Question

I have read that the Einstein-Cartan theory introduces torsion into general relativity in a way that produces coupling between gravity and the spin of particles. Then, the gravitational field is able cause the precession of this spin axis.

But what about spinless particles? Wouldn't there be a difference between the way gravity acts on particles with spin vs no spin? I guess that even for particles with nonequal nonzero spin there would be a difference

If gravity acts differently on the varied kinds of particles, the equivalence principle goes out the window. Plus, I don't know how to make the spin coupling disappear with a simple coordinate change
A) Einstein-Cartan theory maintains the Equivalence Principle by showing that gravity affects particles with spin differently than spinless particles, yet a simple coordinate transformation can nullify the spin coupling.

B) In Einstein-Cartan theory, gravity induces spin precession for particles with nonzero spin, but it doesn't affect spinless particles, upholding the Equivalence Principle without deviation.

C) According to Einstein-Cartan theory, gravity treats all particles uniformly, regardless of spin, thus preserving the Equivalence Principle, and any perceived differences are amendable through a straightforward mathematical transformation.

D) Einstein-Cartan theory establishes a departure from the Equivalence Principle by demonstrating that gravity interacts distinctly with particles of varying spins; however, adjusting the coordinates erases the spin coupling effect, restoring equivalence among particles in gravitational fields.

Answer 1

Einstein-Cartan theory extends general relativity to include spin-torsion interactions, potentially affecting spacetime geometry. This does not automatically violate the Equivalence Principle, but makes the theory more complex and still under continuous research.

Step-by-step explanation:

The student is asking about the implications of the Einstein-Cartan theory on the Equivalence Principle of general relativity, especially regarding particles with spin. In Einstein-Cartan theory, gravity does indeed induce precession in particles with spin, but this does not necessarily violate the Equivalence Principle. To clarify, the Equivalence Principle states that there should be no way to distinguish between an inertial frame in free fall in a gravitational field and one in the absence of gravity.

In Einstein's general theory of relativity, the presence of matter curves the fabric of spacetime, while spacetime tells matter how to move. In Einstein-Cartan theory, an extension of general relativity that includes spin-torsion interactions, spinless particles and those with non-zero spin still move along geodesics in a curved spacetime. However, the torsion generated by the spin of particles can affect the spacetime geometry. Despite these added complexities, the theory attempts to maintain the foundations of the Equivalence Principle, though more advanced mathematics is necessary to explore its nuances fully. It's still an area under study, and not all aspects have been experimentally confirmed. The differences induced by spin could be subtle and require complicated mathematical methods to describe.