Does Zero Net Energy equal Zero Energy?

[Athanatsius]

It seems that some of the new "free lunch" cosmological models promote the idea that if the universe has zero net energy, zero energy was required to create it. However, a closed system can have tremendous potential energy but zero net energy, so the idea seems questionable to me, even if the positive and negative energies add up to precisely zero. For instance one unit of positive energy plus one unit of negative energy equals zero net energy, but a potential energy difference of two units. It does not seem as though the expansion of space could create energy from nothing, either. Otherwise, how could the matter separated by inflation have had kinetic or gravitational potential energy without the law of the conservation of energy being violated? So what do you think? Am I on track in thinking that the creation of the universe probably required energy, such as a powerful quantum fluctuation of tremendous energy, as Tyron assumed with his original proposal, or off base here? if I am off base, please try to explain it to me in simple terms that a non-scientist like me can understand.

 

[PeterDonis]

a closed system can have tremendous potential energy but zero net energy

How?

one unit of positive energy plus one unit of negative energy equals zero net energy, but a potential energy difference of two units.

How? What model of potential energy are you using?

how could the matter separated by inflation have had kinetic or gravitational potential energy without the law of the conservation of energy being violated?

The law of conservation of energy in a non-static universe doesn't work the way you are thinking it does. Sean Carroll has a good article explaining this:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

 

[Athanatsius]

"How?"

Suppose a strong man is pulling your left arm, and and another strong man is pulling your right arm in exactly the opposite direction. You then have zero net energy pulling at you, but certainly not zero energy, or you would not feel that your arms are about to be pulled out of their sockets!

"How? What model of potential energy are you using?"

That potential energy is the energy difference between the energy of an object in a given position or state and its energy at a reference position or state. If the reference position or state is -1 and the rest position or state is +1, then the potential difference is two.

In regard to that article by Sean Carroll, I have always been under the impression that if the universe is a closed system, then the conservation of mass and energy must hold true. Carroll seems to be saying that while this holds true locally, it does not globally. But doesn't that really depend on exactly what you define as energy, for which there is a variance of opinion? And can this contention be experimentally verified, or is it simply something required to make some favored cosmological models work? How can something being moved with space rather than through space gain kinetic or potential energy by this, unless energy is being expended? After all, don't we call the force that is stretching out space dark energy? Doesn't it require energy to give something kinetic or potential energy? Please help me to understand. Is Carroll saying this because in some cosmological models, inflation is considered to be an exception to this? In other words, is it believed that inflation gave the universe gravitational and potential energy without any expenditure of energy being required?

 

[PeterDonis]

Suppose a strong man is pulling your left arm, and and another strong man is pulling your right arm in exactly the opposite direction. You then have zero net energy pulling at you

No, you don't. The reason you don't is exactly what you say: your arms are being pulled out of their sockets, so clearly there is nonzero energy present.

What is zero in this scenario is the net force on your center of mass; your body as a whole does not move. But your body is not just a point particle at its center of mass; it's an extended object, and parts of the object can be subjected to forces that the object as a whole is not, like the forces pulling your arms out of their sockets. Those forces have energy associated with them, but energy is not a vector; it doesn't have a direction associated with it. So energies due to forces pulling in opposite directions don't cancel out, even if the forces themselves do, as far as their effect on the motion of your body as a whole is concerned.

That potential energy is the energy difference between the energy of an object in a given position or state and its energy at a reference position or state.

Ok so far.

If the reference position or state is -1 and the rest position or state is +1, then the potential difference is two.

I assume you mean, if the energy in the reference position or state is -1 and the energy in the other position or state is +1, then the potential energy difference is two. This is true as you state it, but you've left out something very important: the zero point of energy is arbitrary; only energy differences matter. So in your scenario, we could adjust the zero point of energy so that the energy in the reference position or state was 0, and the energy in the other position or state was 2, for the same difference of two units. But now there is no "negative energy" anywhere.

I have always been under the impression that if the universe is a closed system, then the conservation of mass and energy must hold true. Carroll seems to be saying that while this holds true locally, it does not globally.

Correct.

But doesn't that really depend on exactly what you define as energy, for which there is a variance of opinion?

Yes, in the sense that (as Carroll says in his article) there are different ways of interpreting what the equations say, and some of them include an interpretation of "energy" for which it is conserved, while others include an interpretation of "energy" for which it isn't. But the physics is the same either way; the difference is only one of how we choose to describe the physics in ordinary language. No predictions of experimental results are changed.

can this contention be experimentally verified, or is it simply something required to make some favored cosmological models work?

The equations and their predictions can certainly be experimentally verified, and have been. But you can't experimentally test an interpretation, because the whole point is that different interpretations agree on the experimental results; they only disagree on how to describe them in ordinary language.

How can something being moved with space rather than through space gain kinetic or potential energy by this, unless energy is being expended?

This question can't be answered as you ask it, because you're asking it in ordinary language, not math. Ordinary language is too imprecise for this purpose; that's why we can have different ordinary language interpretations of the same math and physics. The math and physics are not imprecise at all; but there a lots of questions that sound meaningful in ordinary language but turn out not to be when you try to translate them into math.

don't we call the force that is stretching out space dark energy?

