Big Bang for beginners-14: Does the Big Bang theory violate the second law of thermodynamics?

(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.

In the previous post, I showed that the creation of the universe does not, as is sometimes thought, violate the law of conservation of energy, otherwise known as the first law of thermodynamics.

Another supposed problem that disappears under close examination deals with entropy. Entropy is a quantity that has a precise definition in science but whose meaning has not become as familiar to the layperson as other scientific terms like energy. It can be loosely related to what we call the level of disorder or the loss of information or the amount of ‘useless’ energy (i.e., energy that cannot be utilized to perform work). So for example a system that is more disordered (a sock drawer in which the socks have been unceremoniously dumped) has a higher entropy than an ordered system (where the socks are neatly arranged in matching pairs.) Similarly a state in which information decreases or the amount of useless energy increases can be said to be a state in which entropy in increasing.

The second law of thermodynamics says that the entropy of a closed system must either increase or stay the same. It cannot decrease. Any closed system (i.e., one in which no energy is allowed to enter or leave) that is left to itself will approach an equilibrium state, its entropy increasing until it levels out at the maximum value once equilibrium is reached. So for example, if you take a closed container of (say) helium gas into a closed room and open the lid, the helium that was at that instant just in one region of the room (a state of partial order) will approach equilibrium by diffusing until it occupies the entire room, at which point the disorder is greatest and entropy is maximum.

The second law of thermodynamics is considered to be inviolate on a macroscopic scale and is what rules out the possibility of creating perpetual motion machines. As Arthur Eddington, famous for his experiment testing Einstein’s theory that light could be bent by gravitational fields, said in his 1927 Gifford Lectures (The Nature of the Physical World (1928), p. 74.)

If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

The Big Bang seems, at first glance, to violate the second law. It starts off as a dense almost perfectly homogeneous gas (thus at almost maximum entropy) and then seems to separate into clumps that formed stars and galaxies. Hasn’t order increased and thus the entropy decreased, and since the universe is a closed system, hasn’t this violated the second law?

The solution here is that because the universe is expanding it keeps getting shifted out of equilibrium, and in the drive to reach a new equilibrium state, you can get pockets of order occurring without violating the second law, because the maximum allowable entropy also keeps increasing.

Back to our helium example, even after the gas has completely occupied the room, if we now increase the volume of space available to it by opening the door that connects to an adjacent room, then the gas is now suddenly in partial order again because it is in only one part of the total space allowable to it. It is thus far from equilibrium and needs to start diffusing again to reach the new equilibrium where it uniformly occupies both rooms. In other words, its entropy increases even though it was at maximum entropy before the door was opened. This happens because the increasing volume accessible to the gas also increases the maximum entropy available to it.

In more technical terms, if we consider the universe to be a sphere of radius R that is increasing, the maximum allowable entropy increases as the square of R, while the actual entropy of the universe increases less rapidly, only linearly with R. Thus even if the initial universe was at maximum entropy for its size, as the universe expands its entropy can increase while still being easily able to accommodate the increasing order we see. In fact, calculations done assuming that there exist ten planets per star, 100 billion stars for every galaxy and 100 billion galaxies (which are our best current estimates) show that the ordering of the planets produces changes in entropy of only one part in 1011 of the total current entropy. Victor Stenger (Has Science Found God?, 2003, p. 152) summarizes the situation:

No violation of the second law of thermodynamics was required to produce the universe.

I don’t want to give the impression that these explanations are the last word on the subject and that all the problems are solved. Entropy is a tricky concept and there are disagreements (as is usually the case with research at the frontiers) on how to calculate it for the early universe. For example, some argue that the maximum allowable entropy of the universe remains constant even as the universe expands, and that the reason that the entropy can increase is because it started out with a small value at the Big Bang, well below the maximum. So the second law of thermodynamics is not violated in this case either.

The point is that blanket statements that the Big Bang violates the first and second laws of thermodynamics, and thus the only explanation is that it is due to the actions of a creator, are simply not true.

Next: The essential tension in science – puzzle or paradigm shift?

POST SCRIPT: Mr. Deity and Eve

The Bible never warned us that she was such a ditzy drama queen.

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.

Big Bang for beginners-12: Measuring the rate of expansion of the universe

(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.

We seem to be living in a runaway expanding universe. Given that we are confined to such a tiny region of what seems like an infinite space, how can we know so much about it? It is indeed a tribute to the doggedness of the scientific endeavor that we can investigate the universe so methodically and tease out answers to questions that at first glance might seem hopelessly out of reach. In this post, I want to give some further background about how we have figured out some of this information.

For example, how do we know the speeds of distant galaxies? The speed with which a distant galaxy is receding from us can be obtained from something called the ‘red-shift’ of the light emitted by it.

To understand how that is done, we first need to know that each element (hydrogen, oxygen, or whatever) emits a characteristic pattern of wavelengths of light (denoted by the symbol λ) that is unique to it and can be measured in the laboratory. So by observing the pattern of wavelengths emitted by a star we can tell what elements that star contains. If the universe is expanding (or contracting), then between the time that the light was emitted by that distant star and the time it reaches us, space would have expanded (or contracted) and the wavelength of the light would have also increased (or decreased) because of the expansion of the space. This difference Δλ=λ(received)-λ(emitted) tells us, if it is a negative number, that the star is ‘moving’ towards us (i.e., space is contracting) or, if it is a positive number, that it is ‘moving’ away from us (i.e., space is expanding). In the former case, the light is said to be ‘blue-shifted’ and in the latter case, it is ‘red-shifted’. The size of Δλ tells us the rate at which the space is changing.

