers, one can notice a law, and some can't.
Math alone (without data) leads nowhere.

Last edited: Nov 10, 2013
12. Nov 10, 2013

### kye

What is another term for the Standard model 19 free parameters? Are they called Constants of Nature or just Free Parameter? What terms should be used to distinguish them to others that can be derived from them.

Is it required for any unified theory program to derive the 19 free parameters from equations or calculate them? For example. Is it the hope of string theories to derive them from the vibrational modes of strings, branes and extra dimensions? Or are there parameters that just can't be derived? If so. Why are some parameters not possible to derive even in principle. And last. Why is say the charge of electron the same value here and say Andromeda? Where is the value or information stored? Your computer and I both have same windows bootup because it is stored in hard disc. How about the primary constants or parameters, how are they stored? what is the present consensus on this?

13. Nov 10, 2013

### lpetrich

I'm far from alone in calling it numerology. Consider Go To Hellman: Fundamental Constant Numerology It's essentially a form of overfitting.

14. Nov 10, 2013

### HallsofIvy

Staff Emeritus
Last edited: Nov 10, 2013
15. Nov 11, 2013

### kith

You can't calculate them from these three constants.

In the SI system, we have the five basic units m, s, kg, A and K which are arbitrary definitions derived from everyday values of physical quantities. To get to the more natural set of the Planck units, we set the five important constants c, h, G, ε0 and kB equal to one. This only works because these constants are independent of each other.

16. Nov 14, 2013

### lpetrich

Proposed redefinition of SI base units - Wikipedia
BIPM - New SI
BIPM = French initials of International Committee for Weights and Measures

The units have gone through these redefintions:

Length: Earth size - platinum bar - Kr-86 electronic transition - defined in terms of time by fixing the vacuum speed of light, c

Time: Earth solar day - Earth year - Cs-133 hyperfine transition

Mass: Water density - platinum cylinder - (proposed) defined in terms of time by fixing c and Planck's constant, h

Temperature: Water freezing and boiling - Water triple point - (proposed) defined in terms of time by fixing c, h, and Boltzmann's constant kb

Elementary charge e and electric permittivity of the vacuum ε0: e measured, ε0 defined - (proposed) e defined, ε0 measured

Fixing h and e will fix the Josephson constant in the Josephson effect, and also fix the von Klitzing constant in the quantum Hall effect. This will be convenient for precision measurements of voltages and currents with these two effects.

17. Nov 14, 2013

### dauto

Minor quibble: Usually Planck units are defined by setting h = 2π, and ε0 = 1/(4π).

18. Nov 14, 2013

### dauto

To the OP. Yes ideally a "theory of everything" should reduce the current number of parameters down to just a few. Even string theory has a few parameters. Grand unified theories have been partially successful in reducing the number of parameters from the standard model. Notably, the three gauge coupling constants of the standard model g, g', and gs are replaced by a single unified gauge coupling constant gU. These GUT models are also typically able to unify some (but not all) of the Yukawa coupling constants of the standard model. A more thorough understanding of those Yukawa constants would (should? ) explain the pattern of masses for the fundamental particles seen in nature. That would be huge progress towards a truly unified theory.

Last edited: Nov 14, 2013
19. Nov 15, 2013

### lpetrich

Back to the Standard Model, here's how its free parameters split up:

Quark masses and mixing: 10
Lepton masses: 3
Lepton masses with massive neutrinos: 10 or 12
Gauge interactions: 3
Strong CP violation: 1
Higgs-particle mass and self-interaction: 2

Gauge unification in grand unified theories reduces the 3 gauge-interaction parameters to two: one parameter value and one energy scale.

Axions, if they exist, would replace the strong-CP parameter with at least two.

-

The elementary-fermion masses and mixings have a big ambiguity problem. These masses are due to the elementary fermions' interaction with the Higgs particle:

Lint = yijφψLiψRj + hermitian conugate

where φ is the Higgs field, ψ is the EF fields, L is left-handed, R is right-handed, i and j are summed over EF generations, and the y's are Yukawa-coupling matrices. These matrices are completely general, being arbitary matrices of complex numbers without any constraints. One gets

(masses) = (Higgs VEV) * (absolute values of y eigenvalues)
m = v*|y|

(quark mixing matrix) = (L to R eigenvector matrix for up-like quarks)-1 . (L to R eigenvector matrix for down-like quarks)

Neutrinos may have seesaw-mechanism-generated masses, and that mechanism adds some complexity that I'll avoid for now.

For quarks, the generations mix, meaning that y(up) and y(down) cannot have eigenvectors orthogonal to each other. They cannot both be diagonal matrices at the same time. CP violation means that they cannot both be real matrices at the same time. So one is stuck with full generality, 36 parameters. Imposing symmetry gives 24 parameters, and there's been a lot of work on possible "textures", setting some elements of the y's to zero and other such things.

-

Let's see what GUT's predict. I'll use shorthand:
yu = y(up quark), yd = y(down quark), yn = y(neutrino), ye = y(electron)

SU(5): ye = transpose(yd)
Tau lepton and bottom quark masses ought to be equal at GUT energies

SO(10) ye = yn = yd = yu -- is symmetric
Too successful: no cross-generation decay, no seesaw mechanism. These two effects must be generated by violations of SO(10).

20. Nov 17, 2013

### kye

Do you guys believe that in the Final Theory, the speed of light c, planck constant, Newton G for example have to be derivable from equations? What if they can't be derived and just given. Do you consider it ad hoc and won't you accept it?