8. The Ultimate Causes of Cosmic Order and Structure

What emerged at the Big Bang as a quantum fluctuation was an energy field, with no structure. But so much order and structure has emerged and evolved since then: Elementary particles, atoms, molecules, stars, galaxies, life, and so on. All this can be attributed to the following factors: the universe is expanding; the universe is cooling; the gravitational interaction was present right from the beginning; and ultra-minute quantum fluctuations occurred during the so-called 'inflation' period, ~10^-35 seconds after the birth of the universe. These fluctuations got amplified over time and were the original source of the cosmic structure we see today, including galaxies and clusters of galaxies.

Gradients of various types get created because of the expansion and the cooling of the universe. And these gradients are a measure of departure from equilibrium. The tendency to move towards equilibrium, so as to achieve stability, creates much of the order and structure. In addition, the inflation mentioned above was a one-off episode which created gradients, and its effects continue to affect the evolution of our universe.

I have already introduced the notion of free energy in Part 6. The second law of thermodynamics says that phenomena occur because their occurrence lowers the overall free energy. In particular, PHASE TRANSITIONS can occur for lowering the free energy. I consider the case of water to illustrate the notion of phase transitions. Above 100^oC water exists as steam (at atmospheric pressure). Between 100^oC and 0^oC it exists as liquid water, and below 0^oC it is ice. Thus there are three phases of water, namely steam, liquid water, and ice, each stable in an appropriate temperature (and pressure) regime. There is a change or transition of phase (or phase transition) from steam to liquid water on cooling to 100^oC, because liquid water is more stable than steam below this temperature. Another phase transition occurs on cooling to 0^oC, when liquid water changes to crystalline ice.

Let us begin at the beginning, and take a look at the figure below. It depicts the main events in the history of our universe. The time scale is not linear. The temperature rises as we go backwards in time towards the Big Bang, and physical processes happen more rapidly.

In the beginning the temperature was so high that no structure or order was possible, and there was only an energy field. As the very hot universe expanded after the cosmic explosion, it also cooled. 10^-43 seconds after the Big Bang the temperature was ~10³² K (here K stands for 'Kelvin'; 0^oC = 273 K; no temperature can be equal to or lower than 0 K). The gravitational interaction was present at this stage.

The next important event in our cosmic history occurred 10^-35 seconds after the Big Bang, and the technical term for it is INFLATION. During this very brief episode the rate of expansion of the newly born universe was much much higher than what it settled for after a while. In a way, it was this event which provided the real bang in the Big Bang.

As I said above, this inflation was one factor responsible for the later formation of structure in the universe. Why? The rate of expansion during the inflation was so very high that even the tiniest of quantum fluctuations got amplified and was enough for the nucleation and growth of structure. The temperature was ~10²⁷ K, and matter ('quarks', 'leptons', 'gauge bosons', and several other elementary particles) appeared, as also 'antimatter'. The appearance of matter and antimatter can be attributed to quantum fluctuations in the density of the universe, amplified by the effects of gravity. Even a miniscule increase in local density could attract more matter towards it, with a corresponding decrease in the surrounding density. That is how cosmic inhomogeneity arose and evolved.

At a certain stage of the inflation episode, a cosmic phase transition occurred, which freed enormous amounts of trapped energy (rather like the release of latent heat when steam condenses to water). After this prelude of inflation and cosmic phase transition, the normal (much slower) expansion of the universe set in, and has continued ever since.

During the inflation prelude, the universe grew extremely rapidly from a volume smaller than that of the nucleus of an atom to the size of a tennis ball. Why have cosmologists postulated the occurrence of inflation almost right after the Big Bang? With the postulation of the inflation episode certain cosmological mysteries get resolved. For example, when the universe was just the size of a tennis ball, regions that are very far apart today could have been in communicable contact then, resulting in the observed near-homogenization of the universe.

