Bob Walance said:
I’m an electrical engineer. When explaining gravity in GR terms to my peers, and I get to the part about there being no net force acting upon an object that’s “free falling” in curved spacetime, I have difficulty countering the argument:
“Yeah, you can’t measure a net force because gravity is pulling on all parts of the free falling matter equally.”
The fact that photons are affected by curved spacetime doesn’t seem to impress them as much as it does me, and so while I’m content believing that there are no net external forces acting on a free falling object, trying to convince others has proven to be a difficult task.
I know how to build accelerometers that show that there are no external forces during free fall, but does anyone out there know of any better techniques or arguments?
Thanks.
Bob Walance
If your students think there is some way to distinguish between a force that is pulling on all parts of the falling object equally, as opposed to saying that there is no force, it should be up to them to come up with an experiment that will distinguish the two cases.
If there isn't any way to distinguish the two cases, the whole issue becomes a pointless philosophical argument. (Which is what I see it as being).
Perhaps you might mention the principle of equivalence. There are several forms that this takes, the one of specific interest is that gravity acts on any sort of body so that it accelerates equally, i.e. so that the gravitational mass is always equal to the inertial mass. This is not explainable with the Newtonian point of view, but is a natural consequence of GR. If one views gravity as some sort of "force", it's just an accident that the gravitational mass of bodies is always equal to their inertial mass. (And force being proportional to mass is the requirement for the fact that bodies accelerate uniformly under gravity, indpendent of their composition, i.e. that a brick made of gold falls at the same rate as one made of wood).
To give deeper meaning to this observed fact, one must say that it is a fundamental law, and not just "coincidence". This is what GR does, and what Newtonian theory (and apparently your students) does not do.
On a slightly different tack:
One thing that might be interesting to note is that GR and Newtonian theory both predict that there will be small tidal forces on a free-falling body. This means that if you mount your accelerometer in the center of mass of your free-falling body it will read zero, but if you mount it somewhere else, you'll get a very small reading.
Forward mass detectors is another very sensitive way of measuring gravity gradients (i.e. tidal forces).
For an free-falling observer, tidal forces can be directly related to components of the Riemann curvature tensor of GR. Tidal forces are the simplest link between the mathematics of GR (the Riemann tensor), and familiar physical "forces".
