Joshua said:
> Anything close to accurate?
Not too bad.
> Anyway, my question: does anyone have any idea how the concept of mass
> as caused by the Higgs field maps to GR's notion of mass causing
> distortions in spacetime? The "billiard balls on a rubber sheet"
> analogy make perfect sense to me until we rip the masses out of the
> picture as a fundamental property of matter. Help!
The thing that causes curvature of spacetime is something called the
"stress-energy tensor", which measures how energy and momentum are
flowing at a certain point (mass just being a type of energy). If you
have a field then you can work out its stress-energy tensor and then
work out how that affects spacetime.
While we're on the subject, here's something I wrote for the Culture
when the subject of the Higgs boson came up over there:
All our theories of particle physics are based on "local gauge
symmetries", which are rules for changing the properties of the various
fields independently at each event in such a way that the laws of
physics are unchanged (the changing of properties is the "gauge" part,
the unchanged bit is reflected in the "symmetry" part and "local" means
"at each event"). For instance, if you take the law of motion of a
particle and try to modify it so that it has a "local U(1) symmetry"
(i.e. so that the law is unchanged by arbitrary changes of phase) then
you're forced to modify the "derivatives" that tell you how properties
vary from event to event so that they take into account the changes in
phase. The extra bits that you have to add to the derivatives in the
equation are so-called gauge fields, and they're responsible for forces.
To go back to the local U(1) symmetry, for example, the gauge field you
have to introduce turns out to obey Maxwell's equations, and so it's the
electromagnetic field! Similarly, it turns out that the strong and weak
nuclear forces are also based on (less simple) gauge symmetries.
However, there's a problem: if you try to do all this for particles with
mass then it just doesn't work. The mass terms in the equations turn out
not to be symmetric under the local gauge change, because it's an
experimental fact that the weak gauge fields only interact with "left
handed" fermions (i.e. fermions whose spin is pointing in the opposite
direction to the direction of their motion). The Higgs mechanism is a
way of sorting this out: what looks to us like the particles having a
rest mass is really the energy associated with the interaction between
the particles and the Higgs field. When you do a local gauge change, the
Higgs field transforms in such a way that the "mass" term in the
equation is also invariant. The mass of a particle is thus a measure of
how strongly it interacts with the Higgs field. Why the various
interaction strengths should take the values they do is currently
utterly mysterious.
Now, just as the electroweak field has quantised excitations called
"photons", "W+/- bosons" and "Z0 bosons", and the strong force field has
excitations called "gluons" (and, of course, the excitations of the
matter fields are particles like quarks, electrons and neutrinos), so
the Higgs field has excitations called Higgs bosons. The Standard Model
of particle physics constrains the mass of these Higgs boson to be low
enough that they should be detectable in the next generation of particle
accelerators (or else the particle physicists will have to come up with
some clever new ideas about mass). It's just possible, though, that the
Higgs particles might have a low enough mass to be found by our current
accelerators, and the recent fuss in the news concerns the possibility
that Higgs bosons have been found by the Large Electron-Positron
accelerator at CERN (which found the W and Z bosons in the 1980s). LEP
was due to be shut down about now so that the tunnel can be used to
build the more powerful Large Hadron Collider, but it's been reprieved
for a couple of months to see if they've really found Higgs bosons. If
they have, then we'll have found all the particles predicted by the
Standard Model and can go looking for more exotic things.
Rich
GSV Not An Expert
