Accelerational gravitoelectromagnetism

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Accelerational gravitoelectromagnetism


Accelerational gravitoelectromagnetic effects are the dragging effects (or spacetime distortion effects) that are expected to appear when a body is forcibly accelerated (forced to change speed by anything other than gravitation). The effect creates a distortion around the accelerated body.

Machian derivation of acceleration effects

Mach ... A body must experience an accelerating force when neighbouring masses are accelerated, and, in fact, the force must be in the same direction as that acceleration.

... There is an inductive action of accelerated masses, of the same sign, upon the test body. ...

— Albert Einstein, Princeton Lectures 1921    

Suppose that we sit in the cockpit of a rocket-ship and ignite the engines. As the ship accelerates, the gee-forces push us back into our chair.

  • Under Eighteenth-Century Newtonian physics, we say that the existence of these gee-forces shows that our acceleration is not just a matter of relative physics which can be transformed away by mathematics and a choice of coordinate system: there is a physical consequence to our acceleration wrt the background stars, which entitles us to refer to the change in motion as "real", or "absolute". It is a case of "absolute" motion referred to in Newton's Principia.
  • Under a Mach-Einstein model, we are entitled to say that the apparent gravitational effects that we feel are, for us, real gravitational effects. We are entitled to argue that, according to what we see, the universe appears to permeated by an actual gravitational field, whose reality can be demonstrated by the fact that the rest of the universe is "falling" in this field, and undergoing free-fall acceleration in the direction pointed to by the tail of our spaceship. Outside observers are not able to feel this field because they are all in freefall, we are able to sense the field because we are not in freefall – we are able to remain stationary and maintain our position, resisting the field, only by firing our rocket engines.


The immediate objection to the Machian interpretation of acceleration is that it is merely an empty reinterpretation of existing known physics.

However, if we argue that the result is not a "special" one, and must be generalisable, we can start to derive new results from it. For instance, if the relative acceleration of the stars wrt our spaceship causes a dragging effect on the ship, then the relative acceleration of the ship wrt the stars, must also cause a (correspondingly smaller) dragging effect on the stars.

When we forcibly accelerate a mass, the region around that mass should feel a gravitoelectromagnetic effect pulling in the direction that the mass is being forcibly accelerated in. The region around the mass is distorted by a real gravitational field. Since this induced curvature is intrinsic curvature, the (agreed for all observers) forced acceleration of the mass is accompanied by an (agreed for all observers) distortion of the region's spacetime.

This is an important result for a geometrical theory of gravity - where we might be tempted to say that since different motions of the observer can result in the apparent appearance of non-appearance of a field, all such fieldsmust be unphysical, in fact, the opposite is true: this is a situation where changing the observer's state of motion does not merely translate the same physics and the same geometry between different projections, obtained with a mathematical transform ("accelerated frame" vs "inertial frame") – changing the way that the observer moves can physically change the geometry of spacetime around the observer's position.

So ... a forcibly-accelerated mass causes deviations from flat spacetime.

Further reading

  • Albert Einstein, The Meaning of Relativity (1922)