# Velocity-dependent gravitoelectromagnetism

GEM

#### Velocity-dependent gravitoelectromagnetism

Velocity-dependent gravitoelectromagnetic effects are the dragging effects (or spacetime distortion effects) that are expected to appear between relatively-moving bodies.

The status of GEM-v effects is difficult to establish –

• On the one hand, these effects were assumed not to exist in Einstein's 1905 theory, as a way of simplifying the geometry ... since SR assumes of flat spacetime, a curved-spacetime description invalidates the SR proofs. In GEM-v effects exist, then special relativity is the wrong theory of relativity – this is enough to convince many physicists that GEM-v effects cannot be real.
• On the other hand, GEM-v effects appear to agree with the available experimental evidence, and general gravitational arguments and the general principle of relativity, appear to insist that GEM-v effects must exist in order for gravitational theory to be logically consistent.

This leaves us in an awkward situation, where SR requires the effects not to exist, and the GPoR requires the opposite. Assuming that we can take special relativity's side and suspend the GPoR, more fundamental gravitational arguments also seem to require GEM-v, and so apparently, does compatibility with quantum mechanics.

## GPoR-based arguments for GEM-v

If we assume that rotational GEM dragging effects are real (Mach, Einstein 1921, Gravity Probe B), then:

• The dumb-bell argument copies an argument by Galileo and says that if we change the shape of a rotating gravitational body until it takes the shape of a dumb-bell, and have the two parts of the dumb-bell rotate at exactly the right speed to co-orbit, so that we can remove the central connecting bar without obviously affecting the physics, then since the original body drags light, each of the two resulting circling bodies should also drag light, even for short sections of path that appear indistinguishable from a straight line, apparently giving a description of GEM-v.
• The ring argument similarly says that if we mould a rotating spherical gravitational mass into the form of a ring or torus, gravitational dragging ought to occur alongside the rotating limb – both inside and outside the ring, and also above and below it. If the ring's orbital speed matches the speed required for self-orbiting (if there are no significant stresses within the ring), we can compact the ring until it is arbitrarily thin, and then break it into segments which follow the same path as before, orbiting a common centre. Each of these small pieces should still exert a dragging effects on nearby matter, even though, if we zoom in far enough, they may each appear to be moving in a straight line at constant velocity.

More generally, while SR requires the absence of velocity-dependent gravitoelectromagnetism, rotational GEM, which is considered to be an accepted and experimentally verified part of mainstream physics, does include a GEM velocity component.

## Frame-dragging and gravitational aberration arguments

We can argue that, regardless of theory, the absence of GEM-v effects is known as an empirical fact, due to the operation of Newton's First Law ("N1L"). If moving masses drag light and matter, then a body moving at speed wrt its background environment ought to be attracted more strongly by the receding stars behind it than the approaching stars before it. Bodies moving wrt the background starfield would then be expected to slow until their average speed wrt the starfield approached zero. This does not happen, therefore GEM-v effects do not exist.

A parallel argument applies to gravitational aberration effects. Theory suggests that the gravitationally-sensed position of a star ought to correspond to its optically-observed position ... but if stars exerted an attraction to their apparent locations, then the aberrated starfield seen by a moving observer would appear more concentrated in the forwards direction, and a moving body would accelerate. This does not happen, therefore the effect cannot exist.

HOWEVER, both the first decelerative effect and the second accelerative effect seem to have the same magnitude but different polarities. This suggests that rather than our manually overriding both effects sequentially on the basis of empirical evidence, if we allow both effects, they appear to cancel out. If we accept this, then N1L and apparent background flatness in inertial physics is not something that we have to force onto relativity theory, they are emergent effects that appear from deeper curved-spacetime principles as a special case of cancellation in 3+1 dimensions.

Rather than saying that GEM-v cannot be correct because of N1L, we are then saying that GEM-v is a necessary compensating mechanism required for the emergence of N1L, and that without it, gravitational physics doesn't work. *

## General gravitational arguments for GEM-v=

• Time-domain argument – If we define the effective gravitational differential between an initial position and the surface of an attracting body "pragmatically", by the change in velocity that a test particle undergoes as it falls to the surface, then this change in velocity is greater if the gravitational source recedes and smaller if it approaches. While we can argue that this is a trivial time-domain effect (the receding mass creates a greater delta-vee, because it gets to act on the test mass for longer), the uninterpreted result is that the receding mass creates a greater delta-vee than the approaching mass. If we take this outcome and describe it in the gravitational domain rather than in the time domain, we obtain a description in which a moving gravitational field includes a velocity component that attracts in the direction of motion (GEM-v).
• black hole horizon argument – The r=2m radius of a stationary black hole represents an effective horizon, and also (under GR1960) an absolute horizon. Light-rays originating at r=2M and aimed outwards, remain at 2M.
If we now consider the same black hole from the point of view of an observer for whom it is receding, we require these "critical" rays to recede at the same speed as the hole. This means that they now point away from the observer (parallel to the hole's worldline), meaning that if the angle of observer-aimed rays is a function of distance from the hole (tipped light-cones), the critical surface at which rays aimed at the observer appear "frozen" (pointing only in the observer's time direction) is some distance outside r=2M. The effective horizon surface is further from the hole's nominal centre of gravity if the hole recedes than if it approaches (corresponding to an apparent stronger pull by the hole if it moves away rather than towards the observer).

