The speed of light is not constant

The speed of sound in air is sometimes said to be 343.2 metres per second or 768 miles per hour. But actually, it varies. It usually decreases with altitude up to about 11 kilometres above sea level. That’s about 36,000 feet, which is typical for a passenger jet. At that altitude the speed of sound is circa 295 m/s or 660 mph, which is one reason why passenger jets don’t fly as fast as you might like. Interestingly enough, the speed of sound typically decreases with increasing altitude, so sound tends to get refracted upwards. It’s similar for sound waves in the sea, but there the speed of sound typically decreases with depth. So a horizontal sonar wave tends to get refracted downwards:

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

The sonar waves “veer” rather like a car veers when it encounters mud at the side of the road. The mud slows down the wheels on the left, so the car pulls to the left. You steer a tank to the left in a similar fashion, by slowing down the track on the left.

It’s c for celeritas which means speed

See Wikipedia and you can read that the speed of sound “is conventionally represented by c, from the Latin celeritas”. Celeritas means swiftness or speed, which varies according to the properties of the medium. The speed of sound in sea water is circa 1500 m/s or 3,355 mph. In steel it’s circa 6000 m/s or 13,421 mph. In diamond it’s circa 12,000 m/s or 26,843 mph. It’s similar for seismic waves. Wikipedia says the propagation velocity depends on the density and elasticity of the medium, and is up to 13 km/s in the deep mantle. That’s 13,000 m/s or 29,080 mph. Of course in seismology we have P-waves and S-waves. The former are “primary” longitudinal waves like sound waves. The latter are “secondary” transverse waves like light waves. The equation for the speed of a transverse seismic wave is given as csolid,s = √(G/ρ), where G is the shear modulus and ρ (rho) is the density. The equation for the speed of light in the vacuum of space is given as c = 1/√(ε0μ0) where ε0 is vacuum permittivity and μ0 is vacuum permeability. There’s a reciprocal because permittivity is a “how easy” measure rather than a “how hard” measure. Other than that, the equation takes the same general form, and the speed of light in space, in “vacuo”, is said to be 299,792,458 m/s or 670,616,629 mph.

The speed of light in space is said to be constant

Note that the speed of sound in air varies, the speed of sound in water varies, and the speed of seismic waves in rock varies. But it is said that the speed of light in space does not vary. Search the internet and you can find lots of articles saying this. See for example Luke Mastin’s article on the speed of light and the principle of relativity. He talks about the Michelson-Morley experiment, which “unexpectedly demonstrated that light travels at the same speed regardless of whether it was measured in the direction of the Earth’s motion or at right angles to it”. Mastin also says when light moves from one medium to another, its speed “can of course change depending on the new medium’s index of refraction, and this “bending” of light is essentially how lenses work”. However he doesn’t mention gravitational lensing. Instead he says regardless of the speed of a light source and regardless of your speed, the “light still travels at a steady 300,000 km/s, completely contrary to classical physics and common sense”. He also says it was the young Einstein’s genius to explain why. And that in 1905, Einstein realized that “the whole idea of aether as a medium for light to travel in was totally unnecessary”. It sounds good. Especially since “the constant speed of light was to become one of the two main planks of his Special Theory of Relativity”. Unfortunately there’s a problem. A big problem. How big? The size of Texas.

When a clock goes slower

If you had a clockwork clock that was running slow, and I told you it was because time was running slow inside the clock, you’d laugh in my face. You’d know that it was due to some issue with the mechanism. Perhaps the oil was drying out and gumming up the works. Whatever the reason, you’d know that your clock was going slower because the clockwork was going slower. So, what if I showed you an optical clock going slower? An optical clock is typically an atomic clock which employs ytterbium atoms instead of caesium atoms, and visible light instead of microwaves. It isn’t some cosmic gas meter with time flowing through it. Nor is a clockwork clock. When a clockwork clock goes slower it’s because the clockwork goes slower. And when an optical clock goes slower, it’s because the optics goes slower:

ytterbium lattice double clock image from NIST

And when does an optical clock go slower? See the interview with David Wineland of NIST: “if one clock in one lab is 30cm higher than the clock in the other lab, we can see the difference in the rates they run at”. An optical clock goes slower when it’s lower. This is said to be the hard scientific evidence for gravitational time dilation. But it’s really the hard scientific evidence for light goes slower when it’s lower.

Einstein’s postulate only lasted two years

Yes, Einstein said the speed of light is constant in 1905 when he was doing special relativity, but by 1907 he was broadening his horizons and looking into what would become general relativity. That’s when he wrote a paper on the relativity principle and the conclusions drawn from it. He used Φ (phi) to denote gravitational potential, and he said this: “These equations too have the same form as the corresponding equations of the nonaccelerated or gravitation-free space; however, c is here replaced by the value c[1 + γξ/c²] = c[1 + Φ/c²]. From this it follows that those light rays that do not propagate along the ξ-axis are bent by the gravitational field”. Only two years after his special relativity postulate, there’s Einstein talking about a speed of light that varies with gravitational potential. This wasn’t some one-off. He said the same thing in 1911. That’s when he wrote a paper on the influence of gravity on the propagation of light. He said this: “If c₀ denotes the velocity of light at the coordinate origin, then the velocity of light c at a point with a gravitation potential Φ will be given by the relation c = c₀(1 + Φ/c²). The principle of the constancy of the velocity of light does not hold in this theory in the formulation in which it is normally used as the basis of the ordinary theory of relativity”. He said the principle of the constancy of the velocity of light does not hold. And it’s clear from the context that the word velocity is as per “high velocity bullet”. It’s the common usage as opposed to the vector quantity. Einstein was talking about the speed of light, which is why he was referring to c.