No. No force is required for the universe to expand. Dark energy has the effect of making the expansion accelerate, rather than decelerate, as it would if there were only ordinary matter and energy present; but even this is not best viewed as a force, since the accelerating expansion is manifested by objects (galaxies and galaxy clusters) which are in free fall, feeling no force.

Is Carroll saying this because in some cosmological models, inflation is considered to be an exception to this?

No. Inflation is no different in this respect from the expansion the universe is undergoing now.

is it believed that inflation gave the universe gravitational and potential energy without any expenditure of energy being required?

This is another question that sounds meaningful in ordinary language, but turns out not to be when you try to translate it into math.

 

[Athanatsius]

I read through Carroll's article again and it is making sense to me now. What I was reacting to was the following by Vilenken:“The way the universe gets around that problem is that gravitational energy is negative. That’s a consequence of the fact, mathematically proven, that the energy of a closed universe is zero: The energy of matter is positive, the energy of gravitation is negative, and they always add up to zero. Therefore, creating a closed universe out of nothing does not violate any conservation laws.” [http://discovermagazine.com/2013/september/13-starting-point]

Hawking has also said something very similar.

What Carroll is saying is that it's better to just tell people that "Energy isn’t conserved; it changes because spacetime does."

So, since some cosmologists do claim that no conservation laws are violated, doesn't that mean that my point that zero net energy does not equal zero potential energy is still applicable, at least in regard to what they are saying?

 

[Athanatsius]

Peter, thanks for taking the time to answer.

No, you don't. The reason you don't is exactly what you say: your arms are being pulled out of their sockets, so clearly there is nonzero energy present.

What is zero in this scenario is the net force on your center of mass; your body as a whole does not move. But your body is not just a point particle at its center of mass; it's an extended object, and parts of the object can be subjected to forces that the object as a whole is not, like the forces pulling your arms out of their sockets. Those forces have energy associated with them, but energy is not a vector; it doesn't have a direction associated with it. So energies due to forces pulling in opposite directions don't cancel out, even if the forces themselves do, as far as their effect on the motion of your body as a whole is concerned.

OK, I see your point that energy is not a vector. Perhaps I used a poor example, but I think you see my point that if a negative and positive energy cancel out such that there is zero net energy, there can still be a potential energy difference between them.

I assume you mean, if the energy in the reference position or state is -1 and the energy in the other position or state is +1, then the potential energy difference is two. This is true as you state it, but you've left out something very important: the zero point of energy is arbitrary; only energy differences matter. So in your scenario, we could adjust the zero point of energy so that the energy in the reference position or state was 0, and the energy in the other position or state was 2, for the same difference of two units. But now there is no "negative energy" anywhere.

I agree, and in the same way, isn't infinity adopted as a reference point in order for gravitational energy to be considered negative?

This question can't be answered as you ask it, because you're asking it in ordinary language, not math. Ordinary language is too imprecise for this purpose; that's why we can have different ordinary language interpretations of the same math and physics. The math and physics are not imprecise at all; but there a lots of questions that sound meaningful in ordinary language but turn out not to be when you try to translate them into math...This is another question that sounds meaningful in ordinary language, but turns out not to be when you try to translate it into math.

I would appreciate it if you tried to answer it in ordinary language anyway. Sometimes, the act of finding a clear way to summarily explain something complex can be of great benefit not only to the listener, but even to the explainer.

No. No force is required for the universe to expand. Dark energy has the effect of making the expansion accelerate, rather than decelerate, as it would if there were only ordinary matter and energy present; but even this is not best viewed as a force, since the accelerating expansion is manifested by objects (galaxies and galaxy clusters) which are in free fall, feeling no force.

Doesn't this relate to my question, though? How can the expansion of space produce kinetic energy locally if there is ultimately no expenditure of energy behind it?

 

[PeterDonis]

since some cosmologists do claim that no conservation laws are violated

No cosmologists claim that conservation laws are violated. Carroll is not saying that; he's saying that, on his interpretation, there is no global conservation law to begin with. Saying "conservation laws are violated" is tantamount to saying that the laws of physics are violated; no cosmologist says that. All of them, to repeat, are using the same laws of physics, and making the same experimental predictions, and those predictions are valid. The only difference is in what ordinary language they use to describe what they are doing. Ordinary language descriptions are not physics.

oesn't that mean that my point that zero net energy does not equal zero potential energy is still applicable, at least in regard to what they are saying?

No. Even on the interpretation where the kinetic and rest energy of ordinary matter and radiation in the universe is positive, and gravitational potential energy is negative, and the two exactly balance to net out to zero, things don't work the way you are thinking they do. See below.

I think you see my point that if a negative and positive energy cancel out such that there is zero net energy, there can still be a potential energy difference between them.