The shift is usually measured by the quantity z, obtained by dividing the change in the wavelength of the light by the wavelength of that same line as measured in the laboratory. i.e., z=Δλ/λ. So for example if we measure a spectral line for a given element in the laboratory to be 630 nm (λ) and we measure the same line from a distant star and find it to be red-shifted to triple its value (1890 nm), then Δλ=1890-630=1260 nm and hence z=1260/630=2.0.

If space is stretched in a short interval of time, then the increase in separation distance of two objects embedded in space will be proportional to the distance separating them, as can be seen by our old raisin bread analogy. So the speed of separation v (obtained by dividing the increase in separation distance by the time taken) will also be proportional to the separation distance d for the two objects. This gives Hubble’s law, that the speed v of a receding galaxy is related to its distance from us by v=Hd, where H is the constant of proportionality and is called the Hubble constant. (See this paper titled The redshift-distance and velocity-distance laws, Edward Harrison, The Astrophysical Journal, 403:28-31,1993 January 20.)

If the rate of expansion of the universe is constant in time (i.e., H does not change with time), it can be shown that v/c=z (where c is the speed of light), so measuring z gives us the value of the recessional speed v. Note that z can be greater than 1, so we can have speeds that are greater than the speed of light. This is not a violation of the laws of relativity because the speeds we are talking about are the speeds due to the expansion of space and there is no limit to that. It is the local motion of objects relative to space that cannot exceed the speed of light. (Note: There are different ways of defining time and distance (and hence velocity) for the expanding universe. But while these may give different values of each quantity, the basic idea holds that recessional speeds due to the expansion of space can exceed the speed of light.)

Measuring the distance to distant galaxies is much more difficult (which I will not go into) but it can be done, though it has higher uncertainties associated with it, By obtaining the values of z (and hence deducing v) and d for a large number of distant galaxies and plotting the straight-line graph with v on the vertical axis and d on the horizontal axis, we can obtain the value H from the slope of the graph.

Note that although we refer to H as the Hubble ‘constant’, what that means is that we use the same value for all the observable objects at one particular time. It is possible that the value of H is changing with time. If so, at a different age of the universe, the speeds of separation may be more or less, and for each of those times we would have to (in theory) calculate the value of the Hubble constant from the slope of the graph, though we cannot do so directly in practice because the only time we have is now, so we have to infer its variation from theory. But since the value of H can vary with time, the value for the present time is customarily written as Ho.

If the recessional speed v of any given galaxy has been constant over the age of the universe (i.e., the space of the universe has been expanding at a steady rate), and if all the galaxies started out together at one point in space, then v=d/T, where d is the current separation distance and T is the age of the universe. Hence by combining this with v=Hd we get the simple relationship that T=1/H. So measuring the Hubble constant as the slope of the v-d graph immediately enables us to obtain an estimate for the age of the universe. The current value of H is 2.37×10-18s-1, which gives an age of the universe that is 4.22×1017seconds or 13.4 billion years.

Of course, this result depends on the assumption that the speeds of all the galaxies have been constant over the age of the universe. If the rate of expansion has been slowing down so that the speeds in the past were greater than they are now, the actual age will be less than 13.4 billion years. If the expansion has been speeding up, then the age will be greater. The current best estimates for the age of the universe place it as 13.73 (+/- 0.15) billion years.

The measured value of the red-shift z also tells us when the light was emitted by the distant galaxy, as a fraction of the time that has elapsed since the Big Bang. i.e, as a fraction of the age of the universe. The relationship is a complicated one that depends on the relative domination of matter versus the cosmological constant in the universe. As a rough approximation for a flat universe, this fraction is given by 1/(1+z)3/2. So in the case of a star or galaxy that has the value of z=2.0, this fraction works out to 0.192. If we take the age of the universe as 13.7 billion years, the star must have emitted its light 2.6 billion years after the Big Bang, or 11.1 billion years ago.

The current record for the highest observed red-shift is z=8.2 from an object known as GRB 090423, where GRB stands for ‘gamma ray burst’ and is believed to be emitted by a dying star. A value of z=8.2 corresponds to a source that emitted its light at about 1/28 the age of the universe or about 490 million years after the Big Bang. More precise calculations place the figure at 630 million years, so we are seeing something that happened almost at the beginning of our universe.

That’s all for the mathematical background (except for the post-script below). In the last few posts in this series, I will get back to the verbal descriptions.

Next: Where did all the stuff in the universe come from?

POST SCRIPT: The Doppler shift

At the risk of getting too much into the weeds of theory, I want to deal with an issue that is confusing about the cause of the galactic red-shifts.

The shift in wavelengths above was described as being due to the expansion of space itself. But the shifting of light wavelengths is normally associated with something called the Doppler effect that says that if a source of light and the detector of light are moving relative to each other in a fixed space, the wavelength of light measured by the detector will also be different from the wavelength of light emitted by the source. The main point to bear in mind with wavelength shifts due to the Doppler effect (when compared to the expansion of space itself) is that in this view, speeds can never exceed the speed of light.

If the source and detector are moving towards each other, the detected wavelength is shorter than the emitted wavelength (this is called a ‘blue shift’) while if they are moving away from each other, the wavelength gets longer (called a red-shift), which is similar to the effects due to the expansion of space.

In the case of Doppler shifts, the relationship of z=Δλ/λ to the speed v of the moving objects is given by

z=√[(1+v/c)/(1-v/c)] -1.

We can turn this around to get


So knowing the speed v, we can get z and vice versa. So for the above case of z=2.0, the speed of the galaxy is given by v/c=0.8 and thus the galaxy is moving at four-fifths the speed of light.