Einstein’s VSL attempt in 1911

There’s a Wikipedia article on the Variable Speed of Light, which is often abbreviated to VSL. If you take a look at an old version dating from 2014, you can see a section entitled Einstein’s VSL attempt in 1911. This says Einstein first mentioned a variable speed of light in 1907 and reconsidered the idea more thoroughly in 1911. However it then goes on to say Einstein abandoned the idea in 1912 because it only predicted half the deflection of light by the Sun. However it isn’t true. Einstein didn’t abandon the idea. That’s why you can find him saying the same thing year after year:

1912: “On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential”.

1913: “I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis”.

1914: “In the case where we drop the postulate of the constancy of the velocity of light, there exists, a priori, no privileged coordinate systems.”

1915: “the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned”.

1916: “In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity”.

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”.

The last quote is the English translation of what Einstein said in German in 1916: “die Ausbreitungsge-schwindigkeit des Lichtes mit dem Orte variiert”. That translates to “the propagation speed of light with the place varies”. Einstein never did abandon his variable speed of light. The people who tell you that grew up before the Einstein digital papers were online. The general relativity they were taught wasn’t the same as Einstein’s.

A shift in interpretation

As to why, see Clifford M Will’s paper The Confrontation between General Relativity and Experiment. On page 4 he refers to a period of hibernation between 1920 and 1960, and a golden era between 1960 and 1980. On page 9 he says special relativity only became mainstream in the late 1920s. That sounds odd. Something else that sounds odd is something in the Wikipedia history of general relativity article. It says Kip Thorne “identifies the “golden age of general relativity” as the period roughly from 1960 to 1975 during which the study of general relativity, which had previously been regarded as something of a curiosity, entered the mainstream of theoretical physics”. So, special relativity wasn’t mainstream until circa 1930, and general relativity wasn’t mainstream until circa 1960. There’s more, because during this golden age, “many of the concepts and terms which continue to inspire the imagination of gravitation researchers and the general public were introduced”. All in all it would seem that something was changed, and something was lost.

The speed of a light wave depends on the strength of the gravitational potential along its path

As for when I’m not sure. But Irwin Shapiro was talking about the variable speed of light in 1964. His paper was all about what we now call the Shapiro delay. Wikipedia faithfully quotes what Shapiro said, which is that “the speed of a light wave depends on the strength of the gravitational potential along its path”. That’s in line with Einstein and the evidence of optical clocks going slower when they’re lower. And yet when you google it, you find people saying the Shapiro delay is caused by the distance between source and emitter being longer”. And you find people saying the unchanging speed of light in a vacuum is a foundational fact of relativity. There’s a huge contradiction between what Einstein said and what many physicists say today. So much so that general relativity today sometimes feels like an ersatz imitation of the real thing, authored by people who advocate time travel.

The prevailing opinion is wrong

However with a nudge from yours truly, the Wikipedia Variable Speed of Light article now talks about Einstein’s proposals after 1911. It says this: “there is no other way to interpret the velocity of light in this usage except as a variable scalar speed”. It also says Peter Bergmann did not agree with Einstein, but left the dispute out of his earlier book in 1942 to get Einstein’s endorsement”. Peter Bergmann was Einstein’s research assistant in Princeton between 1936 and 1941. He wrote the first textbook on general relativity in 1942. But after Einstein died “Bergmann wrote a new book in 1968 claiming that vector light velocity could change direction but not speed. This has become a prevailing opinion in science”. I’m afraid to say that this prevailing opinion is wrong.

The tautology

Of course, not all physicists say the speed of light in vacuo is constant. Two who don’t are John Moffat and João Magueijo. In their 2007 Comments on “Note on varying speed of light theories” they said this: “Can c vary? Could such a variation be measured? As correctly pointed out by Ellis, within the current protocol for measuring time and space the answer is no. The unit of time is defined by an oscillating system or the frequency of an atomic transition, and the unit of space is defined in terms of the distance travelled by light in the unit of time. We therefore have a situation akin to saying that the speed of light is “one light-year per year”, i.e. its constancy has become a tautology or a definition”. They talked about a tautology. To appreciate this, take a look at the NIST caesium fountain clock:

Image courtesy of NIST

It’s used to define the second as “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom”. The radiation is microwave radiation, which is light in the wider sense. In essence you count light waves going by, and when you get to 9,192,631,770 you say a second has elapsed. Then you use the second along with the light to define the metre as “the length of the path travelled by light in vacuum during a time interval of 1 ⁄ 299,792,458th of a second”. You use the motion of light to define the second and the metre. And then you use them to measure the motion of light. That’s why you always measure the speed of light to be 299,792,458 m/s. It doesn’t matter how fast the light is moving, you will always end up saying the speed of light is 299,792,458 m/s. That’s the tautology. The speed of light is defined to be constant, and it is absolutely amazing that this is not generally recognised. Can you imagine what you’d think if somebody tried to tell you that the speed of racehorses was constant? And that the winning horse won because time flowed faster for it? You’d think they were crazy, or stupid, or both. But that’s what they tell you about optical clocks, and about light.

The reality that underlies gravitational time dilation

Imagine you repeated your definition of the second and the metre at a lower elevation. Light goes slower when it’s lower. When the light goes slower the second is bigger. Then the slower light and the bigger second cancel each other out such that the metre is unchanged. You will still say the speed of light is 299,792,458 m/s. Then you might be tempted to say 299,792,458 m/s at one elevation is the same as 299,792,458 m/s at another, even though the metres are the same and the seconds aren’t. That’s clearly wrong. It’s like saying 100 metres per second is the same as 100 metres per second and a half. But people will insist that 299,792,458 m/s at one elevation really is the same speed as 299,792,458 m/s at another, even though they know the seconds are different. They insist even though they know that optical clock rates vary and there isn’t any actual time flowing through them. Even though they know that the things that move inside optical clocks are things like light. At times the resistance is dogged. At time it’s almost mindless, as if Morton’s demon is sitting on their shoulder. You have to make things extremely simple to corner the reluctant ego. The simplest thing I’ve found is the parallel-mirror light-clock. It’s employed in the simple inference of time dilation due to relative velocity, and it can also be employed to demonstrate the simple reality that underlies gravitational time dilation. See this gif:

Gif image by Brian McPherson

The two light pulses aren’t going at the same speed. If they were, the parallel-mirror light clocks would stay in time. And if they did, the NIST optical clocks at different elevations would stay in time too. Only they don’t.

