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.


This Post Has 21 Comments

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

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

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