Science Sundays with John Duffield: Dark Energy.

Dark energy is usually peddled as something mysterious, because mystery “sells”. But if you’ve read what Einstein said, it isn’t mysterious at all. On page 185 of The Foundation of the General Theory of Relativity, Einstein said this: “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. That’s dark energy. And it’s right there in the room you’re in, right in front of your face.

Let’s tuck you out of harm’s way, then take the air out of that room. Then we can line it with lead to keep out the cosmic rays, and make it cold and dark so there’s no particles in there.   But there’s still a gravitational field in there. There’s still energy there.

Some will say there’s virtual particles there, but there aren’t, not in any real sense. Check out Matt Strassler’s website and note this: A virtual particle is not a particle at all”. Virtual particles are like accounting units, like you divide the field into squares and say each is a virtual particle. They aren’t real particles. They don’t pop in and out of existence. Hydrogen atoms don’t twinkle. Magnets don’t shine. There are no particles in your cold dark empty room. But there is energy there. And it is dark.

Some will say it’s just field energy, but they aren’t giving you the whole story. For that, you have to read Einstein talking about field theory in 1929. He was referring to electromagnetic fields and gravitational fields, and he said this: “It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds”. Did you catch that? According to Einstein, a field is a state of space. It isn’t something separate to space, it’s a state of space. So field energy is really spatial energy. The energy of the gravitational field is the energy of space itself. You can’t see this energy. It isn’t made up of particles. The only thing that’s there is space. And like Einstein said in his Leyden Address, space isn’t nothing.

It’s really important to appreciate this. And the way to do that is to appreciate that waves run through it. If you’ve ever looked at displacement current you’ll know that Maxwell talked about transverse undulations. A ripple in a rubber mat is a transverse undulation. It’s a transverse wave. So are light waves. So are gravitational waves, which you can read about at LIGO. See where they talk about the two arms of the interferometer forming an L shape? See where they say “if the two arms have identical lengths”. The thing about waves is this: if a seismic wave moves through the ground, the ground waves. If an ocean wave moves through the sea, the sea waves. And if a gravitational wave moves through space? Space waves. Yes, space waves. And when it does, the two arms of the LIGO interferometer are no longer the same length.

If you’ve got a rubber mat, give it a shake and watch the wave run through it. A wave in space is like that, but in a three-dimensional bulk. Like I was saying, space can be likened to a gin-clear ghostly elastic jelly. To emulate a gravitational field you insert a hypodermic needle and inject more jelly to represent the E=mc² energy of the Earth. The surrounding jelly is then pressed outwards, and now there’s an energy-pressure gradient in it. Because of this “the speed of light varies with position”. And because of that, light curves. That’s what Einstein said. Light curves like a car veers when it encounters mud at the side of the road:

BlackHoleSpaceLight

Did you notice anything about that jelly analogy? Something deep and fundamental? I said space is like some gin-clear ghostly elastic jelly. And that you inject more jelly to represent energy. The thing that’s deep is this: at the fundamental level, you just can’t separate space and energy. It’s like energy and space are the same thing.

Take a look at the clear night sky. Don’t look at the moon or the stars. Just look at the space between those stars. Dark, isn’t it? What are you looking at? Dark energy. And get this: space isn’t just some gin-clear ghostly elastic jelly with pressure gradients in it. The whole shebang is under pressure too. It’s like the whole universe is some squeezed-down stress-ball, only you’ve opened your fist. So it expands, something like this:

universeexpands

Note that the squares aren’t flattened, so there’s no overall gravitational field in the expanding universe. And remember what Einstein said: a gravitational field is a state of space. It isn’t something that sucks space in, so the universe was never going to collapse under its own gravity. Also note that conservation of energy tells you that the cosmological constant can’t stay constant over time, because it’s “the energy density of the vacuum of space”. This is obvious once you know about “the strength of space”, which is mentioned on page 5 of this paper: http://arxiv.org/abs/0912.2678. If you’ve ever watched the Discovery Channel you’ll have seen the balloon analogy. The expanding universe is likened to an inflating balloon. But it ought to be a bubble-gum balloon. As it expands, the skin gets thinner and weaker, and less able to resist the expansion. The dimensionality of energy is pressure x volume, the pressure drops, the volume increases, so energy is conserved. Only the balloon doesn’t stop expanding because the skin gets weaker and weaker.

