Natural Science Forum / Physics / Relativity / March 2007

We live in a Newtonian world of Einsteinian physics ruled by Frankenstein
logic.

-- David Russell

--
Ahmed Ouahi, Architect
Best Regards!

That's basically what he ended up with, albeit with a set of highly
nonlinear differential equations where the metric tensor plays a role
analogous to the potentials.

The simplest problem with this is that in electrodynamics, like charges
repel, while in gravity, like masses attract (and there are no negative
masses, as far as we know).  If you only had to deal with a Coulomb-like
interaction, this would just be a matter of changing a sign in the force
law.  But of course, the Coulomb interaction is only good if the sources
are at rest.  As soon as you allow sources to move, and go to the full
Maxwell equations, you find that this sign change is disastrous -- it
makes the energy carried by the field negative.  For gravity, this would
give gravitational waves carrying negative energy, which would lead to
drastic instability of gravitating systems.

I'm not an expert on the history of general relativity, but I would guess
that for Einstein, another factor was as important.  We know, both from
theory (the equivalence principle) and from experiment, that all forms
of energy gravitate.  For this to be put into a theory of gravity, one
needs the whole stress-energy tensor as the source of gravity.  This is
not compatible with a Maxwell-like theory, in which the source is a vector
rather than a tensor.

(In a little more detail: in electromagnetism, the basic source of the
field is charge.  This is, observationally, a scalar under Lorentz
transformations.  This means that under a Lorentz boost, the charge
*density* picks up a factor of gamma: charge density is charge divided
by volume, and the volume is Lorentz contracted.  This behavior implies
that charge density is the time component of a four-vector.  This is right
-- the spatial part is the current density -- and it makes Maxwell's
equations relativistic.

In gravity, the basic source of the field is energy.  This is,
observationally, a component of a vector, the four-momentum, under
Lorentz transformations.  This means that under a Lorentz boost, the
energy *density* picks up *two* factors of gamma: one from the volume,
as in electromagnetism, and a second from the behavior of energy itself.  
This behavior implies that energy density is the time-time component of
a rank two tensor.  This is right -- it is a piece of the stress-energy
tensor.  But you can't put such a tensor on the right-hand side of
Maxwell's equations; you need a "spin two" field, like the metric in
general relativity.  In fact, Deser has shown that if you start with
such a field and ask for Coulomb-like behavior of static sources, and
also require that the field's own energy also acts as a source (gravity
gravitates), you are automatically led to general relativity.)

Since Einstein, a number of physicists have looked at what would happen
if you added an "Maxwell-like" piece to the gravitational interaction.  
The answer is that it's experimentally ruled out, unless the interaction
is *much* weaker than gravity: it gives violations of the equivalence
principle that would be seen in Eotvos-type experiments, along with the
wrong deflection of light by the Sun and a variety of other observationally
wrong predictions for the Solar System.

Steve Carlip

Take a look at a powerpoint presentation by James Espinosa, in which
he talks about a guy who did just what you're asking about.

Einstein's Tests of General Relatiivity through the Eyes of Newton
http://www.phys.unt.edu/Espinoso.ppt

Bob Fritzius

Well, the maxwell equations were used by Lorentz (1900) and Poincare
(1905) to explain gravity. See their papers:

Lorentz: http://www.historyofscience.nl/search/detail.cfm?pubid=260&view=image&startrow=1
Poincare: http://www.soso.ch/wissen/hist/SRT/P-1905.pdf
http://en.wikipedia.org/wiki/Speed_of_gravity

But obviously it doesn't work. See this discussion for further details
and look on Steve Carlip's respond:
http://groups.google.com/group/sci.physics.relativity/browse_thread/thread/ada26
85f7d418427
And a paper by Deser: http://arxiv.org/abs/gr-qc/0411023

Dietmar Hainz