<blockquote>
  <p>Is blue light not travelling faster then red light in space?</p>
</blockquote>

<p>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.      </p>

<blockquote>
  <p>I just can't understand why light and other massless particles are not traveling at different speeds?</p>
</blockquote>

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

<blockquote>
  <p>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.</p>
</blockquote>

<p>Gravity doesn't just affect anything with mass. Light is massless, but gravity affects it. As to why, see what Einstein said in <a href="https://einsteinpapers.press.princeton.edu/vol7-trans/156?highlightText=%22spatially%20variable%22" rel="nofollow noreferrer">1920</a>: <em>“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”</em>.</p>

<p>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:</p>

<p><a href="https://i.sstatic.net/r6dpT.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/r6dpT.jpg" alt="enter image description here"></a> </p>

<p><sup>Image from FAS and the US Navy, see <a href="https://fas.org/man/dod-101/navy/docs/es310/syllabus.htm" rel="nofollow noreferrer">course ES310 chapter 20</a></sup></p>

<p>Also see Professor Ned Wright’s <a href="http://www.astro.ucla.edu/~wright/deflection-delay.html" rel="nofollow noreferrer">Deflection and Delay of Light</a> article. He says this: <em>“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”</em>:</p>

<p><a href="https://i.sstatic.net/DU50e.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DU50e.gif" alt="enter image description here"></a></p>

<p><sup>Gif from Ned Wright’s Deflection and Delay of Light</sup></p>

<p>That delay ties in what Einstein said. Which ties in with the Shapiro delay. See the <a href="https://en.wikipedia.org/wiki/Shapiro_time_delay" rel="nofollow noreferrer">Wikipedia article</a> on that, and note this: <em>"according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path"</em>. It doesn't matter what the wavelength is, the light curves the same regardless of wavelength. </p>

<p>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 <a href="https://arxiv.org/abs/physics/0508030" rel="nofollow noreferrer">https://arxiv.org/abs/physics/0508030</a>. That ought to tell you that what you usually hear about light and matter  <em>"following the curvature of spacetime"</em> is just <a href="https://en.wikipedia.org/wiki/Lie-to-children" rel="nofollow noreferrer">lies to children</a>.  </p>

CC BY-SA 4.0
2019-04-17T22:58:00.550Z
The bending effect on massive particles in GR asymptotically approaches that of massless particles as $v \rightarrow c$. (e.g. https://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.
ProfRob
CC BY-SA 4.0
2019-04-18T10:24:08.250Z
@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 https://arxiv.org/abs/1508.06478 and [What is spin?](https://staff.fnwi.uva.nl/m.renzo/materials/WhatIsSpin.pdf) 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
CC BY-SA 4.0
2019-04-17T13:51:20.553Z
2019-04-18T10:48:56.760Z
2019-04-18T10:48:56.760Z
John Duffield
<p>Photons are massless. This doesn't depend on their energy, so doesn't depend on their frequency or wavelength.</p>

<p>Massless particles travel at the speed of light.</p>

<p>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.</p>

<p>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.</p>

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

<p>The gravitational bending of light <em>must</em> 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 <span class="math-container">$c$</span>) 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 <a href="https://arxiv.org/abs/gr-qc/0311010" rel="nofollow noreferrer">Barrabes &amp; Hogan 2004</a> (see their eqn 4.5). The reason, as discussed by <a href="https://press.princeton.edu/titles/11169.html" rel="nofollow noreferrer">Misner, Thorne &amp; Wheeler</a> (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 <em>space</em>; but their tracks through space-time have the same curvature. </p>