It’s all pretty simple when you see it right. When you know about the speed of light and gravity and Einstein’s stress-energy tensor, you soon catch the general drift. Space is like some ghostly gin-clear elastic, it’s the same stuff as energy, and there’s a lot of it about.

And space, of course, is dark:

darkMatterPie-590

16 comments on “Science Sundays with John Duffield: Dark Energy.

  1. shorelark
    October 27, 2013 at 8:22 pm #

    Hi DJ; I’ve been wondering when you would get here. Let’s start with:

    Einstein said this: “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”.

    Sounds quite biblical; “Let there be dark energy /matter” rather than “Let there be light”, I think I prefer light to dark. It makes it easier to see what’s going on.

    “And the way to do that is to appreciate that waves run through it.”

    OK, but it would be better if that could be shown. LIGO has nothing to say on this score, for it never actually saw anything.

    Regards

  2. duffieldjohn
    October 28, 2013 at 8:52 am #

    That’s what Einstein said, shorelark. Check it out.
    Hmmn, maybe I should look into gifs re showing “waves run through it”. As for LIGO, it’s an interferometer. Michelson and Morley had an interferometer. Could be it’s just a rubber ruler.

  3. jdseanjd
    October 29, 2013 at 10:17 am #

    Whoosh, you did it again, straight over my head.

    There’s this cute little black bird, lives around the corner.
    She has a twinkle in her eye & a curvy derriere.

    Now that’s the kind of dark energy I go for. 🙂

  4. B. Prior
    October 30, 2013 at 10:25 am #

    “Dark energy is usually peddled as something mysterious, because mystery “sells”. But if you’ve read what Einstein said, it isn’t mysterious at all. On page 185 of The Foundation of the General Theory of Relativity, Einstein said this: “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. That’s dark energy. And it’s right there in the room you’re in, right in front of your face.”

    No, that isn’t dark energy. Dark energy is a component of the stress energy tensor with a negative pressure. Gravitational energy is forbidden from being in the stress energy tensor – the gravitational effects of the field energy are a result of the nonlinearity of the equations. It has to be described in a pseudotensor.

    “He was referring to electromagnetic fields and gravitational fields, and he said this: “It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds”. Did you catch that? According to Einstein, a field is a state of space. It isn’t something separate to space, it’s a state of space. ”

    Duffield is at best misleading here. Clearly electromagnetic field energy and gravitational field energy are quite different. And electromagnetic and gravitational waves are clearly quite different.

    “The whole shebang is under pressure too. It’s like the whole universe is some squeezed-down stress-ball, only you’ve opened your fist. So it expands, something like this:”

    No no no. The expansion of the universe is not driven by the material in it being under positive pressure. It happens because of whatever early in the universe started it happening – it’s a continuing event, much as a football continues to move because it was kicked. It is true that dark energy is making this expansion accelerate now, but that is a *negative* pressure, not a positive one, and it acts gravitationally and not through the pressure itself. A compressed stress-ball may be trying to expand, but gravitationally speaking it has a little more energy because you worked to squeeze it, and that little bit of energy gravitates just like its mass does. Dark energy’s pressure, if it were to be exerted on a material, would pull in not push out, but gravitationally (when you work out what Einstein’s equations are telling you) it tries to accelerate an expansion.

    “Also note that conservation of energy tells you that the cosmological constant can’t stay constant over time.”

    This is quite wrong. If you have a piston filled with air and you push in on it, you do work on the air inside and it gains a little bit of energy, and therefore if you like a little bit of mass – its density goes up slightly. Immeasurably so for an everyday piston of course. A cosmological constant exerts negative pressure and is pulling in. The bit of work you *gain* by allowing it to pull in exactly compensates for the change in volume, allowing it to stay at a constant density. Now this does leave the perfectly reasonable question of how you can have a universe double in size, say, with a cosmological constant in it, because it then seems like you have twice as much energy and have therefore violated the conservation of energy. The short answer (which I’m sure Duffield won’t like but I’m afraid is true) is that the conservation of energy in general relativity is at best more complicated and at worst not really valid. Read http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html (which also covers what I said about the gravitational energy not being part of the stress energy tensor).

    “The expanding universe is likened to an inflating balloon. But it ought to be a bubble-gum balloon. As it expands, the skin gets thinner and weaker, and less able to resist the expansion. The dimensionality of energy is pressure x volume, the pressure drops, the volume increases, so energy is conserved. Only the balloon doesn’t stop expanding because the skin gets weaker and weaker.”