In the early days of cosmology, space was assumed to be fixed and the red-shift of distant galaxies was thought to be caused by the Doppler shift as they moved away in space. But now it is more common to say that the red shift is caused by the expansion of space, not the motion of objects in space, so the interpretation of z is different and its relationship to the recessional speed is different such that there is no restriction that the recessional speed be less than the speed of light.

So how do we reconcile these two views? If we want to think of the positions of galaxies changing with time, rather than space itself expanding and the galaxies fixed in space, then we can use the Doppler shift but we have to add to that the additional shift due to the photon traveling through a gravitational field on its way to us. If we do that, then the end result is the same in both cases. As cosmologist Edward Wright says:

This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views.

Big Bang for beginners-11: Relativity theory

(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.

So far I have been simply describing what the Big Bang theory says without giving much of the theoretical background. But Einstein’s General Theory of Relativity (like Darwin’s theory of evolution by natural selection) has had such a profound effect on our relationship with the rest of the universe that I feel obliged to give readers, at least for cultural purposes, a glimpse of what the theory is and why it is so powerful, even if it remains obscure in its details. So for the sake of greater completeness and for the benefit of those who want to know more, in this post and the next I will give some of the theoretical background to what I have been saying so far, and hope that even those who are averse to algebra will stick with me through it and get some of the flavor of how the theory works.

A word of caution, though. This is not my field so I cannot guarantee that this is error-free or state-of-the-art knowledge. My goal here is to give a simplified understanding of how the important field of cosmology operates. In order to provide a narrative I will largely ignore the fact that this is a field in which there are spirited debates and disagreements over many of the details. I strongly recommend reading more authoritative works by real scholars in the field for a more complete understanding of all the alternative points of view.

The basic paradigm that the field of cosmology operates under is Einstein’s General Theory of Relativity which generates the Einstein Field Equations:

Rij – (1/2)Rgij = (8πG/c4)Tij – Λgij

Without worrying too much about what each individual term means, the main idea is that the terms on the left of the equal sign (Rij and R) represent the curvature of space while the terms on the right (Tij and Λ) represent the mass and energy in the universe that causes this curvature. The quantity Tij is called the stress-energy tensor and in it is contained all the information about how all the mass and the ‘normal’ energy (i.e., excluding dark energy) is distributed throughout all space. Λ is what is called the cosmological constant and determining its value that has been the source of all the excitement within the last two decades. The quantity gij is called the ‘space-time metric’ and defines how space and time are related. So the above equation represents the fundamental relationship between the mass-energy of the universe and the curvature of space.

G is the universal gravitational constant and c is the speed of light and since these are such fundamental and important quantities, they have been measured with great precision and are found to have the values G=6.67×10-11Nm2/kg2 and c=3×108m/s. (For the most up-to-date and comprehensive compilation of data, see the work of the Particle Data Group at Lawrence Berkeley Laboratory, which has a section on astrophysics and cosmology that contains a very useful data table.)

If we treat the universe on a large enough scale as if all the mass and energy is homogeneously spread out (like a uniform gas or liquid) and ignore the clumping on small scales that make up the stars and planets, the equation above simplifies considerably by mathematics standards, although it is still difficult to solve. In that case, Λ is related to the density of the energy (ρΛ) of the ‘vacuum’ by Λ=(8πG/c2Λ, and it is this vacuum energy that is referred to as dark energy and is driving the accelerating expansion of the universe. The vacuum of space used to be considered as inert ‘empty’ space, but that is no longer the case.

The total energy density of the universe ρ is thus made up of what we might call matter density ρM (comprising regular matter such as protons, electrons and the like, plus electromagnetic energy and dark matter), and the energy density associated with dark energy. i.e., ρ=ρM&Lambda.

The critical density ρc that we encountered earlier and that determines the curvature and ultimate fate of the universe is something that we can calculate theoretically and is given by the expression ρc=3H2/8πG, where H is the Hubble constant (more about this and how it is measured in the next post). So &Omega=ρ/ρc, where Ω>1 gives us a positive curvature and a universe that will eventually stop expanding and start contracting, Ω<1 gives us an open universe that will expand forever, and Ω=1 gives us a flat universe that will also expand forever.

Hence &Omega = ρ/ρc = (ρM + ρ&Lambda)/ρc = ΩM + ΩΛ,

where ΩM = ρMc and ΩΛ = ρΛc.

The results obtained from the WMAP satellite say that the density of our universe is currently exactly equal to the critical density thus making Ω=1.0, and is made up of 4.6% ‘ordinary’ matter and energy, 23.3% dark matter, and 72.1% dark energy. This means that our current best estimates are that ΩM=0.28 and ΩΛ=0.72.

Note that since we know the values of G and H (more on this in the next post), the value of the critical density ρc=3H2/8πG can be calculated and it works out to be 1.0×10-26kg/m3. This is an extremely small number reflecting the fact that the universe is mostly empty space. This highly dilute distribution is one major reason why it is not easy to directly detect things like dark matter and dark energy.

When it comes to calculating the total energy density of the universe, the dark energy is added up with the other energies from ordinary matter and dark matter. But unlike those other forms of energy, its effect on cosmic expansion is to push outwards and increase the rate of expansion of the universe, and not pull on it and slow it down.

In those particular inflationary models that assert that Ω will always equal 1.0 for all time, since ΩM gets less as the universe expands and gets more dilute, the value of Ω&Lambda must increase with time to keep Ω=1, so that the outward pressure will ultimately win out over the gravitational attraction. In this model, we live in essentially a runaway expanding universe, with everything moving away from everything else with increasingly rapid speeds.