[Yes, the universe does look remarkably uniform or homogeneous in all directions (though not completely homogeneous). The present age of the universe is ~13.7 billion years. There are regions (e.g. the opposite sides of the horizon) that are so far apart that even light (the fastest moving signal anywhere) cannot travel from one end to the other in 13.7 billion years; so they cannot possibly be causally connected. But even they exhibit the same degree of homogeneity. This is known as the 'horizon problem'. The inflation hypothesis solves it.]

As you will see as we progress in this series of posts, an enormous number of facts about the evolution of order and complexity, as also the emergence and evolution of life, can be understood in terms of the following ultimate causes (in conjunction with the laws of quantum mechanics, relativity, and thermodynamics):

• Expansion and cooling of the universe.
• Emergence of the gravitational interaction at the birth of our universe.
• Occurrence of the very rapid and brief cosmic inflation soon after the birth of the universe.
• Occurrence and consolidation of quantum fluctuations during the inflation period.

Irony of Life

* Most 'First Class' students get seats in technical colleges, some become engineers and doctors.

 

* The 'Second Class' pass, then get an MBA degree, become administrators, and control the 'First Class'.         * The 'Third Class' pass, enter politics, become ministers, and control both of the above.  * Last, but not the least, the 'Failures' join the underworld and control all the above.

And those who do not attend any school become 

Swamis and Gurus, and everyone follows them.

Icy Delights

Icebergs in the Antarctic area sometimes have stripes, formed by layers of snow that react to different conditions.

Blue stripes are often created when a crevice in the ice sheet fills up with liquid water and freezes so quickly that no bubbles form.

When an iceberg falls into the sea, a layer of salty seawater can freeze to the underside. If it is rich in algae, it can form a green stripe.

Brown, black and yellow lines are caused by sediment, picked up when the ice sheet grinds downhill towards the sea.

7. Of Bosons and Fermions

The Higgs boson is in the news these days, but what exactly is a boson?

The Earth is a massive object, so it exerts an enormous gravitational pull on you. Have you wondered why is it that you do not get pulled all the way down to the centre of the Earth?! It is because of a principle in quantum mechanics, called the PAULI EXCLUSION PRINCIPLE, which says that no two electrons (or other 'fermions') can have the same set of 'quantum numbers', or occupy the same 'quantum state'.

Any atom has a positively charged 'nucleus', and one or more electrons around the nucleus. Positive and negative charges attract, so why do not all the electrons get sucked into the nucleus, and thus reduce and eliminate the distance between the positive charges and the negative charges? This is because of another principle of quantum mechanics, namely the Heisenberg uncertainty principle (cf. Part 3).

The diameter of the nucleus is ~10^-15 meter. The nucleus comprises of protons and neutrons, and each of them is ~2000 times heavier than an electron. If an electron were to get sucked into the nucleus because of the force of electric attraction (also called Coulomb attraction), it would be confined to a length of the order of 10^-15 meter. This would be the uncertainty ∆x in its position. We can plug this into the inequality embodying the uncertainty principle, namely ∆x.∆p_x ≥h/(4π), to get the corresponding uncertainty in its momentum p_x. From this momentum if we work out the kinetic energy (= p_x²/(2m)), it turns out to be so large that the electron just cannot remain bound inside the nucleus (by contrast, a proton or a neutron can remain bound inside the nucleus because for it the kinetic energy is ~2000 times lower, because of the larger mass m).

So the electrons are outside the nucleus, and each atomic species (hydrogen, helium, carbon, etc.) has a distinctive distribution of electrons in specific orbits around the nucleus, and a distinctive 'valence' or proclivity for chemical bonding. The distinctive structure of atoms of any type (say carbon) is because electrons belong to a class of particles called 'fermions', and for fermions the Pauli principle says that no two of them can be in the same quantum state; so they separate out into more than one orbits. [The term 'fermion' is in honour of Enrico Fermi.]

All fundamental particles are either fermions or bosons ['bosons' in honour of S. N. Bose]. These two classes differ in a quantum parameter or number called SPIN. The spin of any fundamental particle can be either an integer (in a certain system of units), or a multiple of 1/2. That is, it is either integral (0, 1, 2, 3, ...) or half-integral (1/2, 3/2, 5/2, ...).