The speed of light varies in the room you’re in

See Is The Speed of Light Everywhere the Same? It’s a PhysicsFAQ article by Don Koks. He talks about laser gyroscopes and the Sagnac effect, and later says “Einstein talked about the speed of light changing in his new theory”. This new theory was of course general relativity, which concerns non-inertial reference frames. The article goes on to say the room you’re sitting in right now is a very high approximation to a non-inertial reference frame. And that whilst an observer stationed at the ceiling will measure the speed of light to be c, as will the observer stationed at the floor, the “global” observer will say that light at the ceiling travels faster than light at the floor. You aren’t situated at the ceiling, or at the floor. You’re sitting in your chair. You are that global observer. What this means, is that the speed of light varies in the room you’re in. If it didn’t, your pencil wouldn’t fall down. Pick up your pencil, hold it up at head height, then drop it on your desk. The speed at which it hits the desk depends on the difference between the speed of light at head height, and the speed of light at desktop height. The speed of light varies like the speed of other waves vary. Just like Einstein said.

The ascending photon speeds up

The situation is similar to sound waves in the sea, where the speed of sound typically decreases with depth. That’s why a horizontal sonar wave bends downwards. In similar vein the horizontal light wave bends downwards because the speed of light decreases with elevation. However the vertical sonar wave does not bend downwards, and nor does the vertical light wave. Imagine you had a torch that could emit a single photon. Imagine you aimed it straight up and pressed the button. What happens to the ascending photon? It isn’t like an ascending brick. The speed of light at the ceiling is greater than the speed of light at the floor. So the photon doesn’t slow down as it ascends. Au contraire, the ascending photon speeds up. This is, of course, a matter of some gravity.


This Post Has 73 Comments

  1. Before forming a logical conclusion on (constancy of) linear speed of light, it is essential to know what is light and its constituents? How does it move? and what is its moving mechanism?

    1. It moves like other transverse waves moves, Nainan, due to the properties of the thing it moves through. In a few weeks I shall post an article called What is a photon? It will show you the scientific evidence that tells you that the photon has an E=hf wave nature, but is neither a wave train nor a wave packet. Nor is it an electric wave and an orthogonal magnetic wave that generate one another. Instead it’s a singleton soliton electromagnetic wave with a “quantum” nature.

  2. Johnk90

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    1. Sorry John, I don’t have any tips. I’m new to this blogging game, I’m still finding my feet. I just set up the website on Godaddy then followed some instructions to allow “crawlers” to scan it, then logged onto Bing to tell them about the website. Can you give me a link to what you saw on Yahoo News? I couldn’t find anything there about it. Just a search result. (Search on Google and what comes up is the PSYCHIC detective, tsk). Thanks for the compliment by the way, much appreciated.

  3. Jim

    “the unchanging speed of light in a vacuum is a foundational fact of relativity”
    The unchanging top speed through space in a vacuum, C, is a foundational principal of *Special* Relativity. General Relativity is based on a different principal: that acceleration and gravity are equivalent (crudely speaking).
    It is important to be clear which theory you’re discussing in this context.
    What general relativity says is that gravity affects which paths light takes. Astronomers benefit from that effect when studying distant objects through a “gravitational lens”
    This is similar to the speed of light altering when it travels through, say, water. The reason for the “slow” down is not that photons are actually moving slower, but rather that they’re being absorbed and re-emitted by electrons. The Dirac equation tells you the physics.

  4. Johnk274

    Very efficiently written post. It will be valuable to anyone who usess it, as well as myself. Keep doing what you are doing i will definitely read more posts. gedkabaeddde

    1. Jim

      @Johnk274 – do not get your physics from this blog, because this blog says thinks like “the speed of light is not constant” which is misleading. Although beams of light might not have a constant rate of propagation through materials, that’s due to photons being absorbed and re-emitted. Photons themselves travel at C – which is measured to be constant, not a variable, to high precision.
      Let me say that again – the speed of photons is constant, as is the speed of all zero-mass particles. C.

      1. Jim: I’ve given you Einstein saying the speed of light is not constant, plus Irwin Shapiro, plus Ned Wright, plus Joao Magueijo and John Moffat, plus Don Koks. I’ve also told you that a clock is not some cosmic gas meter with time flowing through it, so an optical clock doesn’t go slower when its lower because time goes slower when it’s lower. Now if you’re going to dismiss all that and cling to notions like gravitational lensing is caused by the absorption and re-emission of photons, and then tell people they shouldn’t get their physics from this blog, you and I are going to fall out. Follow my links, read the original material by Einstein etc, and do your own research and think for yourself.

  5. Andy Hall

    The speed of light constant in vacuum is an interesting combination of two ideas. One that the speed of light is constant and two, that there is a vacuum. There is definitely space. It is observable and obvious. The dark thing between the illuminated stuff in the sky is space. However, it is not nothing. Light goes through it, which makes it not empty. How much light goes through it? Enough to allow us to see everything visible and, presumably enough to make sure all the visible stuff stays where it is. There is a scary amount of idealism that passes for fact and masks the consideration of the real nature of things. Can there even exist a perfect vacuum devoid of light? If there is no perfect vacuum, then all of the light travelling through the near vacuum will interact locally with any other light it encounters. It will also interact with the effect of mass on space in the vicinity of the mass. Hence, gravitational lensing due to the effect of mass increasing the local energy density in its vicinity. I generally can’t find fault with the sentiments and factual direction of this blog. It chimes with both my gut feel and my interpretation of the facts of which I am aware.

