The principle of equivalence and other myths

Once you know that an optical clock goes slower when it’s lower because light goes slower when it’s lower, you soon understand why light curves. Not because it follows the curvature of spacetime. Because the speed of light is spatially variable, like Einstein said. Then once you know about the wave nature of matter and electron spin, you soon understand why matter falls down, and why the Newtonian deflection of matter is only half the deflection of light. Then once you know how gravity works, you soon understand why there is no magical mysterious action at a distance, like Newton said.

The equivalence principle is only valid in the infinitesimal

You also come to understand is that the principle of equivalence is something of a myth. In the Wikipedia equivalence principle article you can read that “being on the surface of the Earth is equivalent to being inside a spaceship (far from any sources of gravity) that is being accelerated by its engines”. However the two situations are not exactly equivalent, because standing still in inhomogeneous space is not exactly the same as accelerating through homogeneous space:

Reference frame pictures by me

Yes, when you’re in a windowless room either on Earth or in the accelerating spaceship, you might say light curves and matter falls down. But like Wikipedia says, the room has to be small enough so that “tidal forces may be neglected”. As for how small, note that in chapter 20 of Relativity: The Special and General Theory Einstein said it’s impossible to choose a body of reference such that, as judged from it, the gravitational field of the Earth (in its entirety) vanishes”. You cannot “transform away” the Earth’s gravitational field. That isn’t true for the accelerating spaceship, That’s why in Fundamental ideas and methods of the theory of relativity Einstein said the special theory of relativity is “nowhere precisely realized in the real world”. He said it’s only valid “in the infinitesimal”. Your room has to be an infinitesimal room for the principle of equivalence to apply. So it doesn’t apply at all.

The midwife should be buried with appropriate honours

This is why on pages ix and x in his 1960 preface to relativity: the general theory, John Synge said the equivalence principle performed the essential office of midwife at the birth of general relativity, but should “be buried with appropriate honours”. It started in 1907 with Einstein’s happiest thought, wherein the falling observer doesn’t feel his own weight. This was Einstein’s train ticket to understanding, to be discarded once he reached his destination. That’s when he appreciated that exact equivalence demanded an infinitesimal room. However the equivalence principle is said to have been successfully tested on multiple occasions:

Image from the 2010 paper Quantum tests of the equivalence principle with atom interferometry from the QUANTUS team

That’s because the waters have been muddied. The Eötvös experiment is said to be a test of the equivalence principle, but it was first performed in 1885, to test whether different materials were equivalently affected by gravity. It’s the same for the Eöt-Wash experiments, which tested “the universality of free fall”. What they tested was the weak equivalence principle, which is not Einstein’s equivalence principle. See Kevin Brown‘s mathspages article on the many principles of equivalence where you can read that the equivalence principle has undergone several changes over the years. Brown talks about the strong equivalence principle, and says this: “the modern statement of the strong equivalence principle, of the assertion that the laws of physics are the same for all frames of reference (i.e. independent of velocity) is also conceptually quite distinct from the original meaning of Einstein’s equivalence principle”. OK, but see the Einstein equivalence principle in the Wikipedia equivalence principle article. It says “the outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime”. That isn’t Einstein’s equivalence principle either. It doesn’t square with what Einstein said in 1907. Or with what he said in 1939 about light rays taking an infinitely long time to reach a black hole event horizon. Which doesn’t square with the idea that an object falling from infinity will be moving at the speed of light when it crosses the event horizon.

The fine structure constant is a running constant

The Wikipedia article also says the fine-structure constant must not depend on where it’s measured. That doesn’t square with the fine structure constant being a running constant. It “depends upon the energy at which it is measured”, and so must surely vary with gravitational potential. Solar probe plus was going to test this alleged violation of the equivalence principle, and so would be a “test of relativity”, but it looks like it’s now going to be purely a heliophysics mission. That’s a shame, because it might have brought the issue to a head. It’s an issue that’s been around for way too long. John D Norton talked about it in his 1985 paper what was Einstein’s principle of equivalence? He said it was a special relativity principle that dealt only with fields that could be transformed away. He talked of an old view and a new view, and said “the equivalence of all frames embodied in this new view goes well beyond the result that Einstein himself claimed in 1916”. This new view is why there’s so many papers on testing the equivalence principle when the old view doesn’t apply at all. Unfortunately the new view doesn’t apply either. We don’t have gamma ray bursters for nothing.

The ascending photon does not lose energy

Something else that doesn’t apply is gravitational redshift. Not the way they say. Take a look at page 149 of Relativity, the Special and General Theory. Einstein said an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated. When the ascending photon ascends, its E=hf energy does not reduce, and nor does its frequency. There is no magical mysterious outflow of energy from the photon. It doesn’t get redshifted at all. That’s a myth. Instead the photon was emitted at the lower frequency at a lower elevation. Conservation of energy applies. It appears to have less energy at the higher elevation because that’s where optical clocks go faster, along with everything else. So we measure the photon frequency to be reduced, even though it didn’t change at all.

But it does speed up

Another myth is a gravitational field that’s so strong it can drag light back down. It’s a myth that’s been around for a long time now. See for example Stephen Hawking’s paper singularities and the geometry of spacetime dating from 1966. On page 76 Hawking talked of such a strong gravitational field that even the ‘outgoing’ light rays from it are dragged back”. This is incorrect, because a gravitational field is a place where the speed of light is spatially variable. It varies in the room you’re in. That’s why your pencil falls down. The speed of light at the ceiling is greater than the speed of light at the floor. Hence the ascending photon doesn’t slow down as it ascends. Au contraire, it speeds up.

Black and white falling gif by James Zanoni, inverted and cropped by me

If I could somehow make the gravitational field in your room much stronger, there would be a much bigger difference between the speed of light at the ceiling and the speed of light at the floor. So the ascending photon would speed up all the more. We don’t measure it as speeding up because we use the local motion of light to define our second and our metre, and then we use them to measure the local motion of light. So we always say it’s 299,792,458 m/s. But nevertheless that ascending photon does speed up. It doesn’t slow down. It isn’t like an ascending brick.

The mass deficit

Talking of which, when you throw a 1kg brick up in the air you do work on it. You give it kinetic energy. Whilst conservation of momentum p=mv means there is an effect on the Earth, it’s very slight. The kinetic energy KE=½mv² is not shared equally because the Earth doesn’t move in any detectable fashion, so the brick gets virtually all of the kinetic energy. It’s akin to what happens when you fire a projectile from a cannon, only more so:

Image drawn by me

As the brick ascends it slows down, because gravity converts the brick’s kinetic energy into gravitational potential energy. Note that this gravitational potential energy is in the brick, not in the gravitational field, and not in the Earth-brick system. You did work on the brick. There is no magical mysterious mechanism outflow of energy from the brick. The kinetic energy you gave to the brick merely gets converted into potential energy, which is in the brick. This potential energy is mass-energy. Hence when the brick is at the top of its arc, its mass is greater. Then when the brick falls back to Earth the situation is reversed. Gravity converts potential energy, which is mass-energy, into kinetic energy. Once the brick hits the ground this kinetic energy gets dissipated, and you end up with a mass deficit. See the mass-energy relation section of the Wikipedia binding energy article: “a bound system is typically at a lower energy level than its unbound constituents because its mass must be less than the total mass of its unbound constituents”. Binding energy is not some actual thing that consists of negative energy. It’s the reduction in the mass-energy of the real things that consist of positive energy. Hence the mass of the brick at rest on the ground is less than the mass of the brick at the top of its arc.

Escape velocity means the kinetic energy leaves the system

You can check this by throwing the brick upwards at 11.7 km/s, so giving it escape velocity. It will end up leaving the system, taking the original 1kg worth of mass-energy away, along with 11.7 km/s worth of kinetic energy. This gets converted into gravitational potential energy, which is in the brick, increasing its mass. You did work on the brick. Once the brick escapes the Earth’s gravitational field, it leaves the system, and so does the kinetic energy that is now mass-energy. Hence the mass of the brick at rest on the ground is less than the mass of the brick in free space.

The mass of an electron varies

The same applies to a 511keV electron. When you throw the electron up in the air, you do work on it. You give it kinetic energy, and gravity turns this into gravitational potential energy, which is mass energy. Hence the mass of the electron at rest on the ground is less than the mass of the electron at the top of its arc. In similar vein the mass of an electron in a hydrogen atom is less than that of a free electron. The proton is only 1836 times the mass of the electron, so the situation isn’t quite so unequal as the Earth and the brick. But if it was, when an electron “falls” towards a proton to form a hydrogen atom, some of its mass-energy gets converted into kinetic energy, which gets dissipated as a 13.6eV photon:

Image from Rod Nave’s hyperphysics

The electron mass is then circa 13.6eV less than 511keV, and this 13.6eV is the binding energy. Unfortunately there’s a myth that says the electron has an invariant mass of 510.9989461(13)keV. The irony of course is that invariant mass varies. It varies even more in a Helium-4 nucleus which consists of two protons and two neutrons. The binding energy there is circa two million times greater than the electron-proton binding energy.

