# Alan Guth thought experiment about negative energy and gravity

1. Feb 2, 2014

### Herbascious J

Recently, I watched a lecture with Alan Guth. He made an interesting statement. He said that to create an electric field requires work, because the like-charges prefer to repel one another, therefore this requires energy to bring them together. However; because gravity is attractive, it requires no work to create a field, simply because the particles attract to one another, and will assemble themselves into a large gravity field without work. He went on to say that it is even possible to extract energy from a system while a gravity field is being created in this way (falling matter can render energy and do work, leaving behind a large gravity field). By this definition he claims that the resultant gravity field must have a negative energy associated with it, while an electric field must have a positive energy by nature of its configuration. He uses this argument to demonstrate part of his inflation theory, in that the gravitational force increases while new particles are being created during inflation. This creates the tremendous momentum of expansion along with the huge quantities of mass, in a kind of cosmic trade off, where total energy equals zero.

I'm having trouble with this concept, because It doesn't seem intuitive. It seems that the gravity field is already there just separated out with each particle. And the new resultant field is simply these separate fields being assembled. So no new field has been created right? At least not in the sense that more energy (or negative energy) had to be added to the field. Thoughts?

2. Feb 2, 2014

### Simon Bridge

The gravity field is already there - means that there is no work required to get a bigger on as two particles come together. However - as two objects gravitate towards each other, you can extract energy as work ... just look at a water wheel. Where does this energy come from?

3. Feb 3, 2014

### Herbascious J

I believe the energy of a water wheel comes from water moving from high to low in the earth's gravity field. But that doesn't change the gravity fields density itself, at least not significantly (I realize each drop of water has its own field). So by moving the water vapor up in the atmosphere, the sun does work and expends real energy. Then the water is then allowed to flow back to the ocean, via a river, and passes the water wheel. The wheel slows the motion of the water and extracts energy. This is potential energy.

Ok, so separating objects gravitationally requires energy, just like gathering like charges requires energy. So does this truly mean that the gravity field itself is made of negative energy, which can be used to cancel the existing matter energy of the universe?? It doesn't seem right, because the energy of the field between two unlike charges, say a positron and an electron would also be a negative energy field, but we know that electrical fields contain a positive type of energy. Does this mean that attempts to use gravity as the trade off for positive energy in the universe are not really well founded?

4. Feb 3, 2014

### Simon Bridge

In general - from two masses getting closer together by gravitation.
There's no such thing as insignificant this time ... remember the cosmological scale that we are talking about? However, there are problems defining what we mean by the gravitational energy density ...
classically it goes like this:
http://en.wikipedia.org/wiki/Gravitational_energy
... spot the minus sign.
iirc there is no such thing in general relativity though.

And where did the Sun get that energy from? We could go on like this - treat it as rhetorical.
You are actually on the major objection to the usual analogy.
That minus sign depends on where we choose to put the value of zero.

What I want to encourage you to do right now is try to understand how someone would feel that it makes sense to treat gravity as having a negative contribution to the Universes energy-balance sheet.

If you prefer, go right to considering how the matter in the Early universe got it's energy?
What was doing work on it to separate it out like that? i.e. where is the cosmological analogy for what the Sun does to the water?

Do you see the difference between needing energy to bring like objects together vs needing energy to move like objects apart? The change in energy kinda seems to have an opposite sense doesn't it?

I think care needs to be made to distinguish between "negative energy" (in GR) and the contribution that gravity makes to the total energy-balance of the Universe.

I also think you should bear in mind the intended audience for the lecture ... Guth was making some simplifications. It is valid to think of gravity as having a negative contribution to the total energy of the Universe, it is one of the ways you can get something from nothing, but iirc it's not the whole story.

The discussion usually crops up in the context of getting something from nothing ... so I have some more accessible reading for you now I have a better idea where you are coming from:

<<deleted>>
... overview of less speculative ways you can get something from nothing.

