> A vibrating star is a star that is literally moving back and forth relative to an observer
What physical process would cause this? Have we ever observed it?
Large bodies of matter don't just "move back and forth" of their own accord. Try shaking any heavy object, it takes a lot of energy.
Do you mean ringing like a gong or a pond with ripples? Then "moving back and forth" is a confusing poor choice of words. Do you mean "orbiting a black hole in such a way that it comes nearer to us and then further again?" Then why not say so?
How would the mode be out of synch with our own, whatever that even means?
> The jargon of science is one of her bugbears and she is trying to demystify it.
By introducing new and incomprehensible jargon that is literally mystical?
> oscillating in a mode which is out of phase with the motion of the detector
Are you saying that undetectable EM radiation exists because of modes / phases? This is complete hand-wavy mysticism.