Gravitational field energy is positive

Another myth is that gravitational field energy is negative. It’s arisen because people historically set Newtonian gravitational potential energy to be zero at infinity. That means it’s deemed to be negative at sea level. Only it isn’t really negative, it’s still positive. That’s why you can drop a brick into a hole and convert some more of that gravitational potential energy into kinetic energy. That’s not the end of the world, but unfortunately gravitational potential energy then gets confused with gravitational field energy. On page 82 of his 2002 book The Theory of Everything, Stephen Hawking said this: “in a sense the gravitational field has negative energy. In the case of the whole universe, one can show that this negative gravitational energy exactly cancels the positive energy of the matter, so the total energy of the universe is zero”. It isn’t true. In his 1916 Foundation of General Relativity Einstein said “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. Gravitational field energy is positive, just like electromagnetic field energy. And when you drop a 1kg brick into a black hole from some “infinite” distance, the black hole mass increases by 1kg. It doesn’t decrease by 1kg. It would be similar if you dropped stars and planets and everything else into a single supermassive black hole. Hence the zero-energy universe is just another myth. As are some other things in cosmology. I’ll talk more about them at a later date.

Misinterpretations of the theory

For now, see Peter Brown’s 2002 paper Einstein’s gravitational field. He quotes John Synge and John Ray on page 20. He also says Einstein’s general relativity and modern general relativity differ, and the latter suffers from contradiction and confusion. Chung Lo says essentially the same in 2015 in his rectification of general relativity. He blames Wheeler and others: Wheeler led his school at Princeton University while his colleagues, Sciama and Zel’dovich (another H-bomb maker) developed the subject at Cambridge University and the University of Moscow”. Lo goes on to say the misinterpretations of the theory and errors such as the singularity theorems have been accepted as part of the faith”. The bottom line is that the general relativity that is taught today, is not the same as Einstein’s general relativity. Instead it’s like some kind of doppelganger from Invasion of the Body Snatchers. What’s more like Einstein’s general relativity is the polarizable vacuum proposed by Robert Dicke and then Harold Puthoff: “in essence, Dicke and Puthoff proposed that the presence of mass alters the electric permittivity and the magnetic permeability of flat spacetime”. Dicke’s 1957 paper was Gravitation without a Principle of Equivalence. Puthoff’s 1999 paper was Polarizable-Vacuum (PV) representation of general relativity. Both Dicke and Puthoff refer to Harold Wilson’s 1921 paper an electromagnetic theory of gravitation. I am reminded of Julian Schwinger’s 1949 paper quantum electrodynamics II : vacuum polarization and self-energy.

Perhaps the past, if looked upon with care and hindsight, may teach us where we possibly took a wrong turn

There’s more, much more, but we’ll come on to that later. For now, there’s a more pressing lead to follow, and it’s this: a gravitational field is not a place where space is curved. Instead it’s a place where space is neither homogeneous nor isotropic. It’s inhomogeneous in a non-linear way, in line with the inverse square rule. So if space isn’t curved where a gravitational field is, where is it curved? To answer that we need to look elsewhere. We also need to take careful note of Bert Schroer’s 2003 essay on Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics. Because on page 9 he says this: “in times of stagnation and crisis as the one we presently face in the post standard model era of particle physics, it is helpful to look back at how the protagonists of quantum field theory viewed the future and what became of their ideas and expectations. Perhaps the past, if looked upon with care and hindsight, may teach us where we possibly took a wrong turn and what alternative path was available”. You bet Bert.


Edit 21/06/2020

I didn’t say anything about the wavelength of the ascending photon above. But I had an interesting conversation about that recently:

We start with the photon in special relativity. A series of identical photons are released at point A, and you’re at point B. You measure the photon energy along with the frequency and wavelength, wherein E=hf and E=hc/λ. Then you accelerate away from point A until you reach some speed v. Then you repeat your measurements. The photon energy appears to have descreased, as does the frequency, whilst the wavelength appears to have increased. But those identical photons haven’t changed one jot. Instead you’ve changed.

We then move on to general relativity. A series of identical photons are released upwards at point A, and you’re above them at point B. You measure the photon energy along with the frequency and wavelength, wherein E=hf and E=hc/λ. Then you climb upwards away from point A until you reach some elevation C. Then you repeat your measurements. The photon energy appears to have decreased, as does the frequency, whilst the wavelength appears to have increased. In my conversation I said those identical photons haven’t changed one jot. Instead you’ve changed.

But I think I was wrong. Because the second is defined 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”. In essence you count light waves going by, and when you get to 9,192,631,770 you say a second has elapsed. So if the light goes slower the second is bigger. 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”. Note here that if the light goes slower the second is bigger, and these two opposites cancel each other out. So the metre is unchanged. The second changes, but the metre doesn’t.

So, when you’re at the higher elevation your seconds are shorter. So it looks like the photon frequency has  decreased. Even though it didn’t. It also looks as if the photon wavelength has increased. But your metre hasn’t changed. So that should mean that the wavelength really has increased. Interesting stuff.

This Post Has 162 Comments

  1. Jim

    “light goes slower when it’s lower” – Be very careful here – although a beam of light is slowed down in a field or transparent material, it does not mean that photons themselves do not always travel at the speed of light C. Photons ALWAYS move at speed C. What slows down the beam of light is that indifidual photons are being absorbed (destroyed) and then re-emitted (recreated) after a tiny delay, which we perceive as a slow-down of the beam.
    Photons travel at one speed and one speed only – C.

  2. Jim

    “It doesn’t square with what Einstein said in 1907. Or with what he said in 1939 about light rays taking an infinitely long time to reach a black hole event horizon. Which doesn’t square with the idea that an object falling from infinity will be moving at the speed of light when it crosses the event horizon”
    The equivalence was talking about non-gravitational experiments. You’re trying to square that with gravitational experiments that involve black holes.
    You seem to be badly confusing Special Relativity and General relativity throughout this blog. It’s critical to be clear on which you are discussing and to not mix them up.

  3. Jim

    [the fine structure constant] “must surely vary with gravitational potential” – that’s not correct (at least ignoring the unknown theory of quantum gravity). It’s a constant regarding electromagnetism. A gravitational potential will affect the physics of particles for sure, but that doesn’t mean the fine structure constant is not a constant. All you’ve done is add another field on top of the system.

    1. The fine structure constant is a running constant. That means it isn’t constant. See where you can read this: “Thus α depends upon the energy at which it is measured, increasing with increasing energy, and is considered an effective or running coupling constant. Indeed, due to e+ e- and other vacuum polarization processes, at an energy corresponding to the mass of the W boson (approximately 81 GeV, equivalent to a distance of approximately 2 x 10-17 m), α(mW) is approximately 1/128 compared with its zero-energy value of approximately 1/137. Thus the famous number 1/137 is not unique or especially fundamental”.

  4. Jim

    “Hence the ascending photon doesn’t slow down as it ascends. Au contraire, it speeds up.” – this is wrong! The speed of a photon is C – period. You cannot speed up or slow down a photon. This is basic physics, the foundation.

    1. It’s wrong Jim. Your foundation is wrong. Read the opening paragraph again, and remember what I said about faith. You are clinging to conviction, and you need to be empirical instead. A clockwork clock doesn’t go slower because time’s going slower inside it it, and nor does an optical clock.

      1. Jim

        Hi John,
        Massless particles travel always at C. If you’re saying that this is wrong, then by consequence, you’re saying that Einstein’s Special Relativity is wrong. Last time I checked, the Einstein equations are in perfect agreement with precision experiments.
        Have you an experiment that disproves SR?

        1. No, but I will say this: massless particles always travel at c, but c is not constant. See the Shapiro delay article on Wikipedia: “according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path”. Also see this page of the Einstein digital papers. I’ve highlighted the “spatially variable”. Now cast your eyes down a couple of lines. See this: “The theory of special relativity, therefore, applies only to a limiting case that is nowhere precisely realized in the real world”. Isn’t that interesting? They didn’t teach you that in college, did they? I’m afraid to say some of what you were taught was wrong Jim. Sorry.

