Imagine observing the frequency of light which is directed to the center of a gravitational field such as a planet. According to the gravitational-blueshift-effect, the frequency increases while getting closer to the center. Is this progress continuous?
If so, how does that fit with the photoelectric effect, which says the energy of light is quantized?
If not, would that mean light skips the states of energy in between? How would that work? Would that mean either time or space or both are quantized as well?
Please comment whatever comes to your mind about that problem or tell me if I made a big mistake in my thoughts. Thank you very much.