    1. John Duffield

      Thanks Andy. When you appreciate that Einstein, Shapiro, and many others have been saying the speed of light is not constant since 1907, it more than just chimes.

      It strikes you that the speed of light is constant is a myth, and yet physicists believe in it. So much so that they don’t know how gravity works, and think a gravitational field is curved space. Then when it comes to classical electromagnetism and quantum electrodynamics, they’re lost, with no concept of the underlying reality. Worse, they don’t know that they’re lost, and won’t look beyond the streetlight.

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  9. CG

    Thank you!
    Thank you very much for this blog!
    The past couple of months I (i.e. someone who is acquainted with natural sciences only from an “outside-look”) was devoting way too much time searching for online articles to straightening out + clarify some of the things that just would not add up for me, within the [perceived] current status quo of nowadays astrophysics; too many arrogant students regurgitating what they read, copying the “understanding” of what they’ve been taught, to then talk down on any doubter (the illusion of education = intelligence/understanding); as if being born later automatically elevates them above historical misunderstandings, and thus could not be wrong, while anyone not tied into the mysteries they were inaugurated into, was automatically wrong, an imbecile, a .
    I slept quite bad, thinking about the M.Morley-experiment and the crude “conclusions” drawn from it, which seemed more like a cheat (Lorentz-transformation) than the actual relative movements of corresponding particles (maybe the misunderstanding still solely lies with me); and even though this article is more concerned with general relativity rather than special, it did help; and restored some of the respect I had for Albert Einstein and his theories… “so it really was the detractors which now pose as his heirs… huh! – how history again and again tends to repeat itself when it comes to progress and the reception of great minds and ideas…”.
    So, once again: thank you!

    Anyways; I often wondered: was there ever a scientific experiment to clarify, if polarized light bends differently, according to the polarization? that is to say: weaker for the light polarized transverse to the gravitational source, and weaker for the one being polarized vertically. — or in other words: do black holes polarize light, by bending some parts less so than others?!?

    PS: I’m German; if anything I just said sounds crude/odd/not right (grammatically that is), attribute it to the fact that my native tongue isn’t English 🙂

  10. My pleasure CG. I hope you find these articles useful. Yes, there are some arrogant people regurgitating what they’ve been taught without thinking for themselves. I think it’s rather sad, especially since Einstein had his “miracle year” when he was only 26.
    Sorry, I don’t know of any scientific experiment that demonstrates that polarized light bends differently. I haven’t heard of any scattering associated with gravitational lensing.
    Your English is just fine. And a whole lot better than my German!

  11. CG

    It’s not like I have heard about that effect, either; it’s just one of those interpretations that seem natural to me to assume — given some other assumptions… — as such i’d like to falsify or verify my suspicion (clarity is a nice thing to achieve), whatever it should turn out to be!
    Thanks for the answer!
    PS: IQ usually is highest earlier on; it’s not entirely unusual, for any thinker, to come up with his/her best ideas in their late 20’s; even though they may only come to full fruition later on, when one has worked out all the flaws.
    + I am a bit jaded when it comes to the many who do not think for themselves, even from within the realms of higher education. Seen it too often, and albeit being strongly disappointed, it does not surprise me any more. Just makes me very, very quiet at times…”Für mich nämlich gibt es an dieser Stelle viel zu schweigen. –” (F.N.)

  12. Yes, there is much to be said. Once you’ve read some of the old papers I refer to here, and come to certain conclusions, I suspect you may be very very quiet for quite some time. For example, see what Schrödinger said on page 27 of his 1926 paper quantization as a problem of proper values, part II. About light rays influencing one another and showing remarkable curvature.

  13. hiroji kurihara

    Speed of Light : Reexamination

    Plane waves of light (wavelength is constant) are coming from just above. An observer is moving horizontally at different speed. Speed relative to the waves does not vary. But speed relative to photons or light ray will vary (both will be real existence). With the formula : light speed = f λ, speed of waves can be shown. However, speed of photon and light ray will not be shown. Because of large speed of light, this problem is not noticeable.

    In outer space, plane waves of a star light are coming. An observer is at a standstill. Speed of light waves and photons (light ray) relative to the observer will not be the same (in general). By the way, speed of light waves and of photons (light ray) relative to the aether frame will be the same (as a physical constant : not c, maybe).

    Sorry, I cannot receive E-mail. I do not have PC.

    1. John Duffield

      The speed relative to the waves does vary, hiroji. That’s because the descending photon slows down. Optical clocks go slower when they’re lower because light goes slower when it’s lower. However you always measure the local speed of light to be the same because of the wave nature of matter. See The Other Meaning of Special Relativity by Robert Close:

  14. David

    “And that whilst an observer stationed at the ceiling will measure the speed of light to be c, as will the observer stationed at the floor, the “global” observer will say that light at the ceiling travels faster than light at the floor.”

    So this is equivalent to say that the speed of light is always locally constant, i.e. in a region of space sufficiently small so that space-time can be considered flat? (it is what I understood from GR)
    But then, if say I measure the speed of light at half the height of the room (which should be c0=299’792’458 m/s), and then observe a ray of light emitted at the top of the room towards the ceiling, I would deduce (using general relativity equations) that the speed of light is larger than c0 on top of me and slower beneath me ?

