Re: Lost Mass in Chemical Reactions

From: Franz Heymann (notfranz.heymann_at_btopenworld.com)
Date: 02/03/05 

Date: Thu, 3 Feb 2005 15:41:48 +0000 (UTC)

"Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
news:1107425184.140856.324390@g14g2000cwa.googlegroups.com...
> Franz Heymann wrote:
> > "Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
> > news:1107419265.283350.31930@l41g2000cwc.googlegroups.com...
> > > Franz Heymann wrote:
> > > > "Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
> > > > news:1107378095.841131.187810@l41g2000cwc.googlegroups.com...
> > > > > Franz Heymann wrote:
> > > > > > "Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
> > > > > >
news:1107304573.203720.128920@c13g2000cwb.googlegroups.com...
> > > > > > > Franz Heymann wrote:
> > > > > > > > "Richard Tobin" <richard@cogsci.ed.ac.uk> wrote in
> message
> > > > > > > > news:ctot9f$2ovr$1@pc-news.cogsci.ed.ac.uk...
> > > > > > > > > In article <cton64$7u2$1@hercules.btinternet.com>,
> > > > > > > > > Franz Heymann <franz.heymann@btopenworld.com> wrote:
> > > > > > > > >
> > > > > > > > > I'm confused about the terminology for mass,
invariant
> > > mass,
> > > > > etc
> > > > > > > > > so please take the questions below as serious
> questions.
> > > > > > > > >
> > > > > > > > > >Please let us not have this yet again. The term
> "mass"
> > of
> > > > a
> > > > > > > system
> > > > > > > > is
> > > > > > > > > >used nowadays to refer to the energy of the system
in
> > its
> > > > CM
> > > > > > > > > >coordinates.(Divided by c^2).
> > > > > > > > > >
> > > > > > > > > >A photon always travels at a speed c. Only if its
> mass
> > is
> > > > > zero
> > > > > > > can
> > > > > > > > > >that be achieved without emdowing it with an
infinite
> > > > amount
> > > > > of
> > > > > > > > > >energy.
> > > > > > > > >
> > > > > > > > > So a photon has no mass, but a system of two photons
> > > > travelling
> > > > > > in
> > > > > > > > > opposite directions does have mass?
> > > > > > > >
> > > > > > > > That is quite correct.
> > > > > > > >
> > > > > > > > Mass is not an additive property of a particle.
> > > > > > > >
> > > > > > > > > And if I take a box containing a particle and its
> > > > > anti-particle,
> > > > > > > > does
> > > > > > > > > its mass change when they collide? Presumably not,
and
> > the
> > > > > mass
> > > > > > of
> > > > > > > > > the matter is now the mass of the energy of the
> > resulting
> > > > > > photon.
> > > > > > > >
> > > > > > > > Let's get a small thing out of the way first:
> > > > > > > > The final number of photons which result from an
> > annihilation
> > > > via
> > > > > > an
> > > > > > > > electromagnetic interaction has to be 2 or more. Now I
am
> > in
> > > a
> > > > > > > > position to say that the CM energy of the two
particles
> > which
> > > > > > > > annihilate is the same as the CM energy of the
resulting
> > > > photons.
> > > > > > > >
> > > > > > > > Dividing both sides by 2 says that the mass of the
> photons
> > is
> > > > the
> > > > > > > same
> > > > > > > > as the mass of the initial particles. As an addendum,
> > > > rermember
> > > > > > that
> > > > > > > > the mass of the initial particles may well be more
than
> > the
> > > > sum
> > > > > of
> > > > > > > > their indiviual masses.
> > > > >
> > > > >
> > > > > >>>This is because the mass of the initial
> > > > > > > > particles is the total energy in their CM system
(divided
> > by
> > > > > c^2).
> > > > > > > If
> > > > > > > > they are in relative motion in their CM coordinates,
> their
> > > > energy
> > > > > > > will
> > > > > > > > be more than the sum of their rest masses (times c^2)
> > > > > > > > Franz
> > > > >
> > > > > > > Ah not one of Franz's better posts, but there's
> > > > > > > sufficient junk in it to skip replying.
> > > > > >
> > > > > > Apart from saying "2" instead of "c^2" in one place, I
defy
> > you
> > > to
> > > > > > find any error in that post.
> > > > > > Franz
> > > > >
> > > > > Well that "2" did confuse, but letting that pass
> > > > > you're a bit ambiguous otherwise.
> > > > >
> > > > > A good analogy is using an Atomic bomb,
> > > > >
> > > > > It starts with a rest mass, and after detonation
> > > > > has less rest mass but more kinetic energy.
> > > > >
> > > > > What reamins the same is
> > > > >
> > > > > Energy = p_0*gamma = an invariant constant.
> > > >
> > > > Energy is not an invariant. It is one component of a
> four-vector.
> > > It
> > > > is conserved in any given inertial frame.
> > > > >
> > > > > where p_0 = rest mass.
> > > > >
> > > > > Prior to detonation gamma=1, afterward gamma>1.
> > >
> > > > > The diff is evidently a lot of heat and kinetic energy.
> > > >
> > > > Both heat and kinetic energy can contribute to mass.
> > >
> > > That's right, put the bomb in a box on a weigh
> > > scale, then blast it, of course nothing goes in
> > > or out of the box then,
> > >
> > > p = p_0 *gamma = p'_0 *gamma' = invariant.
> > >
> > > The primed are the same bomb but detonated, and
> > > have a substantial kinetic energy component from
> > > the latent rest mass energy denoted by p_0.
> > >
> > > gamma=1, gamma'>1, p_0 > p'_0, p is invariant.
> >
> > Previously you said "Prior to detonation gamma=1, afterward
> gamma<1."
> > Which do you consider to be right?
>
> Oh-poop it was an obvious typo, I corrected it,
> move on...life is short.

Unfortunately both gamma <1 and gamma > 1 are wrong in this case, so
where do you go from here?
>
> > I offer you the following:
> >
> > The initial and final momenta of the system are both zero and the
> > gamma of the CM of the system is 1 before and after the
detonation.
>
> Of course, momenta is vector sum, kinetic energy is
> magnitude sum, i.e. a function of v^2.

I take it then that you agree that gamma is 1 both before and after
the detonation.

> > > Also note gamma = dx^0/ds.
> >
> > Why should I note this?
> > And whose x0 are you talking about?
>
> x^0 = ct, and s^2 = (ct)^2 *(1-v^2/c^2)
> where gamma = 1/(1-v^2/c^2).

About whose x0, s and gamma are you talking?
And you still have not said why I should note what the value of that
gamma is.

> > > For the serious reader, see P.G. Bergmann's
> > > "Intro ...Relativity", Eq.(6.19), I recommend
> > > the entire chapter 6. If anyone wants to discuss
> > > it I'd be more than happy to.
> >
> > You should read it quite a few more times before committing
yourself
> > to such a discussion.
>
> Evidentally you don't own that book,
> as any serious researcher would,

As an even more serious ex-researcher and ex-teacher I prefer
d'Inverno.

> Evidentally

I presume the word you want is evidently.

> you don't own that book,
> as any serious researcher would, don't
> be so damn cheap. I bought the soft cover
> Dover edition when I was a punk back in
> the 70's for $5.00 when the revised edition
> of it first came out.

You beat me there. d'Inverno is a later book and it cost me roughly
ten times as much as yours.

> If you can't afford
> the damn book I'll pay for it. It's the
> least I can do to prop up that impoverished
> welfare state aka germany.
I have heard it said that Bergmann's book is quite reasonable, so you
would probably benefit by reading it as well as owning it.

Franz

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