Are gravitons and gravitational waves analogous to photons and EM radiation?
In a sense yes. Keep in mind that gravitational waves are dominated by higher order multipole terms than electromagnetic waves are.
Since gravity bends EM radiation, why would it not also slow down EM radiation?
All kinds of weird effects can happen to EM radiation on a global scale due to curvature of space-time. It only travels at ##c## relative to inertial observers on a local scale.
Not to be argumentative or semantic but if spacetime can curve how can it be nothing.
Is "curvature" just a figure of speech?
The curvature is most certainly not a figure of speech - it's real.
You can detect curvature by looking for things like parallel lines that intersect (if I draw two parallel lines at the equator and pointing due north they'll intersect at the north pole) and triangles whose interior angles don't add to 180 degrees.
It's something of a jump to conclude that the presence of these curvature effects means that spacetime has to be "something" instead of "nothing". All we really have is a mathematical object (the "metric tensor") that tells us the distance between two nearby points; large-scale effects like the intersecting or not of parallel lines are derived from the metric. Some metrics correspond to flat manifolds and others to curved ones; neither tell us much about whether there's something there to curve.
This is highly dependent on what "nothing" means.
Consider that we cannot detect spacetime, we cannot measure it, cannot touch it, etc. We can only detect and interact with things within spacetime, which is why its called the "framework" that everything sits within. If you want to go ahead and say that spacetime is "something", then feel free. Just realize that your definition of "nothing" and "something" may be different than someone else's. In the end whether you call it nothing or not changes, well, nothing. It's just arguing over definitions.
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