Although classical analogies can be very inadequate for explaining quantum mechanics, imagine a spinning top. We can associate an angular momentum with it: The faster the top spins, the higher is its angular momentum. And the angular momentum of a classical top can have any arbitrary value. Not so in quantum mechanics. Only discrete (or quantized) values are possible here, although quantum spin indeed has the identity or 'dimensions' of angular momentum. What is more, the spin value for an electron can be either 1/2 or -1/2, and nothing else.

Whereas the Pauli principle prevents electrons and other fermions from occupying the same quantum state, there is no such restriction for bosons. Unlike fermions, bosons can have the same set of quantum numbers. [A quantum state is specified by a set of quantum numbers. Spin is an example of such a quantum number; there are many others.]

How do electrons get distributed in various specific orbits (or 'energy states') around the nucleus if they cannot all occupy the same orbit? The answer lies in the wave nature of electrons. An electron would tend to be as close to the nucleus as possible, but the smallest orbit can be that which allows a wave to close back on itself smoothly and repeatedly, as shown in the figure below, on the right.

The Pauli principle allows the smallest orbit to be occupied by two electrons, one with spin 1/2, and the other with spin -1/2. If there is a third electron, it must occupy the next permissible larger orbit, and so on. Only orbits which are compatible with the formation of 'standing waves' are possible. This is what defines the specificity or uniqueness of the orbits.

An atom of sodium has 11 electrons around the nucleus. The first orbit (or shell) can take only two. The next shell can take 8, and the 11^th electron must go to the third shell.

Similarly, an atom of selenium has 34 electrons, and has the distinctive electron distribution shown below.

Protons and neutrons are also fermions, with spin = 1/2. By contrast, photons are bosons (spin = 1). The Higgs particle is expected to have spin = 0; that is why it is called a boson.

So, you and I exist because electrons and other fermions obey the Pauli principle, leading to the existence of distinct types of atoms and molecules. And it is the Pauli principle again which prevents the Earth from pulling us all the way down to its centre; electrons and other fermions (unlike bosons) just cannot come too close together in 'phase space'.

Why are all fundamental particles either bosons or fermions? According to quantum 'field theory' (to be discussed in a separate post), when 'matter' particles interact with one another, they do so by the emission and absorption of 'field' particles. For example, the electromagnetic interaction between two electrons is via an exchange of photons. And all matter particles are fermions, all field particles are bosons.

Sea Spectacular - 2/2

Shape of Things to Come!

President Obama and the Canadian PM are shown a time machine which can see 50 years into the future. They both decide to test it by asking a question each.

President Obama goes first: "What will the USA be like in 50 years’ time?"

The machine whirls and beeps and goes into action and gives him a printout. He reads it out: "The country is in good hands under the new president, José Fernandez.... Crime is non-existent, there is no conflict, the economy is healthy. Vice President Jin Tao has declared Chinese language mandatory in all US schools There are no worries."

The Canadian PM thinks, "It's not bad, this time machine, I'll have a bit of that" so he asks: "What will Canada be like in 50 years’ time?"

The machine whirls and beeps and goes into action, and he gets a printout. But he just stares at it.

"Come on, David," says Obama, "Tell us what it says."

David: "...I can't. It's in Punjabi."

6. How can Order Emerge out of Disorder Spontaneously?

As explained in Part 5, the second law of thermodynamics says that, for an isolated system, the state of maximum disorder is the most likely thing to happen, given enough time. All gradients tend to be obliterated, and ultimately a zero-gradient or equilibrium state is attained if there is no input/output of energy or mass.

The important thing to understand is that the above statement of the second law is for an ISOLATED system; i.e. a system which cannot exchange energy or matter with the surroundings. By contrast, an OPEN system is one which can exchange energy and matter with the surroundings. Your own body is an example. You are alive because you are exchanging energy and matter with the surroundings. Any living organism, if kept fully isolated from everything, would die eventually. It would be reduced to a final state of total equilibrium and stability, with no gradients of any kind. EQUILIBRIUM IS DEATH.

