Science on Sunday with John Duffield: Gravity

The thing about physics is that once you understand one thing, it’s easy to understand another. A couple of weeks back I was talking about time being derived from motion. Once you understand that, it’s easy to understand that the speed of light isn’t constant. Then once you understand that, it’s easy to understand gravity. Straight up. You’ll be familiar with the rubber-sheet analogy. The Earth is like a bowling ball in a rubber sheet, like this:

GNU FDL image by Johnstone, see Wikipedia commons

GNU FDL image by Johnstone, see Wikipedia commons

You probably know already that one problem with this picture is that the Earth looks like it’s being pulled down by gravity. It’s no good using gravity to explain gravity, that’s circular. But the picture isn’t totally wrong. Imagine you’ve placed a whole lot of parallel-mirror light-clocks in an equatorial slice through and around the Earth. When you plot all the clock rates, your plot resembles the rubber-sheet picture because clocks go slower when they’re lower. Then the curvature you can see does relate to Riemann curvature, which relates to curved spacetime. And yes, you measured those clock rates, so yes, it’s a curvature in your metric. But it’s important to remember that the curvature is just a curvature in your plot of clock rates, and those clocks measured the motion of light through space. So what the rubber-sheet analogy is really depicting, is the variable speed of light.

It’s also important to note that the clocks nearer the Earth don’t run slower because your plot is curved. In other words, they don’t run slower because spacetime is curved. Spacetime is an abstract mathematical space, and it is static. It’s the plot, the map, and the map is not the territory. Spacetime is not what space is. The clocks run slower when they’re lower because the space down there is different. That’s because a concentration of energy in the guise of the matter of the Earth “conditions” the surrounding space, the effect of this diminishing with distance. Einstein talked about this in his 1920 Leyden Address, where he also talked about inhomogeneous space. That’s the reality that underlies curved spacetime. And like I was saying last week, he didn’t say light curves because spacetime is curved. He said light curves because the speed of light varies with position.

I don’t know if you know, but there’s another couple of problems with the rubber-sheet picture. One is that it depicts tension instead of pressure. Einstein’s stress-energy tensor has an energy-pressure diagonal, and to envisage pressure you need to step up from a rubber sheet to three-dimensional space. Imagine it’s like some gin-clear ghostly elastic jelly, and  you insert a hypodermic needle and inject more jelly to represent the mass-energy of the Earth. The surrounding jelly is pressed outwards rather than being pulled inwards. The other  problem is that the Earth is spherical, which really muddies the water when we’re talking about Einstein’s inhomogeneous space. To get past that, we need to zoom in a little, like this:

Image credit: NASA  (I removed the moon and added the lattice lines)

Image credit: NASA (I removed the moon and added the lattice lines)

The height of each square relates to your clock rates. Remember they’re light-clocks, so the height of each square relates to the speed of light at that position. And because the speed of light varies from top to bottom, a beam of light going across the picture will curve like a car veers when it encounters mud at the side of the road. Like this:


Hence Professor Ned Wright’s Deflection and Delay of Light wherein “the delay experienced by light passing a massive object is responsible for the deflection of the light”. That’s easy to understand. And of course, once you understand why light curves, it’s easy to understand why matter falls down. There’s only one other thing you need to know about, and that’s the wave nature of matter. You can make an electron along with a positron out of light in pair production. And you can diffract an electron. Plus in atomic orbitals electrons exist as standing waves. So just think of an electron as light going round and round. Then you can simplify it to light going round a square path. Try drawing it, like this:


Now imagine it’s in a gravitational field. The vertical parts of the path are still vertical, but the horizontal parts bend down a little. So the electron falls down. Like this:


In essence the reducing speed of light is transformed into the downward motion of the electron. You can diffract protons and neutrons too, so the same principle applies to matter in general. From this you can even understand why the general-relativity deflection of light is twice the Newtonian deflection of matter. It’s because for matter, only the horizontals bend down. Yes, it’s pretty simple really. It’s a bit like riding a bike. Once you’ve the hang of it, it’s easy. But as for why this isn’t common knowledge, I don’t know. It should have been common knowledge for about three hundred years, because in Opticks queries 20 and 21 Newton said this:

“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? …Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?”

That’s Newton telling you how gravity works. Whilst he didn’t know everything we do and he got the density thing back to front, in Opticks query 30 he did say “Are not gross bodies and light convertible into one another?” He managed to make the connection between light curving and matter falling down. And yet here we are, three hundred years later, and it’s like it never happened. It’s like Einstein’s variable speed of light never happened either, or the wave nature of matter. Yes, most physicists and cosmologists will confirm that something called the coordinate speed of light varies in a gravitational field. But many of them talk of point-particles, and insist the speed of light is absolutely constant, despite the patent evidence of optical clocks, despite what Einstein said. They don’t appreciate that the locally-measured speed of light is only constant because we use the motion of light to define the second and the metre, which we then use to measure the motion of light. Some of them even confuse curved space with curved spacetime. That’s despite John Baez’s website, where you can read that gravity is ”not the curvature of space, but of spacetime. The distinction is crucial”. It’s a bit of a mess really. But hey, we’ll get there in the end.

