Saturday, January 28, 2012

12. The Four Interactions

There are four types of forces or interactions in our universe. The first is the gravitational interaction, or the gravitational force field. It is very weak, but is always present between any two particles or bodies. It is proportional to the product of the masses of the objects interacting. Since most of the celestial bodies are very massive, the gravitational force becomes very significant for them. Your weight is the gravitational force with which the Earth attracts you towards its centre.

Like charges repel, and unlike charges attract. Similarly, like magnetic poles (north-north or south-south) repel, and unlike magnetic poles (north-south) attract. Research showed that the electric interaction and the magnetic interaction are really two aspects of the same underlying phenomenon, so the term electromagnetic interaction was coined. This is the second of the four interactions.

The third is the 'weak nuclear' interaction. It is operative, for example, inside the nuclei of radioactive materials, and is responsible for the emission of alpha-particles, beta-particles, etc. from inside such nuclei.

Lastly we have the 'strong nuclear' interaction, which is very strong but very short-ranged, and is responsible for the large binding energies of nuclei: A rather large amount of energy is required for extracting a proton or a neutron from inside the nucleus of an atom.

Maxwell's theory of the electromagnetic interaction was a classical theory. So also was Einstein's theory of the gravitational interaction, namely the general theory of relativity. Quantum effects become very significant at sub-atomic length scales. Moreover, the early universe (at and immediately after the Big Bang) was also of very small dimensions. We therefore need a quantum formulation for all the four interactions.

In quantum theory, not only are the elementary particles quanta of mass/energy, even the force fields or interactions among the particles are mediated by quanta. For example, when two electrons interact, the fundamental particle which mediates the interaction is the photon. One electron emits a ('virtual') photon and recoils in the process. The other electron absorbs the photon and also recoils. This back and forth exchange of photons constitutes the electromagnetic interaction. Quantum field theories have to be formulated for all the four interactions.

Historically, the electromagnetic interaction was the first to be cast in a quantum-mechanical form, and this subject goes by the name of quantum electrodynamics (QED). Richard Feynman, who played a major role in the development of QED, had also formulated a sum-over-histories version of quantum mechanics (see Part 4). He used his famous path-integrals for working out the details of QED. But the QED theory ran into a conceptual problem. The summation over the infinitely many possible histories resulted in an infinite mass and charge for the electron, which was an absurd result. Feynman got over this problem by a procedure called renormalization, but I shall not go into its technical details here.

Why are there four different fundamental interactions, and not just one? The fact is that there was indeed only one interaction to start with, but as the universe expanded and cooled, symmetry-breaking transitions occurred, resulting in the successive appearance of different and less symmetric interactions. Attempts continue to be made for 'unifying' the four interactions to see what kind of a theory emerges when this has been achieved. Such efforts run parallel to those for obtaining quantum-field-theoretic formulations for the four interactions.

The first to be unified were the electromagnetic interaction and the weak-nuclear interaction, resulting in what is called the electroweak interaction. A bonus point of this unification was that the renormalization procedure could be successfully carried out for the unified interaction for obtaining its quantum field theory (without encountering the 'infinities' problem mentioned above), whereas it was not achievable for the weak interaction separately.

The quantum field theory which successfully achieved renormalization for the quantum version of the strong nuclear interaction is called quantum chromodynamics (QCD). In this theory the proton and the neutron, as also some other particles, are envisioned as made up of a more fundamental set of particles called quarks. Quarks come in three 'colours' (nothing to do with the usual meaning of colour): red, green, and blue, along with the respective 'anticolours'. The quarks cannot exist as free, stable particles. Only those combinations of them can exist as free particles which do not have a net colour. For example, a colour and its anticolour cancel, giving a neutral net colour. Composite particles in which this occurs are the particles called mesons.

Another possibility is that all three colours (one each), or all three anticolours, occur together in a composite particle. The name for such a composite particle is 'baryon'. Protons and neutrons are examples of baryons.

In addition to colour, quarks have quantum parameters like 'up' (u), 'down' (d); 'charm', 'strangeness'; and 'top', 'bottom' (do not pay attention to the literal meanings of such words; they are just labels, with no literal meaning). Two up quarks and a down quark make a proton, and two down quarks and one up quark make a neutron.

The information given in this post is part of what is called the STANDARD MODEL of particle physics. In it, the electromagnetic interaction and the weak-nuclear interaction have been unified into the electroweak interaction, and a quantum version for it has been established. In addition, there is a quantum-mechanical formulation for the strong nuclear interaction (QCD), but no entirely satisfactory unification with any of the other interactions. The gravitational interaction has been neither quantized, nor properly unified with other interactions. I shall return to the Standard Model in the next post.