<<deleted>>
... it's basically a book review but hang in there - two approaches are considered, with the "negative gravity" one coming second. You may just prefer the first one.
After setting the stage and describing the two deals the author complains that the book has a bad title ... so you can probably stop there.
When physicists set out with questions starting "why" we don't mean literally "why" - that's not really our job, but the author is a philosopher so ....

here's a better discussion (see the links also)
<<deleted>>

Basically it's an idea being taken seriously so it is worth making an effort to come to grips with it.
Unfortunately it is not a short story that can be summed up in a few posts.

Last edited by a moderator: Feb 4, 2014
5. Feb 3, 2014

### Jano L.

The gravitational energy is negative, but it is not certain whether it has to be the same in magnitude as the rest of the energies to product null energy as a result.

Energy of electrostatic field between two oppositely charged bodies is positive in macroscopic theory, but it increases as the bodies are being separated in a similar way to gravitational energy. Only the absolute values have different signs, changes of energy have the same sign. This is because the macroscopic Poynting energy is defined as integral of positive quantity. For point particles, one can define energy in a different way, to obtain negative energy density too (when some constant positive terms are discarded).

6. Feb 3, 2014

### Chronos

All 'work' done in the universe is due to entropy.

7. Feb 3, 2014

8. Feb 3, 2014

### BruceW

Think of just two massive particles to begin with (to make it simple). energy is required to pull them apart due to gravity. and for two opposite charges, also energy is required to pull them apart. So if you're going to say gravity is a negative energy, then also the electric field between these opposite charges is also negative energy.

9. Feb 3, 2014

### Staff: Mentor

No. If you start with two opposite electrical charges together the field is 0. As you pull them apart you do work and the field becomes non-zero. So work is required in order to increase the field, therefore the field has positive energy.

If you start with two masses together the field is non-zero. As you pull them apart you do work and the field decreases. So work is required in order to decrease the field, therefore the field has negative energy.

10. Feb 3, 2014

### BruceW

no, in the limit of the two oppositely charges particles being very close together, you get an electric dipole field, which is definitely not zero. Also, as you pull the two charges further apart, the field decreases. So work is required to decrease the field.

11. Feb 3, 2014

### Staff: Mentor

I was talking about two identical charge distributions exactly on top of each other, not a dipole. Also, the dipole field is less than the field of two widely separated charges, so pulling a dipole apart also increases the field.

12. Feb 3, 2014

### BruceW

the dipole field tends to infinity, in the space between the charges, when the charges are brought closer together. Similarly to how the gravitational field tends to infinity, in between the two masses as they are brought closer together. (neglecting general relativity or quantum physics, of course).

If we're talking about identical (and opposite) charge distributions, then yes when they overlap, you must do work to increase the field. But once they are no longer overlapping, you must do work to decrease the field (same as in the case of point particles).

13. Feb 3, 2014

### Staff: Mentor

That is a mathematical artifact of using point charges, which are not realistic. I do recognize that for small but finite sized charges your general point is correct that the field becomes high as the small charges are brought together.

However, you seem to be forgetting that we are talking about an energy density, so the important quantity is not the maximum of the field but rather the integral of the field (actually the integral of the norm squared of the field) over its volume. This tends to zero, not infinity. You get a small amount of energy concentrated into a very small volume for a high energy density but low total field energy.

No, the work is always done to increase the field (norm squared integral), regardless of whether or not the distributions are overlapping. I can post a calculation if you like.

Last edited: Feb 3, 2014
14. Feb 3, 2014

### BruceW

hmm. I was talking about the maximum of the field. But yeah, the integral of the norm squared is probably a more interesting question. What volume should we use for the integral? If we use a cubic volume inbetween the two charge distributions (i.e. for when the two charge distributions are not overlapping), then I'm fairly sure the integral of the norm squared will be greater when the two charge distributions are further away from each other. OK, I see what you meant now. But this is also true of the integral of norm squared of the gravitational field. So still, the gravitational field has the same 'sign of energy' as the electric field has in this case.

15. Feb 3, 2014

### Staff: Mentor

In principle, you have to integrate over all space, otherwise you neglect some portion of the energy. In practice, you just have to go far enough out that your fields are negligible.