    I’m afraid this is simply nonsense. Space doesn’t get thinner, and the pressure of dark energy doesn’t apparently drop (cosmologists are still trying to measure its precise behaviour, but if it is a cosmological constant then it is, unsurprisingly, constant).

    I’m afraid anyone who has been reading John Duffield’s blog entries here and have been taking him seriously as someone who knows what he’s talking about has been misled.

    If John Duffield was right, he would be able to take the content of the universe and derive the amount of dark energy that should come from its gravitational field, shouldn’t he? But it’s not known why there is the amount of dark energy there is. If he could do this he’d be a rather well known physicist by now, since this is actually something of a major problem in theoretical physics.

    • shorelark
      October 30, 2013 at 11:45 am #

      Hi BP; I like the way you reason. One point though. particle physicists and big band theorists have conspired to persuade us that they can calculate how much mass there should be in the universe. Not enough it seems, by a very large margin.

      So they have obtained a “good” estimate of the amounts of dark matter and dark energy required to fill the gap.

      A more reasonable person might simply argue that the big bang model is wrong. What happened to all the anti-matter?

      • B. Prior
        October 30, 2013 at 12:27 pm #

        Well, dark matter and dark energy are certainly hypotheses that fill gaps. However, they fill those gaps very well and different lines of evidence agree (with sometimes a few tensions at the bleeding edge of observations) with how much of what there should be. It is very reasonable to suggest that there might instead be a flaw in our understanding of gravity, and there are cosmologists working on such ideas. Milgrom’s work on MOND as an alternative to dark matter is a classic example of this (e.g. the paper John Duffield linked to).
        The question of where all the antimatter went (or better, why was there more matter than antimatter early on so we got some of that left over) is also very reasonable, and we don’t have a good answer to that yet.
        Our understanding of the big bang, dark matter and dark energy are without a doubt incomplete, but that does not mean that the basic ideas of them must be wrong. I have no problem with people looking for alternatives, but the alternatives need to be at least as good as what we have right now.

      • duffieldjohn
        October 30, 2013 at 8:22 pm #

        @B Prior: I’ve just written my next article. It is of course on dark matter. I mention MOND and say Milgrom doesn’t get it right, but there is a sense wherein he’s on the right lines. PS: I know what happened to the antimatter.

        @shorelark: once you understand the fundamentals, you work out that space just has to expand. Which means there was a big bang of sorts. Though perhaps not quite the way it’s usually portrayed.

  5. duffieldjohn
    October 30, 2013 at 8:13 pm #

    @B Prior:

    Dark energy doesn’t have a negative pressure. That’s a fallacy. It causes expansion. The dimensionality of energy is pressure x volume. The energy is positive, the volume is positive, so the pressure is positive too. It is said to be negative pressure because gravity, which involves positive pressure, causes attraction rather than repulsion. However gravity is a pressure gradient.

    I’m not misleading you about Einstein describing a field as a state of space. Or about electromagnetic field energy and gravitational field energy being related. An electron doesn’t have two different fields.

    The expansion of the universe IS driven by pressure. You think it’s a negative pressure. I’m afraid it isn’t. Think it through for yourself from first principles.

    Energy is conserved full stop. The Baez article is not a good one. Light doesn’t lose any energy as it climbs out of a gravitational well. Yes, Einstein argued that all energy has mass [equivalence], and all mass acts gravitationally: and you cannot transform that gravitational field away.

    The reducing strength of space isn’t nonsense. It’s just unfamiliar to you. What is nonsense is energy being magically created ex nihilo as the universe expands.

    The universe doesn’t have a gravitational field. On the large scale it’s homogeneous. A gravitational field is inhomogenous space.

    You need to backtrack a few weeks. Start with time travel, then the speed of light, then gravity. I’m not just making this stuff up. Everything I’ve been saying is true to Einstein. I’m afraid what you’ve been taught isn’t.

    • B. Prior
      October 30, 2013 at 10:22 pm #

      “Dark energy doesn’t have a negative pressure. That’s a fallacy. It causes expansion. The dimensionality of energy is pressure x volume. The energy is positive, the volume is positive, so the pressure is positive too.”

      Anyone can look online or ask their friendly neighbourhood cosmologist to determine whether you or I are correct about this. And everything else. I encourage readers to do their own research and find out if what John Duffield says here is true, and find out his reputation elsewhere as a physicist.

      My opinion is that The Bogpaper hasn’t got a columnist here of the calibre they thought.