In fact, these theories suggest that the universe is expanding so rapidly that galaxies are disappearing from sight over the far horizon so we will see less and less of them as time goes by. So if we had happened to come along a hundred billion or so years later than we did, the only things we would see in the night sky would be the merged result of own Milky Way and the Andromeda galaxy, which are predicted to collide in the future. The sky would be really boring because the rest of the sky would be dark and people would have thought that there was nothing else in the universe. We would not have had the vast amounts of observational data that we have now that enable us to learn so much by making all these great inferences.

Lucky us!

Next: Measuring the universe.

POST SCRIPT: Mr. Deity has a better equation than Einstein’s one

Big Bang for beginners-10: The cosmological constant

(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.

To understand what is going on with dark energy, we need to look at something called the cosmological constant.

Einstein’s General Theory of Relativity, when expressed as equations in their most general form, contains a constant term (called the cosmological constant) whose value is unspecified by the theory itself but influences how the universe evolves with time. A positive value for this constant would have the effect of acting like an outward pressure trying to ‘push’ the universe apart, counteracting the gravitational attraction that is trying to pull it together. A zero value would do nothing, leaving gravity as the only (attractive) force. A negative value would be like a ‘pull’, adding to the attractive force of gravity.

There is nothing mysterious about such constants. Their appearance is common in scientific theories (they are sometimes called parameters) and their values are determined by experiment. Once the value of such a constant has been calculated using some data, it is fixed and the same value must be used in all applications of the theory which is why it is called a ‘constant’. For example, our normal everyday theory of gravity also has such a constant G called the universal gravitational constant whose value is found by measuring the size of the gravitational attractive force between two objects that have mass. But once that has been done for any two masses, the same value of G is used everywhere and ever after, which is why such constants are so important and thus measured with great care and precision.

When Einstein first used his General Theory of Relativity that he developed in 1915 to build a model of the universe, he too needed data to obtain the value of the cosmological constant. He, like most people of that time, assumed that the universe was static and so he gave a positive value for that term, choosing it to have such a value that its repulsive force would exactly balance the attractive gravitational force. This choice gave him the static universe solution he thought he needed to get, although it was soon pointed out that the static solution he obtained was unstable and thus problematic. (The Runaway Universe, Donald Goldsmith (2000), p. 12)

The catch with the cosmological constant term lay in trying to interpret its physical meaning. Its behavior in the equation is like that of an energy density and giving it a positive value implied that the universe was filled throughout with something that had the same units as energy. But it could not be the same kind of massless energy that we are familiar with (which is electromagnetic) since we know how to detect that and this new form of energy (like dark matter) seemed to be invisible to us, except for its large scale gravitational effects.

Einstein’s Special Theory of Relativity had just a decade earlier convinced scientists to abandon belief in the ‘ether’, which had for a long time been assumed to exist and to also permeate all of space while remaining undetectable. So one can see why people would be wary of introducing a new substance with ether-like elusiveness that might also turn out to be spurious. So having a non-zero cosmological constant term, while not violating any laws, was not something people at that time were particularly happy with and it was tolerated simply because there seemed to be no other way of obtaining a static universe.

Fortunately, the problem seemed to go away by itself. When around 1930 it was realized that the universe was not static but expanding, the need for a cosmological constant disappeared and it was assigned the value zero, in essence removing it from the equations. The theory of gravity that emerged resulted in an expanding universe solution, but one whose expansion was slowing down due to the unopposed gravitational attraction of the rest of the universe. It is like the way that a ball thrown upwards slows down because of the gravitational attraction of the Earth below it.

This remained the standard model until recently. But measurements made in 1998 of the speeds of distant galaxies and supernovae (which consist of massive stars exploding at the end of their lives and becoming so extremely bright that they can be seen at immense distances) suggest that rather than slowing down due to this gravitational attraction, those distant objects are actually speeding up. We seem to be living in a universe whose rate of expansion is increasing, not decreasing.

The emergence of observations supporting both a flat and accelerating universe has brought the cosmological constant back into the spotlight. It turns out that one can explain both these features by adding the cosmological constant back into the equations governing the laws of gravitation and giving it a positive value. But this once again raises the question of the physical meaning of this term. Since it behaves like an energy density, some scientists have postulated that in addition to dark matter (invoked to explain the otherwise anomalous behavior of the stars in spiral galaxies), the universe must also contain vast and uniform amounts of something they call ‘dark energy‘ that we have not as yet been able to detect directly.

This dark energy is even more mysterious than dark matter. Like the electromagnetic energy associated with the photon that I discussed earlier, it may have no mass but it cannot be the same kind of energy as that because we are familiar with that form of energy and know its properties well and so would be able to identify its presence easily. So if dark energy exists, it must be a new kind of energy.

If we take the dark matter and dark energy hypotheses at face value as the explanations for the spiral galaxy and the flat and accelerating universe problems, then the results provided by the WMAP satellite has made highly precise measurements of them possible. The best current estimates are that the Universe today is made up of about 72.1% dark energy, 23.3% dark matter, with the remaining 4.6% being all the other matter that we are familiar with and know exists.

Next: Some background on dark energy, how it acts, and where it originates.

POST SCRIPT: Why don’t we have more advertisements like this?

John Cleese shows us how it might be done.

Big Bang for beginners-9: Dark 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.

In addition to the appearance of dark matter, another interesting development arose when observers tried to determine the curvature of the universe, an important fact in determining the ultimate fate of the universe.