          1. Jim

            I already covered that, when I said that photons are absorbed by fields, such as gravitational fields, then re-emmitted. Even though the photons are always going at the full maximal C, the light beam is slowed down because there is a delay between absorbtion and re-emmission.
            So even in a gravitational field, C is constant, photons travel at C – but the beams of light are slowed by the medium / field, very much like light through water. The photons are not slowed, but the overall beam is due to absorbtion / re-emmission. This was figured out by Dirac with his famous equation.

  5. Jim

    “Gravitational field energy is positive” – this is semantic games. What phycisists are talking about when discussing negative potential energy is different from what you seem to think it is.

  6. Jim

    “Perhaps the past, if looked upon with care and hindsight, may teach us where we possibly took a wrong turn and what alternative path was available”. You bet Bert” – this has been done to death. You don’t think phycisists read Einstein’s papers? WTF?
    Also remember that Einstein himself fought strongly against the predictions of his own theories and spent most of his life persuing a doomed research programme. So to idolise him as you do, whilst sweeping his mistakes under the carpet, means you’re not learning from history but repeating its mistakes.
    The major problem that physics faces is that we have insufficient experimental data to give us clues as to what Nature is up to beyond the Standard model. String theory has just wasted a lot of time on a research program that should have been scaled right back in the 1990s.
    So we have a situation where quantum mechanics / standard model agrees with experiment. A huge success of physics. Likewise the relativity theories are also holding up to astonishing precision. Yet we cannot reconcile these, nor find more fundamental theories of particle physics.
    Without huge clues from experiment, humans did not dream up relativity nor quantum mechanics, not in 3000 years of thinking. And now we’re missing the next huge idea. That’s not because physicists are mis-interpreting the Einstein papers!

    1. No, gravitational energy being positive isn’t mere semantics. And no, physicists don’t read the Einstein papers. If they did, they’d know that a curvature of light rays occurs only in spaces where the speed of light is spatially variable. They wouldn’t say you cannot speed up or slow down a photon, and that this is basic physics, the foundation. But they do, and then they flatly dismiss what Einstein said, and the hard scientific evidence of optical clocks. And then in the same breath they claim that physicists are not misinterpreting the Einstein papers.
      You can’t find more fundamental theories of particle physics because you aren’t looking at the fundamentals. If you did, you’d be able to tell me what a photon is, how pair production works, and what an electron is. When you can, you’ll understand what a “huge success” really is.

  7. Jim

    What a photon is was explained by Maxwell, see Maxwell’s equations. Quantum mechanics tells us how pair production happens. It tells us which particles can morph into other particles – fully in agreement with experiment.
    Given that agreement witih experiment continues – over many decades, to be perfect, I’d say that those theories are continuing to be perfect.
    And the path of individual photons are not “curved” by gravity. They travel is straight lines, until absorbed. Then they are re-emmitted after a delay. It is that effect that slows down the overall light beam, which, as a consequence, follows a bent trajectury.

    1. Quantum mechanics doesn’t tell you how pair production happens. If you think it does, write it down here, or refer to a description. And I’m afraid the path of an individual photon is curved by gravity. Gravitational lensing does not involve the absorption and re-emission of photons.

      1. Jim

        “Gravitational lensing does not involve the absorption and re-emission of photons.” – oh really? Show me the proof!

        1. The Physics Detective

          I can’t really prove a negative Jim, but I can offer this: when photons interact with the electrons in glass, the shorter-wavelength photons interact more. Hence in a prism the shorter wavelengths are refracted more than the longer wavelengths. Hence we see a rainbow:

          Public domain image by Lucas V Barbosaso, see Wikipedia

          We don’t see any rainbows in gravitational lensing. That’s because the bending of light is not caused by the interaction of photons with electrons. Empty space is not full of electrons. Whilst some will tell you they’re constantly popping in and out of existence, it isn’t true. Virtual particles only exist in the mathematics of the model. Instead the light bends because the speed of light is spatially variable

          1. Jim

            The photons in the glass are moving at full light speed – C. The diffraction is caused by photons being aborbed then re-emmitted by electrons. That slows down the beam of light at different rates per energy – causing the prism effect.
            Photons move at full C and only at full C. See Maxwells equations and the Dirac Equation and also Special Relativity. If you think about it, it makes sense. The material is absorbing and re-emmitting the photons, otherwise how else would the photons interact with the electrons?

  8. Amrit Sorli

    Light diminishes speed a bit when it is lower (closer to the stellar object where gravity is stronger) because when you move towards the centre of stellar object energy density of space diminishes……

    1. The Physics Detective

      I think it’s the other way round, Amrit. However Newton agreed with you. See Opticks query 20: “Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines?”

  9. Amrit Sorli

    Shapiro experiment confirms in stronger gravity light speed diminishes a bit. In stronger gravity space is less dense.

  10. hiroji kurihara

    Composition of the vector : Free fall

    Vector of gravity and inertial force is possible to compose. It seems to show that the two are inviolable and non-interference each other (it will be the same on two gravity). It will be the same also on vector of gravity and inertial force that act at an optional point of an elevator cabin in free fall.

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

    1. The physics detective

      Hi Hiroji. I see you have a lot of material about the variable speed of light on your web page. Do you know that the speed of light varies in the room you’re in? And do you know who said this?
      “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”.
      “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”.
      “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.

      See this:

  11. Hiroji Kurihara

    Turn your eyes to accelerated motion and inertial force. It does not matter what gravity is.

  12. 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 ?

  13. 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. The number of waves hitting the bars is the same. Lorentz contraction is unthinkable. And also,time dilation will be denied.

  14. Hiroji kurihara

    Time dilation

    A light source is shinning (frequency is constant). Two observers are receding from the light source at the same speed (in the opposite direction). Two observers receive the same frequency. Where is the time dilation ?

    Below is new URL of my web site. Service of Yahoo japan ends on Mar 2019.

  15. Hiroji kurihara

    An elevator is in free fall.

    In it, action and reaction are working. The two are equal as a whole and at the selected infinite small area. By the way, in an elevator accelerated horizontally (no friction), the two are equal at every area.

    Sorry, I cannot receive email. I don’t have pc.

  16. Hiroji kurihara

    Equivalence principle

    Every inertial force measurable. Every gravitational force is measurable also. Principally. In an elevator in free fall, there is no exception.

    1. That’s true Hiroji. But standing on a planet in inhomogeneous space is not exactly the same as accelerating in a rocket through homogeneous space. In the former situation your ball accelerates downwards due to gravity, in the latter situation you accelerate upwards due to rockets. When you know how gravity works, you know why the ball accelerates downwards, so you don’t need the principle of equivalence any more. You appreciate that the principle of equivalence was merely an enabling principle. It was “Einstein’s ticket to understanding”, to be discarded once he reached his destination.

  17. Hiroji kurihara

    A site on anti relativity
    A web site written by member volunteers of Japan science council is now being published (in Japanese). Below is URL.

    1. The physics detective

      It’s nice to see that it says this: in general relativity, the spacetime continuum is not homogeneous. I used Google translate. Which has a 3000 character limit. Tsk.

  18. Hiroji kurihara

    Equivalence principle
    Two forces the same vector in strength are acting on a particle from the opposite. The two are inertial force, tension and gravity. Different combinations are three. Forget the equivalence principle.

    Thank you for your reply so much.

  19. Hiroji kurihara

    Inertial force

    On a slope (no friction), a body m is sliding down. Action of gravity is mg. Then, how about the reaction ? It is resolved to two vectors. Inertial force is not fictitious.

    1. The physics detective

      Imagine two bodies the size of planets. They fall towards one another. There’s action and reaction. Make one body smaller, and you don’t notice the reaction so much. Make one body the size of a brick, and you might not notice it at all. But it’s still there.

  20. Hiroji kurihara

    Thanks for your reply, The physics detective,

    Inertial force is not fictitious

    On a plane, there are two bodies. One is at a standstill, the other is accelerating. Acceleration (a) and inertial force (ma) both are not fictitious.

    There are two disks. One is not rotating, the other is rotating. Acceleration and inertial force both are not fictitious.

    1. The physics detective

      Correct, Hiroji. Inertial force is not fictitious. Nor is acceleration. But a non-inertial reference frame is.

      1. Hiroji kurihara

        To The physics detective,

        But….from nothing, a does not emerge, I think.
        P.S. Aberration proves the existence of aether.

  21. Hiroji kurihara

    Space is rest frame

    Into space, let us draw plural vectors of acceleration a. Space will be rest frame.

    1. The physics detective

      Space is like some kind of gin-clear ghostly elastic solid, Hiroji. Waves run through it. A field is a spate of space. Space isn’t nothing.

      1. Hiroji kurihara

        Thanks so much ! Yes, space is not nothing !