    • B. Prior
      October 31, 2013 at 1:26 pm #

      I hadn’t caught this before but:
      ” The dimensionality of energy is pressure x volume. The energy is positive, the volume is positive, so the pressure is positive too.”

      The dimensionality only tells you the units, not the sign. This is a pretty profound misunderstanding of dimensional analysis.

      Readers will be familiar from school that pressure is force per unit area. Consider a piston of gas with an area on the piston head of ‘A’, and a pressure of the gas inside of p (positive pressure, we will all agree). You push on this, and the force is p x A (force per unit area, as above). You move the piston head a distance d, and the volume in the piston therefore shrinks by A x d. The work you do on the gas is the force times the distance d, so p x A x d. You should be able to see that the energy goes up in the gas as the volume goes down. Written as a derivative, p = -dE/dV and this is a more useful definition of pressure (strictly you’d want to make this a partial derivative, but this will do here). You can see the equivalent in the ideal gas table at http://en.wikipedia.org/wiki/Table_of_thermodynamic_equations – where W is the work done by the gas, rather than the energy put into the gas so dW=-dE.

      For positive pressure, dV is negative (the volume shrinks) and dE is positive (the energy increases), so the minus sign is put in to give you a positive answer for p.
      For a cosmological constant, the volume change would be negative, and the density inside stays constant so the total energy must have gone down. Therefore p in this case must be negative. There’s no wriggle room – it fundamentally differs from a normal gas in which way the energy flows when it is compressed.

      • duffieldjohn
        November 2, 2013 at 11:39 am #

        The dimensionality does tell you the sign. If you have more volume and the same pressure you have more energy. If you have the same pressure and more volume again you have more energy. If you have more volume and more pressure you have more energy again. It’s that simple.

        I’m afraid you’ve confused yourself. When you push down your piston you are opposing the internal gas pressure, as does the skin of the balloon. This features tension, which is indeed negative pressure. Please read the essay again, then ask yourself why you adhere to a confused textbook canard that “fundamentally differs” so much that it relies upon the magical creation of energy from nothing.
        As regards asking your friendly local cosmologist, I’m afraid science is not conducted by popular vote.

  6. shorelark
    October 31, 2013 at 4:08 pm #

    Hi BP: Two points here:

    “I have no problem with people looking for alternatives, but the alternatives need to be at least as good as what we have right now.”

    At the time Einstein was formulating his general theory, astronomers imagined all the matter in the universe was contained in what we now call ‘our galaxy’. It was a small universe cosmology, akin to Aristotle’s.

    In Newton’s cosmology, space is flat and the universe is infinite in extent. This forms the framework for all matter- antimatter theories, including mine..

    The reason there isn’t enough matter in ‘our universe’ to bring its expansion to a close is that almost all of it disappeared in the annihilation of matter with anti-matter in a local big bang. Only the small initial excess of ‘matter’ remains. There isn’t any a priori necessity for dark matter or energy. (Occam)

    “Anyone can look online or ask their friendly neighbourhood cosmologist to determine whether you or I are correct about this. And everything else.”

    It all depends whether you are looking for a correct exposition
    and understanding of the theory or seeking to establish or prove whether it is false. I think JD is attempting to provide the former. If you are concerned with the latter, I can only say that science does not proceed by consensus. (nullius in verba)

  7. duffieldjohn
    November 2, 2013 at 11:56 am #

    Shorelark: there’s a surprise or two when it comes to antimatter. And note that in the early universe the energy density of the whole universe was very high. Much higher than the energy density of matter. But that didn’t stop the universe expanding. And it didn’t collapse either.

    Yes, I’m attempting to provide the correct understanding of general relativity. I’m afraid to say that some cosmologists have an incorrect understanding of some aspects of it.

    Well said re science does not proceed by consensus. I’m reminded of Planck saying: “science advances one funeral at a time. I’m also reminded of Clifford M Will’s Confrontation between General Relativity and Experiment* where he mentions that special relativity wasn’t accepted by mainstream physicists until the late 1920s. Sometimes, consensus actively hampers scientific progress.

    * http://arxiv.org/abs/gr-qc/0510072

Trackbacks/Pingbacks

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    […] evidence that the universe is expanding, and when you know a bit about relativity and space and energy, you end up reasoning that the universe just has to expand. Space has an innate pressure, and […]

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  3. Science Sunday with John Duffield: Quantum Gravity | Bogpaper.com - December 1, 2013

    […] fair enough. But if you read what I said about dark energy you might recall Matt Strassler saying this: “A virtual particle is not a particle at all”. […]

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