Energy Is Not Golden Holy Cow Urine
    By Sascha Vongehr | October 19th 2010 09:30 AM | 14 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    Energy (E) is a useful quantity. It has certain properties and connections with other such measures, like momentum p. E is in a certain sense paired with time t, much like momentum p and distance x are such a pair. This pairing is known from classical mechanics and it shows up in relativity: The merging of t and x into one entity, space-time, leads straight to such a melting also of E and p; they mingle up correspondingly. In quantum physics, the uncertainty Δx ~ 1/Δp is a very important formula, and it translates into Δt ~ 1/ΔE, too. Meaning: Their properties all correlate.

    If space-time, i.e. x and t, has certain symmetries, for example if they are much like a static box, unchanging by what you put inside, then p and E are conserved, which can come in very handy. You can use this to solve some questions much faster than by calculating what a system actually does in detail, which may be difficult. All you need is to know that in the end, E must still be the same.

    Energy – something mysterious?

    Esoterics tell us that “everything is energy”. E is somehow mysterious, much more mysterious than p, and the conservation of E has become a dogma. E has become like god’s urine, a mystic ever lasting essence. However, we know for almost a century now that space is not static and that there is no reason to even expect p or E to be fundamentally conserved. But humans are religious by nature and E is holy now. There are many who come up with desperate attempts to save E from the antichrist.

    They try to rescue holy E by coming up with some sort of reservoir, some potential where it came from, some latrine bucket where it went to. It is inside the gravitational potential maybe, although there is no gravity in general relativity, just curved space-time. Or it gets smeared around the cosmic horizon and made negative so that the overall E of the cosmos is zero and thus truly conserved - even if the universe itself should disappear, holy E remains the same.

    I think the answer is psychology. Calm down, have a cup of warm chocolate, and look at it rationally. E is not even supposed to be conserved if space-time is not static.

    E is often closely related to curvature. Think of particles being knots in space-time (not true, but still). More curvature of space time, more E. Also quantum mechanically: If a wave function has more curvature (higher frequency), then the associated E is higher. There may be more overall E in a space-time that expands - there is surely more opportunity for curvature.

    “Laws” of nature are not some holy rules handed down. They are symmetries. Angular momentum is quantized. Why? It is momentum inside a space that has a certain symmetry, here being rotational symmetry leading to the angle of zero degrees being the same as 360 degrees. Angle space is periodical, thus the momentum that is paired with it, the angular momentum, is quantized. Is this a holy quantization? No! Take the symmetry away, and momentum is no longer quantized. It is that easy.

    Classically, space-time is static, and so E is conserved, which means if some is missing, we better find out where it went. However, energy in general relativity is not even expected to be conserved. If it is missing and we know well why it is missing, why not?

    If E is not conserved, a perpetual motion machine becomes possible. The universe is a perpetual motion machine of the worst kind. It not just creates E, it creates space out of nothing, violates the second law of thermodynamics, all of it. Why should it not? Certain “laws” are applicable when certain symmetries are present for the system under investigation. These symmetries that describe the physics in our backyard may not hold for the universe as a whole. They should not even be expected to hold.

    I like to put in these "not even expected" terms to counteract the usual lore that certain circumstances are terribly counter intuitive and unexpected. For example, we should not even expect two twins having taken completely different paths through space-time to have aged equally! The twins meeting again and having aged the same way needs some symmetry that insures such an unlikely feat. Them being the same age is what is actually unexpected.


    Previous entries on energy in general relativity and the boring universe:

    Don’t Stop the Presses: Energy Conservation Law Questioned Again

    The Space-plunger

    The Boring Universe: Is Inflation Incredibly Fast Or Painfully Slow?

    Stumble It!


    "Our Judeo-Christian desperation for everlasting life is under attack if E is not conserved."

    The irony here is that life isn't everlasting in a world where energy is conserved.

    Life needs sources of low entropy, not energy.
    In an energy-conservative world thermal gradients tend toward slopes of zero, and in time entropy everywhere in the system will become too high to support life. Life does need energy; energy in storage and energy in the process of being taken out of storage.

