Gravitomagnetism
In
relativity theory, gravitomagnetic effects
are inertial or gravitational field effects that might be expected when
there is relative
motion between bodies. Some of these effects are currently
included within
standard "core" physics, some aren't.
The
name comes from an analogy with electromagnetism,
where the motion of an "electric" charge produces "magnetic"
sideeffects. In gravitomagnetism,
the "moving charge" is
inertialgravitational, and the "gravitomagnetic" effect can be
considered as being due to a distortion of a body's surrounding
inertialgravitational field. These effects can be considered
consequences of the finite speed of gravitational signals: if a body
changes its location or velocity while its previous signals are in
flight, the way that its signals are distributed though space should be
affected. If we consider the inertia of a
body to be partly or wholly determined by its interactions with its
environment, then interfering with the way that it communicates with
that environment might alter its apparent inertial properties.
The
name "gravitomagnetism" is slightly misleading, in that it
doesn't have anything directly do do with electromagnetism, or with
conventional magnetism.
Standard effects
acceleration
A
forciblyaccelerated observer feels geeforces
that appear to them as evidence of an apparent gravitational
field.
Applying the general principle of relativity, the
observer is entitled
to blame the existence of this field on the relative acceleration of
the rest of the universe. The observer can say: "When
the
background
stars accelerate, I feel an associated gravitational field".
The
principle of relativity then requires that the effect be mutual ("democratic
principle"),
so, as a result of the general principle of
relativity, if we forcibly
accelerate a mass, the acceleration is smudged out into the surrounding
region, and should cause light and particles near to the mass
to undergo a certain amount of acceleration, too.
As
the body resists the applied acceleration, it tries to grab onto its
surrounding region of spacetime, and nearby bodies in that region get
pulled along. The forced acceleration of a body effectively causes a
gravitational field around that body, acting in the same
direction
as the acceleration. From the point of view of the "forcibly
accelerated" observer, it is this same effect, applied to the relative
acceleration of all the background stars around them, that produces the
apparent gravitational field and the geeforces that they feel.
rotation
Similar
arguments say that a body should be more gravitationally attractive in
its
equatorial plane if it is seen to be rotating, and that this attraction
should be strongest towards the side of the body that moves away from
us. The observer can say, "When I see the
background
stars to be circling around me, I feel associated
gravitational fields pulling me outwards in the rotation plane, and
around in the sense of the rotation".
When
we fire a rocket directly upwards from the
Earth's equator, the centrifugal effect makes it easier for the rocket
to escape the Earth's gravity, and from the point of view of the Earth
observer, we can redescribe the effect by saying that the shell of
stars and galaxies rotating around the Earth appear to create an
outwardpointing centrifugal field
within it (with the
centrifugal forces usually felt by rotating or swept objects being
considered to be the results of these fields). If we then apply
topological arguments to turn this effect inside out, or apply the
principle of mutuality to say that the background stars must feel the
Earth to produce a similar effect, we find that rotation must make a
body more gravitationally attractive. We can make a parallel
argument that this additional gravitational mass is a consequence of
the energy bound up in the object's rotation w.r.t its
environment, E=mc^{2}
The
second effect that we
notice with our launched rocket is that, if the rocket proceeds
in pretty much a straight line with respect to the background
stars, then
from the point of view of the Earth observer, the rocket is moving away
from the Earth in an expanding spiral that makes it circle the
Earth,
EasttoWest, once every every 24 hours. For the Earth observer, the
launched rocket was originally traveling in a straight line, but had
its
path deflected into a spiral by the rotating shell of surrounding
matter.
This tells us that a rotating shell of
matter must generate inside itself a Coriolis field
that pulls other objects around with it, and if we then again turn the
description inside out, or apply the principle of mutuality, we
conclude that the general principle of relativity predicts that
rotating bodies should twist gravitational fieldlines, so that
nearby objects and light are pulled around.
Both
effects can be visualised as fieldline effects: the results of the
finite speed of gravity plus
relative rotation causing a body's gravitational
fieldlines
to twist around it when it rotates relative to its environment.
The
"twist" causes the rotating object's gravitational centre of gravity to
appear offset towards its
receding side, and as a result, when we surround the body with
observers and ask them to point towards where the body's gravitation
appears to be centred, those indications no longer point to the same
location, but to locations that are all offset in the rotation plane,
away from a common centre. The idealisation of a rotating mass is no
longer a point, but a ring, and this is part of why we say that
rotating black holes under GR1915 are idealised as containing a ringsingularity
at their centre, instead of a pointsingularity.
In current physics, this
rotational dragging effect is referred to as framedragging,
and the effect that this should have on orbiting gyroscopes is referred
to as the LensThirring effect. An
orbiting
experiment to test this for this effect ("Gravity Probe B"),
was launched in 2004, with the (delayed) results now hoped for some
time
in 2008.