        Every motion is possible to show as a motion relative to luminiferous aether. This rest frame cannot be emerged by means of dynamics. But space will be uniform isotropic field also to dynamics.

        1. The physics detective

          I’m sorry Hiroji, I’m not sure what you mean by that. But the CMB gives us the rest frame for the universe, and a field is a state of space. When space is homogeneous and uniform there is no field. When space has a vertical inhomogeneity akin to a density gradient, that’s a gravitational field. When space is twisted, that’s an electromagnetic field, and so on. I’ll talk more about this sort of thing in my next article. To understand it you ought to read the recent articles starting with this one:

  22. Hiroji kurihara

    Equivalence principle (I say again)

    Vector of inertial force is is shown by an arrow. Vector of gravity cannot be shown by an arrow generally. The two are different as facts of physics.

    P.S. To Physics Detective,
    On 25 Nov (on my post). Second line is true. It is shown in my website clearly.

    1. The Physics Detective

      No problem, Hiroji. I don’t make much of a distinction between the luminiferous ether and Einstein’s gravitational aether. Space is not nothing. A field is a state of space.

  23. Hiroji kurihara

    Dear Physics Detective,
    I also don’t make much more distinction between the luminiferous aether and real state of space (not nothing).

    Accelerated frame and non- accelerated frame

    There are plural accelerated frames and plural non- accelerated frames. The two will not be relative.

    1. the physics detective

      Agreed re space being the aether, Hiroji. As for frames, I consider myself a relativity guy, but I have to say this: reference frames do not actually exist. I can stand with you under the clear night sky and point out the moon. I can also show you the stars. But I can’t show you a reference frame. A reference frame is little more than a state of motion.

  24. Hiroji kurihara

    To the physics detective,

    I think, reference frame (aether) can be shown by aberrations. Annual aberration is eclipse. But this eclipse will be warped by the motion of linear motion of the solar system. And, all is caused by aether.

    Equivalence principle

    Difference between acceleration and nonacceleration seems to be more basic. If so, equivalence principle must vanish. This difference will be caused by the reference frame.

  25. Hiroji kurihara

    Perihelion shift of Mercury

    Mercury revolving is divided in two (hemisphere A facing the sun and the other B). Inertial force is A<B and gravity is A>B.

    Above must be the most natural explanation of perihelion shift of Mercury. Because the value of perigee movement of the moon is remarkable (around 8.85 years). On the other hand, value of asteroids will not be found. Common explanation (main cause is other planets) is not acceptable.

  26. Hiroji kurihara

    Perihelion shift of Mercury

    Perihelion shift moves forward constantly. It cannot be explained by gravity of other planets.

    On asteroids, no perihelion shift will be observed. Some size is needed.

    Cause of perigee movement of the moon is written to be the sun. Not understandable. Because it will be the same phenomenon to perihelion shift of planets.

  27. Hiroji kurihara

    Allow me Sir to post one more on Mercury.

    The value of perihelion shift of planets is constant. This will not be three body problem or many body problem.

  28. Hiroji kurihara

    Inertial force is not fictitious

    Three passenger cars are moving in different accelerated motions. These are shown with the formula, F = ma, 2F = m2a, 3F = m3a. Inertial force will not be fictitious (even for those in the passenger car).

    All about inertial forces

    A body is hung by a string from the roof the passenger car accelerating to the right. The string is leaning to the lower left. The leaning of the string depends on the equilibrium of forces. The string is under tension. The leaning of the string is the same for one outside the car and for the other inside the car. Inertial force is not fictitious to them.

    1. The physics detective

      Hiroji: I didn’t say an inertial force is fictitious. As you said, the string is under tension, and it’s leaning. There is a force on it due to gravity, and another force due to the acceleration of the car.
      However F=ma is not ideal when it comes to gravity. There’s a force on a falling brick making it fall faster and faster, because gravity is converting internal kinetic energy into external kinetic energy. That means the m is diminishing, hence the mass deficit. Once the kinetic energy has dissipated, you’re left with a brick with a smaller mass. The opposite happens when you lift the brick back up. You do work on it. You add energy to it. You increase its mass. This mass change makes it clear that gravity is not some fictitious force. So this is totally wrong:
      “Following up on this insight, Einstein was able to formulate a theory with gravity as a fictitious force and attributing the apparent acceleration of gravity to the curvature of spacetime. This idea underlies Einstein’s theory of general relativity”.
      This is not:
      “There exists some confusion, as evidenced in the literature, regarding the nature of the gravitational field in Einstein’s General Theory of Relativity. It is argued here the this confusion is a result of a change in interpretation of the gravitational field. Einstein identified the existence of gravity with the inertial motion of accelerating bodies (i.e. bodies in free-fall) whereas contemporary physicists identify the existence of gravity with space-time curvature (i.e. tidal forces). The interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with.”

  29. Harry

    How do we explain the Michelson – Morley experiment proving the constancy of the Speed of Light? Wouldn’t they find some change depending on the path and so interference?

    1. The physics detective

      Harry: Einstein came up with special relativity to explain it. Have a look at Robert Close’s paper the other meaning of special relativity. It’s the wave nature of matter, and we use the motion of waves to calibrate our rods and clocks. It’s something like trying to measure the length of your shadow using the shadow of your stick. You always get the same answer, whether it’s dawn or dusk or noon.

  30. Harry

    I am awfully sorry to return to this, I know that the experiment established once and for all that the speed of light is constant. This was the main postulate that led to the special relativity theory. My point was: you content that light speed is not constant. How do you square your assertion with Michelson-Morley.

    1. The physics detective

      Harry: the Michelson-Morley experiment didn’t establish that the speed of light was constant. All it did was demonstrate that the variation wasn’t measurable using an interferometer. See and note all the Einstein quotes. He said the speed of light varied with gravitational potential, and he said it year after year. In addition, take a look at and note what Irwin Shapiro said: “according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path”. Also see where Joao Magueijo and John W. Moffat talk about the tautology. That’s where we use the local motion of light to define our seconds and our metres, then we use them to measure the local motion of light. So we always measure the same speed, even though the speed varies.

  31. Thomas Brannan

    Since light increases velocity as it goes up (away from the gravitational center) and since matter is made of light, isn’t that enough to predict the expansion of the universe?

    1. The physics detective

      Thomas: no, because the space around the Earth is inhomogeneous. It isn’t expanding. Nor is it contracting, or falling down as per the waterfall analogy, which I mention here. What I think is enough to predict the expansion of the universe, is general relativity. It’s not totally unlike continuum mechanics, featuring the stress-energy momentum tensor because space is treated as a gin-clear ghostly elastic solid. And since stress is directional pressure, it’s a compressed gin-clear ghostly elastic solid. Think in terms of a stress ball, and see what you make of

  32. Zbigniew Modrzejewski

    Dear John, do you really BELIEVE space to be: ” a gin-clear ghostly elastic solid ” ?!
    If so, I would like you to write a blog post : THE NATURE OF SPACE.
    Unzicker argues how space and time are an illusion :
    ” Alexander Unzicker is a theoretical physicist and writes about elementary questions of natural philosophy. His critique of contemporary physics Bankrupting Physics (Macmillan) received the ‘Science Book of the Year’ award (German edition 2010). With The Mathematical Reality, Unzicker presents his most fundamental work to date, which is the result of years of study of natural laws and their historical development.The discovery of fundamental laws of nature has influenced the fate of Homo sapiens more than anything else. Has modern physics already understood these laws? Many puzzles formulated by Albert Einstein or Paul Dirac are still unsolved today, in particular the meaning of fundamental constants. In this book, Unzicker contends that a rational description of nature must do without any constants. A methodological and historical analysis shows, however, that the underlying problem of physics is deep, unexpected and fatal: the concepts of space and time themselves, the basis of science since Newton, could be fundamentally inappropriate for the description of reality, although—or precisely because—they are so easily accessible to human perception. A new understanding of reality can only arise from mathematics. By exploring the three-dimensional unitary sphere, which could replace the concepts of space and time, the author presents a mathematical vision that points the way to a new understanding of reality.” —
    In general, I agree with Unzicker, albeit I need to read his book, yet, to examine his specific argumentation.
    John, please don’t get me wrong. It is not that I am in love with Unzicker and with everything he says, and this is the basic psychological reason why I can’t see the obvious fact that space is a gin-clear ghostly elastic solid.
    You might be aware that lately the mainstream opinion has shifted towards : ” elastic fluid”. This is nothing else than just resurrection of the good old ether, a XIX-th century ghost from the Museum of Scientific Blunders.
    I don’t know Unzicker’s argumentation in details, but I have done my own research into the nature of space, and I would love to present my own argumentation up for a scientific debate.
    John, I am pretty sure that you will remain unmoved and unconvinced by my argumentation, and likewise, even though I do believe in ghosts :
    I doubt that you could have any strong arguments supportive of space being a gin-clear ghostly elastic solid or fluid, other than the most popular argument : ” it GOTTA be so, because space can’t be an empty vacuum made of nothing. ”
    And if space has to be made of something at all, well, then clear Gin (with some Tonic) is my top choice! :-))


  33. Jay Reed

    Gravitation is a central field of force. Two bodies dropped to earth fall in convergent paths. A mechanical field of force; generated by the well-known accelerating rocket, is rectilinear in its action. Two dropped bodies on the rocket will fall in parallel paths to the floor. The effect in this example will be slight; but the two different fields of force can be identified.