To understand this consider, as an analogy, a ball thrown upwards from the surface of the planet. It will slow down as it goes up due to the gravitational attraction of the planet’s mass. But will the ball eventually fall back to the ground or will it escape from the planet and go on forever? The answer depends on both the speed of the ball and the size of the planet. For a given speed of the thrown ball, if the mass of the planet is below a certain value, its gravitational pull on the ball is not sufficient to bring it back and the ball will escape and travel out in space forever.

The same feature holds for the universe. We currently know the speeds of the galaxies as they move apart form each other. We know that the gravitational field of the other galaxies is trying to slow them down. Whether the expansion eventually stops and the universe starts collapsing again or whether the expansion of the universe goes on forever depends of the combined mass of all the other galaxies, or more precisely, the density of the universe. And in turn, the density of the universe determines the shape of the universe.

If the density of the matter in the universe is below a certain value that we can calculate (called the ‘critical density’), the standard Big Bang theory predicts that the universe curves at every point in the shape of a saddle (called negative curvature) and will expand forever.

If the density of the universe is greater than the critical density, theory predicts that the universe curves the opposite way like a sphere (called positive curvature) and will stop expanding at some point and then start to collapse back into itself, like a thrown ball falling back to Earth.

Curved space.jpg

Thus the ultimate fate of the universe is dependent on the curvature of the universe, which in turn is directly related to whether the actual density is greater or less than the critical density. The ratio of the actual density to the critical density is given by the Greek letter Ω and if this quantity is greater than 1, the universe is said to be closed (finite), if it is less than one it is said to be open (infinite and saddle shaped), and if it is exactly equal to one, it is said to be flat (and infinite). This figure from a NASA website provides a visualization by analogy with 2D space.

So clearly, knowing the curvature of the universe would give us important information about the ultimate fate of the universe. There are two ways to do this: measuring the density of the universe, calculating Ω, and thus inferring the curvature as above, or by directly measuring the curvature itself. Measurements of all the visible matter in the universe seems to indicate that the density of the universe is well below the critical density, signaling a saddle shape, and that we will have perpetual expansion. Even adding in all the postulated dark matter still gives a density that is only about 20-40% of the critical density.

But it is also possible to directly measure the curvature of space. How does one directly measure the curvature of space while living within that space? An analogy with the Earth may help. We currently live on the surface of the Earth. People have known for more than two thousand years that the Earth was a sphere. For most of that time, they inferred it indirectly, by observing eclipses, ships sinking over horizon, and so forth. In more recent times people have had direct confirmation for its spherical shape as a result of having circumnavigated the globe and viewed the Earth from outer space.

But it is theoretically possible for someone to determine the curvature of the Earth even if they never leave their living room or look outside, provided they have very precise measuring instruments. All they would have to do is draw a triangle on a sheet of paper that is laid flat on the ground (as shown in the figure), measure the three angles, and add them up. As all students are told, the total should be 180 degrees. But what many don’t know is that this result is a very special case that only occurs if the sheet of paper is flat.

If the surface of the Earth is curved into a sphere (and the sheet of paper follows that curvature), the sum of the angles will be greater than 180 degrees. You can easily see that this is true by imagining that we could draw a triangle large enough that one of its vertices is the North Pole and the other two vertices are on the Equator. We see that the two angles formed at the equator are each 90 degrees, which means that the sum of the three angles must be greater than 180 degrees. If the surface of the Earth had been saddle-shaped, the sum would be less than 180 degrees. The sum of the angles of a triangle drawn on a small sheet of paper would differ from 180 degrees by only a tiny amount, which is why you need precision instruments to measure the curvature of the Earth’s surface this way.

To directly measure the curvature of space in an analogous manner, a satellite called the Wilkinson Microwave Anisotropy Probe (WMAP) was launched in 2001 and the surprising result that it returned (with an astoundingly low 2% margin of error) was that the universe is neither saddle shaped nor spherical but flat, which meant that Ω=1 and hence the density of the universe must be almost exactly equal to the critical density. The unlikely coincidence of the actual density being equal to the critical density cries out for an explanation.

The ‘inflationary model’ of the universe, which is an add-on to the standard Big Bang theory, says that the very early universe underwent an extraordinarily rapid expansion within a tiny fraction of the very first second of life of the universe. This theory has gained widespread acceptance because a ‘flat’ universe would be an outcome, in addition to also solving what is known as the ‘horizon’ problem, which I will not go into.

So assuming that the universe is indeed flat, what is the source that is making the density of the universe exactly equal to the critical density? The solution that has been proposed is that space is filled with something called ‘dark energy’ that fills the entire universe (dark matter is assumed to only be present in galaxies) and this provides the amount of energy needed to make the universe flat.

But what is this new form of energy? And where did it come from?

Next: The cosmological constant and dark energy.

POST SCRIPT: Crazy health care opponents

I have not been writing recently about the health care issue even though it is important because a lot of recent activities was pure theater, mainly posturing and parliamentary maneuvering. But I will get back to it after the Big Bang series ends.

But what amazed me watching the process unfold me was the irrational and over-the-top rhetoric that was being thrown around by reform opponents. This video clip of the people at the demonstration last weekend gives a taste of the ignorance and selfishness prominently on display.

Big Bang for beginners-8: Star formation and dark matter

(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.

In the study of our universe so far, one fact becomes resoundingly clear. Humans occupy a tiny volume of the universe. All our scientific theories have been discovered using data that has been generated within that volume. What gives us the confidence that these same laws can be applied to distant regions as well? One answer is that we have no choice but to make that assumption. Another is that when do make such an extrapolation we get a reasonably satisfactory understanding of the behavior of distant stars and galaxies, thus justifying our decision.

