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S14b. Does the standard model predict chemistry?
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The standard model is widely believed to be in agreement with
all we know about matter and radiation on earth, within the range of
accessible energies, as long as gravitational effects can be neglected.
But this does not mean that it has a high predictivity, except
on the level of high energy elementary particle scattering.
The reason is that we can compute from it almost nothing at the scales
of interest in nuclear, atomic, or molecular physics.
Lattice gauge calculations show that the standard model implies the
existence of baryons such as proton and neutron with masses that
match the experimental masses with an accuracy of about 5%.
This is far too low to be of use in chemistry or even in nuclear
physics. The accuracy of the effective forces between them is even
poorer.
We have very little control over confinement, which is essential to
get useful forces at the energies relevant for nuclear physics.
Thus predictivity of the standard model for nuclear information
is almost nil.
And indeed, nuclear physicists do not use the standard model
(except for paying religious lip service to it), but work with
their own phenomenological models. They just borrow some of the
symmetries. These were of course known long before the standard
model was born, and built into the latter to match reality; so they
cannot count as predictions from the standard model.
If we had only the standard model and the numerical estimates
for the constants of effective actions computed from it,
this would give _very_ poor predictions of properties of protons,
neutrons, and their bound states.
One can show that the effective dynamics of protons and neutrons is
governed by effective field theories whose form can be derived
from the standard model (but also follows from assumed symmetry
principles built into the standard model) but whose coefficients
are derived by fitting calculations to _measured_ data about form
factors of proton and neutron, which have _not_ been calculated
from the standard model but must be put in by hand as additional
information.
From this, one can calculate the energy of the nuclei, using a combined
droplet/shell model. We understand the structure of nuclei, in agreement
with the standard model, but _not_ derived from it.
If we had only the standard model and the numerical estimates computed
from it, this would give _very_ poor predictions of nuclear properties.
There would be neither nuclear energy nor nuclear weapons based on
knowledge derived form the standard model only.
Even knowing the properties of proton and neutron from measurement
and the effective equations (but nothing else) does not allow to get
highly accurate predictions for the properties of larger nuclei.
At atomic distances from the nucleus (for QED-dominated phenomena),
one can further approximate the theory by Dirac-Fock equations,
or, for light nuclei, by Schroedinger's equation
for electrons and nuclei together with relativistic corrections.
The details of the nuclei become irrelevant for atomic physics and
chemistry, except for their atomic weights. These cannot be derived
accurately enough from lower levels, and must again be supplemented by
additional experimental information.
If we had only the standard model and the numerical estimates computed
from it, this would give _very_ poor predictions of most chemical
properties of everything including the hydrogen spectrum.
Only starting on this level, _assuming_ the properties of the nuclei
and the electron, we are able to predict much of macroscopic physics:
We can solve the Dirac equation exactly for hydrogen, and
compute the radiation corrections from QED and other corrections from
the Standard Model. It agrees with the experimental measurement of
hydrogen spectra to extraordinary accuracy. We can understand why the
periodic table works, and predict the properties of even large
atoms (such as the color of gold) reasonably well using the Dirac-Fock
equations.
From this level on upwards, one has enough experimental data to
calculate chemical information for small molecules that is predictive
in the sense that it may give quantitative information that is
reasonably accurate and not put in by hand.
But already for proteins, one again needs to complement the theoretical
input by measurements to get predictions of reasonable accuracy.
Thus the standard model is a very inaccurate tool for chemistry.
It is useful only for elementary particle scattering experiments.
At each higher level, one needs additional information from
experiment to complement the predictions of the lower levels.