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# Zero Energy Universe?

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# Zero Energy Universe?

February 13, 2014 8:41 AM Subscribe

Stephen Hawking has proposed that our universe has a total energy of zero, which allowed it to Bang into existence without violating any laws. Is this thesis falsifiable? If so, what is an example of something that might happen, which would contradict the zero-energy hypothesis?

Hawking writes: "If the total energy of the universe must always remain zero, and it costs energy to create a body, how can a whole universe be created from nothing? That is why there is a law like gravity. Because gravity is attractive, gravitational energy is negative: One has to do work to separate a gravitationally bound system, such as the earth and moon. This negative energy can balance the positive energy needed to create matter, but it’s not quite that simple. The negative gravitational energy of the earth, for example, is less than a billionth of the positive energy of the matter particles the earth is made of. A body such as a star will have more negative gravitational energy, and the smaller it is (the closer the different parts of it are to each other), the greater the negative gravitational energy will be. But before it can become greater than the positive energy of the matter, the star will collapse to a black hole, and black holes have positive energy. That’s why empty space is stable. Bodies such as stars or black holes cannot just appear out of nothing. But a whole universe can." [Hawking (2010),

Hawking writes: "If the total energy of the universe must always remain zero, and it costs energy to create a body, how can a whole universe be created from nothing? That is why there is a law like gravity. Because gravity is attractive, gravitational energy is negative: One has to do work to separate a gravitationally bound system, such as the earth and moon. This negative energy can balance the positive energy needed to create matter, but it’s not quite that simple. The negative gravitational energy of the earth, for example, is less than a billionth of the positive energy of the matter particles the earth is made of. A body such as a star will have more negative gravitational energy, and the smaller it is (the closer the different parts of it are to each other), the greater the negative gravitational energy will be. But before it can become greater than the positive energy of the matter, the star will collapse to a black hole, and black holes have positive energy. That’s why empty space is stable. Bodies such as stars or black holes cannot just appear out of nothing. But a whole universe can." [Hawking (2010),

*The Grand Design*, p. 180]

With a lot of theories, the ultimate fate isn't so much "It's false" as "It's interesting but useless". That seems likely to be the fate of this one.

The ultimate test of any physics theory is whether it can become the basis for some kind of engineering. We know that quantum theory is true because computers work. We know that special relativity is true because nuclear weapons work. We know that Maxwell's Equations are true because generators and motors work. And so on.

This zero-energy theory will remain in the realm of interesting-but-useless until and unless it eventually results in other theories which can become grounds for new kinds of engineering.

posted by Chocolate Pickle at 10:13 AM on February 13 [4 favorites]

The ultimate test of any physics theory is whether it can become the basis for some kind of engineering. We know that quantum theory is true because computers work. We know that special relativity is true because nuclear weapons work. We know that Maxwell's Equations are true because generators and motors work. And so on.

This zero-energy theory will remain in the realm of interesting-but-useless until and unless it eventually results in other theories which can become grounds for new kinds of engineering.

posted by Chocolate Pickle at 10:13 AM on February 13 [4 favorites]

This is a pretty common question, and you can find a lot of answers on various physics sites addressing it. Basically, my opinion is that whether the totally energy of the Universe, once you include the gravitational field, is ill-defined, and I haven't seen a calculation that resolves the issue. There is a definition of the energy in general relativity that would appear to be zero, but this is something of a trivial statement (you're looking for the classical solution to an equation of motion, which forces the thing you're calling the energy to be zero in GR, but is that the right thing to do?). It obviously an interesting and evocative idea, but its really not clear to me that we have a way to define the energy of the vacuum (including gravity) which lets us know whether it is correct.

Its also not clear to me that the answer to this question is stable over time. That is, maybe the Universe started with zero total energy (correctly defined, whatever that means), but doesn't have zero total energy now. Or maybe it started with non-zero energy, and now has zero, and a few trillion years from now will have some other non-zero value. This is because the Universe is dynamical in time, and as a result, does not have to conserve energy.

