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Thread: Gravity and Negative Energy

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    Gravity and Negative Energy

    I keep reading that the total energy in the Universe may be close to zero beause a gravitional field can be thought of as negative energy.

    How can this be?

    Also, the Universe started out really hot and really small. How does this equate to zero energy.

    If the Universe contracted to a big crunch, it would be really hot and really smal again. I can't see how it could then disappear back into the quantum vacuum.

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    Quote Originally Posted by sdsperth View Post
    I keep reading that the total energy in the Universe may be close to zero beause a gravitional field can be thought of as negative energy.

    How can this be?
    Can you cite some reference where they state that?
    Perhaps you migh have misread it and what they meant is that due to energy conservation, total variation of energy in the universe equals zero?
    The gravitational field has been considered a form of negative energy in different contexts. But I don't know how that would lead to zero total energy.

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    That idea is really just fanciful speculation. The idea is that get something by splitting nothing into equal and opposite parts, one positive, one negative. Think of it assests and liabilities, sort of like how Central Banks "create money". The central bank's balance sheet sums to zero. It creates money out of nothing on the promise to repay in a process known as "monetizing debt". The gravitational field negative energy is the debt, and the positive energy that makes up everything else is the money created.

    Again, this is just fanciful speculation and has no more grounding than the psychological notions that are money and wealth anyway. In General Relativity, there is no such thing as gravitational field energy, although the field can carry energy and momentum away via gravitational radiation, but that is nothing like the Newtonian notions of field energy. Indeed, in GR, no general invariant notion of that energy can be defined anyway, although in limited, restricted cases of space-time it can be. But it doesn't work in general.


    -Richard

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    I will attempt to explain why this idea of 0 energy is wrong.

    Around here we can not detect the expansion rate of the universe. Its not happening quickly or at a great rate. Almost 0.

    Thats correct. BUT, when you look into deep space. Some billions of ly distant. Its rushing away at a frightening pace. Are both correct ? Yes.

    Understand ... that we do not know from where the energy comes that is expanding the universe. Why and by what mechanism ? Unknown.

    As long as we perceive a eccelorating expansion ( and we do. ) The energy does not equal 0. There is no balance.

    an acceleration of the whole mass of the universe does not seem to have an equal and opposing force...

    If it ever did. That situation changed about 13.7 billion years ago and for infinitum....<<<< continues.

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    Quote Originally Posted by publius View Post
    That idea is really just fanciful speculation. The idea is that get something by splitting nothing into equal and opposite parts, one positive, one negative. Think of it assests and liabilities, sort of like how Central Banks "create money". The central bank's balance sheet sums to zero. It creates money out of nothing on the promise to repay in a process known as "monetizing debt". The gravitational field negative energy is the debt, and the positive energy that makes up everything else is the money created.

    Again, this is just fanciful speculation and has no more grounding than the psychological notions that are money and wealth anyway. In General Relativity, there is no such thing as gravitational field energy, although the field can carry energy and momentum away via gravitational radiation, but that is nothing like the Newtonian notions of field energy. Indeed, in GR, no general invariant notion of that energy can be defined anyway, although in limited, restricted cases of space-time it can be. But it doesn't work in general.
    Richard, you've been spending way too much time with the Black Monday thread.

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    It was a great post, and I like to use money analogies for energy too, but it occurs to me that we may have reached the point where general relativity is actually easier to understand than global economics! Perhaps I can add another way to look at it, which is that when you drop something, kinetic energy seems to appear out of nowhere. Newton fixed that "something from nothing" problem by inventing gravitational potential energy, which we imagine is "already there" before you dropped the object. How do we know it was already there? We don't, we just wanted it to be there, because we prefer to not get something from nothing. We do that in physics, we set things up so that it is like we want it to be, and makes sense to us. Same with a "zero energy universe"-- but either way, it is we who are doing it, not the universe. Maybe someday there will be a theory of gravity where this "zero energy" idea will seem inescapably natural, but for now, I have to agree with publius that it seems like our fingerprints are all over the idea, so take it or leave it as you wish.

    There is one additional subtlety though-- when you pull two gravitating bodies apart, you do work on the system. That means you put energy into the system, and by mass-energy equivalence, that means you must increase the mass of the system. That further means you must increase the gravity from the system. So gravitational potential energy does appear to be showing up somewhere physical, and I believe that this is quite important in the stability of neutron stars-- when you make a neutron star, you release a whole ton of gravitational potential energy, which noticeably reduces the gravitational mass of the system (when that energy escapes as light), and that weakens the star's tendency to implode into itself and make a black hole. The general relativity of all that is beyond me, and it's not a cosmological application (it's a very different kind of local geometry than a whole universe), so I can't comment any more on the connections between the energy stored in separated bodies that is released (or counted as negative) when the bodies are very compact (like the early universe).