Since this apparent gravitational velocity component ought to shift the energy of light, we find that:

• If the motion shift of a gravitational body nominally obeys special relativity, then when the additional curvature effects are taken into account, the equations of motion have to diverge from special relativity ...
• * ... but if the shift relationships for a gravitational body diverge from SR, then since we require lightsignals to obey the same velocity-shift relationship when passed between a "gravitational" and a "non-gravitational" body regardless of which is supposed to be "really" moving, the same divergence must then appear for nominally non-gravitational bodies. If we start by assuming the correctness of SR and its flat-spacetime derivation, we conclude that all signals sent between moving masses must obey a different, modified set of equations ("SR is nominally correct, but does not describe reality").
• On the other hand, we may like to argue that the "gravitational" velocity component does not act in addition to the conventonal motion shift, but actually is the conventional motion shift, described within the gravitational domain.
• This would mean that our equations of motion would not need to be modified by an additional GEM-v effect, since it would already be built into the equations. However, we would then need to derive those equations of motion by assuming that velocity-dependent curvature was an intrinsic part of inertial physics (Cliffordian universe). Since SR and Minkowski spacetime depend so critically on the assumption of flatness, it would seem that a relativistic derivation that assumes curvature must arrive at a different set of relativistic equations to those of SR.

## Experimental evidence for GEM-v

If velocity-dependent dragging effects are real but cancel with gravitational aberration effects for a uniform background, we should still expect to see physical dragging effects when the distribution of matter is not uniform

1. We should expect a body skimming a moving star or planet to be dragged (to "undergo momentum exchange") with that larger moving body, and
2. We should expect light-signals skimming atoms to be influenced by the atoms' motion.

In reality we find that:

1. If we throw a space probe at the rear edge of a moving planet, the probe emerges from the encounter with a deflection in the direction of the planet's motion, having acquired some of the planet's momentum (indirect collision, via the field). This is the basis of the slingshot effect used by NASA to accelerate probes across the solar system.
Although we can describe this effect in terms of the planet's velocity-dependent gravitoelectromagnetic field component accelerating the probe, we find it more convenient to carry out slingshot calculations using Newtonian gravitational theory, in the time domain (tracking how locations vary with time).
2. If we try to magnify the measurable effect of a single moving atom on light, by shining light through a region containing a co-moving body of atoms (water flowing in a tube, a spinning glass or perspex block, etc.), we find that the velocity of light passing through the moving particulate medium does appear to be dragged – light crosses the distance more quickly when it is travelling in the same direction as the particles, than when it is moving the other way - the GEM-v light-dragging behavior appears to be real.
Proponents of SR can counter that:
1. Special relativity does not claim validity in particulate media, only in "empty space", and,
2. Special relativity's velocity-addition formula can be used to model light-dragging, with light within the media treated as operating under a different set of rules, and not required to have a speed of $c$ for all onlookers.

However, the first argument says that special relativity, which is supposed to be a theory that predicts how observers and masses interact, is allowed to be wrong if the observers or masses are particulate – which they pretty much always are. This weakens the special theory's experimental falsifiability ("disproofs don't count if they involve particles").

The second argument includes an ad hoc rule added from experience ("lightspeed is not c or isotropic when significant numbers of particles are present, not because we derive this from SR, but because we already know it to be true, and override SR's "vacuum" behaviour accordingly"). Einstein's relativity book suggests that the Fizeau experiment physics provides compelling evidence for SR's model, thanks to the SR velocity addition formula applied to light as if it was a non-luminal velocity. However, the simplified SR equation provided by Einstein as having been verified turns out to be the exact equation already derived by Fresnel in the early C18th, derived from a dragged-light model.

The experimental effects that we would expect to see if moving matter dragged light, both at the lab scale and at astronomical scales, appear to be real. On the other hand, there seem to be no experimental confirmation for the absence of short-range dragging effects around matter, to support SR's geometry. Given that GEM-v can be regarded as a classical field theory implementation of statistical mechanics (the "smudging" of a body's mass and momentum, implemented as a field), it might even be impossible for counter-evidence to exist.

## Notes

• While SR and GEM-v effects do seem to be incompatible, the fact that we live in a universe that includes gravitation and allows relative motion between gravity-sources suggests that if we have to choose between SR and GEM-v for "expulsion" from physics, SR seems to be the weaker of the two. General arguments seem to require the existence of GEM-v, but no corresponding arguments seem to require that relative motion needs to be a "flat" problem. **
• SR's assumption of flatness seems to have been made to obtain the simplest possible solution to inertial physics in the context of a theory that did not address gravitation or assume that the principle of relativity applied generally. However, the simplest solution for a restricted range of phenomena is not necessarily the simplest solution for a wider range. A general theory does not have to reduce perfectly to a more limited theory, if the founding principles of the two theories aren't compatible.