Torsion Vs Frame Dragging

[Dubbelosix]

I know more than anyone, that torsion has been treated differently to frame dragging, and many a great conversation has happened from knowledgeable people online detailing specifically, that the two are separate phenomenon. They argue, ''frame dragging was predicted by general relativity, in absence of torsion (purely symmetric theory).''

 

This is in fact true, except the thing we call frame dragging can very well be interpreted as a torsion in the weak field limit. This will buzz many peoples heads, in either a positive way or a negative way, and I appreciate both. I am aware of an experiment called the Lense-Thirring effect, which does in fact show, that the direction light takes in respect to the rotation of a planet like earth, is significant, that the photon has more length to pass through when moving against the rotation of Earth. 

 

This surely is an example of a very weak torsion field? It seems the photon has more length to move when making a full journey around the Earth, when in opposite direction to the Earths spin and it appears, the only logical way to explain this is by stating that space itself is being dragged, which is the same definition as a torsion field. Cartan argued, that a symmetric theory may not explain reality and in fact, this assumption could not be closer to the truth, since rotation and torsion are both features of the full Poincare group, which was one motivation for me a while back to consider the universe may have possessed a primordial spin. 

 

The rotation of the planet and the length of time it takes for a photon to make a full revolution, is predicted by gravielectromagnetic theories. The reason we may require this has roots within analogies found in standard electrodynamics theory. 

 

 

In fact, the issue of rotation is more accurately related to ''Mach's Problem'' and [is] supported at least in principle with electrodynamics: Consider a stationary cylinder, the electromagnetic field inside is zero and a wire inside of it, also a rest, will have no voltage. If you put a cylinder in motion by spinning it, the wire will experience a coupling to the magnetic field as [math]\mathbf{B} \times v[/math], becoming a Lorentz force! This suggests the rotated cylinder generates a voltage across the wire, so the rotating dynamics certainly are non-trivial.  The implication is clear, a purely symmetric theory of general relativity is only an approximation, and it may come to your interest, there was no underlying law or presumption of fundamental nature that willingly led Einstein to ignore these corrections, the biggest reason why he ignored them was because he could not understand what the precession of a particle in a torsion field would even look like. 

 

The only logical explanation for me for the Lense Thirring effect is a direct analogy to the twisting of space in the presence of matter. If anyone wants to challenge this with a reasonable debate, I would welcome it.

[Dubbelosix]

Be mindful as well, concerning the inter-relationships between torque and torsion, as they help to define each other. 

 

1.  Torque is defined as the tendency of a force to rotate an object about an axis

 

2. Torsion is the deformation of objects (or a metric like spacetime since it is dynamical) due to a pair of equal and opposite torques

[Dubbelosix]

The idea that spacetime is being dragged in opposite direction to the path the light takes, is in fact related to another interesting concept, concerning the photon travelling in the direction of rotation. Once again, we find the speed of light varies locally while in the gravitational field of a spinning rotating mass, to one that would be stationary, since the spacetime curvature can be argued to ''flow in the direction'' in which the moving photon is in. This concept must be related to the Ricci flow, which is the heat equation for a Riemannian manifold. 

Edited October 14, 2018 by Dubbelosix

[Dubbelosix]

To be fair, the phenomenon of frame-dragging and a concept of torsion is implemented in the models of supermassive black holes that have a spin (its likely all supermassive black holes spin as they spin the direction of their host galaxy). The black hole, swallows spacetime, a little bit like a planet... the force you feel sitting on Earth, is in fact spacetime ''pushing you down.'' This force is amplified by the strong gravitational and magnetic forces of a spinning black hole. It was as early as work made in 1985 that I first read about how black holes swallow spacetime as if it were a drain sucking in water. The presence of spin to a black hole, simultaneously drags spacetime along with it - some have speculated that black holes will be the only objects in nature to show visible presence of this spacetime torsion, whilst I see the Lense-Thirring effect as an indirect mathematical consequence of the same physics concerning even small masses like Earth. 

 

Certainly, it has been shown that torsion removes singularities in the universe, along with explaining other dynamical properties which seem to solve many other problems, such as a primordial rotation solving the dark energy problem in a natural way, instead of explaining inflation which Penrose showed, doesn't solve anything and actually requires a fine tuning. 

[Vmedvil2]

Ya, isn't frame dragging just torsion upon time-space that is caused by rotation of a massive object. Time-space would have decreased distance in the direction of the rotation due to the kinetic energy of the rotation, where as in oppose the direction of rotation time-space would have its natural length not being length contracted by the kinetic energy of the rotation.

 

Edited October 14, 2018 by VictorMedvil

[Dubbelosix]

Ya, isn't frame dragging just torsion upon time-space that is caused by rotation of a massive object.

 

 

It does actually seem obvious, and while predicted by relativity, the same thing could be explained in the antisymmetric extension of torsion. The remarkable thing is that Einstein did predict this, but in a sense, he understood concepts like ''gravitational locking'' but he did not understand clearly a role of torsion... If though, we base frame dragging effects on the Lense-Thirring model, we see clear analogies to the dragging of space as a torsional effect with that of the extreme local phenomenon of frame dragging.