Is the Energy of the Universe Really Zero?

[da_willem]

I read that the energy of the entire universe might be zero, by an argumnet of the positive energy matter content balanced by the negative gravitational potential energy (see e.g. ttp://www.astrosociety.org/pubs/mercury/31_02/nothing.html).

How does this argument go from a GR point of view? As far as I understand, it does not work with gravitational potential energy, or even forces at all. Does the 'zero energy universe' place some restriction on the energy momentum tensor or something?

Finally, is there some experimental evidence for this claim?

 

[ptalar]

If the net energy were zero then why is the Universe still expanding? It is my understanding that the size of the Universe is proportional to the amount of energy in it. If the energy were balanced between dark energy, matter, dark matter, vacuum energy then the Universe would stabilize and stop expanding.
Any thoughts?

 

[Chronos]

A similar paradox exists for the preponderance of matter v anti-matter. It has been proposed that gravity negates the presence of matter. But that presupposes a need to counteract anything. We live in a lumpy universe, which is in an embarrassingly difficult position for any universe to explain. Other universes are pointing fingers at ours, as we speak, whispering to their children 'that's the one with the infection'.

 

[da_willem]

A similar paradox exists for the preponderance of matter v anti-matter. It has been proposed that gravity negates the presence of matter. But that presupposes a need to counteract anything. We live in a lumpy universe, which is in an embarrassingly difficult position for any universe to explain. Other universes are pointing fingers at ours, as we speak, whispering to their children 'that's the one with the infection'.

But as to the orginal question, how does this claim follow from GR?!

 

[pervect]

As I recall, some means of computing the Hamiltonian of the universe get zero for an answer. This is not actually a useful formulation of the theory of GR, solving Hamilton's equations with a Hamiltonian of zero doesn't make any actual physical predictions.

I believe that this is where the original claim came from, but I could be wrong. It's actually better for the originator of a claim to track it down (this would be the person with the question - while we can guess where someone might have read something some of the time, it's much easier if they can find the source themselves).

Anyway, from what I recall reading it was this "vanishing Hamiltonian" that gave rise to these sorts of speculations.

There are useful global defintions of energy in GR for closed systems, but the FRW cosmologies are not closed systems, and there isn't any useful global definition of energy that applies to an expanding FRW universe as far as I know.

For some general references, see http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

about the issue of energy in GR, also you might want to see

http://en.wikipedia.org/wiki/Mass_in_general_relativity (note that I wrote it, so it's not an independent source). This also talks about the general issue of energy in GR, and specifically about the "mass of the universe".

The textbook quote in the Wikipedia article is also relevant, but note though that it's about the mass (or rather, the lack of same) of a closed universe, while current models put us in an open universe.

Anyway, I would say that the bottom line is that nobody has found any way of making this sort of statement about "total energy" of the universe useful in the full theory of GR according to current theory.

 

[hellfire]

This zero energy idea is also related to inflation, at least at some very speculative level. See for example this and search for "zero energy" (Alan Guth's "free lunch").

 

[xantox]

How does this argument go from a GR point of view?

The argument arises from the fact that in general relativity there is no preferred frame, and the time coordinate is reparametrizable. This condition applies to the classical gravity and matter action, leading to a constraint equation setting the total hamiltonian density to zero. It is also assumed that there are no boundary terms in the case of the universe as a whole.

 

[litewave]

Is this idea of zero total energy of the universe a proven fact or just a speculation? Here's a list of quotes from scientists who make this point, including Stephen Hawking:

http://www.infidels.org/library/modern/mark_vuletic/vacuum.html

Does it mean that -mc^2 where m is the total mass of the universe should be equal to gravitational potential energy of each particle with respect to all other particles in the universe? Does it follow from general relativity?

 

[litewave]

If we imagine a simple universe with two particles with masses m1 and m2 then we can calculate these two types of energy of the universe:

1) energy of matter = (m1+m2)c^2

2) potential gravitational energy = -2Gm1m2/r (where G is gravitational constant and r is the distance between the two particles)

The formula for potential gravitational energy has zero potential level at r=infinity, because that's the only position where the gravitational force affecting either particle is indeed zero. As the universe expands and the two particles get further apart, the expanding force does work against the gravitational force and thus increases the potential gravitational energy - until it reaches zero where the distance r is infinite. Which means that at any finite distance between the particles the potential gravitational energy is negative.

