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Do the Newtonian laws imply that the angle of bending/inflection of a photon moving near earth does not depend on its energy which depends on its frequency/wavelength?
I know that gravity translates to different momentum and energy of photons (red-shift, blue-shift). How does this change of momentum and energy include or exclude the change of direction of photons from the sun the prophecy of which Einstein got famous by? Intuitively, I cannot think of sun rays being bent in different angles by Earth's gravity - I only know of atmospheric refraction named Raleigh.

I know of the equivalence of energy and mass. Just like hammer and feather, any photon should undergo identical acceleration which, with photons, translates is red- and blue shift. Accordingly, all kind of photons should be defracted identically.

In your answer please consider that the Newtonian formula on gravitational force includes the masses of both bodies involved - does it matter, in the context of electro-magnetic waves, that the gravitational force on hammer and feather appear not to be exactly the same?

Is there a formula that describes both bending and shift of frequency (redshift/blueshift) brought about by gravitation?

(First paragraph deleted, according to comments below, for erroneously assuming that gravitation is described by Newton's three basic laws of motion.)

Related:

Does "special relativity + newtonian gravity' predict gravitational bending of light?

Peter Bernhard
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1 Answers1

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Basics of Newtonian gravitational force

  • Bodies are attracted by gravitational source. If the body initially does not move towards the center of force, its trajectory will be curved.
  • A higher initial velocity causes a lower curvature.
  • The component of motion perpendicular to the center of force remains constant (in airless space).

Basics of the constancy of the speed of light

  • All photons move with the same velocity. Thus, they all follow gravitogeodesic paths.

Basics of Einstein's understanding of gravitation

  • Gravity exerts an attraction on other bodies, but is not a force. On the falling body no acceleration acts (we are always weightless at the free fall in the airless space!, we feel no force).
  • The gravitational potential is not only composed of the surrounding masses but is self-amplifying, the larger the surrounding masses are.
  • With c, the gravitational potential in the space can be described unambiguously.
  • With increasing gravitational potential the speed of light slows down (from an external observer far away from the point of changing gravitational potential).

To your question about the redshift

  • The geodesic of bodies changes seriously with the changing value of the mass of the central body.
  • The geodesic also changes seriously, if the body is in relation to the other gravitational source in the same order of magnitude.
  • The geodesic changes - not so seriously - also still because of the self-amplifying gravitational effect. For example, our earth orbit would be more curved in the area of an umpteen times heavier sun than to be expected with the Newtonian formula.
  • What has this to do with the redshift of photons? Emitted photons of heavier masses (etalon: our earth) are redshifted.

To your question about the geodesic of photons of different frequency

  • The gravitational potential between two bodies is self-amplifying (thus not simply additive).
  • If another body is added, the speed of light decreases (as always, of course only for an external observer from a space area with invariable gravitational potential).
  • If one agrees that also the presence of energy increases a gravitational potential, thus photons of different energy content change the gravitational potential differently and thus also the local c. But this effect is purely academic and will play a role at most for gamma bursts etc..
HolgerFiedler
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