notes@ucbcad.UUCP (10/26/83)
#N:ucbcad:22400002:000:311 ucbcad!kalash Oct 25 22:36:00 1983 A question a couple of friends and I came up was, how do you convert energy into mass? We can figure out, and know about how to convert mass into energy (drop it inside a hydrogen bomb for one), but can anybody do the reverse? We couldn't come up with any examples out side of the Big Bang. Thanks, Joe
guy@rlgvax.UUCP (Guy Harris) (10/27/83)
Since, in relativistic terms, mass and energy are not separate things which
are interconvertible but are actually the same thing (ignoring the question
of whether mass as measured by the force required to accelerate something -
"inertial" mass - is the same as mass as measured by the force exerted on
the object by gravity - "gravitational" mass), the distinction between mass
and energy is more a distinction between the form of the mass/energy.
Generally, "mass" refers to the "rest mass" of something with significant
rest mass, where most of the energy that the object has is due to its rest
mass - if you make a ball go faster its mass increases because its energy
increases, but the difference is extremely small relative to the "rest energy"
of the ball. Something having a mass of 10 grams has a rest energy of 10 grams
times C^2, which is (3E10 cm/sec)^2, giving 9E21 grams-cm^2/sec^2. Such an
object moving at 4.5E3 cm/sec, which is 100 mi/hour, has a kinetic energy
of 1/2 m*v^2, which is 1.01E8 grams-cm^2/sec^2, which is about 18 orders of
magnitude less than the rest energy. "Energy" in the case you mention
generally refers to the energy of something with no rest mass; i.e. electro-
magnetic radiation. As such, a nuclear explosion (or a chemical explosion)
converts the rest mass/rest energy of the explosive materials into the
kinetic energy of what's left after the explosion (although all that kinetic
energy *does* remain as mass, because the flying pieces have greater mass due
to their greater kinetic energy) and into the kinetic energy of electromagnetic
radiation from the explosion (which, since it has no rest mass and can't
stop moving, has only kinetic energy).
One process which goes the other way would be that of breaking up the
products of a fusion or chemical reaction, or fusing the products of a
fission reaction, with the addition of electromagnetic or strong nuclear
energy. In a chemical reaction which requires energy input, the final products
would have more mass than the inputs (although the same 18 orders of magnitude
would come in and you'd need the kinetic energy of 1E18 balls moving at 100MPH
to produce an increased mass equal to the mass of one of those balls). One
other such reaction is "pair production". A photon of electromagnetic energy
interacts with the electromagnetic field of a nucleus and becomes a pair of
a particle and its antiparticle, such as an electron and a positron. This
is probably the purest form of the kind of reaction you're looking for, as
it converts a photon (which has no rest mass and acts more like what people
conventionally think of as "pure energy" than most anything else) into
particles of the type that make up everyday matter.
Guy Harris
{seismo,mcnc,brl-bmd,allegra}!rlgvax!guyjames@umcp-cs.UUCP (10/27/83)
I think that, impractically speaking, one procedure is to get an extremely high frequency laser, shoot out a cosmic ray, and some small percentage of these rays will spontaneously turn into an electron and a positron. To lower your expenses, make sure to collect the other cosmic rays a short distance away, and feed them back into the laser again. I think some cosmic rays will turn into a pair of electrons, but I'm less sure of this. --Jim O'Toole
james@umcp-cs.UUCP (10/27/83)
Guy: Your statement concerning increased mass in energy-consuming chemical reactions doesn't make sense to me. I think the popular interpretation (mine, at least) is that the energy absorbed by the reaction is still 'present' in the form of potential energy. In other words, some electron or another (or all the electrons collectively) is 'farther away' from the nucleus (i.e. in a higher energy state), and thus has more potential energy. I think an example of this would be the expected value of the potential energy operator in the ground and first-excited states of the hydrogen atom. Surely a photon causing the electron to move into the first-excited state would consume energy. The value of <V(r)> = <Y|V(r)|Y> would be higher for the first-excited state wave function, so I would say that is where the energy went. --Jim O'Toole
guy@rlgvax.UUCP (Guy Harris) (10/27/83)
I think the popular interpretation (mine, at least) is that the
energy absorbed by the reaction is still 'present' in the form of
potential energy.
Yes, this is correct, but in the new state the higher potential energy will
relativistically translate into a higher mass for the products of the
reaction.