  34. The Physics Detective

    Good stuff Jay. I so dislike the way people claim exact equivalence between the accelerating rocket and the gravitational field, even though Einstein didn’t. I also dislike the way people claim that Lorentz invariance always applies, absolutely, no matter what. IMHO there’s no place in science for such articles of faith.

  35. Jay Reed

    Some relativists consider the deflection of light near gravitating bodies to be an original thought of Einstein’s. A close historical study of Eddington’s measurements will reveal some insights into some “slight of hand” to obtain unquestionable proof of Einstein’s GR. It is also interesting to see that the deflection concept was first espoused by Newton. Also before 1800 the deflections were being investigated. See, for example, Joh. Soldner, “On the deflection of a light ray from its rectilinear motion,” (Berlin, March 1801). This subject is very far from being settled; and does not prove any aspect of GR.

    1. The Physics Detective

      Jay: thanks that for that I see the Soldner paper is on Wikipedia:
      I haven’t talked about the Gerber controversy here, or how Einstein didn’t credit any of the other relativity guys in 1905. But I do refer to Newton in saying this:
      So did Newton, see Opticks query 20: “Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines?
      For myself, I think the biggest issue with GR is that “modern” general relativity features a constant speed of light, whilst Einstein said repeatedly year after year that the speed of light varies with gravitational potential.

  36. Hiroji kurihara

    Gravitational time dilation
    Allow me to post an essay,

    Laser beam (frequency is constant) emitted from the ground is reflected by the mirror at the top of the high tower, and returned to the ground. Frequency at these three points is the same. There is no time dilation.

    1. the physics detective

      Agreed, Hiroji. Time doesn’t go slower when you’re lower. There is no thing called time moving in an optical clock. The thing moving in the optical clock is light. Light goes slower when you’re lower. Then, because of the wave nature of matter, so do you.
      Sorry and no offence, but I won’t let you post an essay. It’s a can of worms.

      1. Hiroji kurihara

        I am seeing worms also. I must say, sorry !

  37. Hiroji kurihara

    Acceleration & non-acceleration
    Allow me to post an essay

    A passenger car is moving in a uniform accelerated motion to the right. In the car, a ray of light emitted downward from the roof will be bent to the left (as a parabola). Defference of acceleration and non-acceleration is not relative (but absolute).

  38. Hiroji kurihara

    Acceleration & non-acceleration
    Allow me to post an essay

    A passenger car is accelerating to the right. In the car, lights (frequency is constant) are emitted from light source settled on rear and front walls, and at the center of the car, interference fringes are observed. Varying of interference fringes will reflect varying of acceleration. Sagnac effect like will also occur in a straight line.

  39. Jay Reed

    The Physics Detective stated his appreciation for my comment on the deflection of light by a gravitational field. That being said he and possibly others might be interested in Olinto De Pretto’s investigation and publication of the “Mass-Energy Equivalence,” published in November of 1903. De Pretto’s paper was later favorably received by the Royal Society, and listed in their “International Catalogue of Scientific Literature.” It is most interesting to note Einstein was living in Italy when this paper was first published.

    1. The physics detective

      Thanks for that Jay. I learn something new every day. I will look into this, starting with Wikipedia. I’ll try to find his paper.
      There are a number of issues surrounding Einstein’s work. He didn’t credit Voigt, Fitzgerald, Lorentz, or Poincare at all for special relativity. There’s the Gerber dispute re the perihelion formula, the Hilbert issue, and then there’s the mystery as to why Einstein achieved very little after about 1920. Sometimes I wonder if “my hero” Einstein was a tainted hero. I’m afraid nothing would surprise me when it comes to physics. The more I learn about it, the more problematic it seems to be. I used to be a Feynman fan, but now I’m not.

  40. Jay Reed

    In further reference to the “Principle of Equivalence,” there is another method of distinguishing a gravitational field of force from an inertial field of force. The inertial field is produced by mechanical means such as the well-known rocket with acceleration “g.” As a body falls, under a true gravitational force, it will experience a slight increase in acceleration due to the effect of the inverse square law. On board the rocket, the object falls in a rectilinear path, as discussed earlier, and experiences no increase in acceleration as the inverse square law is non-existent in the inertial field.

    1. Jay: agreed.
      Why anybody would think otherwise absolutely beats me. But there again, they don’t understand how gravity works. And what’s worse, is that they don’t seem to want to.

  41. Jay Reed

    The worship of false gods has always been a problem.

      1. Leon

        “Einstein said “an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated“. When the ascending photon ascends, its E=hf energy does not reduce, and nor does its frequency. There is no magical mysterious outflow of energy from the photon. It doesn’t get redshifted at all. That’s a myth. Instead the photon was emitted at the lower frequency at a lower elevation. Conservation of energy applies. It appears to have less energy at the higher elevation because that’s where optical clocks go faster, along with everything else. So we measure the photon frequency to be reduced, even though it didn’t change at all.”

        Doesn’t this imply that redshift cannot be used to infer distances? But only regions where the gravitational potential is stronger (“denser space”)? Hence completely throwing out of the window accepted cosmological evolution models?

        I’m not disagreeing with the hypothesis, but what could be an experimental verification, that favors this interpretation over the commonly accepted one? If I got it right, it’s quite the implication.

        1. The physics detective

          Doesn’t this imply that redshift cannot be used to infer distances?
          No. Take a look at the Tamara Davis Sci-Am article at the bottom of . The CMBR photons have not actually redshifted, but we can still use the thing we call cosmological redshift to plot the expanding universe.

          1. Leon

            All I see in the article is that this is an equivalent interpretation if we assume a flat space time locally at any point along the photon’s path, which is very reminiscent of the infinitesimal room of the equivalence principle. I’m not sure we can assume that globally space time is flat, but maybe you can convince me otherwise.

            The article itself directly contradicts one of your first replies to my inquiries:
            “ Also, in GR global energy is just not well defined. Locally it’s always conserved, but globally it isn’t necessarily the case.
            That’s a myth peddled by those who would tell you a) the total energy of the universe is zero, and b) the universe has an evil twin where time runs backwards.”

            I think it’s a bit weird that you cite this one.

            In any case, we still shouldn’t be able to infer a distance if there’s no direct way of measuring the total gravitational field of the galaxy of origin of the photon, because two galaxies at the same distance from earth but with a different total gravitational field would emit photons at different frequencies, hence making redshift unreliable.

            If your theory on the origin of dark matter is true, and it is simply an increase in the energy density of space, then redshift should be directly affected. But then, since the older galaxy clusters have more “dark matter”, we conclude that closer galaxies (whose light reached us first) should be redshifted the most, if not for the fact that Since expansion is a thing and closer galaxies tend to move slower with respect to us, there’s less Doppler shift. The two effects (gravitational redshift and Doppler redshift) combine to give the overall redshift. Depending on how fast the expansion is happening, the combined effect is different: at the right expansion rate, the redshift could even remain constant! But of course this is not what we observe.

            I’m just terribly confused by the whole ordeal.

  42. Jay Reed

    Re: Past posts on the Principle of Equivalence. “We… assume the complete physical equivalence of a gravitational field and a corresponding acceleration in the reference system (the ubiquitous accelerating rocket).”
    Einstein 1907

    1. The Physics Detective

      They aren’t completely equivalent, Jay. What I’ve heard is that the principle of equivalence was akin to a train ticket, to be discarded at Einstein’s destination. The man falling off the roof was allegedly his happiest thought, because for the falling observer who doesn’t know he’s falling, it’s like there’s no gravitational field. Once Einstein reached his destination, which was General Relativity, he didn’t need the principle of equivalence any more, and said it only applied to a region of infinitesimal extent. See

  43. Jay Reed

    Re: Past posts on the “Principle of Equivalence.” As the man falls off the roof; he is falling in a gravitational field, which certain experiments will reveal. I understand the Principle of Equivalence to be the foundation of GR. A MIT physicist gives a lecture on GR on “Youtube,” and in the first opening of the lecture is the declaration of exact equivalence between gravity and uniform inertial acceleration. He made no mention of the principle being a convenient, incorrect, and infinitesimal expendable as he journeyed to his destination.