  15. David: yes, the speed of light is deemed to be locally constant. But that’s because when light goes slower, so does the observer, because all electromagnetic interactions go slower at the lower elevation.
    You have to be cautious about spacetime can be considered flat. Spacetime curvature is the second derivative of potential, and is associated with the tidal force. This is not detectable in the room you’re in. Spacetime can be flat and level, whereupon your pencil doesn’t fall down, or it can be flat and tilted, whereupon your pencil does fall down. See the next article where I talk more about this.
    Yes, you should deduce that the speed of light is larger than c0 above and slower below. Rather counter-intuitively, the ascending light beam speeds up. The descending light beam slows down.

    1. Chris

      In this context, what does “lower” mean?

    1. Good stuff Roger, thanks. I’ll correct that and make a note pointing to your paper.
      As for people saying Einstein said the speed of light is constant, I think it’s more than just a translation error. I think it’s 1960s physicists doing their own thing and appealing to Einstein’s authority whilst flatly contradicting the guy. Einstein said the speed of light varies in a gravitational field. He said it time and time again, year after year, starting from 1907. And yet, what do I read? I read things like Einstein showed us that the speed of light was constant.

      1. Roger

        Hi John, its a domino effect (i.e cumulative effect) where an initial mistake/error is made and more mistakes are then built on top. SRT is supposed to be his 1905 paper, and between 1905 and GRT in 1915 that is supposed to be him struggling with entwurf theory; the entwurf theory gets ignored i.e. the mindset of them is to ignore the 1907 quote you mention as not being SRT and not being GRT.
        Example of Einstein being mistranslated at: in the part two : it all boils down to one German word being mistranslated – the German which Einstein wrote as “nun” got mistranslated as the German “nur”. Resulting in the difference that (one way) lightspeed (in vacuum) can optionally be treated as constant, versus the usual belief that it is compulsory constant.

        1. Roger

          Hi John

          Now found that there are so many mistakes with what we have been told about relativity, that it must have been his wife who wrote it, and what we got from Einstein was a distortion, see:

          1. I wonder if there was some international politics in it Roger. Or plagiarism. Einstein built on the work of Voigt, FitzGerald, Lorentz, and Poincaré, but he didn’t acknowledge them at all.
            Just you wait until you find out about the mistakes that were put into general relativity in the sixties. It makes the issues in special relativity look minor.

            1. Roger

              Of course there was politics involved. It was a group of influential scientists that called themselves the X Club that wanted science based on atheism, and so championed Darwin’s theory. I think they probably championed Einstein as well, because Newton’s theory could be viewed as God in control of a clockwork universe; thus viewed Einstein as dethroning Newton to give atheist physics. Einstein eventually started saying things like “God does not play”, and I think then they withdrew their support for what he was later saying, but kept the relativity+etc from his earlier days. (Einstein not giving references etc all helped to cut ties with what others had said in the past.)

              1. I read somewhere that the international politics was such that German science didn’t want to acknowledge the contribution from non-German scientists. Or something like that. I’ll have to look it up.

  16. Hiroji kurihara

    About MM experiment

    In a moving passenger car, MM experiment is being done. On the ground, an observer stands. To this observer, are constancy of light speed and Lorentz contraction compatible ? And also, are constancy of light speed and time dilation compatible ?

  17. Hiroji kurihara

    About speed of light

    Brawnian motion shown by many particles will be a model of the real world. And a measure of time and space will be invariable. Even when a light ray is passing by.

  18. Hiroji Kurihara

    Lorentz contraction

    Plain waves of light (wavelength is constant) are coming from the upper right 45 degrees.Two bars of the same length are moving to the right and the left at the same speed. Number of waves hitting the bers is the same. Lorentz contraction is unthinkable.

    1. You won’t find me telling people about Lorentz contraction, Hiroji. I simplify your bar to a single electron, then I simplify that to light going round in a circle, like this: O. Then I turn it sideways, so it looks like this: | . Then when you move this thing, it’s liking stretching one turn of a coil spring. You go from this | to this /\. That electron is smeared out. It gets longer. So do you. That’s why you see other things looking length contracted, even though they haven’t changed.

  19. Doug Cox

    I believe the speed of light is a constant in a vacuum because I also believe that measurement between anything in a vacuum CAN change to keep the speed of light a constant whenever time is changed per the General Theory of Relativity. This belief is backed up by a belief that the Inflation of the universe just after the “Big Bang” was real, and that both the measurement between things in space and time changed together at a speed that seemed faster than our constant speed of light but was actually both the measurement AND time that changed together to keep the speed of light constant.

    1. The trouble with that Doug, is that people define the second using the local motion of light. Then they use the second to measure the local motion of light. Then they say the speed of light doesn’t change. Even though optical clocks go slower when they’re lower. Even though the thing that’s moving in those clocks is light, not time.

      1. Chris

        Are you saying time is a stationary membrane and light, matter, etc moves through it? Or are you saying that the speed of “time” is an irrelevant here, as it is the thing being measured and can’t be used also to explain speed discrepancies because that is logically circular?

        1. No. Light and matter move through space. Time is just a cumulative measure of that motion. See the nature of time. If you use the local motion of light to calibrate a clock, and then use that clock to measure the local motion of light, your definition of the local motion of light is circular.

  20. Akis

    Hi John, I just bumped onto this excellent video on VSL from Dr Alexander Unzicker.
    If you haven’t seen it I suggest you have a look. It explains that the ‘curved space with constant c’ is just a different way to describe ‘flat space with variable c’.. Its just a different view of GR. Goes on to say the two different versions are equivalent :

    The paper he mentions from Jan Broekaert (2008) is a very nice read too.

    Kip Thorne in his interviews also acknowledges that the constant speed of light is something Einstein and we simply chose to go with for simplicity / practical reasons.
    So it seems that the VSL GR is not really a different thing..just maybe a harder way to compute things…compared to the model where we use a constant speed of light to do the math/computations/simulations etc.., thats also according to Kip Thorne but I am not sure if this is true though.

