Brother Hugh raises some questions that deserve more
analysis than they have heretofore received.
Notion A: Invariant mass.
Notion B: Mass deficit: The mass of a deutron is
measurably less than the mass of its contituents.
Note: This isn't about terminology. What
used to be called "rest mass" is nowadays
just called "mass", and it's invariant.
But as usual, terminology isn't the main
issue. There's real physics lurking here.
So we face the question: Is mass invariant or isn't it????
1) For starters, we need to ask, invariant with
respect to WHAT? The mass, being the length of
a 4-vector, is invariant w.t.t boosts and rotations.
So we need to restate notion (A) as follows:
Notion A2: Mass is invariant w.r.t Lorentz transformations.
Assembling a deuteron requires a lot more than
just a Lorentz transformation. Therefore there
is no conflict between Notion (A2) and Notion (B).
Notion (A2) just doesn't cover all the ground that
needs to be covered.
2) Suppose we glue a 1kg chunk of steel to a 1kg
chunk of brass ... and the result is more than 2kg.
That wouldn't bother anybody; we assume the excess
is just the mass of the glue.
We face difficulties applying this picture to the
deuteron, because the whole is _less_ than the sum
of the parts, and it's hard to imagine that the
"glue" has negative mass.
3) We need the notion of "dressed states". You
can consider the mass of a proton to be at least
partly due to the self-energy of the fields that
it produces. When you drag the proton around,
you have to drag the fields along with it, and
they contribute to the inertia.
In the deuteron, the nuclear field of the proton
is partially cancelled by the nuclear field of
the neutron. This is analogous to the hydrogen
atom in which (in the far-field regime) the
electric field of the proton is nearly cancelled
by the electric field of the electron. In either
case, there is less energy and less inertia in
the fields.
4) Relativity has some very specific things to
say about conservation of mass + certain forms
of energy. This is nontrivial. It is by no means
a simple corollary of the Lorentz invariance
mentioned above (Notion A2). If you think you
fully understand this, please have a look at http://www.monmouth.com/~jsd/physics/gravity-source.htm
In this case things are pretty simple, and you
can use E=mc^2 to connect the deuteron's mass
deficit to its energy of formation.
This posting is the position of the writer, not that of Bert, Ernie,
Oscar, or Elmo.
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.