But perhaps the most important reason is the Hubble result discussed earlier, that every distant galaxy is moving away from us with a speed that is proportional to the distance from us. This could only happen if either the Earth occupied a privileged place in the universe or if the universe was such that there is no such privileged place at all and every point in the universe is equivalent. The former option has been abandoned ever since the Copernican revolution. Since the location of the Earth is no different from any other point, the laws we discover here must be the same laws that apply everywhere.

This leads to what is called the Cosmological Principle, the idea that the universe is homogenous (i.e., is the same irrespective of which point in the universe we may happen to find ourselves in) and isotropic (i.e., looks the same irrespective of which direction in the sky we choose to look). But it is not assumed that the density of the universe is a constant in time, which distinguishes it from the Perfect Cosmological Principle that led to the Steady State theory. In fact, the Big Bang theory explicitly argues that the universe is continuously expanding and getting less dense as it does so.

Of course, the homogeneity and isotropy of the universe is true only on a large enough scale. On small scales, we see all kinds of non-uniformities. After all, most of space is empty with just a few pockets of dense matter consisting of stars, planets, and galaxies. For example, there is no planet like Earth anywhere near us, and when we look out at the night sky, the direction that contains the plane of our local galaxy (the Milky Way) looks very different from what we see when we look in other directions.

Furthermore, even on a large scale, the universe cannot be perfectly homogenous and isotropic because that would not have allowed for the matter that existed at the time of the Big Bang to eventually separate into the clumps that eventually led to stars and galaxies. In order to explain star formation, cosmological theories predict that the early universe must have had slight inhomogeneities and that there should be visible traces of this history. If we look out into the universe and measure its temperature in all directions, there should be very slight variations in temperature, of the order of one part in a hundred thousand. The Cosmic Microwave Background Explorer (COBE) satellite was launched in 1989 to investigate this and its results released in 1992 found just this variation, further supporting the Big Bang theory. In the image below, the changes in color show the minute temperature variation of the cosmic microwave background radiation, which corresponds to the density variation.


Although the Big Bang cosmological theory has been very successful, along the way some problems have arisen that have led to interesting developments. One problem was with the motion of stars on the outer edges of rotating spiral galaxies. If we apply established theories of gravity and assume that all the mass in the universe is what we can ‘see’ (i.e., matter we are already familiar with and can be observed by our detectors because they emit electromagnetic radiation), then we can calculate the speeds those stars should have. But the pattern of speeds that were observed does not agree with those predictions. The problem can be solved if we assume that there exists matter that we cannot see, i.e., matter that is outside the detection range of our detectors, although it still exerts gravitational forces since it has mass. For this reason, this new form of matter has been given the name ‘dark matter’.

This so-called ‘dark matter’ has still not been directly detected but fairly strong circumstantial evidence has convinced most physicists that it should exist and that there is a lot it around. The amount of dark matter present is currently estimated to be about five times the visible matter that we know about and can see. Of course, if it is the dominant form of matter in the universe, then it becomes vital that we learn more about it and major efforts are underway to try and detect it. The difficulty with this endeavor, of course, is that while this dark matter may consist of things that we are familiar with (such as dust grains, nuclei, and small rocks), it is also quite possible that this matter consists of entities unlike anything that we have encountered before. So we are in a very real sense searching in the dark, not really knowing what we are looking for, how we should look, and how we will know if we have detected it. All we really know is that there seems to be a hell of a lot of it.

But that is just the kind of puzzle that scientists relish and major efforts are currently underway to solve it.

Next: If the dark matter puzzle isn’t enough to keep scientists busy, we now have dark energy.

POST SCRIPT: Honoring death wishes

From That Mitchell and Webb Look.

Big Bang for beginners-7: What lies beyond the edge of the universe?

(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.

The idea of an infinite space that has always existed and in which everything else just moves around seems intuitively reasonable, at least to those who are comfortable with the concept of infinity. But the idea that there is no edge or boundary to the universe is much harder to grasp.

Going back to our raisin bread analogy, asking the question “What is beyond the edge of the universe?” is akin to asking what exists outside the space occupied by the dough. The answer is that there is no space outside the dough. The dough is all the space there is. This is where the raisin bread analogy starts to be misleading because we cannot help but view the dough as expanding inside the space of the oven, and it is hard to eliminate that unwanted extra image of oven walls. (If we wish, we can envisage a small portion of the dough and speak of the boundary of that portion alone, but that is not the boundary of space as a whole. It would be like speaking of the boundary of our Solar System or the Milky Way galaxy.)

To try to shake ourselves of the idea that the universe must have an edge (and center), let us try another analogy and imagine the old days when people thought the Earth was flat. A couple of natural questions for them would be to wonder where the center of the Earth was and what lay beyond the edge. There are three ways in which questions about center and edge become meaningless, as illustrated in the figure on the right which is taken from a NASA website.

Curved space.jpg

One is the bottom figure in which the flat Earth extended to infinity, so that there is no edge and no way to determine where the center is, since the location of the center of any object (such as a circle or sphere or anything else) is dependent on its relationship to the boundary of the object. No boundary means no center.

The second way to eliminate the edge and center as meaningful concepts is if the Earth is neither flat nor infinite in size but curved into a sphere, like the top figure. The idea of a center and an edge becomes meaningless here too. After all, what would it mean to refer to the edge of the surface of the Earth? Where on the Earth’s surface would a center be located?

