Big Bang for beginners-16: Concluding thoughts

(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.

As is often the case when I am writing about something, I get a little carried away and the series seems to go on forever. But we have actually reached the last post in this series where I want to look at the broader implications of what all these scientific advances with the Big Bang theory means, particularly for religion. I hope that those who stuck with me through to the bitter end have obtained a deeper understanding than they had before.

Religious apologists often argue that the only or simplest solution to the question of what existed before the Big Bang and what caused the universe to come into being is god. They are wrong on both counts.

It is not the only solution because there is nothing deeply mysterious about the time at which the Big Bang occurred. It has been assigned the value of zero time but that choice is arbitrary, just as our calendar is arbitrarily numbered according to the legend of Jesus’s birth. We could just as easily have fixed the zero at some other time and said that the Big Bang occurred in the year 4760 or -9384.

There are theories about what could have existed before the Big Bang (see Has Science Found God? by particle astrophysicist Victor Stenger, chapter seven: The Other Side of Time) just as there are theories about how our universe came into being (chapter eight: The Laws of the Void). For example, one version of the multiverse theory says that as universes evolve, one can have small regions ‘pinching off’ (via the same kind of quantum fluctuation that created our universe) to create new universes. These things could have been going on forever and what we call the ‘beginning of time’ is simply the beginning of ‘our’ time, when our particular universe came into being. There is nothing more special to it than that.

It is true that these are more speculative theories than what we usually work with in science and will need more work and data before we can transform them into viable theories. When workable theories come into being, they usually bring along with them suggestions of what to measure and how to measure them to see if the theory has any merit. But the important thing to bear in mind is that our present universe is not some deeply mysterious entity whose existence and properties are baffling. As Stenger points out, there is a lot we do know already and all of it undermines the need for any supernatural agency:

We have seen that zero external energy was required to produce the mass and energy of the universe. We have seen that order can spontaneously arise from disorder. We have seen that complexity can evolve from simplicity. We have seen that time has no fundamental arrow, and so the very concept of cosmic beginnings and causal creation are problematical. No known scientific principles are necessarily violated in a model of our universe that is causally self-contained, in which everything that happens, happens within. (p. 188, my italics)

The origin of the universe is not a deep mystery. It is simply a puzzle that is already being scientifically investigated. What might have existed before the Big Bang is also being investigated, as is the question of why it has its current properties. So the idea that god is the only way to explain these things is simply incorrect. God is simply unnecessary.

The argument that god is to be preferred as an explanation because it is a simpler solution than these fancy-schmancy scientific theories is also fallacious. Religious people think that just because god is a three-letter word and the concept of god is a familiar one, that therefore it constitutes a ‘simple’ explanation. It is far from it. You can see why if, instead of using the short word ‘god’, someone gave his or her ‘solution’ to any scientific problem (such as the origin of the universe and life) by saying:

First we must postulate the existence of an complex, intelligent, omnipotent, omniscient, and everlasting entity that either exists throughout all of our universe or outside of it, created all the matter and laws that govern their behavior and yet can overrule the laws of science that it created on a whim, is made up of a totally undetectable substance, and is able to act in ways that seem indistinguishable from the working of natural laws.

Second, we postulate that this entity then did whatever we cannot explain, but that we don’t know how.

That’s not much of an explanation, is it? It is definitely not ‘simple’. It would be like explaining to a child that the reason the sun ‘moves’ across the sky during the day is because there is a huge man (whom we cannot see because the sun is too bright) whose job it is to push it along its path. It is a ‘simple’ solution in the sense that a child might understand it because ‘man’ is a simple three-letter word and the basic concepts of ‘man’ and ‘push’ are already familiar to the child. But it is not a solution at all in the scientific sense because it does not explain how a man could be up there and act this way. It merely shifts the problem to a different and more difficult level. Saying that god always existed and does not require an explanation for his own origins would be like telling the child that the huge invisible man always existed and needs no further explanation. Only a naïve and trusting child would believe such nonsense.

