# Trying to understand linear frame dragging

1. May 17, 2010

### jaketodd

See "linear frame dragging" here: http://en.wikipedia.org/wiki/Frame-dragging
Two small masses, initially the same distance from a large mass. One of the small masses has a propulsion system that keeps it at a constant distance from the large mass. The other small mass has no propulsion system and falls toward the oncoming large mass. Do both objects experience linear frame dragging? If not, which one does? What effect does the linear frame dragging have on the small mass(es)?

Thanks,

Jake

2. May 17, 2010

### Jonathan Scott

As far as I know, linear frame dragging is related to an accelerating source mass (with changing momentum), and produces a tiny component of acceleration in the same direction. As any gravitational source will produce a much larger acceleration due to the static field, it is very difficult to construct a set-up in which this component might be detectable.

If you look at the approximate analogy with electromagnetism, the usual gravitational field corresponds to the grad phi component of the E field, the linear frame dragging corresponds to the dA/dt component of the E field and the rotational frame dragging corresponds to the curl A = B field. In this (somewhat misleadingly simplified) model the gravitational equivalent of the vector potential A is effectively Gmv/r where v is the velocity, so it is like the potential due to the momentum.

3. May 17, 2010

### IcedEcliptic

Rotational frame dragging is the one that is commonly worked with, although I'd guess that two hypothetical cosmic strings racing past one another would cause linear frame dragging. The thing is, you can model RFD using Kerr black holes and their ergosphere, modeling or observing the linear version in a measurable fashion seems unlikely.

4. May 18, 2010

### jaketodd

He said "as far as I know" so I'm wondering if anyone else agrees with this interpretation.

Thanks all,

Jake

5. May 18, 2010

### Jonathan Scott

Note that linear frame-dragging works like inertia, in that a test object experiences a force proportional to its mass m if nearby objects are accelerating relative to it. It would be very neat if this could be extended so that when everything in the universe is accelerating relative to it with average acceleration a, it experiences a force exactly equal to ma. From the point of view of the rest of the universe, that force would then appear to be due to the inertia of the test object opposing its acceleration (in the opposite direction), and requires an equal and opposite force to maintain the acceleration. This is pointed out in Dennis Sciama's 1953 paper "On the Origin of Inertia". This idea is one of the possible simplifications that would arise from a gravity theory that satisfies Mach's Principle.

Unfortunately, it can be shown that in GR this "Sum for inertia" of the effects of the individual accelerations cannot exactly duplicate this effect, mainly because in GR the gravitational constant G is fixed, but the sum depends on the distribution of the masses of the universe and therefore cannot be fixed. This means that either this neat Mach's Principle model is wrong or GR is wrong. (I personally suspect that GR is an approximation which is very accurate at the solar system scale but very inaccurate at larger scales).

6. May 18, 2010

### jaketodd

So it's an effect that moves small-mass objects in the direction a large-mass object is traveling?

7. May 18, 2010

### Jonathan Scott

It accelerates small-mass objects in the direction a large-mass object is accelerating (which is not necessarily the same as the direction in which it is travelling).