There is also a third option for the Earth and that is that it is infinite but not flat. Instead it is like the middle figure which is shaped at every point in space like a saddle that curves downward in the side-to-side direction (where the rider’s legs dangle), curves upward in the front-back direction, and extends to infinity in all directions. (Apparently mathematicians have also been able to devise equations that represent a space that is saddle-shaped at every point but is finite. (The Runaway Universe, Donald Goldsmith (2000), p. 36.) But I have no idea if such a universe makes sense from a physical standpoint and am not going to consider it further.)

Which of these three models (spherical, saddle, or flat) was true of the Earth was an empirical question that was settled by careful observations and data. We now know that it is a sphere, or to be more precise, a slightly flattened sphere.

Something similar is true for the universe. Either it is infinite (either flat or saddle shaped) or it is finite in size and closed in on itself. All three shapes (flat, saddle, sphere) are analogous to the three possible options that we had for the Earth but much harder (even impossible) to visualize. Since we can see in three dimensions, visualizing a 2D surface as a sphere or flat or saddle-shaped is easy. But in the case of the universe, it is already in three dimensions and we cannot visualize how it curves. We can only deal with it mathematically. But the question of which one of these alternatives for the universe (infinite and flat, infinite and saddle, or finite) is one that can be answered by gathering relevant data. At present, our best estimate is that it is infinite and flat, a point I will return to in later posts.

If the universe is infinite and always has been infinite, what does it mean to say that the Big Bang started out as a ‘small’, highly dense and hot gas of quarks, gluons, electrons and photons? How can an infinite universe be small?

What is meant by ‘small’ in this context is that all the matter that now occupies the visible universe once occupied the small region that we identify as the space in which the Big Bang occurred.

Again we need an analogy to help us get a grip on this idea, though as with all analogies we must not take it too far because all analogies eventually break down. Think of a flat rubber sheet that extends to infinity. In a small region of the sheet, a Big Bang occurs that creates matter that is embedded in the rubber. If the sheet is then stretched in all directions (i.e., as space expands), the matter that is embedded will get pulled apart along with the sheet. So then instead of speaking of the absolute size of the universe at any time (the rubber sheet is and always has been infinite), we can meaningfully speak about by how much any given region of the sheet (i.e., the visible universe) has expanded since the Big Bang. (See here for a more thorough explanation.)

So even if the universe is infinite and always has been infinite, the visible universe that we can see could still have been concentrated in a small region in the distant past.

POST SCRIPT: Paralyzed by choice

Barry Schwartz talks with Stephen Colbert about why while some choice is good, too much choice can be bad, leaving people more dissatisfied.

<td style='padding:2px 1px 0px 5px;' colspan='2'Barry Schwartz
The Colbert Report Mon – Thurs 11:30pm / 10:30c
Colbert Report Full Episodes Political Humor Skate Expectations

Big Bang for beginners-6: The evidence

(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.

Why has the Big Bang theory become the standard model for understanding the origins of the universe? In the 15th century and earlier, most people thought that the Earth was the center of the universe and that the stars were embedded in a celestial sphere beyond the outer planets and that the size of the universe was not much larger than the Solar System. The Copernican revolution (with the publication of his book in 1543) displaced the Earth from the center of the universe. This led to suspicions that the universe could be very large, possibly even infinite, but there were at that time no good theories to explain its origins and structure.

Einstein’s General Theory of Relativity (published in 1915) provided a framework for building more systematic models of the universe and various theories began to be put forth. The initial ones argued for a static universe in which everything had a fixed and unchanging location. But some early data suggested that some galaxies were moving away from us and around 1922 models of an expanding universe were proposed, with some early suggestions that perhaps galaxies were moving away from us at speeds proportional to their distance from us. Soon after, observational data supporting that theory started coming in, most famously that of Edwin Hubble in 1929 that, while somewhat scattered, seemed to support that general idea.

If this steady movement away from us had been the case throughout all of time (a reasonable enough assumption in the absence of contradictory evidence), people inferred that if we looked back in time, then everything must have been closer to each other than they are now. And if we go back in time far enough, everything would have all converged to a single point. Thus was born the idea of a Big Bang, the basic idea of which was floated around as early as 1927 by Georges Lemaitre (a Belgian physicist who was interestingly enough also a Roman Catholic priest) and made concrete by George Gamow in 1948, along with the prediction that if this theory were true, the present temperature of the universe (as measured by the primordial photons left over from that initial state) would be around -268 degrees Celsius (5K).

At around the same time another theory called the Steady State was also proposed. This theory also assumed that the universe was expanding but that new matter was also being produced continuously to keep the density of the universe constant. The underlying idea behind this was something called the Perfect Cosmological Principle which said that the universe should look the same everywhere, in every direction, and at all times. This meant that the density of the universe should not change with time either. The amount of new matter that was needed to keep the density constant as the universe expanded was really small (about one hydrogen atom per cubic meter per billion years) but the key idea that the total matter in the universe was not constant made it radically different from the standard Big Bang model.

In 1964, the temperature of the universe was accidentally measured by scientists who had been looking for something else and was found to be -270 degrees Celsius (2.7K). This gave a huge boost to the Big Bang theory.

Another early prediction of the Big Bang theory was the relative abundance of light nuclei (hydrogen, helium, lithium), all of which depended on just one parameter, the total density of protons and neutrons at the time the nuclei were created. The measured values of the light nuclei are in good agreement with the predictions.

These successes added to the credibility of the Big Bang theory and pretty much eliminated the appeal of any competitors. The theory has since moved from strength to strength as scientists have used this basic model to make new predictions that can be tested. These later evidences include the large-scale structure of the universe and the evolution of galaxies, all of which are in reasonable, though not perfect, agreement with expectations.