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    Quote Originally Posted by Tensor View Post
    Richard, you've been spending way too much time with the Black Monday thread.
    Actually, that was the only example of "something from nothing by splitting into equal and opposite positive and negative parts" that came to mind. Which might tell us something about our faith in our money.


    -Richard

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    Quote Originally Posted by publius View Post
    Actually, that was the only example of "something from nothing by splitting into equal and opposite positive and negative parts" that came to mind.
    I can't think of any others either, except the same thing on the personal scale-- the infamous "I.O.U." (And then there's the old joke, two men are accosted in any alley by an armed figure saying "give me all your money." One man turns to the other and says "here's that twenty bucks I owe you.")

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    While IOUs sound risky, that's all "securities" of all stripes are anyway. "Security" sounds much better than IOU. When companies and governments issue bonds and notes, all they're doing is going into the marketplace and auctioning off IOUs, a promise to repay a given amount at a future date.

    -Richard

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    Quote Originally Posted by publius View Post
    "Security" sounds much better than IOU.
    Doesn't it though? That's why these guys make the big bucks.

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    Quote Originally Posted by Staticman View Post
    Can you cite some reference where they state that?
    Perhaps you migh have misread it and what they meant is that due to energy conservation, total variation of energy in the universe equals zero?
    The gravitational field has been considered a form of negative energy in different contexts. But I don't know how that would lead to zero total energy.
    The latest place I read it was in The Void, but Frank Close.

    On page 140 he writes “The idea is that our universe could be a gigantic quantum fluctuation with total ‘virtual’ energy so near to zero that its lifetime can be huge. This can occur because there are both positive and negative energies in the universe de to the all-pervading attraction of gravity.”

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    Quote Originally Posted by publius View Post
    Actually, that was the only example of "something from nothing by splitting into equal and opposite positive and negative parts" that came to mind. Which might tell us something about our faith in our money.
    Another currently used example of the loan analogy comes to mind , that is only indirectly related to OP (in as mucuh as it deals with energy).
    You are probably familiar with the way Heisenberg, in order to do away with the "inelegant" concept of Paul Dirac's "Dirac sea" came up with the concept of a sufficiently brief loan of energy that would be allowed by the Uncertainty principle, when a pair of virtual particles is created, later that borrowed energy would be paid back at "pair annihilation".
    This financial analogy is still used in QM texts, I think Feynman in his lectures used it too. Certainly in this case noone seems to have a problem with the analogy. That sure tells us something about our faith in money.

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    (That was all before Lehman Brothers. )
    But seriously, I think you have put your finger on what sdsperth is getting at with that Frank Close quote-- the desire to see the universe as having zero total energy connects with attempts to unify gravity (and issues on the largest scales) with quantum mechanics (and issues on the smallest scales). Then the universe can be seen as a quantum fluctuation, as part of a "multiverse" of many such universes. The goal is to unify not just gravity and the other forces, but also the very large and the very small, and at the same time "explain" why our universe has so many finely tuned attributes to allow us to be here (the anthropic principle). So the zero-energy issue is seen to connect with all these other concepts as well-- but a troubling question emerges, relating to publius' use of the term "speculation"-- is any of that actually science, and how could we tell if it is or if it isn't?

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    Quote Originally Posted by Ken G View Post

    There is one additional subtlety though-- when you pull two gravitating bodies apart, you do work on the system. That means you put energy into the system, and by mass-energy equivalence, that means you must increase the mass of the system. That further means you must increase the gravity from the system. So gravitational potential energy does appear to be showing up somewhere physical, and I believe that this is quite important in the stability of neutron stars-- when you make a neutron star, you release a whole ton of gravitational potential energy, which noticeably reduces the gravitational mass of the system (when that energy escapes as light), and that weakens the star's tendency to implode into itself and make a black hole. The general relativity of all that is beyond me, and it's not a cosmological application (it's a very different kind of local geometry than a whole universe), so I can't comment any more on the connections between the energy stored in separated bodies that is released (or counted as negative) when the bodies are very compact (like the early universe).
    This is something I didn't notice at first. This can get a bit tricky and it makes my head hurt to think about sometimes. In EM, the potential energy comes from the field. That is we have a consistent notion of field energy and that's where all mechanical energy comes from. Push two positive charges closer together and the integral of the field energy increases by the amount of work you did. Let the charges move apart and the field energy is decreased. Add radiation in that and it get more complicated, but it all works out. And note the field can pump energy from one system to another.

