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What’s the with Matter?

This is a line that caught my attention in Charles Seife’s highly engaging book, entitled “Alpha and Omega: The search for the beginning and the end of the universe” (Doubleday, Trans world Publishers, UK, 2003). I thought that it would be an apt title to discuss some aspects of matter and energy in the context of physics and cosmology.

Although there is no consensus definition for it, matter can be regarded as anything that occupies space and has rest (or invariant mass). Typically, matter includes and other which have mass, and normally exists in the form of solids, liquids and gases. We all know from Einstein’s work that mass and energy are actually different states of a single energy-matter continuum, and that wave-particle duality is a well manifested phenomenon by light. Quantum theorists have since extended the wave-particle duality to include all matter. The atoms that compose ordinary matter have their associated closely tied to the atoms; occasionally, an gets knocked free, but it quickly attaches itself to another nucleus. But in the early universe, within a tiny fraction of a second after the Big Bang, this was not the case.

The Big Bang was a massive explosion that created all the mass and energy in the universe, as well as its space-time fabric, fourteen billion years ago. What started the big bang still remains unfathomable, but it has been hypothesized that the space-time fabric inflated incredibly rapidly after the cataclysm, and before it ended some 10-32 seconds later, the universe was a seething soup of primitive matter in the form of , and (dominantly the electrons), and radiation, the so-called - plasma. Within a millionth of a second, the soup cooled to ten trillion degrees, and the quarks succumbing to the pull of the gluons tripled up to form the ( and ) and some doubled up with antiquarks to form which did not survive as long. The neutrons and protons thus formed were highly energetic and collided with one another randomly and violently, sticking together and then breaking apart, but as the universe cooled they coalesced forming atomic nuclei. This is the era of nucleosynthesis which lasted for a mere 3 minutes and it was incomplete. Most of the protons in the universe remained unbound; the remainder coalesced with neutrons forming deuterium, helium-3 and helium-4 rand other heavier species. This explains why hydrogen constitutes the bulk (about 75%) of the matter found in primordial gas clouds, with helium being about 25%. As described by Seife, the electrons still remained untied to the nuclei during this period, and this plasma state being opaque to light resulted in scattering and re-scattering of trapping it in a cage of matter that cooled for thousands of years. All of a sudden, 400,000 years after the big bang, recombination hit. The electrons and the nuclei settled down together forming atoms, the opaque universe became clear, and the trapped photons were released from their cage of matter. This is the cosmic microwave background which fills the observable universe almost uniformly and carries a wealth of information that cosmologists still continue to analyse. One piece of information that cosmologists have been able to discern from this cosmic background radiation coupled with analysis of supernova data is the value of Ω, the density of stuff in the universe that includes both matter and energy. This density parameter Ω is related to the shape and fate of the universe and is now thought to equal approximately 1.

The inflationary universe is favoured by most cosmologists, including Stephen Hawking, because “it solves more problems than it creates”. The inflationary burst would have smoothed out all the matter in the early universe to a density that would have allowed the universe to expand as long as ours has. If it had been densely packed with matter at its very start, it could simply have collapsed on itself, like a black hole. If the matter had been spread out too thin in the rapidly growing universe, then it might not have been clumpy enough to form galaxies and it would have drifted away into space. Clearly, the inflationary burst starting from 10-35 seconds and ending at 10-32 seconds was critical in determining the structure of our universe.

There are also a number of other factors which are delicately balanced that have ensured that our universe exists as it does. If the strong nuclear force (vide infra) were any weaker, elements other than hydrogen would not exist; if the strong nuclear force were just a bit stronger than the electromagnetic force, then a di- nucleus would be the only stable entity in the universe and hydrogen, the source of evolution of our stars and galaxies, would not exist. If the constant of gravity, which is 1038 times weaker than the strong nuclear force, were any stronger, our universe would be small and swift and the mass and lifetime of the average star would be so small as to deny the development of complex biological systems. On the other hand, if gravity was less powerful than it is, matter would not have congealed into stars and galaxies.

