In summary, the energy of a gravitational wave can be related to Planck's constant in a quantum mechanical analysis, but not in general relativity. Planck's constant will only come into play when a successful theory of quantum gravity is developed. However, the question itself may not have a clear meaning or significance.
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Leonard Begy
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Can the energy of a gravitational wave be related to Plancks constant?
In a quantum mechanical analysis the energy of everything is related to Planck's constant, so if we're doing a quantum mechanical analysis of gravitational waves Planck's constant would be involved.
However, gravitational waves are predicted by and analyzed using general relativity which is not a quantum-mechanical theory, so Planck's constant isn't involved. It wil only come in when we develop a successful theory of quantum gravity.
I don't think this question is clear. I think you have some idea in mind, but that's not what you wrote.
Planck's constant is a constant. You can always multiply or divide by a constant - just like the number 4. So while the answer to your question is formally "yes", I don't think there is any meaning to it.