Is it true that the energy of matter plus the potential gravitational energy is always zero?

And if it is true then obviously the energy of matter decreases as the universe expands. What should we think about it? Does the mass decrease because the expanding universe is getting cooler (mass = heat/c^2)? Is the heat energy converted into potential gravitational energy as the universe expands?

 

[darlmc]

litewave,
I like your two particle simple universe and would like to comment on it... To overcome their mutual gravitational attraction your simple universe should be loaded with some initial energy to get the particles moving apart (increasing r). This kick need not change their mass however, just their kinetic energy. As the simple universe expands its size is determined by the distance between the particles. Expand as it may however, the simple universe will always contain the two particles. I therefore see the simple universe as cooling with expansion as the energy density decreases, but I also think of its overall total energy content as remaining constant. Thoughts?

 

[litewave]

darlmc,

the total energy content of the universe remains constant but is it zero?

 

[siphon]

And if it is true then obviously the energy of matter decreases as the universe expands. What should we think about it? Does the mass decrease because the expanding universe is getting cooler (mass = heat/c^2)? Is the heat energy converted into potential gravitational energy as the universe expands?

What everyone is leaving out, is the energy output of mass burn due to the nuke reactions in stars. There is more than just gravity in the universe. The mass burn is causing the gravity to lower within stars, as mass becomes energy and energy is released, allowing other matter to go where it couldn't before, i.e., solar dust.

 

[darlmc]

litewave,
Since your simple expanding universe contains two particles with some amount of kinetic energy it is my opinion that its energy content would not be zero. As the simple universe expands its volume increases, its pressure drops and its temperature decreases… but its total energy content should remain equal to the energy inherent in the particles and their motion.

Siphon,
Matter is always driving toward a reduction in gravitational potential. In order to actually move to a lower gravitation potential however (move to a heavier, denser form) matter must indeed give up energy to maintain overall energy balance, as it does within a star. But how can we relate that to an expanding universe? I’m not sure I follow.

 

[litewave]

litewave,
Since your simple expanding universe contains two particles with some amount of kinetic energy it is my opinion that its energy content would not be zero. As the simple universe expands its volume increases, its pressure drops and its temperature decreases… but its total energy content should remain equal to the energy inherent in the particles and their motion.

The energy inherent in particles and their motion is the positive energy of matter (mc^2). Did you also consider the gravitational potential energy? This one is negative and it is claimed to exactly offset the positive energy of matter...

 

[my_wan]

The article does mention the energy of the false vacuum. It's based on the idea that a medium that contains energy will expand. It is very imperfectly analogous to heated gas expanding. However as the Universe expanded and cooled matter condensed out of it, actually more like a phase transition. Once matter formed the matter produced a gravitational field that attracts the mass back together (GR). It was this the phase transition that ended expansionary period that account for todays lumpiness of matter in the standard model. Nobody actually knows if the energy balance is exactly zero between expansionary forces and gravity but many observations indicate that it is very close.

Experimental evidence is very hard to come by but given our assumptions about the laws of physics and the standard model of cosmology observation tend to roughly support it. To be more specific requires more detail about GR.

 

[siphon]

Siphon,
Matter is always driving toward a reduction in gravitational potential. In order to actually move to a lower gravitation potential however (move to a heavier, denser form) matter must indeed give up energy to maintain overall energy balance, as it does within a star. But how can we relate that to an expanding universe? I’m not sure I follow

The mass burn in stars is reducing the amount of matter and converting this to energy. If you look at the sun, its mass lowers with time. Even the solar wind would not occur with just gravity. It uses nuclear energy to defy the solar gravity. The question is whether fusion is what is allowing the universe to expand?