CC BY-SA 4.0
2019-04-16T17:45:04.853Z
That is where I trip up mentally. I can see the 3 dimensional bending of space then why isn't all massless particles effected by mass's presents like hawking radiation?
Muze
CC BY-SA 4.0
2019-04-16T18:48:59.337Z
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
CC BY-SA 4.0
2019-04-17T13:53:30.760Z
So why is the deflection of light twice the deflection of matter?
John Duffield
CC BY-SA 4.0
2019-04-17T14:29:48.923Z
Matter does not travel on null geodesics.
Steve Linton
CC BY-SA 4.0
2019-04-17T23:03:22.240Z
@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
ProfRob
CC BY-SA 4.0
2019-04-18T07:43:51.077Z
@Rob Jeffries : can you show me  where Einstein predicted the GR deflection of matter to be twice the Newtonian deflection of matter?
John Duffield
CC BY-SA 4.0
2019-04-18T10:05:18.693Z
@Rob Jeffries : because he's the author of general relativity. Now, can you show me where he said the GR deflection of matter would be twice the Newtonian deflection of matter?
John Duffield
CC BY-SA 4.0
2019-04-18T10:11:50.373Z
@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..
ProfRob
CC BY-SA 4.0
2019-04-18T10:46:49.337Z
I've amended my answer to say Ned Wright said the GR deflection of light is twice the Newtonian deflection of light. I also said the latter is based on the deflection of matter, see https://arxiv.org/abs/physics/0508030 for an example. You're saying light and matter curve the same because they're following a straight line in curved spacetime. I'm sorry, but that's incorrect. Curved spacetime is associated with the tidal force. The force of gravity g is 9.8m/s² at the floor of the room you're in, and 9.8m/s² at the ceiling. So there's no spacetime curvature. But light still curves downwards.
John Duffield
CC BY-SA 4.0
2019-04-18T11:42:05.903Z
"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.
ProfRob
CC BY-SA 4.0
2019-04-19T08:35:27.320Z
I reiterate, space-time curvature does not cause light to curve. If g is 9.8 m/s², light curves so much, if g is 19.6 m/s², light curves more. If g is 19.6 m/s² everywhere you measure it, there is no spacetime curvature, but light still curves. Einstein never ever said light curves because it follows the curvature of spacetime. Or space. Because it doesn't. It curves because _"the speed of light is spatially variable"_. He also described a gravitational field as a place where space is neither homogeneous nor isotropic. I'm sorry, but MTW is wrong on multiple counts. That's the size of it.
John Duffield
CC BY-SA 4.0
2019-04-19T10:47:09.010Z
@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.
ProfRob
CC BY-SA 4.0
2019-04-19T16:43:04.717Z
@Rob Jeffries: yes, g is slightly lower at the ceiling than at the floor. But that isn't why light curves. The curvature depends on the local value of  g, not on the variation in g. The value of g relates to the local gradient in the speed of light. As [Einstein said](https://einsteinpapers.press.princeton.edu/vol7-trans/156?highlightText=%22spatially%20variable%22) _"the curvature of light rays occurs only in spaces where the speed of light is spatially variable”_. Not for any other reason.So light _doesn't_ curve because spacetime is curved. If MTW says it does, MTW is wrong. Nobels or not.
John Duffield
CC BY-SA 4.0
2019-04-20T08:07:52.580Z
@Rob Jeffries: I've just read section 1.6 of MTW. They start off correctly talking about spacetime curvature in terms of the tidal force. But then they introduce a "higher-dimensional analog" and start talking about spacetime curvature in terms of the gravitational force. However the thrown ball does not travel in a parabolic arc because of spacetime curvature. Ditto for the  bullet. The arc depends on the initial speed and on g, whilst spacetime curvature describes the non-linear vertical variation in g. So I'm afraid this section of MTW is not faithful to Einstein's GR, and is wrong.
John Duffield
CC BY-SA 4.0
2019-04-16T17:34:25.343Z
2019-04-18T12:34:43.977Z
2019-04-18T12:34:43.977Z
ProfRob
<p>I just can't understand why light and other massless particles are not traveling at different speeds?</p>

<p>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.</p>

CC BY-SA 4.0
2019-04-16T17:04:32.953Z
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
CC BY-SA 4.0
2019-04-18T13:30:16.190Z
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
CC BY-SA 4.0
2019-04-23T00:00:38.937Z
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
<redshift><mass><velocity><quantum-mechanics><blueshift>
Is blue light not traveling faster then red light in space?
Muze
# Is blue light not traveling faster then red light in space?

(Asked by: username_0 on 2019-04-16)

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.

**Tags:** redshift, mass, velocity, quantum-mechanics, blueshift
> **Comments:**
> **username_1**: 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.  
> **username_2**: 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"  
> **username_3**: 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  

---

## 2 answers

### Answer by username_5 on 2019-04-16. Score: 7 | Accepted answer

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](https://arxiv.org/abs/gr-qc/0311010) (see their eqn 4.5). The reason, as discussed by [Misner, Thorne & Wheeler](https://press.princeton.edu/titles/11169.html) (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.