As Richard Dawkins keeps saying, invoking the existence of a highly complex entity by fiat raises far more problems than it solves. Real solutions to problems require explaining how complex phenomena arise using simpler entities and concepts. This is what the Big Bang theory does for the universe as a whole, just as Darwin’s theory of evolution by natural selection does for life. Starting with a simple mixture of quarks, gluons, electrons, and a few other particles in a highly dense and almost perfectly uniform gas, we can now understand how the complex structure of the universe came about.

All this has been done using natural laws and physical entities. Those who try to explain all this by concocting a god that does not contradict modern science always end up with something that is superfluous. As physicist Steven Weinberg says, “The more we refine our understanding of God to make the concept plausible, the more it seems pointless.” Religious people can postulate a god if they wish but it would be on the same level as postulating the existence of unicorns or fairies or the Flying Spaghetti Monster or the man pushing the sun.

There are still important unexplained questions as well as questions of detail to be worked out about how the universe and life came about. It is exciting when there are big open questions to investigate because they hold the promise of new scientific discoveries. But what we can say now with considerable confidence is that the nature of physical reality shows no sign whatsoever that we need to invoke a transcendental being or supernatural forces in order to explain anything.

According to modern cosmological theories, universes are being created out of vacuum fluctuations all the time and such events are consistent with all the known laws of science. Occasionally, one will be created that will have the necessary conditions to produce sentient beings like us. As Edward Tryon said back in 1973 in his paper Is the Universe a Vacuum Fluctuation? (Nature, vol. 246, p. 396-397, 14 December 1973.):

[M]y answer lies in the principle of biological selection, which states that any Universe in which sentient beings find themselves is necessarily hospitable to sentient beings. I do not claim that universes like ours occur frequently, merely that the expected frequency is non-zero. Vacuum fluctuations on the scale of our Universe are probably quite rare. The logic of the situation dictates, however, that observers always find themselves in universes capable of generating life, and such universes are impressively large.

In response to the assertion that though we might know how the universe came into being, we do not understand why, Tryon responds with a marvelously laconic understatement: “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.”

While we can look at the magnificence of the universe with a sense of awe, there is nothing about the existence of life and the universe that looks like it has an externally imposed meaning.

POST SCRIPT: The Galaxy Song

Although I posted this recently, I think that this clip from Monty Python and the Meaning of Life is a good way to end this series of posts because it captures the sense of wonder at the amazing universe we live in. I particularly like the line, “Remember when you’re feeling very small and insecure, how amazingly unlikely is your birth” because it reminds me how lucky we are to be alive and able to appreciate it. Why would anyone want anything more?

Big Bang for beginners-15: The essential tension in science

(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.

As I wrote earlier, the state of play is that according to our best estimates, the Big Bang theory predicts that the universe is flat and consists of 72.1% dark energy and 23.3% dark matter, with the remaining 4.6% being all the other matter that we are familiar with and know exists.

But while the Big Bang theory has been hugely successful in explaining so many things, it is important to acknowledge what the standard Big Bang cosmological model does not do. It does not say what caused the Big Bang. It describes the evolution of the universe after it came into being. In that sense it is like the theory of evolution that also does not deal with how the very first replicating molecule came into being but only what happens afterwards.

The standard Big Bang theory is also not designed to answer the question of what existed before the Big Bang or what lies beyond the observable universe because there is no way as yet (as far as I know) to get any data that on these questions.

It is also perhaps a little unnerving that we have directly detected only about 5% of the universe we live in but that is where things stand now. Alternatively, some suggest that instead of invoking the existence of dark matter and dark energy, maybe the basic laws of gravity need to be modified, thus creating a new paradigm. This school of thought argues that perhaps it is time to abandon Einstein’s General Theory of Relativity in favor of a new one that does not require dark matter and dark energy.

