Natural Science Forum / Physics / Research / January 2008

Thus spake Phil Gardner <pej_dg@dodo.com.au>

I don't. If one accepts that gravity is the geometry of space-time, then
a gravitational field is equivalent to the change in the rate of clocks
with respect to position. Although we do not have an accepted
unification of general relativity with quantum mechanics it is natural
to think of this change as being reflected in a change of frequency of
the wave function. Since energy is equivalent to frequency, the
potential energy is still "stored" in the atom.

Regards

Are you drawing your system boundaries appropriately?

Atom plus stimulus to higher energy state
= [nucleus] plus [electron in higher orbit] (speaking "Bohr-ingly")

The equivalent for the gravitational system is particle in a
gravitational well
= [gravitational source ( corresponding to the nucleus in the atomic
situation)] plus [particle in higher gravitational state
( corresponding to the electron in the higher "orbit"/position)]

So in both cases the additional PE is within the full system

Same difference - no?

PE (lol!)

In article <2a740c8a-ca83-4d4e-b78d-4a2658349754
@f47g2000hsd.googlegroups.com>, pej_dg@dodo.com.au says...

There's no real difference between the two scenarios - you are just
describing each in a different way.  You are treating the atom as a
single entity, but you treat the Earth-body system as a collection of
components.

Suppose we added energy to an electron in an atom, moving it (so to
speak) to a higher orbit (a larger orbital) - would we say that this
energy is stored in the electron, or in the electromagnetic field of the
atom?

Conversely, if we consider the Earth plus the body plus the
gravitational field as a single entity (like a giant atom), then we can
add energy to it, maybe causing a body to be raised, and say that this
energy is stored in the entity.

It is simply a matter of perspective; there is no actual difference at
all.  You are just looking at each from a different perspective, but you
can look at either one from either perspective.

There is no direct change of gravitational potential energy in the above
scenario, when both the now slightly less massive atom AND the emitted
photon are taken into account, and still considered to be part of the
system.

Of course we can now start to complicate our accounting by proposing
that the photon is absorbed by a distant entity... but that's all we are
doing; complicating our accounting, and to no obvious purpose.  If the
photon is indeed gone, and no longer part of the Earth-body system, then
that system has lost a little bit of gravitational potential energy, as
well as a larger bit of electromagnetic potential energy.

- Gerry Quinn

TYPO: the last word should be "spring", not "atom".

You suddenly changed perspective. In the first two cases you considered
an entire system, but in this last you only consider part of the system.
Moving a basketball higher in earth's gravitational field does indeed
increase the potential energy of the earth+basketball system, and does
indeed increase the effective mass OF THE SYSTEM. Just like your earlier
examples. After all, you did perform work to lift the basketball.

In all three cases one cannot ascribe the potential energy to the
electron, atoms of the spring, or basketball -- potential energy is not
localized and is a property of the entire system, not its individual parts.

It's not clear what you are asking or what physical situation you have
in mind. When an excited atom emits a photon and transitions to a less
excited state, there is no "gravitational field" involved at all -- this
is purely an electromagnetic (quantum) process.

But you seem to be thinking thus: with a photon detector at height H0 in
a gravitational field, when a specified excited atom emits a photon from
height H0 the detector records an energy E0, but when a similar atom
emits a similar photon from height H1 (>H0), that detector at H0 records
an energy greater than E0. This is true, assuming sufficient measurement
resolutions, etc.

There are several ways to interpret such a physical situation:
 A) the photon gains energy by falling in the gravitational field.
 B) the photon is blueshifted due to its travel between heights in
    the gravitational field.
 C) the energy scales of atom and detector are different, due to
    their difference in gravitational potential; the photon does
    not change energy (or frequency) during its journey, but it
    registers more energy in the detector due to change of scale
    (time scales also differ).

All three interpretations are valid, and correspond to using different
coordinate systems to describe the physical situation. So one cannot say
unambiguously that the photon does or does not change energy, does or
does not change frequency, or that the scale of energy does or does not
change with height.

At base, the difference is due to the non-local nature of this physical
situation in the gravitational field, and the difficulty (inherent
ambiguity) in GR of describing non-local situations. This is traceable
to the problems of doing integrals on curved manifolds, and the result
is that energy is conserved only locally in GR.

But there is an approximation that is often appropriate: if a system is
localized in spacetime and has no outside interactions, then one can
draw a closed boundary containing the system, with no energy or momentum
crossing the boundary and the manifold is asymptotically flat there --
then inside the boundary the total energy and momentum are conserved.
This applies to the original three situations, but one cannot draw such
a boundary between the emitter and the detector in this last situation.

Tom Roberts