Because once you understand time, it’s like pulling a thread with Einstein’s name on it, and out comes a string of pearls.

21 comments on “Science on Sunday with John Duffield: Gravity

  1. cementafriendc
    October 13, 2013 at 10:28 am #

    Is this the same John Duffield who sometimes comments on Just reading Dark Matter, Missing Planets & New Comets by Dr Tom van Flandern. That has a different explanation of gravity. Some of that book explaining paradoxes makes sense. He claims speeds faster than light are necessary in his theory.

  2. duffieldjohn
    October 13, 2013 at 1:20 pm #

    Yes, that’s me. You’ll perhaps be aware that I’m forever referring to Einstein and relativity, and pointing out that the original material doesn’t square with what people say Einstein said.

    I don’t share Tom van Flandern’s support of Le Sage gravity I’m afraid. IMHO it’s based upon a misconception of virtual particles. They aren’t real particles, they’re “field quanta”, or “chunks of field”. Like you divide your field up into squares and say each is a virtual particle. There are no actual photons flitting back and forth between the electron and the proton in the hydrogen atom. Hydrogen atoms don’t twinkle.

  3. James Eadon
    October 13, 2013 at 7:54 pm #

    You’re famous, John

  4. cementafriend
    October 14, 2013 at 1:36 am #

    John, I am just an engineer who looks at empirical results (especially my own) to try and make some sense of what is happening. Theory is not always necessary to come up with a design improvement if there is sufficient empirical results. I have some doubts about photons. I have found that there are electrical, magnetic and gravitational fields There are electrical, magnetic and gravitational waves. I have noted claims of wave-particle duality although I have noted that wave pulses can give the appearance of an energy particle. I am not sure of how heat energy fits into the picture but i know that electrical energy can be transformed into heat energy and vice versa. One can model heat transfer by electrical circuits. Using dimensionless numbers (eg the Reynolds number) one can find similar relations between heat, mass and momentum transfer. I have the feeling that physics has lost its way by proposing a theory and then looking at results to see if they can make them fit with the theory rather than the other way around.
    So-called climate science is an example of people proposing a theory and then denying measured results (eg CO2 measurements over the last 100 hundred years -I have measured CO2 in the various conditions including the atmosphere)
    Call me a sceptic about everything until I can work it out for myself.

    • jdseanjd
      October 14, 2013 at 6:57 am #

      So-called climate science, Mr Engineer is a scam.
      It is designed to give the impression of a global problem, in order to promote the idea of a world govt to solve the problem.

      Unfortunately for the scamsters, our world is not cooperating: there has been no statistically significant global warming for ~ 17 years now. Even our Met office has had to confirm this.
      This is why the scare scam has been rebranded climate change. The scamsters are trying mightily to persuade us that humankind is causing more hurricanes, floods droughts & so on ad infinitum. This is equally fallacious.

      A good site on which to follow the climate debate is Anthony Watts’ excellent which happily presents all sides of the argument: warmist activists, lukewarmers & sceptics.

  5. duffieldjohn
    October 14, 2013 at 9:01 am #

    cementafriend: yes, empirical results are very important. Theory is too, but its value is reduced if it doesn’t come with understanding. Hopefully articles like this will help with that.

    Don’t have doubts about photons, but don’t think of them as billiard-ball particles. Think of them as waves. Think of a photon as something like a seismic wave. Note though that it’s an electromagnetic wave. It isn’t an electric wave or a magnetic wave. See a previous article for something about electromagnetism:

    Heat is an emergent property of motion. The atoms in a container of hot gas are moving fast. Yes, theoretical physics has some issues. I don’t know if you saw the Neil Turok thing recently. I did a blog piece on that too:

    • cementafriend
      October 16, 2013 at 1:38 pm #

      Ok, had a look at your two posts. Noted your comments about Lubos Motl (Some of his posts are Ok but I know little of string theory, -read Shape of Inner Space by Shing-Tung Yau and thought it can work in imagination and mathematics but doubt the reality)
      Have not noted you engaging Prof Claes Johnson (eg I think he has some good thoughts and with Fluid Dynamics is at least comparing modelled computation with empirical results.
      As I said I tend to be sceptical until I can work it out myself from empirical results which I can be certain were correctly obtained and assessed for error.

      • duffieldjohn
        October 16, 2013 at 7:02 pm #

        Lub would do himself a big favour if he was civil and didn’t censor people like me. I don’t know much about Shing-Tung Yau I’m afraid, but note that Riemann curvature is merely the curvature of a plot of the speed of light. That’s all it is. Nothing more. So I can’t enthuse about the Calabi conjecture.