For open systems there is still a second law of thermodynamics, but it has to be so formulated that it includes the possibility of input/output of energy and/or matter.

Any gradient implies that the system is away from a state of equilibrium. Such a system is therefore unstable, and the spontaneous dissipation of the gradient demanded by the second law amounts to a move towards STABILITY. There is a hint here about how to generalize the second law so that it is applicable to open systems also. We have to incorporate two things: The tendency towards disorder; and the tendency to achieve stability by exchanging energy and/or matter with the surroundings (an option not available for isolated systems). We quantify the first part by introducing a parameter called ENTROPY (denoted by S). And the parameter relevant for the second part is INTERNAL ENERGY (denoted by U).

Entropy, or rather change of entropy, is defined as follows. Suppose we have a system at a temperature T, and we add a small amount dQ of heat to it. Then dQ/T is defined as the change of its entropy, and denoted by dS.

Consider a system as having two parts, one at temperature T₁, and the other at a slightly higher temperature T₂. When heat dQ flows from the second part to the first, the net change of entropy is dS = –dQ/T₂ + dQ/T₁ . Since T₂ > T₁, we must have dS > 0 always. Entropy does not decrease.

With the passage of time, T₂ → T₁, and therefore dS → 0. Finally, when T₁ = T₂, we have dS = 0, and equilibrium is said to have been reached. If a system is in equilibrium, it is implied that its entropy has reached the maximum possible value under the circumstances, and stopped changing any further.

So much for the entropy contribution to stability. Let us consider the energy part next. An example will help. Water changes to ice when cooled below 0^oC at atmospheric pressure.

A crystal of ice has a highly ordered arranged of water molecules, arranged nicely on a lattice. This is clearly a case of order emerging out of disorder, so why does it happen? Why does an ordered structure emerge out of the highly disordered or chaotic motion of molecules in liquid water? This happens because the watchword is STABILITY, and not just order vs. disorder. For an open system, since energy and mass can be exchanged with the surroundings, the possibility is available that a higher-stability state may be attained (for example by a stronger bonding among the molecules) even at the cost of a little lowering of entropy locally. In the water vs. ice situation, whereas at high temperatures the average speed of the molecules is so high that they just collide with one another and go their separate ways again, for temperatures below 0^oC the motion is sluggish enough that the molecules are able to stick together and form chemical bonds. The process of chemical binding releases some heat energy, which is transmitted to the surroundings. This loss of energy is possible here because it is an OPEN system. The bonded or crystalline configuration is a more stable situation at the prevailing temperature: Crystalline water, i.e. ice, has a lower internal energy (U) compared to liquid water.

Thus the overall stability is decided by a tradeoff between two energy terms: U and TS. We define a new thermodynamic parameter F as (U – TS). This parameter (called FREE ENERGY) decreases as the entropy S increases (because of the –ve sign in front of the entropy term TS). And it also decreases when U decreases; i.e. when the systems acquires a more stable configuration.

So, for open systems, the second law of thermodynamics has to be stated as follows:

IN ANY PROCESS OR PHENOMENON, THE OVERALL FREE ENERGY CAN NEVER INCREASE; IT EITHER DECREASES OR REMAINS THE SAME.

The tendency towards greater disorder is present in open systems as well, but the overriding requirement in both isolated and open systems is always that of maximum stability. We see so much order and self-organization around us because what we have are systems which are able to exchange energy and matter with the surroundings for achieving maximum-stability configurations. Nature does abhor gradients, but even the abhorrence of gradients is nothing but a tendency towards greater stability: Zero gradient means equilibrium, and therefore stability.

There is so much self-organization occurring in Nature all the time, but there is no violation of the second law of thermodynamics ever.

'If someone points out to you that your pet theory of the Universe is contradicted by experiment, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law, I can give you no hope; there is nothing for it but to collapse in deepest humiliation' (Arthur Eddington, 1944).