Nonstandard effects
velocity
We
can extrapolate from rotational effects to argue that
gravitomagnetic effects should also drag light and matter between
bodies that are moving with a simple velocity. In the rotational case,
the receding, redshifted side of a rotating mass should pull at us more
strongly than the approaching, blueshifted side, and if we turn this
association into a general rule, we'll expect receding redshifted
bodies to pull more strongly than approaching blueshifted ones. This
association is already obviously true when the shift is due to
gravitation rather than motion, and we might even decide that it would
be interesting to treat the conventional motion shifts that we see as
the
result of the
body's associated gravitomagnetic field.
Although
the
expected phenomenology of "velocitydependent" gravitomagnetic effects
seems to
correspond well to the available physical evidence, the status of this
class of
effect under current theory isn't totally clear. The phenomena
that we'd associate with velocitydependent gravitomagnetic effects
seem to already be in place within general relativity for bodies with
strong gravitational fields, and general relativity agrees that a
moving gravitational filed carries energy and momentum, and can "bump"
nearby objects. Moving gravitational masses can exchange momentum with
nearby bodies, and for the effect to be mutual, bodies that would
normally be considered to have insignificant gravity must also be able
to cause the effect. Technically, there should be no distinction
between the rules of physics for stronggravity and weakgravity
bodies.
In
practice, current textbook theory makes a distinction between
"gravitational" and "nongravitational" physics, and assumes that there
is a realm where the interactions of bodies can be modeled by assuming
that these sorts of dragging effects don't occur. Current textbook
relativity theory uses special relativity to model physics in flat
spacetime, and says that general theories need to reduce to
the
physics of SR over small regions to be considered
credible.
The
argument for dividing physics up in this way is that since
small
bodies have such negligible gravitational fields, any effects
due
to modifications of those fields must be even tinier. The
counterargument is that the general principle tells us that inertial
and gravitational mass are different aspects of the same underlying
property, and the inertial mass of a small object is not
insignificant in physics  it's perhaps one of the most important
factors in most calculations. Setting the inertial
mass of bodies to zero destroys most inertial physics. We
also
know that when we send signals between moving water molecules, the
motion of those molecules causes an offset in the speed of light (Fizeau
experiment), so the sort of dragging effect that we'd
expect if our third gravitomagnetic effect was real has already been
verified.
The
velocitydependent gravitomagnetism seems to offer an alternative way
of creating and regulating local lightspeed constancy in situations
involving relative motion. However, since the idea would mean that
special relativity's geometry and derivations were wrong, most
physicists tend to say that we know that this third effect
doesn't
happen, or that if it does happen it must be too weak to bother with,
or that if it does happen to a significant degree with stronggravity
bodies( momentum
exchange, slingshot effect),
that this must be a special effect that only applies when
gravitational fields are strong.
Since
special relativity is founded on the geometrical assumption of flat
spacetime, the third gravitomagnetic effect hasn't been integrated into
TwentiethCentury relativity theory.
General expression
In
its
most general form, gravitomagnetism can be thought of as a simple
"smudging" of a body's kinetic energy and momentum out into the
surrounding region, as a field effect. Gravitomagnetism then allows
passing bodies to exchange energy and momentum via the coupling
of their external gravitomagnetic fields, without undergoing a
direct collision.
However, we don't seem to be able
to apply
this most general
concept of gravitomagnetism within relativistic field theories
based on special relativity. A fullyfledged gravitomagnetic model
would treat movingbody problems as exercises in curved space or curved
spacetime, while special relativity treats them as problems involving
only
flat spacetime.
Quotes on Gravitomagnetism and Field
Theory
"
I hold in fact,
1.
That small portions of space are in fact of a
nature
analogous to little hills on a surface which is on the average flat;
namely, that the ordinary laws of geometry are not valid in them.
2.
That this property of being curved or distorted is continually being
passed on from one portion of space to another after the manner of a
wave.
3. That this variation of
the curvature of
space is what really happens in that phenomenon which we call the
motion of matter, whether ponderable or etherial.
4.
That in the physical world nothing else takes place but this variation
subject (possibly) to the law of continuity. "
W.K.
Clifford, "On
the
SpaceTheory of Matter" (1876)
"
What is to be expected along the line of Mach's thought?
1.
The inertia of a body must increase when
ponderable masses are piled up in its neighbourhood.
2.
A body must experience an accelerating force when
neighboring masses are accelerated, and, in fact, the force must be in
the same direction as that acceleration.
3.
A rotating hollow body must generate inside of itself a
'Coriolis field', which deflects moving bodies in the sense of the
rotation, and a radial centrifugal field as well.