That's a pretty crazy-sounding statement, so let me explain. Every conservation law in physics is due to a symmetry in the underlying theory. This is called Noether's theorem, discovered by Emmy Noether and one of the most beautiful and important pieces of physics I know of. The conservation of momentum, for example, is due to a translational symmetry in Nature: the laws of physics at one point are the same as the laws of physics at another, and so you can prove this implies momentum is conserved. Conservation of electric charge is due to an internal symmetry that allows a redefinition of charged particles in a particular manner. Energy conservation is due to the fact that the Universe is constant over time: laws of physics today look like the laws of physics tomorrow.

However, the Universe is expanding: the "metric" of the Universe is changing over time. Since the metric defines how particles move in the Universe, a changing metric will allow energy to not be conserved. A simple example is the energy of photons from the CMB. As these photons fly through the Universe, the Universe expands, causing their wavelengths to lengthen (they redshift). This causes them to have lower energy, as the energy of a photon is proportional to inverse wavelength. So photons do not have conserved energy, due to the lack of a time-invariance symmetry. (I've said this before, I never want to hear any of you use this comment from me as a defense of bullshit free-energy scams. Unless your energy-violating device works on timescales no less than a billion years, the Universe is essentially time invariant, so energy is effectively conserved. Someone telling you they are getting energy for nothing here on Earth is lying to you.)

What this means for your question is that at this point I don't think there is a well-defined answer to the question "is the Universe's total energy zero?" It's neither true nor false, we just don't know. I guess to steal a Zen term, the answer is Mu.

It is also not at all clear to me that if even if we could unambiguously define the energy of the Universe including gravity that this answer will remain constant over time. Much of the Universe's current energy budget is in this mysterious dark energy, whatever it is, and it increases with the volume of the Universe. Now, this is pretty closely tied in with gravity, so maybe the correct way to do with will end up "subtracting out" the time-variance of the metric, and so we'll find a time-invariant result, but who knows at this point? A better understanding of gravity will likely be required, and that will likely require both theoretical and experimental advances - some of which might be functionally impossible to obtain with the technology of even the longest-term projections I can imagine.

Also, the fact that a piece of physics hasn't led to "engineering," whatever that is, is of course totally irrelevant to its truth-value. Neutrinos and muons are pretty useless for engineering purposes thus far, as is most particle physics probed at a modern collider, but they are "true." A theory will be considered as "correct" or at least "likely to be correct or useful to think in terms of" once it makes it past some combination of reproducibility or falsifiability (I'm sure some philosopher of science will have a heart attack over that hand-waviness, but I don't spend my life worrying about it too much). It may be that questions about the energy density and ultimate origins of the Universe are never falsifiable or testable in any way, but the fact that we never get a fancy new device out of it is not the key part of whether it's science.

posted by physicsmatt at 3:23 PM on February 13 [7 favorites]

Its also not clear to me that the answer to this question is stable over time. That is, maybe the Universe started with zero total energy (correctly defined, whatever that means), but doesn't have zero total energy now. Or maybe it started with non-zero energy, and now has zero, and a few trillion years from now will have some other non-zero value. This is because the Universe is dynamical in time, and as a result, does not have to conserve energy.

That's a pretty crazy-sounding statement, so let me explain. Every conservation law in physics is due to a symmetry in the underlying theory. This is called Noether's theorem, discovered by Emmy Noether and one of the most beautiful and important pieces of physics I know of. The conservation of momentum, for example, is due to a translational symmetry in Nature: the laws of physics at one point are the same as the laws of physics at another, and so you can prove this implies momentum is conserved. Conservation of electric charge is due to an internal symmetry that allows a redefinition of charged particles in a particular manner. Energy conservation is due to the fact that the Universe is constant over time: laws of physics today look like the laws of physics tomorrow.