> **Comments:**
> **username_0**: That is where I trip up mentally. I can see the 3 dimensional bending of space then why isn't all massless particles effected by mass's presents like hawking radiation?  
> **username_6**: 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?  
> **username_4**: So why is the deflection of light twice the deflection of matter?  
> **username_6**: Matter does not travel on null geodesics.  
> **username_5**: @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  
> **username_4**: @Rob Jeffries : can you show me  where Einstein predicted the GR deflection of matter to be twice the Newtonian deflection of matter?  
> **username_4**: @Rob Jeffries : because he's the author of general relativity. Now, can you show me where he said the GR deflection of matter would be twice the Newtonian deflection of matter?  
> **username_5**: @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..  
> **username_4**: I've amended my answer to say Ned Wright said the GR deflection of light is twice the Newtonian deflection of light. I also said the latter is based on the deflection of matter, see https://arxiv.org/abs/physics/0508030 for an example. You're saying light and matter curve the same because they're following a straight line in curved spacetime. I'm sorry, but that's incorrect. Curved spacetime is associated with the tidal force. The force of gravity g is 9.8m/s² at the floor of the room you're in, and 9.8m/s² at the ceiling. So there's no spacetime curvature. But light still curves downwards.  
> **username_5**: "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.  
> **username_4**: I reiterate, space-time curvature does not cause light to curve. If g is 9.8 m/s², light curves so much, if g is 19.6 m/s², light curves more. If g is 19.6 m/s² everywhere you measure it, there is no spacetime curvature, but light still curves. Einstein never ever said light curves because it follows the curvature of spacetime. Or space. Because it doesn't. It curves because _"the speed of light is spatially variable"_. He also described a gravitational field as a place where space is neither homogeneous nor isotropic. I'm sorry, but MTW is wrong on multiple counts. That's the size of it.  
> **username_5**: @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.  
> **username_4**: @Rob Jeffries: yes, g is slightly lower at the ceiling than at the floor. But that isn't why light curves. The curvature depends on the local value of  g, not on the variation in g. The value of g relates to the local gradient in the speed of light. As [Einstein said](https://einsteinpapers.press.princeton.edu/vol7-trans/156?highlightText=%22spatially%20variable%22) _"the curvature of light rays occurs only in spaces where the speed of light is spatially variable”_. Not for any other reason.So light _doesn't_ curve because spacetime is curved. If MTW says it does, MTW is wrong. Nobels or not.  
> **username_4**: @Rob Jeffries: I've just read section 1.6 of MTW. They start off correctly talking about spacetime curvature in terms of the tidal force. But then they introduce a "higher-dimensional analog" and start talking about spacetime curvature in terms of the gravitational force. However the thrown ball does not travel in a parabolic arc because of spacetime curvature. Ditto for the  bullet. The arc depends on the initial speed and on g, whilst spacetime curvature describes the non-linear vertical variation in g. So I'm afraid this section of MTW is not faithful to Einstein's GR, and is wrong.  

---

### Answer by username_4 on 2019-04-17. Score: -7

> 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](https://einsteinpapers.press.princeton.edu/vol7-trans/156?highlightText=%22spatially%20variable%22): *“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:

[![enter image description here](https://i.sstatic.net/r6dpT.jpg)](https://i.sstatic.net/r6dpT.jpg)

Image from FAS and the US Navy, see [course ES310 chapter 20](https://fas.org/man/dod-101/navy/docs/es310/syllabus.htm)

Also see Professor Ned Wright’s [Deflection and Delay of Light](http://www.astro.ucla.edu/~wright/deflection-delay.html) 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”*:

[![enter image description here](https://i.sstatic.net/DU50e.gif)](https://i.sstatic.net/DU50e.gif)

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](https://en.wikipedia.org/wiki/Shapiro_time_delay) 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](https://en.wikipedia.org/wiki/Lie-to-children).

> **Comments:**
> **username_5**: The bending effect on massive particles in GR asymptotically approaches that of massless particles as $v \rightarrow c$. (e.g. https://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.  
> **username_4**: @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 https://arxiv.org/abs/1508.06478 and [What is spin?](https://staff.fnwi.uva.nl/m.renzo/materials/WhatIsSpin.pdf) 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.  

---

