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Re: The energy



Regarding Michael's question:

Well... what exactly was the "big bang?"

The beginning of the expansion of the universe.

Was it not some sort of big "conversion" of energy into matter and
antimatter?

Supposedly a lot of particle-antiparticle pairs were created by the
release of the latent heat associated with the global background
value of the Higgs field dropping its potential energy from the
U(1)xSU(2)-symmetric (zero) value to the symmetry-broken ground
state (nonzero) value that exists today. This transition supposedly
propelled the expansion of the inflationary epoch.

If not, where did the matter and antimatter come from?

From the vacuum (as it transitioned to a lower potential energy
value and as it acquired a spontaneous nonzero background value of
the Higgs field).

And what exactly does E=mc^2 mean?

Actually the equation ought to read E_0 = mc^2. It means that
associated with every object/system of mass m is a rest energy
E_0 that has the value mc^2. This rest energy is the minimal
energy possessed by the object as observed over the entire
set of all inertial reference frames. The inertial frame for which
the energy has this minimal value is the one in which the object
has zero total momentum and corresponds to the inertial frame in
which the object's center of mass is currently at rest. This rest
energy can also be thought of as the total internal energy of the
object/system. This total composite rest energy includes the rest
energies of the system's constituent parts *and* the energies of
relative motion and interaction *among* those parts (including any
thermal energy) as seen in the frame in which the system's center
of mass is not moving.

Doesn't it mean mass and energy are equivalent?

It means that mass and rest (total internal) energy are equivalent.

If the object as a whole is immersed in an externally imposed force
field of some kind the overall total potential energy of the object
as a whole in that force field is not counted toward its
mass/rest energy/total internal energy/ value.

When dealing with the complications of curved space-time the local
inertial frame in which the object is taken to be instantaneously at
rest is one that is freely falling at the instantaneous location of
the object.

If the object is so spatially large that there are substantial
curvature effects over the extent of the object itself then the
notion of the system's own localized mass and rest energy become a
bit ambiguous for an arbitrary general space-time manifold in which
the object resides. But if the system happens to be embedded in an
asymptotically flat externally empty and static space-time then the
ambiguity can be removed by looking at the far field leading order
Schwarzschild correction to the geometry asymptotically far from the
object. This leading correction is proportional to the total mass
energy of that embedded gravitating system/object and that
mass-energy *includes* the gravitational field energy of the object.
Normally the gravitational field's energy is ill-defined in an
arbitrarily curved space-time because the gravitational field is not
a tensor field but is the non-tensorial Levi-Civita connection. But
in the special case of an asymptotically flat externally empty and
static spacetime then the ambiguity can be erased by simply declaring
that the preferred frame in which things are measured is one that is
inertial asymptotically far from the object and which the object is
not globally translating. The mass/energy measurements/calculations
are then done with respect to the background flat Minkowski metric
that the actual metric asymptotically approaches far from the object.

Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu

David Bowman