13

If the energy of light is high, does its curvature differ from that of low-energy light around the Sun? In other words, if the wavelength of the light is shorter than another wavelength of light, then does the bending of the two lights differ around the Sun?

Chappo Hasn't Forgotten
  • 1,213
  • 2
  • 12
  • 27
Red Bel
  • 179
  • 3
  • 2
    No, the amount of bending is the same for all wavelengths. See https://astronomy.stackexchange.com/q/33341/16685 & https://physics.stackexchange.com/q/46996/123208 – PM 2Ring Apr 05 '21 at 04:43
  • 2
    What is dependent on the energy of the beam is how much it bends space (to affect other light beams or matter). – Ross Presser Apr 05 '21 at 14:24
  • @PM2Ring I enjoy taking things to their extreme. What if the photon was so energetic it actually had a significant gravitational pull by itself? – Stian Apr 06 '21 at 12:20
  • 1
    @StianYttervik That's very extreme! As Ross said, in theory, a light beam does affect the spacetime curvature, but the effect is tiny that it's usually neglected, although cosmologists do include the energy density due to EM radiation in their calculations of spacetime curvature and expansion. – PM 2Ring Apr 06 '21 at 13:43
  • 1
    @RossPresser Indeed! But the effect is small. Imagine we could focus the entire light output of the Sun into a cylindrical beam of radius R. The luminosity of the Sun is L=3.828E26 watts, which is equivalent to ~4.259 billion kg/s. The density of the beam is $\rho=\frac{L}{\pi R^2c^3}$. Using the formula here for the surface gravity of an infinite cylinder, $g=2\pi G\rho R$, we get $g=\frac{2GL}{c^3R}$. Using R = 1 mm, Google Calculator says (2*(3.828E26 W)*(6.6743E-11 m^3kg^-1s^-2)/c^3)/(1 mm) is ~$1.8965×10^{-6},m/s^2$ – PM 2Ring Apr 06 '21 at 14:00
  • @PM2Ring Interesting calculation. What about https://en.wikipedia.org/wiki/GRB_080916C? – Peter - Reinstate Monica Apr 06 '21 at 17:43
  • @Peter Yes, that probably bent spacetime a fair bit. ;) – PM 2Ring Apr 06 '21 at 18:12

1 Answers1

18

The amount of "gravitational light bending" is independent of the photon energy (light wavelength).

The reason is that the light follows a path through spacetime that is appropriate for a massless particle and this is unique for a given set of initial conditions.

That this is so is amply demonstrated by the consistent angular displacement of "stars" near the limb of the sun whether observed at optical or radio wavelengths.

As pointed out in comments - there are small effects that must be taken into account, associated with the well-understood phenomenon of refraction in the corona of the Sun. However, these do not affect observations of lensing taken well away from the solar limb - which is easily possible at radio wavelengths and now becoming possible for the same sources using Gaia data.

Further evidence comes from the wavelength-independent nature of gravitational lensing and microlensing seen outside the solar system.

ProfRob
  • 151,483
  • 9
  • 359
  • 566
  • I've seen the experiment of bending light from stars around the sun. But has this been confirmed in any practical experiment? – Robert Andrzejuk Apr 05 '21 at 20:12
  • 1
    "light follows a path" In particular, correct my layperson's understanding as needed, light follows a straight line in curved space. A straight line is a straight line regardless of the nature of what's following it. – Don Branson Apr 05 '21 at 20:40
  • This might just raise the question of whether that particular assumption built into general relativity is in fact correct. How do we know that the motion of an electromagnetic wave packet should follow a well-defined path, which we can define as a geodesic -- regardless of its energy? One possible argument that it must be correct is that classically, we can chop any wave packet into two spatially separated wave packets, each with, say, half the energy. –  Apr 05 '21 at 20:42
  • @DonBranson except that objects with mass also follow "straight lines", but they are different to the "straight lines" followed by light, despite no forces acting upon them. – ProfRob Apr 05 '21 at 22:04
  • 1
    @ProfRob This is a great answer accounting for the bending of light due to gravity, but what about the much larger effect of refraction by the Solar Atmosphere? – Connor Garcia Apr 05 '21 at 22:44
  • 1
    @ProfRob oh, I though they were the same. How are they different? – Don Branson Apr 05 '21 at 22:53
  • 2
    @DonBranson if you shine a laser or throw a ball, they follow different paths through spacetime. Both are geodesics and there is no force on either. – ProfRob Apr 06 '21 at 00:02
  • 2
    @DonBranson The curvature of a trajectory through space is not the same as the curvature of a worldline through spacetime. Please see Why does the speed of an object affect its path if gravity is warped spacetime? – PM 2Ring Apr 06 '21 at 07:44
  • 1
    @PM2Ring - Finally made time to read that question. Thanks, it really clears things up. – Don Branson Apr 27 '21 at 19:25