Chapter2_16 - g = 0 obs obs hf E = Energy conservation...

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PHY3063 R. D. Field Department of Physics Chapter2_16.doc University of Florida Photons and Gravity Photons have a relativistic mass ( i.e. inertial mass) given by 2 2 c hf c E m = = . Let us assume that this is also the photons gravitational mass ( i.e. assume inertial and gravitational mass are the same for photons). Now consider an emitter of photons at rest and a detector of photons at rest a distance d apart in the presence of a gravitational field. The overall energy of the photon at the source is the sum of the kinetic energy plus the gravitation potential energy, U g = mgd, as follows: ) / 1 ( 2 0 0 c gd hf mgd hf E source + = + = . The energy at the detector is also the sum of the kinetic energy plus the potential energy (but at the detector U
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Unformatted text preview: g = 0): obs obs hf E = . Energy conservation tells us that the initial energy (at the emitter) must equal the final energy (at the detector) . Thus, ) / 1 ( 2 c gd hf E hf E source obs obs + = = = and hence ( ) 2 / 1 f c gd f obs + ≈ and ( ) 2 / 1 λ c gd obs − ≈ . These are the same answers we arrived at using the equivalence principle. From this point of view, the photon frequency increased because its kinetic energy increased as it dropped from high to low gravitational potential. Earth M e R e Inertial frame in a gravity field emitter detector Photon Direction E source E observer d This approach gives the right answer for gd/c 2 << 1!...
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