Re: [Phys-l] Relativity Question about spring

[Hugh Haskell <hhaskell@mindspring.com>]

At 11:46  +0800 5/10/07, <carmelo@pacific.net.sg> wrote:
> So, the increase in elastic potential energy of a spring will 
> effectively increase the spring's mass. The increase in 
> gravitational potential energy of a muon will increase the muon's 
> mass. If a muon is moving towards the earth, its mass would 
> decrease. This seems to be John's conclusion. :-)
I don't think so. The issue is, what is the system. In the case of 
gravity, it clearly is the "gravitor" and the "gravitee," if it is 
even possible to make that distinction. That is, the earth and the 
ball become more tightly bound to each other as the ball rolls down 
the incline, and so the mass of the earth *and* the mass of the ball, 
collectively decrease. It makes no sense to talk about either the 
mass of the earth *or* the mass of the ball individually changing, 
although it seems reasonable to me that to the extent one can torture 
the theory to actually talk about the changes in individual masses, 
that this change would be distributed in proportion to the original 
masses of each, in which case, most of the change would have to be 
attributed to the earth rather than the ball. there may be good 
arguments that would allow one to attribute the change to the ball, 
or at least mostly to the ball, but I don't know of them if they 
exist.

In the case of nuclei we don't even try to measure the change of mass 
of the individual nucleons when they go from a free state to a bound 
one. All we ever talk about is the change in mass of both of them 
together, which, contrary to the gravitational case, is readily 
measurable. But no one says that the neutron "loses such and such a 
mass" when it becomes bound to a proton, we only talk about the 
deuteron mass being less than the collective masses of the proton and 
neutron as free particles.

In the case of the spring, the situation is similar, except that it 
represents an increase in the system's internal energy rather than a 
decrease, so it makes sense to talk about an increase in the mass of 
the spring as a whole. In this case the spring is the entire system, 
so it makes sense to talk about the change in mass of the spring, but 
not of any particular part of the spring, except to the extent that 
we can infer how the internal energy we have added to the spring by 
compressing it is distributed within the spring.

In the case of nuclei, again, since the neutrons and protons are of 
approximately equal mass, it makes sense to infer that the change in 
mass is approximately equally distributed among the nucleons, but 
that is hardly required, since we only talk about the mass of the 
nucleus as a whole in normal circumstances, and when we removed a 
nucleon or an alpha particle from a nucleus, we only talk about the 
individual nucleon or alpha in connection with the residual nucleus, 
and not in terms of the still bound nucleons.

Hugh
--

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Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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