No, it doesn't. Consider a spherical shell of charge/mass. Let the radius of the shells be 1 m and let $Q/4\pi \epsilon_0 = \pm 1$ and let $M/8\pi G = 1$ in SI units.

A) If the centers of the shells are separated by 1 m the norm squared integral for the electric field is 12.566 and for the gravitational field is 37.699.

B) If the centers of the shells are separated by 3 m the norm squared integral for the electric field is 20.944 and for the gravitational field is 29.322.

Note that the force is attractive in both cases and work is required to move from configuration A to configuration B. However, note that the electric field increased from 12.6 to 20.9, positive work increasing the field indicating a positive energy density. In contrast, the gravitational field decreased from 37.7 to 29.3, positive work decreasing the field indicating a negative energy density.

16. Feb 4, 2014

### Herbascious J

First, thank you for the great reading, and thorough response. I believe I'm beginning to see more clearly, and much appreciated...

Ok, so I see that the sun got this energy from fusion, which ultimately was released by gravitational pressure and infalling matter, creating a star. Ultimately this energy is gravitational potential energy from the original expansion at the beginning of time, right? (of course the fusion energy is from matter, but the point remains I think).

Ok, so the expansion of the universe, and exactly what Friedmann showed, was that it was a momentum which separated all of the matter. This momentum fought against the gravity of everything, doing 'work', like the sun works on the water. This creates an enormous potential energy in the overall gravity field of the universe, because it wants to re-collapse. So if it takes real positive energy to lift the water, then it must take real positive energy to expand the universe. The source of this momentum, was inflation. Inflation also created matter. I realize that inflation is a form of repulsive gravity so I don't think it's really doing work; the matter is all falling outward without work being done on it. But then inflation decays and the momentum is now working against attractive gravity and there is a tremendous amount of potential energy/kinetic energy locked up in the outward momentum of the universe. It's brilliant, but challenging for me. But I can see from DaleSpam's final comment that the energy density of gravity does in fact appear to be negative in nature.

My final thought; if dark energy operates in much this same way, perhaps it too is a negative form of energy that is appearing. Must this dark energy also deliver some positive form of energy to off-set it as well, like when inflation creates matter (giving a net-zero universe)?

Thanks Simon and all.

17. Feb 4, 2014

### BruceW

what volume integral are you using to calculate these answers?

18. Feb 4, 2014

### Johninch

I don't follow you. I see it like this:

If the universe does not want to collapse, since it is apparently on track to expand forever, then maximum entropy is its natural stable state. If work was necessary to give the universe its dynamic, this was embodied in the singularity. I don’t see that “matter is all falling outward without work being done on it”. The potential/kinetic energy initially in the singularity was released to drive the expansion. Inflation was not the source of the energy to drive the expansion, inflation was the result of the release of the potential energy locked in the singularity. The “energy locked up in the outward momentum of the universe” is declining towards zero and is not locked up.

.

19. Feb 4, 2014

### Staff: Mentor

Hold on Herbascious J, you are going way overboard here and have left of studying to go speculating. You have a lot of studying to do before you are ready to do any speculating (and we don't do speculation here, that is done in the peer reviewed literature).
Momentum doesn't do work. Kinetic energy can do work, or more correctly, an object with kinetic energy can use it do work.

Unfortunately, this reasoning is not necessarily the case. Locally, on a scale where you are lifting water, Newtonian gravity is a good approximation, and Newtonian gravity does have a well-defined gravitational field energy (which happens to be negative). However, on the scale of the universe Newtonian gravity is no longer a good approximation, and the only viable theory that we have right now, General Relativity, does not have a well-defined gravitational field energy for the universe.

Unfortunately, GR is not that simple. In GR there is only a well defined gravitational field energy in very specific classes of spacetime. The spacetime of the universe does not happen to be one of those. There simply is no well defined measure of the energy of the universe.

Yes, for Newtonian gravity.

Please refrain from speculation like this. There is, to our best current theory, no definite value to the energy of the universe. We cannot say that it is a net zero.