    Now just like you say in the flat space with VLS model of the GR the space is not curved, there is no curvature of space.
    On the other hand in the Constant speed of Light model of GR the space is measured to be curved. So seems both ways describe same thing in a different way so to speak depending on how you look and measure things.

    1. Hi Akis. Unzicker is a friend of mine. I haven’t seen this video though, I’ll take a look. The 2008 paper by Ye Xing-Hao and Lin Qiang Inhomogeneous vacuum: an alternative interpretation of curved spacetime is similar. I can see a couple of Jan Broekaert papers on the arXiv including . Isn’t it sad that nobody ever hears about this stuff? In this case, me!
      Can you link me to something from Kip Thorne? I don’t think the two interpretations are exactly the same. If they were, guys like Kip Thorne wouldn’t believe in wormholes and time travel. Check out my black hole article, and remember this: a gravitational field is a place where the speed of light is spatially variable, at the event horizon the speed of light is zero, and light can’t go slower than stopped.

  21. Akis

    Well they are equivalent but not identical. Both approaches are claimed to be valid and can be used to accurately describe reality thats what I understood so far. Again I will refer you to the video from Unzikcker as he explains the differences of the two in quite some detail. He explains how things change in GR calculations when using VLS in practice. Please have a look before jumping into conclusions, a lot of what he mentions was really in agreement with some of the things you have said in your articles.

    Kip Thorne is clearly well aware of the slowing of time near a BH, reaching zero speed at the EH…but is either confused or I ‘m missing something important here..He says that when you fall into the BH and pass the EH, ‘point of no return’, can still observe the universe above you…but those outside are not able to see you and you can’t send signals to them.

    How could that be though if time has stopped at the EH? How do you actually observe the universe above you if time has stopped and photons do not move anymore? how do you..see?..Or in Thorne’s version of things with constant c and curved space , somehow photons do not stop moving eventhough time has stopped at the EH….Confusion is the word..

    As for the VSL Thorne specifically said we/Einstein intentionally chose to use constant speed of light for ease of use. Says we basically defined it to be constant to help things are easier. That was mentioned here in this interview: 3:20 onwards, but its all worth seeing.

    Thorne has also mentioned often resorting to the Einstein digital papers. So I believe he is aware of the VSL GR from Einstein as a concept. As for Wormholes..well when asked in a more serious tone, his answer is that they most probably do not even really exist. Now for film purposes (Contact, Interstellar) wormholes and other crazy ideas were entertained by him and others over the years..I guess these topics sell a lot..I believe he believes the same 😉 But they are hypothetical objects till proven otherwise and unlikely to exist as he even said himself. Anyway..also when asked about Time travel he also mentions that time travel if it were to be possible, it would have to respect the speed of light limit and since time flows towards one direction it would need,to always respect, locally, the forward flow of time..

    As for how black holes fall…..
    Yeah how do they when the time flow at the EH is reaching zero, well I hope I get a chance to ask him directly when I will be visiting a lecture he is giving in couple of days in a nearby Uni and will try to get some input.

    But maybe the analogy on the other thread that you made with the fully crowded deck(where one cannot move in the crowd) which is on a moving a good one and maybe BH do fall /move/orbit and merge etc in a way similar to the areas closer to the BH EH will indeed be ‘frozen’ but the whole BH with its near affected surrounding space can move and drag the ‘frozen’ center along..

    1. All points noted Akis. I’ll watch the Unzicker video. I’ve spoken to him about a few things, and I don’t think I’ve ever found myself disagreeing with him.
      I’ve never had any communication with Kip Thorne, and I find myself disagreeing with lots of things he’s said. Yes, I think he’s confused, because he doesn’t actually understand that “the curvature of light rays occurs only in spaces where the speed of light is spatially variable”. Or that at the event horizon, the speed of light is zero. That means you can’t fall though it. Yes, confusion is the word. He might be aware of Einstein’s VSL, but he hasn’t thought it through. I’m confident that the infalling body never even gets to the event horizon – we don’t see gamma ray bursts for nothing. See my Firewall! article. I’ll watch the interview. I will force myself, because I am not a fan. Interstellar was promoted as serious science, but some of it was pseudoscience junk.
      It might be best if you didn’t ask Kip Thorne about how black holes fall down. He shared a Nobel prize for saying they do: In 2017, Thorne was awarded the Nobel Prize in Physics along with Rainer Weiss and Barry C. Barish “for decisive contributions to the LIGO detector and the observation of gravitational waves”. He might give you a hard time. Or me.

  22. Michael Jude

    Before writing and proposing such elaborate and scientifically fecund theories and opinions about light would it not help to first firmly establish what, exactly, is light ? Then, upon doing so, the things themselves which purportedly affect the speed of light would take on an entirely new meaning and application in everyday human activity…

  23. Hiroji Kurihara

    Speed of light

    They say, it stands up on an observer in every inertial frame. Yes, when the light source shines in that frame, it is true.

    Some man mistook this fact natural for a great discovery. And it is believed widely.

  24. David Proffitt

    Surely there is confusion here between what is locally measured and what is measured from a distant point.
    If I stand at the top of a hill with my standard metre rule, then go to the bottom and measure something with it, am I not correct in assuming my meter hasn’t changed? It is my standard metre, after all. The same argument can be used with time. If I use my standard timepiece at the bottom of the hill it still records seconds. But if I ask my twin on the top of the hill “What is the length of my metre and the behaviour of my timepiece”, he will tell me they have changed. If I go back to the top and check, I can confirm that they remain unchanged.

