mistermack wrote:ChildInAZoo wrote:mistermack, you again ignore the fact that we have different kinds of clocks in the form of physical systems that act according to different kinds of principles. They all agree on time dilation, so you cannot simply appeal to some kind of common physical operation to explain time dilation.
Read that back to yourself, and try to see how illogical it is.
If you have many very different things behaving in an identical manner, you would obviously suspect something common to them all, would you not?
.
CIAZ's point is that the effect must be common to many different mechanisms. Space-time geometry fits. But just for the Hades of it, let's see what physical mechanisms were used to test time dilation.
I'll be using hbar = c = 1, and the fine-structure constant a = e
2/(4*pi) in typical particle-physics units. I'll be including the effects of various other parameters, like particle masses, but omitting factors independent of these, factors which may require large amounts of numerical computation.
Ives-Stilwell - time dilation of atomic spectral lines. Those lines' energies is a result of electrons orbiting nuclei, and to lowest order, those energy values are proportional to m
ea
2.
Atomic-Clock Experiments and GPS - atomic clocks, which use hyperfine transitions: electron-nucleus magnetic-dipole and electric-quadrupole effects.
The magnetic-dipole effects have sizes (electron magnetic-dipole moment) * (nuclear magnetic-dipole moment) / (separation)
3 and are about
m
e(m
e/m
N)a
4
The electron magnetic-dipole moment can be from its orbit as well as from its spin. Likewise for the nucleus, with contributions from both nucleons' spin and protons' orbits.
The electric-quadrupole effects have sizes (electron charge) * (nuclear electric-quadrupole moment) / (separation)
3 and are about
m
e(m
e/m
N)
2a
4
Muon Decay - it happens by way of weak interactions, and its rate is
m
mu(m
mu/m
V)
4
where m
V is the Higgs vacuum-field strength in the Standard Model, which is about 300 GeV.
Further Details. To sum up, we have two electromagnetic effects and one weak-interaction effect.
Furthermore, the masses are determined by other interactions. Lepton and quark masses are y*m
V, where y is the coupling constant between each flavor of elementary fermion and the Higgs particle. For multiple Higgs multiplets, it gets more complicated, but the overall principle is the same. Nucleon masses and sizes, however, are dominated by the QCD energy scale, where the effective QCD coupling constant is around 1.
).