However, the Universe is expanding: the "metric" of the Universe is changing over time. Since the metric defines how particles move in the Universe, a changing metric will allow energy to not be conserved. A simple example is the energy of photons from the CMB. As these photons fly through the Universe, the Universe expands, causing their wavelengths to lengthen (they redshift). This causes them to have lower energy, as the energy of a photon is proportional to inverse wavelength. So photons do not have conserved energy, due to the lack of a time-invariance symmetry. (I've said this before, I never want to hear any of you use this comment from me as a defense of bullshit free-energy scams. Unless your energy-violating device works on timescales no less than a billion years, the Universe is essentially time invariant, so energy is effectively conserved. Someone telling you they are getting energy for nothing here on Earth is lying to you.)

What this means for your question is that at this point I don't think there is a well-defined answer to the question "is the Universe's total energy zero?" It's neither true nor false, we just don't know. I guess to steal a Zen term, the answer is Mu.

It is also not at all clear to me that if even if we could unambiguously define the energy of the Universe including gravity that this answer will remain constant over time. Much of the Universe's current energy budget is in this mysterious dark energy, whatever it is, and it increases with the volume of the Universe. Now, this is pretty closely tied in with gravity, so maybe the correct way to do with will end up "subtracting out" the time-variance of the metric, and so we'll find a time-invariant result, but who knows at this point? A better understanding of gravity will likely be required, and that will likely require both theoretical and experimental advances - some of which might be functionally impossible to obtain with the technology of even the longest-term projections I can imagine.

Also, the fact that a piece of physics hasn't led to "engineering," whatever that is, is of course totally irrelevant to its truth-value. Neutrinos and muons are pretty useless for engineering purposes thus far, as is most particle physics probed at a modern collider, but they are "true." A theory will be considered as "correct" or at least "likely to be correct or useful to think in terms of" once it makes it past some combination of reproducibility or falsifiability (I'm sure some philosopher of science will have a heart attack over that hand-waviness, but I don't spend my life worrying about it too much). It may be that questions about the energy density and ultimate origins of the Universe are never falsifiable or testable in any way, but the fact that we never get a fancy new device out of it is not the key part of whether it's science.

posted by physicsmatt at 3:23 PM on February 13 [7 favorites]

I grant that, if the zero-energy hypothesis is ill-defined, there's little sense in trying to imagine a counterexample.

But is it at least possible to convey the gist of what people like Hawking and Tryon etc. have in mind, so that it makes at least some sense to imagine a counterexample? I don't even care whether a counterexample is verifiable; I am only interested in what a counterexample might be like.

For instance, would it be a counterexample if we were in the sort of world where the top portions of skyscrapers had a lot of gravitational potential energy but very little crushing power in the downward direction?

posted by Eiwalker at 7:08 PM on February 13

But is it at least possible to convey the gist of what people like Hawking and Tryon etc. have in mind, so that it makes at least some sense to imagine a counterexample? I don't even care whether a counterexample is verifiable; I am only interested in what a counterexample might be like.

For instance, would it be a counterexample if we were in the sort of world where the top portions of skyscrapers had a lot of gravitational potential energy but very little crushing power in the downward direction?

posted by Eiwalker at 7:08 PM on February 13

Eiwalker, unfortunately the example you're thinking about doesn't quite make a consistent story. What you are trying to build is a universe where the force of gravity (the "downwards power" you refer to) is the same, but the negative gravitational potential energy is smaller. However, in physics, a force is simply the derivative of the potential, or in less mathy talk, a force is caused by the difference in potential energy between two points (divided by the distance between two points, and the derivative just tells you to consider the differences between two points very close together). So, if you want to dial down the gravitational coupling constant to reduce the potential energy from gravity, you will reduce the potential difference between the top of the skyscraper and the bottom, and so reduce the force that the skyscraper exerts downwards. As a result, gravity just got weaker (as you expect, since you reduced the gravitational coupling constant), and structures like the Earth and stars will be less tightly bound.

