Do magnetic fields affect the speed of light in the Pound-Rebka experiment?

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cragar
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Do clocks tick at different rates in different magnetic fields .
 
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nice , If we try to relate this to the pound-rebka experiment , when they tried to measure the gravitational shift of light , If we wanted to expand this to light traveling from a stronger magnetic field to a weaker one , I don’t think we would measure a shift in the light because photons do not interact with magnetic fields at least i think , But would we measure a shift because the magnetic field has an energy density therefore it would have a gravitational field , so would we then measure a shift in the light .