Then there is also the factor called entropy, which has its origins in the second law of thermodynamics. According to this concept, systems in nature tend to evolve from order to disorder, from complexity to simplicity, with passage of time, and entropy is a measure of this disorder or randomness. We see evidence of increasing entropy all around us – Ice melting in a warm room, cars rusting, people becoming old, mountains eroding, economies going into disarray, conflicts becoming too frequent, the ecosystem increasingly coming under stress and our lives becoming ever more hectic and uncertain. Entropy always goes up with increasing disorder. The entropy of a closed system (isolated such that no matter/energy enters or leaves the system; our universe is an ultimate example of this), always increases. This is the Second Law of Thermodynamics. The entropy of an open system, on the other hand, can increase or decrease, but if it decreases, the entropy of its total environment must increase such that the entropy of the universe increases. Biological systems are open systems for the reason that they can decrease their entropy. Entropy has also found a conceptual application in information theory where it is used as a measure of unpredictability or uncertainty associated with a random variable. For a given context, entropy is a measure of the order or disorder in a sequence that can be regarded as information. Since its first introduction by Shannon (1948), entropy in the information sense has taken on many forms, namely topological, metric, Kolmogorov-Sinai and Renyi. These definitions have been applied, for example, to estimating DNA sequence entropy (of introns and exons) with varying levels of success.

Left to its own devices, entropy goes up as time passes. As a matter of fact, natural decay and the general tendency toward greater disorder are so universal that the second law of thermodynamics has been appropriately dubbed "time's arrow", pointing from past to future.

From the standpoint of entropy, the primordial gas of hydrogen and helium that was uniformly spread out in the nascent universe would have constituted a high entropy physical state, but this state existed only for a time as gravity intervened causing the formation of orderly clumps. It is believed that clouds of gas initially began clumping together due to the accumulation of primordial fluctuations, which were small changes of the density in certain parts of the early Universe. Through gravity, gas was then drawn towards these denser regions of the Universe along with a girdling mass of hypothetical dark matter (vide infra). Gravity continued to wield its critical influence unabated for billions of years turning the clumps into stars and galaxies, “with some lighter clumps forming planets (like the earth), with a nearby star (like the sun) that provided a relatively low- entropy source of energy that allowed low-entropy life-forms to evolve”, to quote Brian Greene (“The Fabric of the Cosmos”; Penguin Books, 2004). As elucidated by Greene, the Big Bang started the universe off in a state of low entropy; this generation of order was more than compensated by the generation of disorder by the heat generated as the gas compressed, and, ultimately, by the enormous amount of heat and light when nuclear processes began to take place.

Still awaiting a consensus explanation though is why matter rather than anti-matter prevailed when the universe was created. There is no experimental evidence for an imbalance in their creation and equal amounts of these would have annihilated each other with no matter to show. An explanation that is currently in vogue is that some reactions specifically involving the weak nuclear force do allow for charge-parity violations, tilting the balance in favour of matter over anti-matter. Another possibility quoted in Wikipedia (http://en.wikipedia.org/wiki/Baryon_asymmetry) is that there may be “antimatter dominated regions exist within the universe, but outside our observable universe” and ”radiation from the boundary of matter and antimatter dominated regions may simply still ‘be on its way’ to Earth, and so cannot be observed.”

Cosmologists tallying up all the matter they could see in all the visible stars and galaxies using the most powerful telescopes have come to accept the fact there is insufficient matter to make Ω = 1; the value they obtained is woefully short at about 0.5% of Ω. This can only mean that most matter in the universe is invisible to telescopes, that is, dark matter. The realisation has also dawned on them that dark matter is of two types, one form is baryonic and the other a more dominant non-baryonic form; together they contribute to about 30% of Ω. The latter includes and other exotic entities such as , , gravitols, etc., which being non-atomic exert no electromagnetic interactions with visible matter. There is also the added mystery unveiled from supernova data of a dark energy that is causing the universe to expand ever faster. This also contributes to the value of Ω, estimated at roughly 70% of Ω.