        I’ve never heard of Claes Johnson I’m afraid. But an initial look at his blog doesn’t have me saying Yes! Yes! I don’t know if you know, but Einstein tried to unify electromagnetism and gravity for decades, and failed. I think that was because he started from the gravity end. Gravitational force is very weak compared to electromagnetic force. IMHO the right approach is to start from electromagnetism. But potential is more fundamental than field.

        Yes, be sceptical, and look out for empirical results. What’s weird is that they’re out there, such as the Shapiro delay, but they are totally ignored. A radar pulse takes longer to go to Venus and back if it skims the Sun. Because the light goes slower there. People will try to airbrush this away by talking of curved spacetime, but don’t be distracted by abstraction.

  6. shorelark
    October 15, 2013 at 1:56 pm #

    Sorry to disagree, but once you reject the notion of space-time, all that is left is the aether. You will never formulate a working theory of gravitation if you assume the aether is less dense in free space. Newton was right, as usual.

    • duffieldjohn
      October 15, 2013 at 7:43 pm #

      Hi shorelark. Einstein formulated a working theory of gravity. Have a look at his 1920 Leyden Address (see blog above). Then search arXiv:

      See all those Einstein aether papers? Check this out:

      “It is ironic that Einstein’s most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed”.

      He spoke of space as “the aether of general relativity”. I was amazed when I found out about this.

      • shorelark
        October 16, 2013 at 1:44 pm #

        Hi dj, I might have expressed myself better in a few more words, “theory of gravitation and photons” perhaps, though some nod in the direction of electromagnetism and light might also be in order. For they impose their own, incompatible requirements on the aether. You may recall how horrified Einstein was to learn this could only be resolved in a five dimensional space-time.

        I would say the problem posed for all the geometrical theories, from special relativity to string theory, is to represent two basic concepts of physics correctly, namely linear and angular momentum. They just pretend they can.


  7. duffieldjohn
    October 16, 2013 at 7:14 pm #

    Shorelark: there is Baldomir and Hammond’s “Geometry of Electromagnetic Systems”. It’s a book, and very expensive. I haven’t read it. But I suspect it’s on the right lines. It isn’t quite Kaluza-Klein, but it is geometry.

    Imagine you’re on a headland looking out across a flat calm sea. You see a wave coming towards you, and you notice that it’s veering to the East because of a salinity gradient or somesuch. The path of the wave relates to curved spacetime. Now look at the wave itself. Where the wave is, the surface of the sea is curved. That relates to curved space. To electromagnetism. See this:

    …by Percy Hammond and note this:

    “We conclude that the field describes the curvature that characterizes the electromagnetic interaction”.

  8. shorelark
    October 18, 2013 at 8:44 pm #

    Hi DJ. Thanks for the link to Hammond’s article; it demonstrates the polarity in this debate very nicely. The first part of the article is a classic exposition of Maxwell’s electromagnetism; the second is a leap into the unknowable.

    Consider: ” Faraday’s discovery ….. drew attention to a topological property which conflicts with the idea of empty flat space used in Newtonian mechanics ……. because space and physical action cannot be separated.”

    My thoughts would be:

    first, Newtonian mechanics is set in flat space, but that space is not empty. Rather it is filled by the physical substance of the aether. The properties of the aether are irrelevant to mechanics, and are invariably ignored. As far as they concern gravity and light, Newton came quite close. I flatter myself to think that a half hour discussion would have put him on the right track.

    second, Weber’s formulation of electromagnetism, which is as complete and sufficient as Maxwell’s, requires only a knowledge of the charges and currents, This makes the field concepts redundant. It isn’t so popular now, needless to say, especially among the mathematically inclined.

    Whether the concept of the aether is useful, and capable of further development is still an open question. As far as an understanding of gravity and light is concerned, it does what it says on the tin.

  9. duffieldjohn
    October 19, 2013 at 1:47 pm #

    I don’t think it’s a leap into the unknowable, shorelark. It’s more like discovering the lost secrets of the ancients. One of my favourites is Einstein’s 1929 field theory address* where he says “It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds”. Then you look at gravitomagnetism** to get the gist of it. When it comes to aether, IMHO it’s better to say space is kind of elastic rather than being filled with something else. And as for Weber, the crucial point is that charge isn’t fundamental. Nor is the electron’s electromagnetic field, and nor is conduction current. You need to go back to four-potential and to displacement current, wherein Maxwell said “light consists of transverse undulations in the same medium that is the cause of electric and magnetic phenomena”. When a seismic wave travels through the ground, the ground waves. When an ocean wave travels through the sea, the sea waves. When a light wave travels through space, space waves.




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