March 30, 2010

Big Bang for beginners-13: Does the Big Bang theory violate the law of conservation of energy?

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

For previous posts in this series, see here.

Although the universe is mostly empty space (leaving aside for the moment dark energy and dark matter), there is quite a lot of matter in it. Some of it is in dense clumps that we call planets, stars, and galaxies. The rest is far more dilute and consists of interstellar gases and dust. And quite a lot of it is in the form of massless photons. So the question naturally arises: where did all this stuff come from? Doesn't it require a massive input of energy right at the beginning that violates the law of conservation of energy (also known as the first law of thermodynamics), one of the bedrock principles of science? The answer is simple: No.

The total energy of the universe consists of the energy due to the motion of all the particles (called kinetic energy), the energy that is stored because of the gravitational forces between the particles (called potential energy), and the energy associated with the mass of all the particles (usually referred to as rest energy).

The key feature to bear in mind is that the gravitational potential energy is a negative quantity. You can see this by realizing that in order to separate two objects, one has to overcome the attractive gravitational force and this requires one to supply positive energy from outside. This is why launching satellites into space requires such huge amounts of positive energy supplied by fuel, in order to overcome the negative gravitational potential energy of the satellite due to the Earth's attractive force.

This negative gravitational potential energy exactly cancels out the positive energy of the universe. As Stephen Hawking says in his book A Brief History of Time (quoted by Victor Stenger, Has Science Found God?, p. 148): "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." In other words, it is not the case that something came out of nothing. It is that we have always had zero energy.

Alan Guth, one of the creators of the inflationary universe model, points out that the fact that "in any closed universe the negative gravitational potential energy cancels the energy of matter exactly" has been known for some time and can be found in standard textbooks. (See The Classical Theory of Fields by L. D. Landau and E. M. Lifshitz, second edition, 1962, p. 378-379.)

But what made the universe and all its mass come into being at all? The suggestion is that the universe began as a quantum fluctuation of the vacuum. It used to be thought that the vacuum was truly nothing, simply inert space. But we now know that it is actually a hive of activity with particle-antiparticle pairs being repeatedly produced out of the vacuum and almost immediately annihilating themselves into nothingness again. The creation of a particle-antiparticle pair out of the vacuum violates the law of conservation of energy but the Heisenberg uncertainty principle allows such violations for a very short time. This phenomenon has observable and measurable consequences, which have been tested and confirmed. (The Inflationary Universe, Alan Guth, 1997, p. 272)

Guth says (p. 12-14, 271-276) that the person who first suggested that the universe and its associated space may have originated as a quantum fluctuation was Edward Tryon in 1973 in his paper Is the Universe a Vacuum Fluctuation? (Nature, vol. 246, p. 396-397, 14 December 1973.) As Tryon says in that paper:

In any big bang model, one must deal with the problem of 'creation'. This problem has two aspects. One is that the conservation laws of physics forbid the creation of something from nothing. The other is that even if the conservation laws were inapplicable at the moment of creation, there is no apparent reason for such an event to occur.

Contrary to widespread belief, such an event need not have violated any of the conventional laws of physics. The laws of physics merely imply that a Universe which appears from nowhere must have certain specific properties. In particular, such a Universe must have a zero net value for all conserved quantities.

To indicate how such a creation might have come about, I refer to quantum field theory, in which every phenomenon that could happen in principle actually does happen occasionally in practice, on a statistically random basis. For example, quantum electrodynamics reveals that an electron, positron and photon occasionally emerge spontaneously from a perfect vacuum. When this happens, the three particles exist for a brief time, and then annihilate each other, leaving no trace behind.

If it is true that our Universe has a zero net value for all conserved quantities, then it may simply be a fluctuation of the vacuum, the vacuum of some larger space in which our Universe is imbedded. In answer to the question of why it happened, I offer the modest proposal that our Universe is simply one of those things which happen from time to time.

Note that our universe likely came into being with just a tiny amount of matter. But after that initial fluctuation triggered the start of the universe, what caused the avalanche that created the massive amount of matter that currently comprise our universe? The inflationary model of the universe takes care of that problem too, although the explanation is a little technical. As Stenger says (p. 148):

[I]n the inflationary scenario, the mass-energy of matter was produced during that rapid initial inflation. The field responsible for inflation has negative pressure, allowing the universe to do work on itself as it expands. This is allowed by the first law of thermodynamics.