I think an example of this would be the expected value of the
potential energy operator in the ground and first-excited states
of the hydrogen atom.
Again, since an atom in an excited state has higher rest energy than the
same atom in the ground state, it will have a higher (rest) mass. If the
quark model of particles like protons, neutrons, and pi-mesons is taken,
since those particles are composite they have excited as well as ground
states. There are families of particles which are considered ground and
excited states of a given quark combination; the excited states have higher
mass.
Guy Harris
{seismo,mcnc,brl-bmd,allegra}!rlgvax!guyquark@dartvax.UUCP (10/27/83)
Yes, you do get an electron - positron pair from photon decay, but electron - electron pairs are impossible because, among other things, charge is not conserved in the interaction. Also, and I'm sorry to seem so picky, but cosmic rays consist of alpha particles, protons, etc. in addition to photons. One can get mass from energy in a fusion reaction (you also get energy), so this isn't all one into the other, but it is another possibility.
CSvax:Pucc-H:Physics:dub@pur-ee.UUCP (10/28/83)
How to convert energy into mass?
For large scale production of mass that is a tricky question
I think. But if you just want to see a little mass being created
you can look at bubble chamber photos and they'll probably show
it.
For example, into the vicinity of other atoms, two photons
(energy) can meet and create an electron & positron (massive).
As to creating mass at the time of the big bang, reading
"The First Three Minutes" by Weinberg.
D. Bartholomew
{decvax}!pur-ee!physics!dubbane@umcp-cs.UUCP (11/01/83)
The most 'concrete' example I can think of is what happens in a collision
between an electron and a positron in a colliding-ring accelerator. The
KE of the two particles ends up as mass in the particles created by the
collision.
--
Arpa: bane.umcp-cs@CSNet-relay
Uucp:...{allegra,seismo}!umcp-cs!banecrandell@ut-sally.UUCP (Jim Crandell) (11/02/83)
Here's an example that's very common, and it doesn't require anything
nearly as exotic as a high-frequency laser that emits x-rays (a spot
of Cs-137 will do nicely). It's been a few years, but I vaguely recall
from working with a NaI scintillation detector that the spectra I obtained
were often rendered faintly misleading by -- though one learns to work
around it -- an irrelevant response peak at about 511 kev. That energy
level just happens to be that of the photons emitted from electron/positron
annihilations. Where did the positrons come from? Well, some of those
1+ Mev photons that the Cs-137 pours out sorta get caught in the web of
that darned ol' NaI crystal, and they sorta lose some energy. Sure, a
lot of them do it by kicking valence electrons out of their orbits or by
undergoing funny kinds of collisions with all those massive particles,
but a few manage to turn about 511 kev of it (there's that number again)
directly into mass in the form of a positron and an electron; you have
to have one of each, because you don't want the crystal taking on a net
charge. Naturally, with all those charged particles around, neither the
positron nor the electron gets very far, and right away (on the average)
you get annihilation, with its attendant "ann. rad.".
By the way, the materials used to make proportional radiation detectors
are certainly NOT the only ones in which pair production occurs; however,
you're not likely to notice it elsewhere, for reasons which I hope are
obvious.
--
Jim ({ihnp4,kpno,ut-ngp}!ut-sally!crandell or crandell@ut-sally.UUCP)speaker@umcp-cs.UUCP (11/05/83)
Hey, I seem to remember a REALLY BAD science fiction film with this as the theme... "We know the secret of one half of the process... how to convert mater into energy. And they know the secret to the other half... converting energy to matter. Now they've come to earth to steal the secret and conquor the universe." Uuugghh! Anyone remember this one? -- - Speaker-To-Stuffed-Animals speaker@umcp-cs speaker.umcp-cs@CSnet-Relay
Shinbrot.WBST@PARC-MAXC.ARPA (11/07/83)
Alternatively, "How to convert energy into mass?" You can just observe a 1 MeV gamma-ray passing through a magnetic field. The 'virtual' positron-electron pairs can be split by the field into actual electrons and positrons. Converting energy into mass without anti-particles is not, to my understanding, possible*. - Troy *although some funny-business can be done, yielding quarks and anti-quarks in boson-pairs [e.g. u(d-) + (u-)d].
Shinbrot.WBST@PARC-MAXC.ARPA (11/08/83)
Corection: *although some funny-business can be done, yielding quarks and anti-quarks in MESon-pairs [e.g. u(d-) + (u-)d].