    Apply the same ideas to Newtonian gravity and it turns out the field energy must be negative. Let two masses come together and you get energy out, yet the field increases. Thus it must be negative (and if you go to GEM-like formulation, the gravitomagnetic field must be negative energy as well).

    In GR, a static "field" has no energy associated with it at all. Consider bringing together a shell of mass "from infinity". It will make a Schwarzschild field of course. Remember our "coordinate rest energy", E(r) = mc^2*sqrt(1 - R/r), where 'm' is the SR notion of the rest mass of particles brought in from infinity. The difference between that and the original mc^2 is what has to be given up for that shell to remain stationary. Thus the "M", the gravitational mass making Schwarzschild will be reduced by that. But it has to go somewhere. And same way with stuff falling into orbits. That excess energy has to be shed. But note is has nothing to do with the gravitational field, it stays with the objects until it is released someway somehow.

    No imagine letting that shell collapse in from infinity. As the mass is falling, it never looses that energy. So a falling shell of some radius would have more gravity than one that was static. Or, if we imagine somehow stopping it from collapsing and storing the energy (say a bunch of springs or something), that energy would stay there and make more gravity.

    It would be nice if it remained that simple, but alas it doesn't in dynamic situations. Gravitational radiation is one. Spherical collapsing shells don't radiate, but other systems do, such as letting a small mass free-fall radially in a Schwarzschild field. It's very small, but there. So some of that original mc^2 energy at infinity gets carried away by radiation. Same thing with inspiralling binary pulsars.

    But then it gets even more complicated. Consider the tidal interaction of the moon-earth system. The tidal interaction is slowing the earth's rotation. Some of that energy goes to friction, but some of it is going to the moon's orbital energy, pushing the moon into a higher orbit. The field does transfer energy from one part to another. Again, in EM, that's all cut and dried, as we have a consistent notion of field energy.

    But in GR, it's very different. That isn't radiation per se, as the energy isn't "thrown away to infinity" but it is transfer, and it comes about from the dynamic nature of the space-time of the earth-moon system.

    Consider an antenna. Alone it will radiate something. Now mover another, "slave" antenna in close. The slave can now couple with the primary and cause it to transfer energy. It goes through the field (the near field). You can look at the Poynting vector flux and see how the energy is flowing, but you still don't consider it radiation really. Just energy being transfered by the field.

    A similiar thing must happen in GR, as the earth-moon tidal dance illustrates. I have no idea how it is treated and it's pretty complicated I'm sure, but it must be there. Static fields don't contain energy, but dynamic fields can transfer it.

    -Richard

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    Ken,

    I was looking around some more, and this does get quite involved indeed. Something of interest is "Bondi's Newtonian Poynting Vector". Bondi defined a Newtonian Poynting vector expression to deal with the transfer of gravitational energy as applicable to the tidal example above. Now, take that concept an extend it into GR. Here's the abstract from a 1969 paper of Bondi's on the subject:

    http://www.jstor.org/pss/77829

    Note the "near field transfer" talk there, which is what I was fretting about. Apparently, just like with gravitational radiation, only a pseudo-tensor can be defined, which means it is not invariant. So even here, we've have the same "global energy definition" mess. In approriate limiting cases, it works out and reduces to the Newtonian limit of course, but in the general case, it is murky.


    -Richard

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    Quote Originally Posted by publius View Post
    A similiar thing must happen in GR, as the earth-moon tidal dance illustrates. I have no idea how it is treated and it's pretty complicated I'm sure, but it must be there. Static fields don't contain energy, but dynamic fields can transfer it.
    These are interesting issues. Even in Newtonian gravity, where the field does have a negative energy, it seems odd that E&M fields have negative energy when the charges are opposite, but gravitational fields have negative energy when the gravitational "charges" have the same sign (as they all do, of course). There seems to be a minus sign built right into gravity. How that goes over into the energy in the field in GR I have no idea, but I'll take your word for it that the field has no energy there. But the people who like to think about the start of the Big Bang as having zero energy, as in the original question (and Stephen Hawking likes to think that way too), must be in some way counting the field as having negative energy there. I, like you, am troubled by the absence of a well defined theory that can actually give these ideas precise meaning, but I think the answer to the original question is that those who like to imagine what kinds of theories will ultimately unify general relativity and quantum mechanics like to imagine such a theory will treat the initial condition in the Big Bang as one with zero total energy. Does that answer your question sdsperth?