The dark energy is responsible for the acceleration in the rate of expansion of the universe, drawing galaxies away from each other, against the pull of gravity. It is a bit like ant-gravity. Two proposed forms for dark energy are the cosmological constant, a constant energy density filling space homogeneously, and quintessence which posits a random distribution of energy in space. First proposed by Einstein as a modification of his original theory of general relativity to achieve a stationary universe, and subsequently abandoned by him in the light of the observation of the Hubble redshift which pointed to an expanding universe, the cosmological constant is physically equivalent to vacuum energy, that is, the energy that exists in free space even when devoid of matter. Most physicists believe that quantum effects ultimately determine the size of the cosmological constant. The vacuum energy corresponds to a state that is subject to quantum fluctuations in accordance with energy- time uncertainty principle - the more you know how much energy a particle has, the less you know about when it has that energy. This uncertainty relation has a very strange consequence. It fills the vacuum with an infinite number of evanescent particles that blink in and out of existence. Vacuum is thus never truly empty, it is seething with particles and energy, and this zero-point energy can exert a force (the Casimir effect) which has been measured.

Cosmologists are convinced that both dark matter and the antigravity dark energy shape our universe. By convention, Ω=1 is taken to mean a flat space-time. If Ω >1, the universe has a positive curvature, like a sphere, and if Ω <1, the universe has negative curvature, like a saddle. The evidence in favour of Ω=1 indicates that the fate of the universe under continued expansion is a cold and icy death with temperatures asymptotically approaching absolute zero temperature. However, new understandings of the nature of dark matter also suggest its interactions with mass and gravity demonstrate the possibility of an oscillating universe. In a cyclic or oscillatory model of the Universe, there will be no end … for matter and energy, that is. But for us and the Universe that we know of, there will definitely be a conclusion.

Particle physics has contributed immensely to our understanding of the structure of matter at the sub-atomic level. Just as the periodic table of elements provides a systematic, coherent picture of the chemical properties of atoms, the overarching theory of the (SM) of describes quite remarkably the interactions of fundamental particles- the (quarks and leptons) and the carriers of the strong nuclear force (gluon), the electromagnetic force () and the weak nuclear force (W and Z ). The SM has 17 fundamental particles: 12 -1/2 fermions (6 flavours of quarks and 6 flavours of leptons) shown in the Table below, 4 spin-1 force carriers (‘gauge’ bosons), and a mass-imbuing spin-0 Higgs , which has not yet been observed. The is needed in the model to give mass to the , consistent with experimental observations. While photons and gluons have no mass ( or electric charge), the W and Z bosons are quite heavy; W can be either positively charged (W+) or negatively charged (W-), while Z is neutral (Z0) and is its own . The W weighs 80.3 GeV (80 times as much as the proton) and the Z weighs 91.2 GeV. The Higgs is expected to be heavy as well (estimated to be >110 GeV). Unlike the force-carrying particles, the 12 fermions have associated antimatter particles.

The strong nuclear force acts on (a collective name for baryons and mesons), but not on leptons. The electromagnetic force is mediated by the photon and acts only on objects which have electric charge. Unlike these two forces, the weak nuclear force acts on both hadrons and leptons. It has the ability to change the flavour of quarks and leptons. For instance, it can turn a into an or a into an electron (or vice versa). Emission and absorption of W+ and W- bosons is the mechanism by which the flavour change is accomplished. The Zo boson does not participate in changing the flavour of quarks or leptons; it can decay either into a quark-antiquark pair or into a -antilepton pair. By way of example, consider the conversion of a to the more stable proton in β-decay. What transpires here is that one down quark in the neutron decays to an up quark - - by the emission of W boson. The W boson then materialises a lepton-antilepton pair, in this case, an electron and anti-.

n → p + e + ̅ e

Such interactions are best represented by Feynman diagrams (shown below), a subject that is discussed in many modern physics texts.