In other words, no energy was required to "create" the universe. The zero total energy of the universe is an observational fact, within measured uncertainties, of course. What is more, this is also a prediction of inflationary cosmology, which we have seen has now been strongly supported by observations. Thus we can safely say,

No violation of energy conservation occurred if the universe grew out of an initial void of zero energy.

In the first century BCE, the Greek philosopher Lucretius wrote that "Nothing can be created from nothing" and this assertion exerted a powerful influence over subsequent philosophers. For a long time, science just did not have a good explanation for the existence of all the matter in the universe and it was assumed that the existence of matter was just a given, an initial condition that we just had to accept and proceed from there. Religious people seized on this "How can something come out of nothing?" question to try and argue that the very existence of the universe violated of the law of conservation of energy and implied the existence of a creator who can violate such laws. In other words, it was a Deep Mystery that science has no explanation for and that could only happen by the will of a creator.

But the hope of religious people that they had finally found a safe niche for god where he no longer risked being flushed out by those pesky scientists has been dashed, just like all the other similar hopes of the past. The creation of the universe does not violate the law of conservation of energy. God is once again found to be superfluous.

Next: Does the universe violate the second law of thermodynamics?

POST SCRIPT:Baby Jesus prayer

From Talladega Nights.


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Mano - thanks for this series; it is very thought provoking and it has raised a number of questions that perhaps you can answer. I also have some speculation and wonder whether it has been considered (I assume it has; minds greater than mine have been pondering this).

What is space? It is not nothing - it can expand, it can be bent by mass. That expansion can exert force - it is dragging whole galaxies away from us. How does it exert this force?

When space expands, is there more space created, or is space stretched, like an elastic band? If the latter, is there the potential for 'snap back', so rather than a forever expanding universe, it will actually start contracting some day?

It seems to me that there is two types of motion - one relative to space (local motion caused by gravitational effects, for example) and one with space (the movement of the raisins as the dough expands). How do these two types of motion interact to give us what we observe? For example, space would not only be expanding on the cosmological scale; it must also be expanding at the quantum level. The space between nucleus and electron must be expanding - I assume nuclear forces are stronger and therefore the electron doesn't move away in the same way, but this is a form of local motion, even if the nucleus is 'at rest'.

At the molecular level, the expansion of space would be acting to pull them apart; something must be holding them together. The space that makes up most of me must be also expanding, trying to drag my matter along - nuclear forces, gravity (?) holds me together?

I don't know if I expressed this clearly, but essentially, if all matter was dragged along with the expansion of space without something resisting it, then everything would be expanding, which means the universe would appear as if it was static. Since it isn't, the Universe is expanding, but I am (thankfully) staying the same size, if you overlook some excessive eating from time to time!

The rate of expansion is accelerating. What is driving this acceleration? Was it initially very fast, slow down and is now accelerating again? Remember in the first three minutes the universe went from a point to 50 light years across (I don't quite know how to reconcile this with a borderless, infinite flat universe - perhaps our universe is simply a locii of expanding space in a sea of space in various states of expansion/inflation/collapse, as suggested by this post). So are we now going faster than 50 light years per three minutes, or did we slow down from this rapid expansion and are now speeding up?

The universe is zero energy, because of balancing potential energy (caused by gravity) against all the other types of energy. Is there any relationship between the expansion of space and all this potential energy? That is, gravity is the local motion working against the 'raisin' motion, thus creating potential energy and thus balancing out the energy sum of the universe?

Ummm...that is not all, but I will stop here. Thanks again for this, it is extremely educational.


Posted by Bill on March 31, 2010 03:53 AM


In response to your first set of questions, you have to realize that the properties of space in the absence of matter cannot be investigated. It is matter than enables us to infer the properties of space So all we see is matter expanding or contracting.

As for the sizes of things, these are determined by the forces holding them together and these are unaffected by the expansion of the universe. So an atom will stay the same size. If they are free particles with no forces between them, then the distance between them will expand along with the expansion of space.

It is believed that within the first minute there was an extraordinary rate of expansion driven by what is known as a 'false vacuum' and then the rate slowed down to the current rate of expansion which is accelerating due to the presence of dark energy which creates a negative pressure acting outwards. All this is pretty technical stuff which I myself can barely get a grip on!

Posted by Mano on March 31, 2010 04:35 PM