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    Quote Originally Posted by publius View Post
    Ken,

    I was looking around some more, and this does get quite involved indeed. Something of interest is "Bondi's Newtonian Poynting Vector". Bondi defined a Newtonian Poynting vector expression to deal with the transfer of gravitational energy as applicable to the tidal example above. Now, take that concept an extend it into GR. Here's the abstract from a 1969 paper of Bondi's on the subject:

    http://www.jstor.org/pss/77829

    Note the "near field transfer" talk there, which is what I was fretting about. Apparently, just like with gravitational radiation, only a pseudo-tensor can be defined, which means it is not invariant. So even here, we've have the same "global energy definition" mess. In approriate limiting cases, it works out and reduces to the Newtonian limit of course, but in the general case, it is murky.
    -Richard
    There are indeed reasons to fret about this matters, but look out, if you push it some more you are in ATM territory, and the rules here seem to be very strict, so far you are on the verge. If you seek solutions you have to delve deep into highly speculative concepts of negative energy and negative states ,like in the FrankClose book mentioned by the OP poster,that are not mainstream by current QFT standards, or you have to resort to the financial analogies that you disliked so much of borrowed energies, loans and things like that. Or rely on pseudotensors, that many people find unsatisfactory. The whole thing looks murky as you say.
    BTW , Bondi had an interesting paper on "Negative mass" from 1950something.

    Regards

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    Yes, I think the OP question gets to the place where M meets ATM so closely that the distinction is hard to make and becomes a question of who you ask and what credentials they can claim. That right there may be the most fundamental answer to the OP there is, unsatisfactory though it may be.

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    Quote Originally Posted by Ken G View Post
    These are interesting issues. Even in Newtonian gravity, where the field does have a negative energy, it seems odd that E&M fields have negative energy when the charges are opposite, but gravitational fields have negative energy when the gravitational "charges" have the same sign (as they all do, of course). There seems to be a minus sign built right into gravity.
    Ah, I missed this. While the EM *potential* is negative for negative charges, the field energy is always positive. That is the field energy is the integral of E dot E (and B dot B) over all space and that sum is always positive and that sum will always be reduced or increased by the work done by moving the charges around against the field.

    Say we have a big blob of negative charge. E dot E gives us some total energy. Now drop a positive charge in. That charge is attracted so we get energy out. Now, once we bring the positive charge in and set it at rest somewhere, we'll find the integral of E dot E has been reduced, and reduced by the amount of mechanical energy we got out.

    Or, say we have zero net charge. We convert zero to equal and opposite positive and negative charges and pull them apart. The work we do will just be the field energy of the separated dipole field configuration. This ignores self-energy of point charges, a vexxing problem, so we'll just assume the charges were really there to begin with, just so close together there was no appreciable external field. Pair creation in QFT works this way of course.

    With gravity, this field energy thing has to be negative (and that does indeed come from the minus sign on the Coulomb/Newton Law). When we assemble masses, we increase the gravity, yet we get energy out. The integral of g dot g will increase. When assembling positive or negative charges, we have to do work and there's no problem with E dot E increasing. Now do anything to get energy back out of the system, and E dot E *decreases*.

    But with gravity, the more energy we get out, the more g dot g increases. So that integral has to be negative. When we extract positive energy, the "debt" increases.

    -Richard

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    Quote Originally Posted by publius View Post
    Ah, I missed this. While the EM *potential* is negative for negative charges, the field energy is always positive. That is the field energy is the integral of E dot E (and B dot B) over all space and that sum is always positive and that sum will always be reduced or increased by the work done by moving the charges around against the field.
    Good point, but as you know, the amount of energy is always ambiguous, because only changes in energy ever matter. When you move two opposite charges closer together, the total field energy (which is positive) drops by exactly the same amount that the potential energy (which is negative) increases in magnitude (so becomes "more negative"). If the charges are the same, moving them closer makes the field energy go up, by the same amount that the (now positive) potential energy goes up. In the first case, if you start and end with stationary charges, the energy and gravitational mass of the system drops, and in the second case, they both increase. I think we agree there, your point is how things are different with gravity.
    But with gravity, the more energy we get out, the more g dot g increases. So that integral has to be negative. When we extract positive energy, the "debt" increases.
    Right, so you are pointing out the Newtonian consequences of that bizarre negative sign built right into the field energy. But it still seems possible to interpret the total energy as zero, if the rest energies equal the negative field energies in a volume. The rest energy in the volume scales like the density, but the field energy scaling seems more complicated, but the two might be equal at the critical density. That might be the kind of thinking going on, to motivate the desirable concept that you can a lot of mass to appear out of nowhere if you also get a negative field energy to appear with it.