    OK, in this case I agree, since "tend to" is a much weaker statement. After all, one could imagine a universe with constant energy (say E_total = 0) yet somehow also sources of order that let life go on for ever. Also, I did not intend to say that E is not needed at all, but just to counteract the popular misconception that life needs primarily energy rather than entropy gradients (many lay people are reading this blog). Sure, once there is entropy and temperature, you may be always by this fact alone be able to define energy and so on, so you could argue that even inside a matrix of cellular automata, intelligent life would necessarily discover an equivalent to energy.

    I actually thought you meant your first comment to say that without inflation/metric expansion, entropy would not start out low in new pocket universes, thus no life.
    "E is often closely related to curvature. In a sense, you could think of particles being knots in space-time. More curvature of space time, more E. Also quantum mechanically: If a wave function has more curvature (higher frequency), then the associated E is higher. What is the big problem with that there may be more overall E in a space-time that expands? Why not - there is surely more opportunity for curvature."

    Sascha, is space-time curvature quantized also? I've often wondered if at very small space-time scales, whether the curvature actually becomes 'faceted'. By that, I mean space-time is always flat, and stores the energy of curvature in vertex's and edges. (Self rated as 'Orange' on the pseudo-science indicator lamp) ;-)

    This is a very difficult question. Some hold that there are no gravitons and that gravity is not quantized in the way that string theory for example has it quantized. However, the alternative approaches, like Loop Quantum Gravity (LQG), quantize (or better, make discrete) space-time as such, so that gravity does not have to be quantized anymore (as you surely know, LQG works with the kind of faceting you think of).
    In this sense, curvature is always quantized, but it is not a satisfactory answer of course to just throw some names of theories around and pretend to know about them. Therefore, I would ask myself, if curvature or space-time were assumed to be not discrete, could I ever confirm so by measurement? One would have to supply infinite resolution to do so, and so it is not possible on principle. Or in other words, the fundamental questions are not ontological ones but epistemic. I am not sure whether this would prove that everything is somehow "quantized" or discrete, but I do know that if it is "really" somehow not (a wording that I think fundamentally is meaningless), we would not be able to confirm it.
    Dr. Vongehr certainly has a knack for coming up with catchy headlines... I knew this was an article of his even before clicking on it.

    You knew it was me but still clicked? You made my day.  :)

    Or maybe you just wanted to make this comment.  :(
    Oh, I definitely know that I will enjoy what I am learning when I click on one of your fun titles, but what I truly value is how you get me really thinking about it all. . .

    > "And this is making the whole so ridiculous, so similar to religion."

    it could be down to a confusion about the nature of the laws that emerge from science. Ie. does science determine the nature of reality or does science model observed behavior. And, are these being deliberately confused in the public's mind? (And even .. are they confused in scientists' minds? ) Ultimately .. do scientists yearn to be regarded as priests?

    You wrote:
    "E is often closely related to curvature. In a sense, you could think of particles being knots in space-time. More curvature of space time, more E. Also quantum mechanically: If a wave function has more curvature (higher frequency), then the associated E is higher. What is the big problem with that there may be more overall E in a space-time that expands? Why not - there is surely more opportunity for curvature."

    But, if spacetime expands it looses curvature so it looses energy, maybe the extra energy it takes by expanding, so the question is maybe there's a global conservation of energy although, you cannot derive the local conservation from Einstein equations anymore...

    "if spacetime expands it looses curvature"
    He he, good point. Although, knots may not unknot and expansion is not necessarily a stretching (content inside space would be stretched, but if it is all space itself, it may conceivably curve up more).
    Hey, I'm interested in this knot analogy... Have you developed the idea of particles as knots of a spacetime tissue or something? Maybe fermions would be trefoil knots and bosons eight-figure knots? I assume they would have an invariant curvature proceding from the moment the particle was created and the temperature/energy density of that moment, unless they go into the gravitational singularity.

    Also, do you think you can separate the so-called "content inside space" from space itself? Is it not space the vacuum and from the vacuum we extract the particles by excitation?

    Ed Witten these days is into knot theory, and it is kind of the next logical step of course if you have strings and membranes in higher dimensional spaces with weird topologies. This can model charges as winding numbers around tubes and so on. But I do not work on such stuff anymore, one of the reasons being indeed that space with knots inside (strings as content) is obviously a dualism that cannot be the fundamental answer.