Charge Flavour

First Generation Second Generation Third Generation

Quarks +2/3 Up U Charm c Top t

-1/3 Down D Strange s Bottom b

-1 Electron e− μ− τ−

Leptons

0 Electron νe Muon νμ Tau ντ neutrino neutrino neutrino

Force Strong nuclear force Electromagnetic force Weak nuclear force

Range (m) 10-15 Infinite 10-17

Force-carrying Gluon (g) Photon(γ) W+, W- , Z0 bosons particle

In addition to the attribute of ‘electric charge’, quarks have also a three-valued ‘colour charge’ – red, green and blue. As with the word ‘flavour’, the word ‘colour’ is not to be taken literally; it is simply a property of the quark. Leptons have no colour, but gluons carry both colour and anticolour and they can have eight colour combinations. Quarks (and gluons) cannot exist freely but must form hadronic bound states. Thus baryons are colourless (R+B+G) as also mesons (R+ antired or B + antiblue or G+ antigreen). A quark can change colour by emitting or absorbing gluons. In fact, they are constantly changing colour by exchanging of gluons with other quarks.

RED quark ⇌ RED-ANTIGREEN gluon + GREEN quark

The notion of colour charge was introduced to explain how quarks could co-exist inside some hadrons in otherwise identical quantum states without violating the Pauli Exclusion Principle. For example, the Delta , Δ2+, which is a composite of 3 up quarks and has an of 3/2, meaning that the spin axes of all the component quarks are all pointing in the same direction. This baryon along with its other varieties (Δ+, Δ0, Δ-), decays via the strong force into a (proton or neutron) and a ( a π-) of appropriate charge. Mesons typically have no spin and with a mean life-time of only 2.2 µs, they are not very stable. The leptons that carry no charge are called neutrinos; their motion is directly influenced only by the weak nuclear force, which makes them notoriously difficult to detect. In contrast, by virtue of carrying an electric charge, the electron, muon, and tau all interact electromagnetically. All evidence suggests that neutrinos have mass but that their mass is tiny even by the standards of subatomic particles. Their mass has never been measured accurately. It is to be noted that second and third generations charged particles decay with very short half- lives, and are observed only in very high-energy environments. Neutrinos of all generations also do not decay, and pervade the universe, but rarely interact with baryonic matter. In general, the heavier a quark or lepton is, the rarer it is. Thus the tau particle is so much rarer than the muon, and the muon is so much rarer than the electron. For the same reasons, the J/psi meson which consists of a and a charm antiquark, as expected is a rare entity, and has only been fleetingly observed in studies such as at CERN, the European particle physics laboratory, that runs the Large Collider (LHC), which is a synchrotron particle accelerator. A synchrotron is a cyclic particle accelerator rather similar to the which accelerates the protons to relativistic speeds using a high frequency alternating voltage and with an applied perpendicular magnetic field (that causes the particles to bend into a closed path) that is time- dependent, being synchronized to the proton beam of increasing kinetic energy. The radiated energy from the accelerated charged particles is called synchrotron radiation; it is proportional to the fourth power of the particle speed and is inversely proportional to the square of the radius of the path. It becomes the limiting factor on the final energy of particles accelerated in the synchrotron. The LHC lies in a tunnel 27km in circumference, as deep as 175m beneath the Franco-Swiss border near Geneva, Switzerland. Two beams of subatomic particles called "hadrons" – either protons or lead ions – travel in opposite directions inside the circular accelerator, gaining energy with every lap. The LHC synchrotron is designed to collide head-on the high energy opposing particle beams [of protons at up to 7 teraelectronvolts(TeV) or 1.12 microjoules per nucleon, or of lead nuclei at an energy of 574 TeV (92.0 µJ) per nucleus (2.76 TeV per nucleon- pair] to recreate the conditions just after the Big Bang. The numerous particles created in the collisions are then carefully analysed by international teams of physicists using special detectors in a number of experiments dedicated to the LHC. vg kumar das (27 July 2012) [email protected]