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    Quote Originally Posted by sdsperth View Post
    I keep reading that the total energy in the Universe may be close to zero beause a gravitional field can be thought of as negative energy... How can this be?
    I think the concept has been mentioned, but nobody has mentioned the ultimate free lunch? I think Alan Guth brought this up first, but in 1990 Stenger wrote a more rigorous article on the topic. (Sorry, can't find a free copy on the web...)
    Everyone is entitled to his own opinion, but not his own facts.

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    That is certainly a crucial reference related to this issue, and no doubt Stenger's appreciation of physics principles is deeply profound, but I'm not really sure the term "more rigorous" applies except in comparison to complete handwaving. From the abstract:
    The fundamental particles and the force laws they obey then come about through a series of random symmetry-breaking phase transitions during the period of exponential expansion in the first fraction of a second after the Universe appears as a quantum fluctuation.
    To me, that reads like "I can understand the origin of the universe in terms of certain principles that I believe are relevant to the laws of physics", not "the origin obeys the laws of physics." Still, it's a lot better than just handwaving, so your reference significantly improves the benchmarks here.

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    Thanks guys. I can see I'm going to need a bit more than high school physics to understand this concept.

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    E_T = 0 = (+E) + (-E) = 0 = (Σ+mc^2) + (-E) = (Σ+mc^2) + (Σ-Gmm/r) = 0

    We can assuming that positive energy and negative energy simultaneously repeat pair creation and pair annihilation microscopically at the vacuum state.

    -E = negative energy
    Negative energy candidate : Gravitational potential energy, Casimir energy, dark energy,

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    Quote Originally Posted by Ken G View Post
    That is certainly a crucial reference related to this issue, and no doubt Stenger's appreciation of physics principles is deeply profound, but I'm not really sure the term "more rigorous" applies except in comparison to complete handwaving.
    Uh, yeah, I did notice that Victor Stenger, though very well grounded in physics, has kind of branched off into philosophy in his later years, which, as you say, is rather antithetical to scientific rigor. I must say, though, I much appreciate what he's trying to do:

    An American particle physicist and author, now active in philosophy and popular religious skepticism. As of June 2010, he has published nine books for general audiences on physics, quantum mechanics, cosmology, philosophy, religion, atheism, and pseudoscience, the latest of which is The New Atheism: Taking a Stand for Science and Reason, which was released in September 2009. Stenger announced that work has begun on a tenth book, tentatively titled The Fallacy of Fine-Tuning: How the Universe is Not Designed for Humanity.
    Everyone is entitled to his own opinion, but not his own facts.

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    That last book sounds interesting-- I wonder if he means it's not designed for humanity in the sense that we are selecting from some kind of multiverse, or if he means that anthropic arguments are not as powerful as made out to be. I'd see more value in the latter argument-- the former always seemed to me like a bit of a cheat.

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    Quote Originally Posted by icarus2 View Post
    E_T = 0 = (+E) + (-E) = 0 = (Σ+mc^2) + (-E) = (Σ+mc^2) + (Σ-Gmm/r) = 0

    We can assuming that positive energy and negative energy simultaneously repeat pair creation and pair annihilation microscopically at the vacuum state.

    -E = negative energy
    Negative energy candidate : Gravitational potential energy, Casimir energy, dark energy,
    icarus2,

    This seems to be an against-the-mainstream view. Please do not post ATM material in the Q&A forum.
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    Quote Originally Posted by Ken G View Post
    That last book sounds interesting-- I wonder if he means it's not designed for humanity in the sense that we are selecting from some kind of multiverse, or if he means that anthropic arguments are not as powerful as made out to be. I'd see more value in the latter argument-- the former always seemed to me like a bit of a cheat.
    Yes, I agree. And I'm hopeful, since he only mentions one universe.
    Everyone is entitled to his own opinion, but not his own facts.

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