    1. Leon

      During uniform inertial acceleration you will never feel tidal forces. Since tidal forces stem from the curvature of the gravitational field, and spacetime is never totally flat in a gravitational field, there will always be a residual almost imperceptible tidal force. This is why the principle is never realized in practice.

  44. Jay Reed

    Re: posts on “Principle of Equivalence” by Reed. For a sample of the instruction on said topic see: Youtube… Relativity 107a: General Relativity Basics – Equivalence Principle and Proper Acceleration.

    1. The Physics Detective

      Jay: the video gave a simplified version, and said it applied to a small region of spacetime, which can be approximated to an inertial reference frame. The situations are not indistinguishable in a larger region which might be referred to as a non-inertial reference frame. That’s because you then notice the tidal force, which is associated with spacetime curvature.
      Wes: note that at 7m 10s the narrator talks about light beams bending in an inertial reference frame. That’s when there is no measurable spacetime curvature. That tells you that light doesn’t bend because of spacetime curvature.

  45. Jay Reed

    Re: Origin of GR. Charles Lane Poor was a Professor of astronomy at Chicago and Columbia. He published a paper (resident on the computer) “Relativity and the Law of Gravitation (1930).” Poor takes the reader through Einstein’s 1915 paper; “Erklarung dre Perihelbewegung des Merkur …” showing Newton’s Law declared as the “first approximation” in the new law of gravitation. Einstein’s original and only known derivation of this most important formula to compute the planetary motion is to be found in this paper. The Einstein paper is obscure. His derivation of the rotation of planetary orbits is not found in any standard work on relativity. Poor’s exposition of this paper is very important in the history of Relativity.

  46. Jay Reed

    Re: Past post on Poor’s paper. Poor’s paper is difficult to find on the computer. However, it seems easy to find if the a search is done on the following title: Charles Lane Poor, “Relativity and the Law of Gravitation,” Astronomische Nachrichten, (1930)

  47. Jay Reed

    Re: The Gerber controversy. Not only is the result exactly the same; but even the symbols are a match. If I did this in school or a publication they would say, without reservation, I was a plagiarist. There would be no story I could tell that would exonerate me from the decision. My transcript would be marked with “Academic Dishonesty.”

    1. The physics detective

      Jay: there was also an issue with special relativity, wherein Einstein gave no credit to Lorentz, Poincare, Fitzgerald, or Voigt. See where you can read this:
      However, most historians of science, like Gerald Holton, Arthur I. Miller, Abraham Pais, John Stachel, or Olivier Darrigol have other points of view. They admit that Lorentz and Poincaré developed the mathematics of special relativity, and many scientists originally spoke about the “Lorentz–Einstein theory”. But they argue that it was Einstein who completely eliminated the classical ether and demonstrated the relativity of space and time. They also argue that Poincaré demonstrated the relativity of space and time only in his philosophical writings, but in his physical papers he maintained the ether as a privileged frame of reference that is perfectly undetectable, and continued (like Lorentz) to distinguish between “real” lengths and times measured by observers at rest within the aether, and “apparent” lengths and times measured by observers in motion within the aether.
      Einstein reintroduced the aether for General Relativity, see his 1920 Leyden Address. You can find me saying that I think there’s a big issue with length contraction. And note that the CMBR gives us a privileged frame of reference. So it’s a grey area I’m afraid. Einstein is still my “hero”, but he’s a tainted hero. He was right about a lot of things, but I don’t think he was a saint. Feynman used to be my hero too, but he was definitely a plagiarist, and now he isn’t.

  48. Jay Reed

    Re: Neutrinos and SR. Check out the paper W.W. Buechner and R.J. Van de Graaff, “Calorimeter Experiment on the Radiation Losses of 2-Mev Electrons,” Physical Review,V70,No.3&4,(Aug. 1 and 15, 1946). Without the Neutrino SR is in a pinch. There is no (as in no) info on how Pauli “invented” the Neutrino to make up for the violation of the conservation of energy; thereby saving SR. This is a very interesting revisit to the beginnings of the tests and politics of SR.

  49. Prestij Meselesi

    I really love your blog.. Excellent colors & theme. Did you build this amazing site yourself? Please reply back as I’m planning to create my own personal website and would love to find out where you got this from or what the theme is named.

    1. the physics detective

      I didn’t build it myself, I used a WordPress theme called OceanWP, then selected various options to generate the blog that you see. It’s hosted by GoDaddy, who are very good.

  50. Vit

    Hi John,
    Do you think that it is possible that the reason why an electron has lower potential energy (lower mass) in a stronger gravitational field is caused by slower speed of light and therefore the energy E=mc2 is smaller?

    1. The physics detective

      Yes, it’s something like that. But E=mc² is not a good expression here because E m and c all vary with gravitational potential. Note that gravitational potential is what’s important. A strong gravitational field is where there’s a steep gradient in gravitational potential. Note that the mass cannot reduce without limit, see for more.

  51. Vit

    I tried to do some math and You’re right. E=mc2 is not good, because m varies with gravitational potential. So I tried energy for wave instead: E=h*c/lambda and I was surprised that this works really well.

    Time dilation on the surface of the Earth can be calculated from the equation: t0 = t * sqrt(1 – 2*G*M/(R*c^2))

    So if the speed of light is variable, then on surface of the Earth it should be:
    c0 = c * sqrt(1 – 2GM/(R*c^2)) = 299792457.7913121259366 m/s
    The speed of light at the height H=1 metre above the surface of the Earth should be little higher:
    c1 = 299792457.7913121586925 m/s

    Let’s say we have a mass of 1 kg. This corresponds to wavelength L = h / (c * m) = 2.2102 * 10^-42 m.
    The energy difference is then E1 – E0 = h*c1/L – h*c0/L = 9.82 J which very well corresponds with expected potential energy E = mgH = 1 * 9.81 * 1 = 9.81 J

    Then I tried to express E1 – E0 for arbitrary height H and with linear approximation I’ve got E1 – E0 = mgH.
    I’ve found interesting that the approach with variable speed of light and treating matter as waves gives this result.

    1. The physics detective

      It ought to, Vit, because the time dilation is only there because the speed of light varies. Have a look at the Einstein links in I give quotes such as 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”. People tend to say that Einstein gave up on the variable speed of light in 1911, but he didn’t. Have a look at an older version of the Wikipedia Variable Speed of Light article: Sadly most of the Einstein references are not in the current version.

  52. Jay Reed

    Re: Learning about GR. I have only looked at GR as a historical question through the years. I am interested, as a novice, to see the answers to practical questions such as the following: GR is reputed to be amazingly accurate in predicting many things. And the reality of experiment and GR prediction are said to compare most favorably. It would be extremely interesting, to me, to see an ephemeris of our solar system orbits overlaid by an ephemeris generated by GR. For example, the orbit of the earth’s moon is known with great precision; what does GR predict for the moon’s orbit? I never see mundane, but interesting information such as this.

    1. the physics detective

      Come to think of it Jay, nor do I. I don’t know where this sort of thing is I’m afraid. I’ve just had a search for GR and the Moon’s orbit, and couldn’t find anything. All I can suggest for now is Clifford M Will’s paper The Confrontation between General Relativity and Experiment : . Merry Christmas and a Happy New Year!
      PS: apologies if there’s a problem with the comments.

  53. G.R.+Leslie

    Test has come thru on my end.

    1. The physics detective

      Happy New Year Steve. I wonder if you’ve got things back to front, and stars burn colder at the galactic core? I say that because the gravitational potential at that location means everything happens more slowly there. Hence the emitted light is at a lower frequency. As for dark matter, IMHO the higher spatial energy density at that location is going to have a gravitational effect. See and

      1. Leon

        I think the issue is that c is inversely proportional to the permeability constant. If c is slower, € is higher, and so the coulomb force is weaker, meaning fusion rates are higher (because nuclei can be brought together more easily). I’m not sure if any effect of time dilation are that strong outside the immediate vicinity of the black hole. Weaker coulomb force also means electrons are less pulled by the nucleus, and so orbitals are bigger and the energy needed for transitions becomes smaller, hence longer wavelenght (lower frequency) photons.

        Which is also an issue, because it means that older galaxies (the ones with more dark matter = higher gravitational potential) should be the ones more redshifted by the gravitational redshift. But we don’t observe that.

