# Is blue light not traveling faster then red light in space?

I just can't understand why light and other massless particles are not traveling at different speeds?

Gravity effects anything with a mass but light has no mass but a black hole, and weak lensing changes the trajectory of light to create more red shifted light more than blue shifted light. That tells me light has mass. Can someone clarify this to me in Laymons terminology? Pictures would be helpful.

• Relativity says that massless particles must have a local speed of c in a vacuum, due to the way spacetime geometry works. You might as well ask why (in Euclidean geometry) are the base angles of an isoceles right triangle always 45°. light has not mass but a black hole Doesn't make sense. weak lensing changes the trajectory of light and red more than blue No it doesn't. I suspect you misunderstood something you read. – PM 2Ring Apr 16 '19 at 17:04
• You are thinking in Newtonian physics terms, but look at this: F= m*a. If the objects are massless that means the acceleration will be infinite irrespective of the force applied being huge or tiny. Note light obeys "causality speed" – jean Apr 18 '19 at 13:30
• I don’t have time to write an answer at the moment but i believe your confusion surrounds how bending light actually happens. Remember, space-time itself is curved to the presence of the black hole (or any object with mass) so from the perspective of the photon, it is traveling in a straight line – dalearn Apr 23 '19 at 0:00

Photons are massless. This doesn't depend on their energy, so doesn't depend on their frequency or wavelength.

Massless particles travel at the speed of light.

Even if we abandon particles and look at classical electrodynamics, we find that the speed of an electromagnetic wave (in vacuum) has a fixed value. It doesn't depend on wavelength.

Gravitational lensing affects light of all wavelengths equally. Lensing is caused by light travelling on null geodesics - basically the "straightest line" it can follow in space-time that has been curved by the presence of mass.

EDIT (Not required for any understanding of my answer, which stands as is, but to address some comments below).

The gravitational bending of light must take into account the curvature of space-time. If that is not done, then one gets the "Newtonian" formula which is half the deflection of a correct GR treatment. For particles with mass (which isn't what this question is about), the appropriate formula for their deflection will depend on their speed. At low speeds, the Newtonian formula will work just fine. At high speeds (approaching $$c$$) the deflection asymptotically approaches that for a light beam (i.e. twice the Newtonian value and the same as light). A mathematical proof of the latter in the Schwarzschild and Kerr metrics is provided by Barrabes & Hogan 2004 (see their eqn 4.5). The reason, as discussed by Misner, Thorne & Wheeler (in "Gravitation", 2017 Princeton University Press, chapter 1, section 1.6 - freely available from the linked site) is that gravitation is not just due to the curvature of space, but the curvature of space-time. The tracks of light and (non-relativistic) particles follow distinctly different paths, with different curvatures, through space; but their tracks through space-time have the same curvature.

• All massless particles are affected by mass's presence. They all travel along null geodesics, which are determined by the shape of space, which is in term connected to what the mass in that area of space is doing. Where does Hawking radiation come into it? – Steve Linton Apr 16 '19 at 18:48
• @JohnDuffield It isn't. The deflection is almost identical if the matter is travelling close to $c$. There is no straightforward factor of 2 difference. You are confused between the difference between the predictions of GR and Newtonian gravity – Rob Jeffries Apr 17 '19 at 23:03
• @JohnDuffield What Einstein said (eventually) was that light would be deflected by twice what Newtonian gravity would predict. Where did he say that matter was deflected by half as much as light? It's your claim, you prove it. And even if Einstein did say that, then he was wrong too! More indisputably, you've also wrongly claimed that Ned Wright supports your statement, which you should remove.. – Rob Jeffries Apr 18 '19 at 10:11
• "Einstein’s first calculation of the gravitational deflection of light, in 1911 (see [4], for a historical account and scientific references), was performed using the Equivalence Principle and the equivalent mass-energy of a photon. The calculation yielded δNG. Only in his second calculation, published in 1916, where he included the effect of space-time curvature, he obtained a value twice as large as his first calculation, i.e., δGR [4]." From the very paper you cite. – Rob Jeffries Apr 18 '19 at 11:42
• @JohnDuffield Can I just point out, amongst the many things you are wrong about (and which Nobel-prize-winning General Relativist Kip Thorne is correct) is that there is space-time curvature in the hypothetical room you introduce and indeed $g$ is slightly lower at the ceiling than it is at the floor. – Rob Jeffries Apr 19 '19 at 10:47

Is blue light not travelling faster then red light in space?

No it isn't. Oddly enough, it isn't travelling faster than red light in a prism either. Here's an analogy: A little old lady scurries along the pavement at 4mph. A tall young man strides along the pavement at 4mph. When the pavement is clear, that's like space. When the pavement is crowded, that's like a prism. Then the little old lady and the tall young man are both moving at 4mph, but the tall young man has big strides so he spends longer getting round the people in his way. So the little old lady makes better progress. So it looks like she's moving faster.

I just can't understand why light and other massless particles are not traveling at different speeds?

As far as we can tell photons and neutrinos travel at the same speed in space regardless of their energy.

Gravity effects anything with a mass but light has no mass but a black hole, and weak lensing changes the trajectory of light to create more red shifted light more than blue shifted light. That tells me light has mass. Can someone clarify this to me in Laymans terminology? Pictures would be helpful.

Gravity doesn't just affect anything with mass. Light is massless, but gravity affects it. As to why, see what Einstein said in 1920: “Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable”.

Did you see what he said about light curving because the speed of light is spatially variable? It's rather like the way sonar waves curve in the ocean:

Image from FAS and the US Navy, see course ES310 chapter 20

Also see Professor Ned Wright’s Deflection and Delay of Light article. He says this: “In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light. The figure below shows a bundle of rays passing the Sun at various distances”:

Gif from Ned Wright’s Deflection and Delay of Light

That delay ties in what Einstein said. Which ties in with the Shapiro delay. See the Wikipedia article on that, and note this: "according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path". It doesn't matter what the wavelength is, the light curves the same regardless of wavelength.

PS: Ned Wright points out that the deflection of light is twice the Newtonian deflection of light. The latter is based on the deflection of matter, see for example https://arxiv.org/abs/physics/0508030. That ought to tell you that what you usually hear about light and matter "following the curvature of spacetime" is just lies to children.

• The bending effect on massive particles in GR asymptotically approaches that of massless particles as $v \rightarrow c$. (e.g. arxiv.org/abs/1512.04037). And you can't blame Ned Wright, because he definitely does not say what you attribute to him in your ps. Lies to children indeed. – Rob Jeffries Apr 17 '19 at 22:58
• @Rob Jeffries : Ned Wright said the GR deflection of light was twice the Newtonian deflection. The latter treats light as if it's matter. I believe the 2015 paper by Xionghui Liu et al is incorrect because you can model matter as a photon in a mirror box, see arxiv.org/abs/1508.06478 and What is spin? by Hans Ohanian. Think of light going round a path like this: □. Only the horizontals curve downwards. Hence the deflection of light is twice the deflection of matter. – John Duffield Apr 18 '19 at 10:24