    1. the physics detective

      There is definitely some confusion here, David. If you stand at the top of a hill with your standard ruler and your standard parallel-mirror light clock, then measure the speed of light at that location, you measure it to be 299,792,458 m/s. Then if you go to the bottom of the hill and measure the speed of light at that location, you still measure it to be 299,792,458 m/s. That’s because both your optical clock and the light go slower at the lower location. You go slower too, because of the wave nature of matter. So you don’t notice that light goes slower when it’s lower. You have to take a step back to see the big picture. Then what you see, is this:

      It’s exaggerated of course, but clocks definitely go slower when they’re lower. Light clocks go slower when they’re lower because light goes slower when it’s lower. However your metre rule doesn’t change. The metre is defined as the distance travelled by light in 1/299792458th of a second. When the light goes slower the second is bigger, and the slower light and the bigger second cancel each other out.

  25. David Proffitt

    I understand your argument and agree. It all depends on your idea of what a ‘standard’ is.

    In general relativity for a Schwarzschild black hole, you can calculate the speed of light for a distant observer and it approaches zero at the event horizon. Since the time coordinate approaches infinity there, we cannot conclude on that basis that c=0 at the event horizon but it has to be true, otherwise photons could reach the outside world. But it can be shown that if c=0 in one frame of reference, then it is true in any frame of reference.
    Someone is sure to cite Hawkins at this point; that relies on quantum mechanics but that was never considered by Misner, Thorne and Wheeler when ‘proving’ the existence of a central singularity.

    1. That’s exactly it, David. The important thing is “the curvature of light rays occurs only in spaces where the speed of light is spatially variable”. This means the ascending light beam speeds up, and a black hole is black because at the event horizon, the speed of light is zero.
      Eddington-Finkelstein coordinates include a schoolboy error that says a stopped observer sees a stopped clock ticking normally “in his frame”. He doesn’t. The clock is stopped, and so is he. See for more. But you might like to look at first, followed by

  26. Hiroji kurihara

    Cconstancy of speed of light

    In an area where propagation of light follows the emission theory, it is constant relative to the light source. In an area where propagation of light follows aether, it is constant relative to aether. So, it cannot be constant relative to moving observers.

    1. John Duffield

      It isn’t constant relative to moving observers, Hiroji. It just looks constant to them, because of the wave nature of matter. Robert Close explained it in The Other Meaning of Special Relativity, which I referred to in the previous article. Maybe I should refer to it in this article too.

  27. Hiroji kurihara

    Reexamination of propagation of light (I say again)

    In outer space, a mirror is reflecting star light ray. Speed of reflected light relative to the mirror is constant. Speed of incident light relative to the mirror is not constant (the latter is constant relative to aether).

  28. Hiroji kurihara

    Light is propagated in two ways.

    Propagation following the emission theory, it is propagated in vaccum space and propagation following aether, it is propagated in aether. A mirror in outer space that is reflecting star light ray shows above.

  29. Andy Hall

    Hi John,

    A question for you that occurred to me. I am happy that light goes slower when its lower. Experiments with clocks at different altitudes demonstrate this. However, with regard to vacuum they appear to separate out an important point. Clocks go faster on GPS satellites than on the ground. This is taken as a result of relativity and time dilation, but I think the point you have made has been more to do with physical effect of vacuum polarisation and the space in and around atoms increasing in density at lower altitudes. I wanted to provide a bit of context to my question but the question is basically this; Is all vacuum created equal or is vacuum affected by altitude?
    The answer to this question could be investigated by using two similar atomic clocks. Each would need to be at the same altitude and located close in the vicinity of each other. One clock would need to be in a vacuum chamber that was evacuated and the other in a similar vacuum chamber but at atmospheric pressure. The experiment could be repeated at a different altitude.
    One impact of a positive result for this experiment would be that vacuum density varies and it affects the speed of light. That would mean that the definition of the speed of light would need to be be defined, in vacuum and at an altitude, not just the speed of light in vacuum. I would be interested in your thoughts.

    1. Andy: GPS clocks are subject to an SR slowing down due to their speed, and a GR speeding up due to their altitude. See Phil Fraundorf’s graph here. The GR effect predominates.
      Is all vacuum created equal? I’m not sure. But I am sure that it’s affected by a concentration of energy in the guise of a massive star. It “conditions” the surrounding space. I think of it as an outward pressure. A pressure gradient and so a density gradient. The density diminishes with altitude.
      The speed of light in air is circa 299,700 km/s, which is about 90 km/s less than c. This would show up in your two similar atomic clocks. But you can’t say that this difference is because the vacuum density varies. Here’s an analogy: imagine you walk at 4mph. If the pavement is clear of people, you walk 4 miles in 1 hour. If however the pavement is crowded with people coming at you, you have to dodge around them. You still walk at 4mph, but after 1 hour you’re only 3 miles down the street. The air molecules are like the people.
      On top of that, If you’re a big guy with big long strides your total path length is more than it would be if you were a little old lady with little steps. So longer wavelengths get refracted more than shorter wavelengths. Whenever you see this wavelength-dependent refraction, you know that the lower propagation speed isn’t just due to a variation in vacuum density.

  30. Andy Hall

    Thanks for your thoughts. Personally, I would really like to see an experiment of the sort I described regarding confirming the properties of vacuum at different gravitational potentials i.e. local field strengths. I think it would speak to the issues supposedly addressed addressed by the Michelson-Morley experiment where they conclude the speed of light is constant in all directions and therefore there is no ether. I disagree. Apart from any other considerations I suspect that the Michelson-Morley experiment was not accurate enough to determine the speed of light sufficiently accurately to rule out the size of changes to the speed of light that might result from vacuum polarization or ether density variation. Until there is some solid evidence I need to keep an open mind but I strongly favour an ether hypothesis where density variation is a possibility.