This is always the essential tension in science. No scientific theory ever explains all the phenomena that it confronts at any given time. There are always disagreements and anomalies. When they inevitably occur, scientists have several choices.

One is to treat the anomaly as a puzzle to be attacked with increasing vigor and focus. In the course of this, new entities and variations on the existing paradigm may be brought into the mix. Dark matter, dark energy, and the inflationary model can be considered as examples of this kind of approach to solving the current puzzles of cosmology, creating new entities and modifications of the theory while still remaining within the same basic framework, which in this case is given by Einstein’s General Theory of Relativity.

Another approach is to set aside the problem for future scientists to deal with either because a solution requires knowledge and skills and technology that are currently unavailable, or because the problem itself is currently seen as uninteresting and not worth devoting human and material resources to.

The third approach is to suggest that the anomaly signals a breakdown in the theory itself, requiring a new one. While one can always find scientists who suggest new theories to solve the anomaly, the scientific community as a whole takes such a drastic step only as a last resort, because doing so requires abandoning a fruitful old theory that has served them well and re-evaluating all its past successes in the light of the new theory to see if they hold up. This is a lot of work. While it does happen in scientific history, it is not undertaken lightly. One needs an acute sense of crisis to trigger such a shift by the scientific community as a whole.

For example, for nearly sixty years after Newton proposed his theories of motion, its predicted motion of the moon’s perigee was only half of what was observed. While some scientists suggested that Newton’s theory be modified or even abandoned, most scientists did not take those suggestions seriously, believing that a solution would be found within the Newtonian framework. And it was, when it was discovered that the mathematics that had been used was wrong. (Thomas Kuhn, The Structure of Scientific Revolutions, 1970, p. 81.)

Newtonian physics was so successful that when it was discovered in 1859 that the motion of Mercury could also not be explained by Newtonian physics, it was assumed that a solution within the Newtonian framework would be found for this too. But it turned out that in this case, the solution actually did require the rejection of Newtonian physics in favor of Einstein’s General Theory of Relativity that came along in 1916.

The point is that the presence of unsolved problems does not mean that they are intrinsically insoluble, and the solution can appear in many ways. But as is usually the case, religious apologists tend to seize on unsolved puzzles du jour in science and elevate a select few to the status of Deep Mysteries for which the only solution is god.

The origin of the universe has been a favorite of religious apologists ever since its inception. As particle astrophysicist Victor Stenger writes in his 2003 book Has Science Found God? (the answer is no, by the way):

The notion of the big bang was first proposed in 1927 by Belgian astronomer and Catholic priest Georges Lemaitre. Well before observations of the cosmic microwave background radiation provided the first good observational support for the theory, Pope Pius XII used the big bang theory to validate Catholic theology. In a speech before the Pontifical Academy, the pope asserted that “creation took place in time, therefore there is a Creator, therefore God exists.” At the urging of academy member Lemaitre, however, the pope stopped short of making this an “infallible” pronouncement. Lemaitre realized how dangerous that would have been, knowing that his theory like any other was not infallible. (p. 84)

More recently, when the COBE results came out showing the slight deviations from perfect uniformity of the cosmic microwave background, religious physicists like Hugh Ross claimed that they fulfilled the prophecies of the Bible (Stenger, p.84).

Religious apologists also argue that the cause of the Big Bang and what existed before it are Deep Mysteries. What is their solution? No surprise here. It is that god always existed and so was around to create the universe with all its matter and laws. They say that this is either the only or the simplest explanation and hence is to be preferred. As I will discuss in the next (and final!) post in this series, they are wrong on both counts.

While the modern scientific community may decide to temporarily shelve a problem, or work within an existing paradigm to solve it, or decide it is time to choose a new paradigm, what it never does is throw up its hands and say ‘god must have done it’.

POST SCRIPT: The Lady and the Gramps

Sarah Palin campaigns for John McCain, but is she helping?

<td style='padding:2px 1px 0px 5px;' colspan='2'Lady and the Gramps
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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
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