        1. steve powell

          Hey Leon, You are correct that the time dilation is tiny but it (redshift) has been measured by Pound and Rebka over just a few feet of elevation change. C being inverse to epsilon is just Maxwell eq. c= 1/sqrt(epsilon*mu)

      2. steve powell

        John, Yep I use gravitational potential inside out. I use absolute value since more here makes better sense than 0 in space and -xyz here. More mass ~ more gp. Also more gp means less dense space, kinda like LeSage gravity.

        1. The Physics Detective

          I agree with that, a negative gravitational potential near the surface of the Earth doesn’t make any real sense. However I’m not a fan of La Sage gravity or negative energy. I’m pretty sure that space is “denser” down near a gravitating body. So light goes slower there. Hence light passing horizontally is refracted downwards, then matter falls down because the horizontal component of what you’d call the matter wave also refracts down. Einstein spoke repeatedly of refraction and the speed of light varying with gravitational potential, and said “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. See for more.

          1. Steve Powell

            Agree with refraction for sure!

            Speed of sound in denser materials is faster than less dense. Steel v air. I know that sound is not transverse wave but that’s “where the light is good” lol

            1. Steve Powell

              Been wrestling w/density concept for a very long time. Came across Dicke’s 1957 paper and realized nature of space is moot. Once you know that epsilon is relative to the gravitation potential the rest is hardwired and you can plug it into some major physics and explain some unexplained observations.
              That said I would like to understand the nature of space and your writings are great. One thing space is not is any sort of matter like we know.

                1. Steve Powell

                  Space is the absence of matter. Better: matter is the absence of space.

              1. Steve Powell

                Yep denser~lower. Can we say that space is less energetic when it’s denser? By e=mc2 ?

                1. The physics detective

                  I think it’s more energetic when it’s denser. When I’ve put on my systems analysis hat to investigate what energy is, I end up thinking that space and energy, at some strange fundamental quintessential level, are the same thing. And matter is made of it.

                  1. Steve Powell

                    Yes I mostly agree. Ever see a calm swimming pool. There is usually a jet of conditioned water which causes tiny whirlpools. Light though the whirl leaves a dark circle shadow on the bottom. I think matter is like those whirls.

                    1. The physics detective

                      Agreed. I and other have been fascinated by Falaco solitons. You dip a plate halfway into a pond and stroke it forward and up and out. This creates a vortex akin to half a smoke ring, and what looks like two whirlpools on the surface. You can emulate attraction, repulsion, and annihilation with Falaco solitons, like Thomson and Tait did with smoke rings. I mentioned Falaco solitons in plus some other articles. Sadly Thomson and Tait were ahead of their time with their vortex atom, and nobody started thinking about the vortex electron. Such is life, but here’s a historical article that might be of interest:

      1. Steve Powell

        Yeah that up down stuff is in every written description except the research itself!

    1. The physics detective

      I thought it started well, but liked it less when they started talking about fibres and proposing their own theories. Also, they don’t know much history. For example they said “Equations describing the relationship between speed of sound closely mirror Maxwell’s equations for electromagnetism”. They don’t know that Maxwell based his speed of light equation on Newton’s speed of sound equation. See the Wikipedia talk page for On physical lines of force. Contributor David Tombe says “the punchline comes at equation (132) where he uses the Weber/Kohlrausch experimental result in Newton’s equation for the speed of sound”.

      1. Steve Powell

        Yeah I read most of the rest and not much there. Sinners in the choir still better than atheists…

        1. The physics detective

          I had fun digging around into Maxwell and guys like Weber, Kohlrausch, and Kirchhoff in the mid nineteenth century. See this: . Apparently Maxwell didn’t know about Newton’s Opticks, which was out of print until 1931. So it would seem that he didn’t know about query 20: “Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines?” So whilst Maxwell unified electricity and magnetism, he didn’t unify electromagnetism and gravity. Well that’s what I reckon anyway.

  54. Cedron Dawg

    I would like to draw everybody’s attention to the “Revisiting Einstein’s Premises” section in my off topic Physics article:

    My main thesis is that Gravity is the net result of refractive acceleration of constituent components of matter. I also postulate the physical nature of these components.

    Finally, there is a shout out to this blog in my second comment, third of the article. Please, everybody read this and pass the link around.

    1. The physics detective

      It’s not a fluid, Cedron. It’s some kind of gin-clear ghostly elastic solid. As per the website Steve linked to. Light waves are transverse waves. You need a solid for that.

  55. Cedron Dawg

    As you note, you need compressibility in your solid to transmit a wave, so the distinction is almost semantic. Technically, window glass is a fluid. Regardless, the speed of the wave is going to be much faster than the underlying medium, analogous to sound waves in a flowing river. Since my thesis employs vortex rings, rapid flow has to be possible, so I will disagree with your statement in a broad sense.

    1. The Physics Detective

      No more, Cedron. Please. Because light is a wave, and this is not a “my theory” website.

      1. Cedron Dawg

        Okay. If anybody wants to reply, my email address is in the bio of my blog, or they can comment on the article.

  56. Cedron Dawg

    I should also emphasize that I am able to derive a complete behavioral description of Gravity based on Refraction, prior to speculating on the underlying physical implementation. My vortex rings hypothesis may not be correct, but it wouldn’t obviate my “Motion Enhanced Gravity” equation, nor my comparisons to GR.

  57. steve powell

    Found it! Einstein at Nottingham –
    “The strange conclusion to which we have come is
    this-that now it appears that space will have to
    be regarded as a primary thing and that matter is
    derived from it, so to speak, as a secondary result.
    Space is now turning around and eating up matter.
    We have always regarded matter as a primary thing
    and space as a secondary result. Space is now having its revenge, so to speak, and is eating up matter.
    But that is still a pious wish.”

    1. The Physics Detective

      Good stuff Steve. You know, I used to think Einstein was overrated, but the more I’ve read about the guy, the more I’ve though he was pretty much spot on, See As far as I can tell, space is the only thing there is, and it’s the same thing as energy. On top of that, as far as I can tell, a field is a state of space. The gravitational field is inhomogeneous space, and the electromagnetic field is twisted space. All plain vanilla stuff once you suss it.

      1. Cedron Dawg

        Great reference! The most significant statement in it for me is: “The problem is nearly solved, and to the first approximations he gets laws of gravitation and electro-magnetics.” As per my comments in the “Speed of Light” article, since there is no way to empirically differentiate Ye & Lin’s solution and the Schwarzschild GR solution, why should we presume the latter to be more correct?

        1. The Physics Detective

          I don’t think we should. But I’d say there are other things that are more incorrect. For example look at the Wikipedia article on the Schwarzschild radius. It says “The physical significance of these singularities was debated for decades. It was found that the one at rₛ is a coordinate singularity, meaning that it is an artifact of the particular system of coordinates that was used”. That’s wrong. The speed of light at the event horizon is zero. Changing your coordinates system won’t change that. To think it will is a schoolboy error. See . PS: I have a discussion forum which you might find useful.

          1. Cedron Dawg

            I don’t think we should either. In fact, Occam’s Razor would select Ye & Lin’s as the preferred one. The r_s is a characteristic value, so it can naturally be used as a normalization factor to make comparison of different sized systems comparable. Calculating other characteristic values in respect to the normalized one is also a valid and valuable technique. But I agree, if it changes the nature of the problem, then you’ve done the math wrong.

            What it means is also confusing. The Wiki defines it as the location of the event horizon which is where light is supposed to stop. But according to the Schwarzschild solution of the index of refraction, the singularity sphere is at r_s/4, which is where the formula for the index of refraction goes to infinity, meaning zero velocity. From a different formula, the radius at which an orbit would go at the speed of light is at 3/2 r_s. The orbital speed at r_s would have to be infinity.

            The Ye & Lin formula gives different results. Under it, there is no event horizon since it occurs at the very center. Obviously, in a physcal situation, there won’t be empty space there. The orbit speed at r_s would be the speed of light, and at 1/2 r_s it would have to be infinity. Clearly this is a more “natural” description, not to mention a much more elegant formula.

            I didn’t know about your forum. I will check it out and lurk a bit before I post.

            1. Cedron Dawg

              Keeping this to the theme of the article. If Ye & Lin’s formula represents reality better, that means the Schwarzschild solution is “not true”. If the argument is “true” (exact derivation), but the conclusion is “not true”, that means at least one of the premises must be “not true”. The rules of logic are pretty firm.

  58. Jay Reed

    Re: The Aether. The USAF repeated the Michaelson – Morley experiment with far more sensitive equipment and obtained a positive result as to the existence of the Aether,

    See: E.W.Silvertooth, “Special Relativity,” Nature Magazine, vol. 322, p.590, (Aug. 1986).