There is one item about the evidence that I listed in favor of the Big Bang that might have puzzled some readers. I said that Edwin Hubble’s initial data and those that came later seemed to confirm early speculations that all the objects in the universe are moving away with speeds that are directly proportional to their distance from us. i.e., if galaxy A is moving away from us with some speed, then galaxy B that is twice as far away will be moving with twice that speed.

The question is why are they all moving away from us? Don’t they like us? Oddly enough, such an issue would not have been a problem to someone living in pre-Copernican times when it was thought that the Earth was the center of the cosmos. But with the Copernican revolution, it has become common to think that Earth does not occupy any special place in the universe. So wouldn’t you expect at least a few galaxies to be moving towards us since we are not located at a special place in the universe? How do we explain this?

Then explanation goes back to the crucial idea that it is space that is expanding as a result of the Big Bang. We need to go back to the raisin bread analogy from yesterday. If we view the dough as space and the raisins as the matter that is dragged along with the dough (space), then as the dough expands uniformly everywhere, it is easy to show that every raisin will be moving away from every other raisin and its speed will be proportional to its distance from that raisin. This is true irrespective of which raisin we choose as the vantage point from which to make measurements of velocity and distance.

The idea that no particular point in the universe has any special significance has been extended to what is called the Cosmological Principle, which asserts that when viewed on a large enough scale, the observed universe will look the same irrespective of where the observer might be situated. This implies that the laws of science will also be the same everywhere in the universe and underlies our belief that we can apply the same laws of physics that we have discovered to work so well in our neighborhood of the universe even to the most distant reaches of it.

Next: What about the edge of the universe?

POST SCRIPT: The Galaxy Song

From Monty Python and the Meaning of Life. It captures the sense of wonder at the amazing universe we live in.

Big Bang for beginners-5: Some conceptual challenges

(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 story of the Big Bang in its essence is quite simple and straightforward, it contains many fascinating subtleties that are worth exploring further. It is good to get some conceptual hurdles and misconceptions out of the way right now.

When we use the words ‘Big Bang’ it immediately conjure up certain images. We immediately think of familiar explosions, like bombs or firecrackers going off. We envisage a big noise and the exploding pieces hurtling away from the center of the explosion and spreading out into the surrounding space at great speed. This image captures correctly the idea of a hot compressed beginning with a fixed amount of matter spreading out through space and getting cooler and more dilute with time. But there are important ways in which the image is inaccurate.

One simple misconception is to think there was a loud noise at all. The very idea of sound at those huge densities is highly problematic and it is not helpful to think in those terms. But this is a minor misconception. The major misconception that people have is the idea that space always existed and extended all the way to infinity and that the Big Bang occurred in one small region of it and the matter that was created then spread out to fill increasing amounts of that pre-existing space.

What the theory actually says is that the only space that exists is the space occupied by the matter produced in the Big Bang and that, as the matter spread out, it did not fill already existing empty space, but instead it was space itself that was expanding, carrying the matter along with it.

To better understand this difficult idea, a good analogy is raisin bread baking in an oven. The raisins occupy more-or-less fixed positions in the dough. As the bread bakes, the dough expands, carrying the raisins along with it.

The wrong way to interpret this analogy to the Big Bang theory is to think of the dough and raisins as the matter expanding into the pre-existing space of the oven.

The correct way to view the analogy is to think of the bread dough as being space and the raisins as the matter. As the bread bakes, the dough (i.e., space) expands carrying the raisins (i.e., matter) along with it. The hard thing for people to grasp is that there is no space outside of the dough. There is no oven for the dough to expand into. So the ‘explosion’ we speak of is not of matter expanding into space but of space itself expanding.

In addition to the motion associated with the expansion of space, there is also what we call local motion caused by the forces between objects. So for example, Earth and the planets orbit our Sun under the influence of gravity, and our solar system rotates in the spiral arm of our galaxy the Milky Way, again under the influence of gravitational forces. Protons and neutrons in nuclei move under the influence of nuclear forces and electrons in atoms move under the influence of electromagnetic forces. All these motions are due to forces acting locally and not part of the motion caused by the expansion of space itself. Back to our raisin bread analogy, the raisins are not rigidly embedded in the dough. In addition to the raisins being dragged along by the expanding dough, they may also move around slightly in the dough due to (say) air pockets near them. But when we speak of the motion associated with the Big Bang, we are referring to the motion due to the expansion of space and not these local motions.

(It should be borne in mind that the well-known assertion that nothing can travel faster than the speed of light is popularly interpreted a little too broadly. That limit applies to the speed of particles and information flow. But there are things like the collapse of the wave function and the phase velocity of wave packets that occur at speeds greater than the speed of light. As I described yesterday, in the case of the early universe, space expanded at a much faster rate than the speed of light but that too is allowed by the theory of relativity. In other words, the dough can expand faster than the speed of light but the speed of the raisins relative to the dough has to be less than the speed of light.)

One consequence of the view that the Big Bang consists of space itself expanding is that it did not occur at a point ‘in’ space (like a blob of dough in an oven) but occurred everywhere in space simultaneously, and that it is space itself that was initially compressed. So it does not make sense to look for a point in the universe where the Big Bang occurred and treat it as the ‘center’ of the universe. There is also no ‘edge’ or boundary to the universe, so it does not make sense to ask what exists beyond the edge either.

I will come back to these last points later because they are undoubtedly hard to grasp, especially the idea about the absence of a boundary.

POST SCRIPT: Will Ferrell tries out for a part in West Side Story