We
shall now show that these three effects ... are actually present
according to our theory. ... "
Albert
Einstein, "The General Theory of Relativity",
1921 Princeton Lectures
translated and published in The
Meaning of Relativity (1956)
"
On the basis of the general theory of relativity, on
the
other hand, space as opposed to "what fills space", which is dependent
on the coordinates, has no separate existence. ... If we imagine the
gravitational field, i.e. the functions g_{ik},
to be removed, there does not remain a space of the type (1),
but
absolutely nothing, and also no "topological space". For the functions g_{ik}
describe not
only the field, but at the same time also the
topological and metrical structural properties of the manifold.
... There is no such thing
as an empty space, i.e. a space without field. ...
Spacetime
does not claim existence on its own,
but only
as a
structural quality of the field. "
Albert
Einstein, "Relativity:
the Special and the General Theory" (1955)
"
… spacetime is not necessarily something to which one can ascribe a
separate existence, independently of the actual objects of physical
reality. Physical objects are not in space,
but these objects are spatially extended.
In this way the concept 'empty space' loses its meaning. "
Albert
Einstein, "Relativity:
the Special and the General Theory" (1955) (note
to the 15th edition)
"
The vision of Riemann, Clifford and Einstein, of a purely geometrical
basis for physics, today has come to a higher state of
development, and offers richer prospects  and presents deeper
problems  than ever before. "
John
Archibald Wheeler, Geometrodynamics
(1962)
"
Einstein's general theory of relativity provides a number of ways to
generate nonNewtonian gravitational forces. ... The three outlined
here were probably known by Einstein before he published his paper on
the principle of general relativity in 1916. They were first
specifically derived by Thirring in 1918, and since then have been
contained in nearly every text on general relativity ...
It
has been pointed out that a rotating mass will exert a force similar to
centrifugal force on a stationary test body; also, if the test body is
moving at some constant velocity v, it will
experience an additional
force which is proportional to the cross product of the angular
velocity of the rotating mass and the linear velocity of the test body.
...
In employing Einstein's Theory to
investigate the
effect of a large accelerated mass on a small test body, it is found
that the accelerated body drags the test body along with it. ... "
Robert L.
Forward, "Guidelines
to Antigravity" American Journal of Physics 31
166170 (1962)
...
the gravitational spinspin force has the same form as the force
between two dipoles in electromagnetism except that its sign is
opposite, i.e., "north pole" attracts "north pole"
in gravitational
spinspin interaction.
Robert
Wald, "Gravitational Spin Interaction"
Physical Review D 6 406413 (1972)
"
In other words, inside a rotating universe, the axes of gyroscopes
rotate in step with the rotation ... they are tied to the directions of
distant bodies in that universe. ... The existence of the dragging of
inertial frames then guarantees that rotation must be defined relative
to distant matter, not relative to some absolute space. ... "
Clifford M.
Will, Was
Einstein Right? (1986)
Chapter 11: "The
Frontiers of Experimental Relativity"
...
Intuitively intrinsic gravitomagnetism may be thought of as that
phenomenon such that the spacetime geometry and curvature change due to
currents of massenergy relative to other matter.
Ignazio
Ciufolini and
John Archibald Wheeler Gravitation and Inertia
(1995)
Section 6.11 "Gravitomagnetism,
dragging of inertial frames, static geometry, and Lorentz invariance"
"
As electric charge, going round and round in a circle, produces
magnetism, so mass, going round and round in a circle, must produce a
new kind of force, gravitomagnetism. ... The quickest way to an order
of magnitude estimate of this EinsteinLenseThirring "frame dragging"
is a line of reasoning invented by Mach which was very influential in
guiding Einstein to his geometrodynamics. ... "
John
Archibald Wheeler, A
Journey into Gravity and
Spacetime (1990, 1999)
Chapter 13: "A
Farewell Look at Gravity"
"
Looking at a "frozen instant" of an object moving through its
environment, we still have a problem of interpretation: the photograph
of the ball certainly could be interpreted as
showing the ball moving, but it could also be interpreted as showing a
ball immersed in a polarised gravitational field. Which interpretation
is correct?
In
a unified model, the two descriptions may be interchangeable. Is the
redshift seen in a receding object due to its recession or to its
gravitomagnetic dragging effect on light? As long as we can do the same
calculations in each case and get the same answer, we really don't
care. "
"
If gravitomagnetic distortions are fundamental, a physical observer's
perception of the apparent alignment of space and time axes is no
longer just a matter of the mathematical projection of different
coordinate systems onto a flat empty region: it becomes a more
physical, visceral interaction between the observer
and their environment. "
Eric
Baird, Relativity in
Curved Spacetime
(2007)
section 9.13: "Zeno
revisited: The 'impossibility' of motion" / "motion
without motion"
section 9.14: "Worldlines
and curvature"
