An attempt to describe what is
meant by "frame dragging" in general relativistic physics is
presented. One of the startling consequence of frame dragging is
that it implies a direct connection to Mach's philosophical approach
torwards relativistic principles within General Relativity.
I've been surprised to learn that there have been a large number of
questions in regards to the Gravity Probe-B mission being conducted by
NASA, I attempt to describe the principles behind this mission in the
hopes of levitating questions to NASA. The best way to begin may
reside with the Machian view of physics, if Point A and B are
connected and there lies a point C only C can tell of relative
positioning difference between A and B to any degree of accuracy.
The problem is the C only seems to hold to any degree of accuracy
when view from A or B or both, when more frames are introduced it only
adds to cloud our views of how these interactions take place,
inevitably this leads to a situation which appears to violate
relativity theory by requiring superluminal communication. Einstein
incorporated these Machian views in such a way which it would not allow
for a violation of the second relativity postulate that c=constant for
all relative observers. Actually by a twist of fate we owe the
Machian agreement with relativistic physics to Sir Isaac Newton, in
classical physics we call this unique effect inertial forces. Confused
yet? Before we even got into what effect Gravity Probe-B is
presently studying, we are all ready dealing with Machian principles,
superluminal data transfer, an internal frame physics, in the end of
our discussion however all should become clear.
O.K. Now Gravity
Probe-B
Well first the name of the mission is indicative to the effect in
question, first the study of gravity and two magnetism, as the magnetic
vector is usually symbolically represent by B. In short the
mission is to measure a composite effect known as gravito-magnetism,
frame dragging, and after the theorist whom predicted them it is also
known as the Lense-Thirring Effect. Lots of names and confusing
terms, but gravito-magnetism is apt named for the cause of the
Lense-Thirring effect, and the consequence of the effect would be the
generation of framed dragged inertial frames. A simple illustration of
this effect would be to stir a viscous fluid such as syrup as you stir
the molecular bonds near the stirring region gets dragged along.
To avoid a lot of circular logic involving Mach's principle let
introduce some mathematical language, in the case of the Earth alone
the amount of implied inertial resistance applied to a body on its
surface is
wdrag~(Mearth/Rearth)~(0.44
cm/6 x 108 cm)~
5 x 10-14 radians/sec
in short the inertial resistance required by Earth's gravitational
disturbance is at such a small magnitude that it will go unnoticed
unless one speaks of subatomic scales with particles traveling at a low
velocity. To translate the above equation it simply suggested
that inertial forces on the ground must counter act the spacetime
distortion formed by the Earth's gravitational field, of course Mach's
principle incorporates the gravitational field of the entire universe
making it a much more complicated problem to deal with. Essentially
what we get from the previous discussion is that effects at great
distances can have an impact on short scales as well, giving a
distorted view of the frames in question, and this is the odd concept
which gravitomagnetism brings to light!
We however skipped the gravitomagnetism effect itself, introducing
Mach's principle first however will prevent confusion later on when one
begins to ask questions regarding the nature of frame dragging.
Gravitomagnetims deals with an electric source vector E=0 (due to html
limitation vector notation is not written but is assumed for this
context), and a moving charge vector representing the magnetic force by
B=-(2/3)(M/R)w, notice the similarity of the
magnetic vector when
Mach's principle is applied to General Relativity? The only
significance between the two is from the added 2/3 this is result of
multiply, contracting and reducing general relativistic tensors, there
are
actually two solutions 2/3's for the exterior of a body and 4/3 for the
interior. Actually graviomagnetism is related to Mach's principle
by the fact that there are geodesic like effects in general relativity
usually described in terms of non-inertial and there also exist
inertial like terms within tensor for to self interaction of
bodies. The motion of rotating body is considered to be following
a non-inertial geodesic path, such that Saua=0,
the problem is that
magnetism feels an inertial force due to the rotation of an electric
field, as such we arrive at the Lense-Thirring Effect when
dS/dt=(4/3) (M/R) w
x S.
Normally the Lense-Thirring effect is to small to notice because it
would take an excessive amount of acceleration to offset the mass of a
body in question, this is due to the Lorentz force law, when given in
terms of a=E-4v x B, so this effect seems to only imply significance to
massive high angular velocity objects such as neutron stars. In
other words the Lense-Thirring Effect is simply the result of the
magnetic field acting to induce a distortion in an otherwise stable
gravitational field, which could also be interpreted as a special
relativistic interference with a general relativistic field.
Now this also illustrates Mach's principle in that a dense ultra
relativistic star such as a neutron local effect, also effects the
region of space near to it (and the reciprocal to a lesser extent), in
this case it effects a bodies geodesic path through spacetime.
Thus the Lens-Thirring Effect implies that for a region with the 2/3
field in place and where the vector of a has a noticeable effect that
the geodesic path will be off set by dS/dt, unless an equal external
inertial force is applied. In simpler terms the magnetic force of
a dense relativistic object causes the local spacetime near the
disturbance to drag, the dragged disturbance is simply termed frame
dragging, and oddly enough it is all tied together with Mach's
principle!
The Importance of
Gravitomagnetism
So why is gravitomagnetism, and its after affect, frame dragging so
important for theorist, for one in provides another test to check the
validity of GR so that we may learn more about the nature of the
universe around us. Second the effect in one way or in other ties into
metaphysics due the apparent relationship between Mach's principle and
frame dragging. Lastly it also tells of a force that is neither
strictly classical such as magnetic the magnetic force, nor does it
describe a force that strictly arises due to mass as we are told by
general relativity alone, it is a combination of the two physical
philosophies. It also gives us clues to the possible structure
behind the very basic building block of the entire universe painting a
picture of the how the universe and matter and energy may have formed,
and what forces a responsible for the present nature of the
universe. Gravitomagnetism may also give clues as to various
other possible behavior which matter and energy may take which are not
known to present science. A prime example being a particle
falling dangerously close to the event horizon of a black hole may
split into two separate particle, one escapes, the other falls in,
however the one that fall in is perceived to have a negative energy
density to an outside observer (due to a violation of geodesic
conservation) and forms the basis of what is known as Hawking
radiation. It also may not be unreasonable to wage that
gravitomagnetism may give some insight into the abundant nature of Dark
Energy reported by cosmologist across the larger scale universe and why
it appears to be practically non existent on Earth. Frame
dragging
is a rather simple effect that has long reaching applications. But
perhaps most interesting consequence of the Lense-Thirring Effect in
regards to gravity probe-B is that if Earth's frame dragging could be
accurately measured and compared to the large scale behavior of the
universe a physical explanation may be given in regards to what forces
act to create inertial resistance. In October of this year [2004] it
was
a preliminary analysis reported that the Earth itself does in deed drag
spacetime around it by Dr.'s Ciufolini and Pavlis, by as much as two
meters in one year (see NASA's
website), gravity Probe-B simply carries this work to the next
phase.