The original question is falsifiable in principle. If we had a well-defined answer to the question of how to define a gravitational energy in GR, then we could in principle calculate the total energy of the Universe at various points in its history. If it converges towards zero (or is zero for all times, but that seems hard to do as I said, but then again, I don't have a good answer to the full question anyway so what do I know), then we could say this idea has merit. If it doesn't then, given our knowledge, we would say this idea is likely to be false. However, futzing with the constants of the Universe (as in your thought experiment) seems like it won't help in this particular case; certainly there are ways to do it that would give a universe with non-zero total energy (again, modulo the problems of defining that), but can we say that such a universe can exist outside of our thought experiment? After all, you are explicitly asking a question about the formation of a universe. If you alter the parameters of the one universe we know exists, how can you be sure that the resulting thought-experiment universe is acceptable? (That said, there are other thought-experiments where dialing fundamental parameters does give insight, or might give insight, but those usually fall into questions of anthropics, and down that rabbit hole let us not go today.)

A very exciting thing would be if the only way to get a universe with zero energy is if the gravitational constant G_newton was what it is in our Universe, or if the cosmological constant had to be the strange value that it is measured to be. It'd be wonderful if we had a reason for these seemingly random constants of Nature. However, I don't think our understanding of these questions is able to give a good answer here yet. My suspicion is that many other universes are possible, as motivated by the multiverse ideas from string theories and inflationary physics, so I'm biased against this being the right answer. But again, I don't claim to have the right answer. The idea is certainly something to think about.

posted by physicsmatt at 6:43 AM on February 14 [1 favorite]

The original question is falsifiable in principle. If we had a well-defined answer to the question of how to define a gravitational energy in GR, then we could in principle calculate the total energy of the Universe at various points in its history. If it converges towards zero (or is zero for all times, but that seems hard to do as I said, but then again, I don't have a good answer to the full question anyway so what do I know), then we could say this idea has merit. If it doesn't then, given our knowledge, we would say this idea is likely to be false. However, futzing with the constants of the Universe (as in your thought experiment) seems like it won't help in this particular case; certainly there are ways to do it that would give a universe with non-zero total energy (again, modulo the problems of defining that), but can we say that such a universe can exist outside of our thought experiment? After all, you are explicitly asking a question about the formation of a universe. If you alter the parameters of the one universe we know exists, how can you be sure that the resulting thought-experiment universe is acceptable? (That said, there are other thought-experiments where dialing fundamental parameters does give insight, or might give insight, but those usually fall into questions of anthropics, and down that rabbit hole let us not go today.)

A very exciting thing would be if the only way to get a universe with zero energy is if the gravitational constant G_newton was what it is in our Universe, or if the cosmological constant had to be the strange value that it is measured to be. It'd be wonderful if we had a reason for these seemingly random constants of Nature. However, I don't think our understanding of these questions is able to give a good answer here yet. My suspicion is that many other universes are possible, as motivated by the multiverse ideas from string theories and inflationary physics, so I'm biased against this being the right answer. But again, I don't claim to have the right answer. The idea is certainly something to think about.

posted by physicsmatt at 6:43 AM on February 14 [1 favorite]

One of the things I was wondering when I posed this question originally is whether the zero-energy hypothesis is a substantive thesis, or a mere result of definitions. However, if the total energy can waver over time (despite the definitions), then the zero-energy hypothesis is not a mere result of definitions. With that said, it doesn't seem like the definitions are really in place anyway (at least in the context of GR), in which case it doesn't currently make sense to imagine it wavering or not wavering over time, let alone being zero at all times (as Hawking imagines: "the total energy of the universe must always remain zero").

This leads to a related question: If GR were false, are there definitions in place in which the zero-energy hypothesis would be well defined?

posted by Eiwalker at 6:31 AM on February 15

This leads to a related question: If GR were false, are there definitions in place in which the zero-energy hypothesis would be well defined?

posted by Eiwalker at 6:31 AM on February 15

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That being said, this is essentially not falsifiable. The reason is that what we see (the visible universe) is only a fraction of what there is. As we can not see the entire universe, it is impossible to know its total energy, nor is it possible to compare our theoretical predictions with what happens outside of the visible universe. By visible universe, I mean places in the universe that are close enough to us that some light coming from those places has had time to reach us since the beginning of time (the big bang).

posted by aroberge at 9:00 AM on February 13 [1 favorite]