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From: cpf@lasspvax.UUCP (Courtenay Footman)
Newsgroups: net.physics
Subject: Re: A question about mass and energy
Message-ID: <391@lasspvax.UUCP>
Date: Sun, 14-Jul-85 15:33:41 EDT
Article-I.D.: lasspvax.391
Posted: Sun Jul 14 15:33:41 1985
Date-Received: Wed, 17-Jul-85 20:33:10 EDT
References: <378@sri-arpa.ARPA> <835@ihlpg.UUCP>
Reply-To: cpf@lasspvax.UUCP (Courtenay Footman)
Organization: LASSP, Cornell University
Lines: 58
Summary: 

>> 
>> In physics I was taught that energy is not a substance and does not have
>> a definite location.
>> 
>> However relativity says that energy is/has mass.  Mass does have a
>> definite location.
>> 
>> If energy is mass, how can it be and not be in a definite location?  If
>> energy has mass, where is the gravitational field caused by that mass if
>> it has no definite location?
>> 
>> Dan
>
>An excellent question.  The answer is simply that energy DOES have a
>definite location (at least if we ignore quantum effects).  In
>elementary physics, concepts such as potential energy prove useful.
>The potential energy is viewed as a property of the entire configuration
>of the system, rather than as a local quantity.  In a more sophisticated
>formulation, we see that the potential energy can be explained as the
>energy stored in the gravitational or electromagnetic field.  The energy
>density of the electromagnetic or gravitational field is well defined
>at every point, i.e. has a definite location.
>-- 
>Bill Tanenbaum - AT&T Bell Labs - Naperville IL  ihnp4!ihlpg!tan
Unfortunately, this is not totally correct.  Most energy can be located
someplace;  for example, electromagnetic energy has a well defined location
(E**2/(8*pi) + B**2/(8*pi).  Since EM energy has a well defined location,
that means that most forms of energy have a well defined location, since
EM accounts for most everyday phenomena (in particular, chemistry).  
Kinetic energy is also not a problem, and so heat is O.K. also.  
    The problem is gravitation.  All other forms of energy have (at least)
one thing in common:  in general relativity, they are source terms on
the right hand side of Einstein's field equation, G = 8piT.  That is, they
curve space, and cause a relative geodesic deviation of nearby world lines
that pass through that region of space.  No such thing is true of any
definable "local gravitational energy" because of the equivalence principal.
The equivalence principal implies that for every neighborhood in space-time
there is a coordinate frame in which all local gravitational fields 
disappear.  (I.e., all Christoffel symbols vanish.)  Thus any attempt
to define a local gravitational energy (or, more precisely, an energy
momentum tensor) will fail.
     Note, however, that gravitation does contribute to the energy;  
the energy of the solar system is less than the energy that the system
would have if its parts were at infinite separation.  That is undeniable.
What is deniable is the localizability of gravitational energy.  
Gravitational energy is a global effect, caused by global curvature.
     This difficulty is why it took seventy years after the discovery of
GR to prove that the total energy in a region surrounded by asymptotically
flat space is positive, because, by choosing an appropriate coordinate
system, you can make the energy at any point whatever you want.

Most of this argument was take from Misner, Thorne, and Wheeler, 
"Gravitation", p466ff.

-- 
Courtenay Footman			arpa:	cpf@lnsvax
Newman Lab. of Nuclear Studies		usenet:	cornell!lnsvax!cpf
Cornell University