Say we had nothing but neutral matter stars without any particle interaction beyond gravity. If I took a big scoop out of every neutral star constantly, their total gravity will continue to lower with time. This may not cause expansion but it would cause contraction to slow. If we also burn the mass we scooped out and thereby remove mass and add energy to the universe, now we have a push.

Stars are much fluffier than they would be with just gravity. The affect of fusion on solar compaction is significant. Without fusion, the sun may end up as a small zone of matter at neutron density. With fusion the sun expands against gravity to billions of times the neutron density size. If you add all the billions of galaxies each with billions of stars, fusion is holding it own against the force of gravity. Maybe this total resistant adds up to the expansion, since the affect of all this fusion is projected outward for us to see with telescopes.

 

[litewave]

The article does mention the energy of the false vacuum. It's based on the idea that a medium that contains energy will expand. It is very imperfectly analogous to heated gas expanding. However as the Universe expanded and cooled matter condensed out of it, actually more like a phase transition. Once matter formed the matter produced a gravitational field that attracts the mass back together (GR). It was this the phase transition that ended expansionary period that account for todays lumpiness of matter in the standard model. Nobody actually knows if the energy balance is exactly zero between expansionary forces and gravity but many observations indicate that it is very close.

Experimental evidence is very hard to come by but given our assumptions about the laws of physics and the standard model of cosmology observation tend to roughly support it. To be more specific requires more detail about GR.

What I am confused about is whether this issue of total energy being zero can be settled by the general theory of relativity alone or whether one needs empirical data to get a conclusive answer. You seem to be saying the latter. In the article at infidels.org there is a quote from Davies that suggests the need for astronomical measurements too. But there is also this quote from Hawking:

In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.

What does "uniform in space" mean? And in the case of such a universe one can show from the theory alone that its total energy is zero?

 

[my_wan]

What I am confused about is whether this issue of total energy being zero can be settled by the general theory of relativity alone or whether one needs empirical data to get a conclusive answer. You seem to be saying the latter. In the article at infidels.org there is a quote from Davies that suggests the need for astronomical measurements too. But there is also this quote from Hawking:

In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.

What does "uniform in space" mean? And in the case of such a universe one can show from the theory alone that its total energy is zero?

Yes you are correct that GR needs empirical data to support the zero energy assumption, though it does appear to be quiet close. I can never be settled by GR alone. All GR can really say is that if these conditions exist in the Universe then this is the solution. GR does not actually specify those conditions. It's like planetary orbits where it does not say we must orbit our satellites in a particular orbit but we have a range of possible orbits to choose from. The Standard Model of Cosmology tries to fill in the rest.

The "uniform in space" seems to be referring to a modeled solution in which the mass is considered to be spread evenly throughout the Universe in just the right density so that gravitational attraction equals the expansion over the long term. Some cosmological models require this balance at a very fundamental level. However it takes more than GR alone to predict this. Generally this is based in Quantum Mechanics (QM) in which particle anti-particle pairs can be created from nothing so long as the total energy of both remains zero. These particle pairs will annihilate each other very soon afterwords. This QM effect is a tested and real effect.

 

[litewave]

Thanks my wan for clarifying this issue. I suppose that the total energy of the universe should be zero because as I imagine, the universe came into being from nothing - from a state with no defined energy - so if the law of energy conservation holds, total defined energy should remain zero.

 

[litewave]

Oh and one more question - is the positive mass-energy of the universe decreasing because of cooling?

 

[yogi]

Thanks my wan for clarifying this issue. I suppose that the total energy of the universe should be zero because as I imagine, the universe came into being from nothing - from a state with no defined energy - so if the law of energy conservation holds, total defined energy should remain zero.

That is an important observation - to embellish upon it one might note that energy, like momentum and velocity, are relative terms - it depends upon how and in what frame the zero point is measured - easy to see in the case of kinetic energies - not always so obvious with other forms such as radiation. Richard Feynman mused over the notion of a zero energy universe (at page 10 - in his book on gravitation). Says Feynman "It is exciting to think that it cost nothiing to create a new particle since we can create it at the center of the universe where it will have a negative gravitaional energy equal to mc^2"