    Also, there is a comment from me visible on November 15th with an equation in it. I was just playing with the MathJax facility in your comments and I deleted the comment after I had made it at the time. I think it has been restored in error. It does not need to be removed, it is an equation from my website, but it is out of context and no relevant as a comment on this page.

    1. the physics detective

      I disagree too. So did Einstein. He reintroduced the aether when he did general relativity. As for Michelson-Morley, they didn’t know about the wave nature of matter. Trying to measure a different speed of light is like trying to measure your shadow using the shadow of your stick. I deleted your comment. I had found it in the bin and thought my spam filter was being too zealous. Apologies!

  31. Hiroji kurihara

    Glass and light (I say again)

    From the right, star light is coming. Two cubes of glass are moving toward the star at the different speed. In the glass, speed of light is c/n : the same. Because in the glass, light emitted from particles follows the emission theory.

    By the way, let’s see the light before arriving (from the glass). Wavelength is the same. Frequently and light speed are not the same.

    1. Funnily enough Hiroji, the speed of light in glass is c when it’s moving between the particles that make up the glass. The particles slow down the shorter-wavelength light more than the longer-wavelength light, hence prisms. It’s similar for water droplets in the air. Hence rainbows. IMHO a crowded pavement is a reasonable analogy: imagine you walk at 4mph. If the pavement is clear of people, you walk 4 miles in 1 hour. If however the pavement is crowded with people coming towards you, you have to dodge around them. You still walk at 4mph, but after 1 hour you’re only 3 miles down the street. Then if you’re a tall young man with long strides you’re affected less than if you’re a little old lady with short strides. Anyway, the wife is calling. Merry Christmas!

  32. william

    It never made sense to me that ‘space’ curves. Always thought that gravity influenced movement. Also thought that ‘time’ , as an influence on anything, is an aberration, an illusion. Time is the notation, or measurement of movement. Slow down movement, time (as a constant) doesn’t change, just measurement changes. All these things you’ve mentioned made sense! (and I’m a 9th grade dropout)

    1. Good man William!
      When you take it one step at a time, you can understand gravity. Then you realise that Einstein described a gravitational field as space that’s “neither homogeneous nor isotropic”. Not curved. Click on NEXT at the bottom of each article to read one article after the other, and hopefully it all builds up into a coherent description that does make sense.

  33. Hiroji kurihara


    Speed of light relative to mediums (such as water or air) is constant. Speed of light relative to aether (physical substance, will be) will be constant also. Aberrations show this.

    But, such a view will have been written by not a few.

    1. Hiroji: the speed of light in air is different to the speed of light in water. The speed depends on the medium, and when the properties of the medium changes, the speed changes. This is why optical clocks go slower then they’re lower. Because in a gravitational field, space is “neither homogeneous nor isoptropic”. Hence “the curvature of light rays occurs only in spaces where the speed of light is spatially variable”.

  34. Hiroji kurihara

    Propagation of light (I say again)

    Light will be propagated in three ways (as follows).
    1 In mediums speed of light is c/n. MM experiment will be invalid.
    2 In outer space, a star light is reflected by a mirror. Speed of incident light is constant relative to aether.
    3 In outer space, a star light is reflected by a mirror. Speed of reflected light is constant relative to the mirror.

    In three pictures above each, speed of light to a moving observer will follow Galilean transformation.

  35. Hiroji kurihara

    Propagation of light (I say again)

    Light will be propagated in three ways (as follows).
    1 In mediums, speed of light is c/n. MM experiment (done in air) is invalid.
    2. In outer space, a star light is reflected by a mirror. Speed of incident light is constant relative to aether.
    3 In outer space, a star light is reflected by a mirror. Speed of reflected light is constant relative to the mirror.

    In three pictures above each, speed of light to a moving observer follows Galilean transformation.

    1. Make sure you read this, Hiroji: the other meaning of special relativity by Robert Close. When you’re made of light along with your rods and clocks, the speed of light always appears to be the same. It’s like trying to measure the length of your shadow using the shadow of your stick.

  36. Andy Hall

    Hi John,
    It has been a while since I was in contact with you but I noticed something today that I would like your opinion on.
    I guess you are aware of the redefinition of the SI system that has been taking place over the last few years resulting in absolute definitions for 7 constant values in the SI system and some second order derived values. The current values are mentioned as defined here with their values. The definition that interests me is the definition of an absolute frequency for a transition frequency for the caesium atom. The implication is that this caesium atom has a property which does not change, anywhere in the universe, under any conditions. However, we are aware of the evidence that atomic clocks go slower when they are lower in the gravitational well. I am generally of what I think is the same opinion as you that the speed of light is spatially variable and certainly varies with position in the gravitational well, or altitude as we would see it on earth. This is the reason that clocks appear to go slower when they are lower. It just strikes me that this frequency based property of the caesium atom should be subject to the same frequency variation. Unless it is such a small signal frequency variation that its magnitude of variation is below the threshold of measurement with respect to the other definitions, one of which is the speed of light in vacuum held as constant everywhere, which also seems to be a flawed assertion.
    Any thoughts?

    1. Andy: it’s like what Einstein said on page 149 of Relativity, the Special and General Theory: “an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated“. The transition frequency of a caesium atom on the floor is less than the transition frequency of a caesium atom at the ceiling. It’s the same for other atoms. That’s why the NIST optical clocks go slower when they’re lower. It was David Wineland of NIST who said “if one clock in one lab is 30cm higher than the clock in the other lab, we can see the difference in the rates they run at”.
      The NIST definition you’re referring to is nonsense. It’s a Humpty-Dumpty definition. It ignores the tautology. It’s saying these two clocks are running at the same rate, even though one’s running faster than the other. We live in a cargo-cult world Andy. An idiocracy. A dark age.

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