Ok. Considering a curvature in spacetime is just a convienience. It is useful to construct field theories because you don't have to worry about the time it takes energy to propagate. You just calculate the field at every point and at any point in time. Then you can ignore the particles that created the field and just consider what happens locally to determine the motion of your particle. In other words, the field is just a construction of a differential (as opposed to integral) form of the force equation.
That being said, photons are most definitely affected by gravity. Gravitational fields are created and interact with energy. Thus photons have a gravitational field and attract each other gravitationally (at least theorically, because the induced gravitional field is both incredibly small and utterly dwarfed by the electromagnetic interation of the photon so we haven't been able to measure it yet). Energy is equivalent to mass (think E=mc^2). It is true that photons have no rest mass, but they do have an effective mass, seeing how they are energy carriers. Electrons have a gravitational field. Electric fields have a gravitational field. Even gravity induces a gravitational field (the self-interaction effect, AKA inertia).
ANYTHING that is deflected by a gravitational field's curved spacetime is by definition interacting with gravity. Curved spacetime IS gravity, not just an effect of it. If two objects don't attract each other gravitationally, then they wouldn't be deflected by a gravitational field. Think neutrons in an electromagnetic field. They have no electric attraction (to first order anyway) and they are, for exactly the same reason, unaffected by a magnetic or electric field (again to first order).
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Ok. Considering a curvature in spacetime is just a convienience. It is useful to construct field theories because you don't have to worry about the time it takes energy to propagate. You just calculate the field at every point and at any point in time. Then you can ignore the particles that created the field and just consider what happens locally to determine the motion of your particle. In other words, the field is just a construction of a differential (as opposed to integral) form of the force equation.
That being said, photons are most definitely affected by gravity. Gravitational fields are created and interact with energy. Thus photons have a gravitational field and attract each other gravitationally (at least theorically, because the induced gravitional field is both incredibly small and utterly dwarfed by the electromagnetic interation of the photon so we haven't been able to measure it yet). Energy is equivalent to mass (think E=mc^2). It is true that photons have no rest mass, but they do have an effective mass, seeing how they are energy carriers. Electrons have a gravitational field. Electric fields have a gravitational field. Even gravity induces a gravitational field (the self-interaction effect, AKA inertia).
ANYTHING that is deflected by a gravitational field's curved spacetime is by definition interacting with gravity. Curved spacetime IS gravity, not just an effect of it. If two objects don't attract each other gravitationally, then they wouldn't be deflected by a gravitational field. Think neutrons in an electromagnetic field. They have no electric attraction (to first order anyway) and they are, for exactly the same reason, unaffected by a magnetic or electric field (again to first order).