Re: Apparent weight

["A. R. Marlow" <marlow@loyno.edu>]

On Thu, 19 Feb 1998, Donald E. Simanek wrote:


 
> ...
> > If gravity is
> > geometry then it SHOULD affect all masses in the same way.
> ...
>
> Ok. I'll bite. *Why* is this assertion true? What experimental evidence
> can confirm it for *all* possible situations? (Not just for gravity.) How
> could this assertion be falsified experimentally? What does it mean to say
> "gravity is geometry"? 

The experimental evidence favoring Einstein's geometric explanation of
gravity over Newton's force theory is becoming more abundant every day
with new discoveries of orbiting pulsars, Etc., but the original pieces of
evidence were the explanation of the extra 40" of arc in precessional
motion of Mercury's orbit, which comes right out of a curvature
explanation of gravitation (but is not explained by Newton's theory), the
correct prediction of the amount of bending light undergoes in passing the
sun, and correct prediction of the gravitational redshift of light.  

To be honest, you do not have to interpret the curvature tensor of GR as a
"geometrical" object, and some quantum field theorists simply regard it as
the best classical field description of gravitation that we have, without
picturing it as geometrical.  However, since it does permit a geometrical
interpretation which most people find very beautiful and simple, most
general relativists seem to espouse that viewpoint.

My apologies if your question was really just limited to the issue of why
curvature should act equally on all masses.  The answer to that is the
same as it would be for a similar situation on the curved surface of
the earth.  The shortest, most economical route from the US to Europe is a
great circle route, and this is true whether you are sailing in a many ton
megaship or a canoe. Geometry does not care what the mass of your vehicle
is.  This analogy can be pushed a little further.  If you did not know the
earth was round and were thinking in terms of a flat surface (Mercator
projection, say)  --  the Newtonian flat space view  --  then you would be
puzzled by the fact that the most economical route to Europe involves a
path that curves first northeast, then east, then southeast.  If you cling
to the flat space view, you might be led to invent a mysterious "force"
field that your ship must tack against to explain the strange curving of
the path of shortest time and most economy.  Such a force would have
strange properties:  it could not be felt, but it affects travel;  it acts
with equal strength on large ships and small.  This is what Newton faced
with gravity without the benefit of curved spacetime.  In the case of the
earth's surface, all mysteries are cleared up once you look at a globe,
and no mysterious "force" is needed.  The same thing happens with
gravitation, once you look at curved spacetime.

> Are electric and magnetic fields also "only
> geometry? What other things in *physics* are "only geometry" and therefore
> conform to this assertion for the same reason? What is the criterion for
> judging whether a thing is only geometry, or is something more? 

Would that it were so, but no one has succeeded in incorporating E&M into
a four-dimensional geometric worldview.  Einstein spent the better part of
his life trying.  The reason is precisely that different charges are
accelerated into different trajectories by the same E&M field.
(Gravitation accelerates different masses in exactly the same way, and so
it could by "geometrized.")  Kaluza and Klein (in the 1920's I think) did
geometrize E&M very neatly, but they had to use 5 dimensions, and this
never caught on too well, but it led to the modern gauge theories of all
forces, which does essentially geometrize all forces (in many dimensions,
however).  
 
> Is it
> possible that we might be clever enough someday to show that *everything*
> is geometry (properly interpreted)? Leave aside the obvious fact that math
> is not physics and physics is not math. I assume you are speaking of
> geometry not as a branch of pure math, but in its historical sense as a
> "science of measurement" and in its modern sense as a science which
> describes the metric of space. 

The gauge theorists are doing this even as we speak.
>

A. R. Marlow                          E-MAIL:  marlow@loyno.edu
Department of Physics, Box 124        PHONE:   (504) 865 3647  (Office)  
Loyola University                                    865 2245  (Home)
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