[IP] more on Brian Greene: That Famous Equation and You

[David Farber <dave@farber.net>]

Begin forwarded message:

From: Vadim Antonov <avg@kotovnik.com>
Date: September 30, 2005 5:26:49 PM EDT
To: David Farber <dave@farber.net>
Subject: Re: [IP] more on Brian Greene: That Famous Equation and You




> From: Brian Sniffen <bts@alum.mit.edu>
> Date: September 30, 2005 2:22:46 PM EDT
>
>
> > Alas, the above are common misconceptions that bear correcting. When
> > one burns gasoline, one doesn't convert any of its mass into energy.
>
> This certainly does involve a change in mass.

That is absolutely correct.


> > It's the equivalent of allowing an anvil to descend from the top of
> > a building to the bottom, and using a rope attached to the anvil to
> > turn a shaft or do other work as it falls. The anvil has precisely
> > the same mass at the bottom as it did at the top; it merely has less
> > gravitational potential energy because it is closer to the center of
> > the Earth. A similar process occurs on a molecular level when a
> > battery is discharged or gasoline is burned.
>
> I *think*, but am less certain, that a dropping anvil also exhibits a
> change in mass.  You'd need to drop an awfully big anvil an awfully
> long way to be able to measure it, though.  That anvil's falling
> deeper into a gravity well, so the potential energy has to go
> *somewhere*.  It goes into rest mass.

The real answer is: the kinetic energy of moving things is stored in
the relativistic icrease of mass (M=m/sqrt(1-v**2/c**2) where M is the
relativistic mass, and m is rest mass).

When anvil crashes down, it transfers its kinetic energy to the kinetic
energy of heat motion in itself and the surface material.

Enegry and the relativistic mass is one and the same.

The physical nature of the gravitational potential energry is not yet
understood, given the absense of a grand unified theory (potential  
energy
of non-gravitational interactions is, basically, equivalent to the  
mass of
the paricles mediating the corresponding force (aka gauge bosons). In  
case
of strong force, pulling apart two bound quarks would eventually  
result in
conversion of the potential energy into a new pair quark/antiquark, thus
"snapping" the stretched tube of color charge).

--vadim



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