Examples Dimensionless physical constant

1 examples

1.1 fine structure constant
1.2 standard model
1.3 cosmological constants
1.4 barrow , tipler
1.5 martin rees s 6 numbers

examples

dimensionless fundamental physical constants include:

α, fine structure constant, coupling constant electromagnetic interaction (≈ ⁄137). square of electron charge, expressed in planck units, defines scale of charge of elementary particles charge.
μ or β, proton-to-electron mass ratio, rest mass of proton divided of electron (≈1836). more generally, ratio of rest masses of pair of elementary particles.
αs, coupling constant strong force (≈1)
αg, gravitational coupling constant (≈10) square of electron mass, expressed in planck units. defines scale of masses of elementary particles , ratio of αg other coupling constants has been used express strength of gravitation relative other interactions.

fine structure constant

one of dimensionless fundamental constants fine structure constant:

α
=



e

2



ℏ
c
 
4
π

ε

0





≈


1
137.03599908


,


{\displaystyle \alpha ={\frac {e^{2}}{\hbar c\ 4\pi \varepsilon _{0}}}\approx {\frac {1}{137.03599908}},}

where e elementary charge, ħ reduced planck s constant, c speed of light in vacuum, , ε0 permittivity of free space. fine structure constant fixed strength of electromagnetic force. @ low energies, α ≈ 1/137, whereas @ scale of z boson, 90 gev, 1 measures α ≈ 1/127. there no accepted theory explaining value of α; richard feynman elaborates:

there profound , beautiful question associated observed coupling constant, e – amplitude real electron emit or absorb real photon. simple number has been experimentally determined close 0.08542455. (my physicist friends won t recognize number, because remember inverse of square: 137.03597 uncertainty of 2 in last decimal place. has been mystery ever since discovered more fifty years ago, , theoretical physicists put number on wall , worry it.) know number coupling comes from: related pi or perhaps base of natural logarithms? nobody knows. s 1 of greatest damn mysteries of physics: magic number comes no understanding man. might hand of god wrote number, , don t know how pushed pencil. know kind of dance experimentally measure number accurately, don t know kind of dance on computer make number come out, without putting in secretly!

the analog of fine structure constant gravitation gravitational coupling constant. constant requires arbitrary choice of pair of objects having mass. electron , proton natural choices because stable, , properties measured , understood. if αg calculated masses of 2 protons, value ≈10.

standard model

the original standard model of particle physics 1970s contained 19 fundamental dimensionless constants describing masses of particles , strengths of electroweak , strong forces. in 1990s, neutrinos discovered have nonzero mass, , quantity called vacuum angle found indistinguishable zero.

the complete standard model requires 25 fundamental dimensionless constants (baez, 2011). @ present, numerical values not understood in terms of accepted theory , determined measurement. these 25 constants are:

the fine structure constant;
the strong coupling constant;
fifteen masses of fundamental particles (relative planck mass mp = 7019122089000000000♠1.22089(6)×10 gev/c), namely:

six quarks
six leptons
the higgs boson
the w boson
the z boson


four parameters of ckm matrix, describing how quarks oscillate between different forms;
four parameters of pontecorvo–maki–nakagawa–sakata matrix, same thing neutrinos.


cosmological constants

the cosmological constant, can thought of density of dark energy in universe, fundamental constant in physical cosmology has dimensionless value of approximately 10. other dimensionless constants measure of homogeneity in universe, denoted q explained below martin rees, baryon mass per photon, cold dark matter mass per photon , neutrino mass per photon.

barrow , tipler

barrow , tipler (1986) anchor broad-ranging discussion of astrophysics, cosmology, quantum physics, teleology, , anthropic principle in fine structure constant, proton-to-electron mass ratio (which they, along barrow (2002), call β), , coupling constants strong force , gravitation.

martin rees s 6 numbers

martin rees, in book 6 numbers, mulls on following 6 dimensionless constants, values deems fundamental present-day physical theory , known structure of universe:

n ≈ 10: ratio of fine structure constant (the dimensionless coupling constant electromagnetism) gravitational coupling constant, latter defined using 2 protons. in barrow , tipler (1986) , elsewhere in wikipedia, ratio denoted α/αg. n governs relative importance of gravity , electrostatic attraction/repulsion in explaining properties of baryonic matter;
ε ≈ 0.007: fraction of mass of 4 protons released energy when fused helium nucleus. ε governs energy output of stars, , determined coupling constant strong force;
Ω ≈ 0.3: ratio of actual density of universe critical (minimum) density required universe collapse under gravity. Ω determines ultimate fate of universe. if Ω ≥ 1, universe experience big crunch. if Ω < 1, universe expand forever;
λ ≈ 0.7: ratio of energy density of universe, due cosmological constant, critical density of universe. others denote ratio




Ω

Λ




{\displaystyle \omega _{\lambda }}

;
q ≈ 10: energy required break , disperse instance of largest known structures in universe, namely galactic cluster or supercluster, expressed fraction of energy equivalent rest mass m of structure, namely mc;
d = 3: number of macroscopic spatial dimensions.

n , ε govern fundamental interactions of physics. other constants (d excepted) govern size, age, , expansion of universe. these 5 constants must estimated empirically. d, on other hand, nonzero natural number , cannot measured. hence physicists not deem dimensionless physical constant of sort discussed in entry.

any plausible fundamental physical theory must consistent these 6 constants, , must either derive values mathematics of theory, or accept values empirical.