Can Light Pressure Energy Influence Momentum and the Doppler Effect?

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Daniel Petka
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Light has no mass. It has a momentum, though. That means it can potentially push things when reflected and therefore lose energy due to the doppler effect, right? Does it mean that it gains energy when it slows down things and doesn't lose any energy if it doesn't push anything? If the whole thing has nothing to do with the doppler effect, then please tell me how it works.

Thanks
 
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You are correct. Light loses energy when it is reflected from an object that is moving away and gains energy when it is reflected from an object that is moving toward the light. In both cases, the Doppler effect is responsible.