No, I don't. There isn't a "potential energy difference" between some negative value of energy for "gravity" and some positive value of energy for "ordinary matter and radiation". That's not what the cosmologists are describing. What they're describing is that the gravitational potential energy of the universe (on their definition) is negative, and the kinetic energy and rest energy of the ordinary matter and radiation is positive, and the two magnitudes are the same, so the total energy, which is the sum of the two, is zero. But the difference if you subtract the two, instead of add them (i.e., instead of E + (- E) = 0, you do E - (-E) = 2E), is not a "potential energy difference"; it's a number with no physical meaning at all. The physically meaningful number (on this interpretation) is just zero.

I would appreciate it if you tried to answer it in ordinary language anyway.

See above. But there will be a point in any such process where the only answer remaining is "look at the math". As Feynman said, "to understand nature, you must learn the language she speaks in."

How can the expansion of space produce kinetic energy locally if there is ultimately no expenditure of energy behind it?

Once again, this question sounds meaningful in ordinary language, but it isn't once you look at the math. I'll try briefly to explain why in ordinary language, but bear in mind my caveat above.

There are two key points you appear to be missing. One is that "kinetic energy" is frame-dependent; it is not an absolute property of an object. You can change an object's kinetic energy by moving relative to it, without doing anything to the object at all. You can even change it simply by changing the coordinates you use to describe the object's motion; that doesn't even change your own motion, let alone anything about the object.

More important, though, is the point that all of the objects--galaxies and galaxy clusters--that we observe in order to figure out that the universe is expanding, are in free fall, feeling no force. Nothing is pushing on them. So any viewpoint in which they gain "kinetic energy" is, to say the least, limited. In Newtonian physics, you could have an object that felt no force even though a force was acting on it--gravity works this way, and in Newtonian physics, gravity is a force. But in GR, gravity is not a force, precisely because objects that are moving solely under the influence of gravity are in free fall, feeling no force. So thinking of the "expansion of space"--which is really just a (somewhat problematic) way of describing the dynamics of a particular solution in GR--as "expending energy" and exerting a "force" on galaxies and galaxy clusters that changes their "kinetic energy" is not a good way to look at it; it's trying to apply Newtonian intuitions in a regime where Newtonian physics simply doesn't apply.

 

[Athanatsius]

Thanks again for your responses, Peter. Are you sure that the difference between "negative" gravitational potential energy and the "positive" kinetic and rest energy of baryonic matter is meaningless? Could it not be reflective of some energy or force that caused or is acting upon the universe - perhaps the energy of the initial quantum fluctuation, for instance? If there is not some relationship between the two, then what is the point of saying that they cancel each other out mathmatically?

I just read a very interesting thread on this forum debating whether or not gravity is a force: https://www.physicsforums.com/threads/general-relativity-is-gravity-a-force.382066/ . I see your point that in GR, objects in free fall are just following the geodesics resulting from the curvature of space. But can't most Newtonian questions be translated into GR? For instance, the Newtonian description of kinetic energy is still a good approximation if velocity is much less than the speed of light.

Even if inflation granted energy and mass to the universe, how do we know that it came from nothing? Could there not have been a cause to it that was equal in energy?

 

[PeterDonis]

Are you sure that the difference between "negative" gravitational potential energy and the "positive" kinetic and rest energy of baryonic matter is meaningless?

Yes.

Could it not be reflective of some energy or force that caused or is acting upon the universe - perhaps the energy of the initial quantum fluctuation, for instance?

No. Once again, you really can't understand this stuff using ordinary language. You need to look at the math. When you look at the math, you will see that these questions don't even make sense; they seem meaningful only because you are using ordinary language, which is imprecise.

can't most Newtonian questions be translated into GR?

Yes, in the sense that, using GR, you can show why the Newtonian approximation is a good approximation in a certain regime (weak fields and slow motion). But the regime we're talking about--cosmology and the early universe--is not such a regime. The Newtonian approximation simply doesn't apply in this regime, so you shouldn't expect Newtonian concepts or descriptions to work.

the Newtonian description of kinetic energy is still a good approximation if velocity is much less than the speed of light.

And if fields are weak. Even if we restrict ourselves to a very small piece of the early universe, so all relative velocities are much less than the speed of light, we still aren't in a regime where the fields are weak. (More precisely, we are not in a regime where all spacetime curvature components are small.) So we aren't in a regime where the Newtonian approximation holds. Just meeting one requirement for that approximation (slow speeds) isn't enough; you need to meet all of them for the approximation to work.

Even if inflation granted energy and mass to the universe, how do we know that it came from nothing? Could there not have been a cause to it that was equal in energy?

The inflation model, as it stands, doesn't tell us what happened before inflation, or how inflation got started. The hypothesis that it originally "came from nothing" (i.e., that there was an initial fluctuation from a state with zero energy that turned into an inflating "bubble" that then became our universe) is one hypothesis about how it got started, but not the only one, and we don't have any good way of testing any of these hypotheses at this point. We can only speculate.

 

[Athanatsius]

Again, thanks for taking the time to reply and clarifying some things for me, Peter.

 

[PeterDonis]

Again, thanks for taking the time to reply and clarifying some things for me, Peter.

You're welcome!