    I wonder why this was not a world-wide headline?

  59. Doug

    Bro,.did you read that “article” you just cited? It’s just few paragraphs, there is no experiment or data or anything. It wasn’t a headline for obvious reasons

  60. Jay Reed

    Re: Doug and the Aether. Go to google scholar and request: E.W.Silvertooth, C.K. Whitney, “A new Michaelson-Morley Experiment,” A complete PDF of the paper will appear and it can be printed or examined for free.

    Anyway, that is one way to get the entire paper for free. Good Luck

  61. Jay Reed

    Re: Use of SR. It is known that SR cannot be used on accelerating systems. When SR is used to find the mass, momentum, etc. of an entity at a relativistic velocity; the entity had to accelerate to reach that velocity. Since SR cannot be used in this required period of acceleration, would there not be some anomaly in the final predicted dynamic state of the entity? Examining this from a slightly different point of view: what happens to the SR predictions in a state of velocity decay (slowing down or particle capture)?

    1. The Physics Detective

      I don’t think special relativity can be used for much, Jay. I don’t think there’s much to it either. The Lorentz factor is just Pythagoras’s theorem. I talked about it in The Nature of Time, where I referred to The Other Meaning of Special Relativity by Robert Close. I reckon he nailed it. Special relativity applies because of the wave nature of matter, but unfortunately this is not a part of the theory. Instead we have reference frames and other abstract things that do not exist. As for SR predictions for a particle slowing down, I don’t know I’m afraid. But I think of an electron as being in essence light going round in a circle: O. Turn it on its side and it looks like this: |. Then move it and the light follows a helical path, that looks like this: /\/\/\/\. Then you use Pythagoras’s theorem again to work out various things.

  62. Jay Reed

    RE: Jay Reed post of 9th Sept. 2022. Charles Lane Poor’s “Relativity and the Law of Gravitation,” Astronomische Nachrichten, (1930) has been hidden and vilified by the “Einstein Fan Club.” It is extremely difficult to obtain Poor’s paper due to their burying technique (I have seen the method before). They even comment on the “sad” state of German science indicated by the publication of Poor’s paper in the above famous journal. What is really “sad” is the censorship of the writings of a keen American scientist.

  63. Jay Reed

    Fermi said, “he could fit an elephant with 4 variables; and with 5 he could make it wiggle its trunk.”
    On a different subject: the advance of Mercury’s orbit is explained by Albert by appending terms supposedly from the realm of special relativity to Newton’s Law of Gravitation. Mercury’s orbit is always accelerating; it also has an additional acceleration due to its advance. So two accelerations are at work. But it is well known special relativity cannot handle accelerating systems. This begs the question as to how Albert got the 43 seconds per century. It is good though to know the answer ahead of time. Reminds me of a Feynman axiom, that “the easiest way to solve a differential equation is to know the answer ahead of time.”

    1. The Physics Detective

      I don’t know Jay. But I have a nasty speaking suspicion he got it from Gerber.

  64. Jay Reed

    Yes, I can see your suspicion when you compare Gerber’s formula with Albert’s formula: the formulas are identical, and Albert even uses the exact same Greek symbols. A person who refuses to admit this has a hidden agenda at work.

    1. The Physics Detective

      There’s also an issue with special relativity, in that Einstein did not acknowledge people like Voigt, Fitzgerald, Lorentz, and Poincare. But note what I said in Nature and corruption about journals. I’ve read that there was a deliberate promotion of “German Science” in the early years of the 20th century, so I don’t know how much fault can be ascribed to Einstein.

  65. Jay Reed

    Re: Just a note; for fun. Stanford University has a linear accelerator. They accelerate particles to relativistic velocities and let them collide in various ways. The debris is examined for any interesting results. The person who is in charge of the accelerator said they have never seen any special relativity effects. This is another case showing SR cannot manifest in accelerating (or deaccelerating) systems. In my humble opinion, I think this problem with acceleration and SR is interesting.

    1. The Physics Detective

      Jay: a lot of accelerator physicists don’t have a clue about fundamental physics. It’s like they’re trying to understand chemistry by watching firework explosions. Have a read of the nature of time and take a look at the section on time dilation. Do follow the hyperlink to read The Other Meaning of Special Telativity by Robert Close. He explains why special relativity works. It’s down to the wave nature of matter. An electron is in essence light in a closed path. Simplify it to a circular path. Then if the electron moves fast, the path is helical. So it takes longer for the light to complete one revolution. How much longer is given by the Lorentz factor, which is just Pythagoras’s theorem. Then scale it up, and the same applies to you.

  66. Jay Reed

    Re:GR revisited. If one examines certain sections of the literature of GR Einstein’s “pseudotensors” will be found. S.J.Crothers ( shows by the developers of tensor analysis, Ricci-Curbastro and Levi-Civita, in 1901 that using the pseudotensors to derive the energy-momentum of the gravitational field violates the laws of pure mathematics. See: T. Levi-Civita, Mechanics. – On the analytical expression that must be given to the gravitational tensor in Einstein’s theory, arXiv:physics/9906004v [physics.hist-ph] 2 Jun 1999. Levi-Civita’s work is also cited elsewhere; but the above translation from the Italian is needed.

    1. The Physics Detective

      Thanks Jay. I’ve tried to talk to Steven Crothers about general relativity, but without success. I see the paper you referred to:

      I’m afraid I can’t look into this now because I’m writing the next article. It looks interesting:
      “While most textbooks of general relativity and research articles discuss at length the relative merits of the pseudo tensors proposed by Einstein and by other authors for representing the energy of the gravitational field, Levi Civita’s definition of a true gravitational energy tensor has succumbed to Einstein’s authority and is nearly forgotten. It seems however worthy of a careful re-examination, due to its unquestionable logical soundness and to the unique manner of propagation for gravitational energy that it entails”.

  67. Jay Reed

    Re: Mach’s Principle. In my opinion, there is an amazingly interesting paper found at: D. W. Sciama, “The origin of inertia.” Also a youtube by Alexender Unzicker explaining the work of Sciama and Foy. Foy saw the important info that had been overlooked or ignored from Scima’s 1952 paper, and added to Scima’s original work. Very interesting indeed!

    1. The Physics Detective

      It might be interesting Jay, but it’s wrong. I can see a link to Sciama’s paper here:
      I will explain why it’s wrong in detail at some point. I can’t do it right now I’m afraid. But you may like to take a look at this:
      The mass of a body is a measure of its energy-content. The wave nature of matter means the mass of a body like an electron is a measure of resistance to change-in-motion for a wave in a closed path. Meanwhile photon momentum is a measure of resistance to change-in-motion for a wave in an open path. Neither measure has got anything to do with the existence of something zillions of light-years away, and there is no instantaneous action-at-a-distance.

  68. Jay Reed

    Physics is a hard mistress.

  69. Jay Reed

    Re: Feynman. You mentioned you soured a bit on Feynman in the past. Did you find any plagiarism? I found the comment interesting; as he seems to be everyone’s darling. I had a friend who had him for a teacher. My friend said, “He smiled too much.”

  70. Jay Reed

    Re: the physics detective 3/2/24. Interesting. I wonder about the mindset of people at such big banquet tables still try to sneak food off others plates. Very puzzling. Maybe admiration is addictive.

    1. The Physics Detective

      I’m not sure it is, Jay. For myself I used to be a Feynman fan because I thought his books were great, and I liked his style. He was humorous and entertaining on TV, and he had a reputation for being “the great explainer”. But when I found out more, things didn’t seem quite so good. He was a total creep with women, see for example Then there are hints that he wasn’t honest. I mentioned the Sudershan thing. Also see where I said this:
      Meanwhile I note that in his Nobel lecture Feynman said he stole the idea of representing positrons as electrons going back in time from his advisor John Wheeler. I also note the popular legend that when Feynman, Schwinger, and Tomonaga were exiting the stage at the Nobel ceremonies, Schwinger quipped, “By the way Dick, professor Stueckelberg wants his lecture notes back”. That’s perhaps a veiled reference to Stueckelberg’s lost paper. You can read about it in various places including the St Andrews Stueckelberg biography written by John O’Connor and Edmund Robertson. They say in the early 1940s Stueckelberg “wrote a long paper outlining a complete and correct description of the renormalization procedure for quantum electrodynamics. He sent it to the Physical Review, but it was rejected”. You can also read Jagdish Mehra quoting Feynman saying Stueckelberg “did the work and walks alone toward the sunset; and, here I am, covered in all the glory, which rightfully should be his”.

Leave a Reply