A total unification of all the four interaction was a distant dream till recently. Now 'string theory' and 'M-theory' have emerged as solutions to some of the pending problems in particle physics and cosmology. I shall discuss them in a future post.

Saturday, January 21, 2012

11. Einstein's General Theory of Relativity

Einstein’s special theory of relativity (cf. Part 10) was followed by his general theory of relativity (1907-1915), which addresses the issue of gravity. He showed that, contrary to Newton’s assumption, gravitational waves, which mediate gravitational attraction between any two bodies, travel at a finite speed, namely the speed of light. The theory explained gravitational interaction in terms of a DISTORTION OF SPACETIME by every object. The larger the mass of an object, the more is this distortion. When one object distorts spacetime, the effect is felt by every other object; this is how gravitational attraction between any two objects occurs.

Newton's second law of motion says that the acceleration (a) produced by a force F acting on an object of mass m is equal to F/m; i.e., F = ma. The mass m that enters this equation is called the 'inertial' mass. To understand why, let us recall Newton's first law of motion, which says that a body continues to be in a state of rest or uniform motion, unless acted upon by a force. Thus, the body exhibits inertia to any change of its state of rest or uniform motion; it resists a change in its state, and the resistance or inertia is proportional to its mass, the 'inertial' mass.

Next, let us consider Newton's law of gravitation. Consider any two bodies or objects, having masses m1 and m2, and a distance r apart. The law says that the gravitational force of attraction between them is F = G(m1m2)/(r2); here G is the 'Gravitational constant', a fundamental parameter of Nature in our universe. [Some other such fundamental parameters are the speed of light c, and the Planck constant, h.] The mass that enters the gravitation-law equation is 'gravitational' mass.

The big question was: Is inertial mass the same as gravitational mass? Newton (and also Galileo) asserted that it is so, and that it is a happy coincidence that it is so. Einstein agreed that the two kinds of mass are the same, but he created a trail-blazing theory of gravity out of this 'happy coincidence', namely the general theory of relativity. The sameness or equivalence of the two kinds of mass goes by the name of EQUIVALENCE PRINCIPLE, an essential ingredient of Einstein's theory.

Einstein argued that the experience of being pulled downwards by the gravitational force on the surface of the Earth is equivalent to being inside a spaceship (far from any sources of gravity) that is being accelerated by its engines.
From this, Einstein deduced that free-fall is actually 'inertial motion' (i.e., constant-speed motion). An object in free-fall really does not accelerate, but rather the closer it gets to an object such as the Earth, the more the time scale becomes stretched due to spacetime distortion around the planetary object. As it approaches the planetary object the time scale stretches at an accelerated rate, giving the appearance that it is accelerating towards the planetary object. An accelerometer in free-fall does not register any acceleration.

When an observer detects the local presence of a force that acts on all objects in proportion to the inertial mass of the object, the observer can be taken to be experiencing an accelerated frame of reference. Imagine two reference frames, K and K'. K has a uniform gravitational field, whereas K' has no gravitational field but is uniformly accelerated by such an amount that objects in the two frames experience identical forces:

'We arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K' are physically exactly equivalent; that is, if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated. This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual (i.e. special) theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course' (Einstein 1911).
Einstein went further than that:
'As long as we restrict ourselves to purely mechanical processes in the realm where Newton's mechanics holds sway, we are certain of the equivalence of the systems K and K'. But this view of ours will not have any deeper significance unless the systems K and K' are equivalent with respect to all physical processes, that is, unless the laws of Nature with respect to K are in entire agreement with those with respect to K'. By assuming this to be so, we arrive at a principle which, if it is really true, has great heuristic importance. For by theoretical consideration of processes which take place relatively to a system of reference with uniform acceleration, we obtain information as to the career of processes in a homogeneous gravitational field' (Einstein, 1911).

He combined the equivalence principle with special relativity theory to predict, among other things, that clocks run at different rates in a gravitational field, and that light rays bend in a gravitational field ('gravitational lensing effect'). This and many other predictions of the theory have been confirmed by experiment.

The central idea of Einstein's theory is that the presence of matter distorts or curves spacetime. Thus gravity is interpreted as not a force, but rather a curvature in the fabric of spacetime, and objects respond to gravity by following (or free-falling along) the curvature of spacetime in the vicinity of an object. This idea has shaped modern cosmology. It also marked a major inroad of geometry into physics.

This video by Richard Feynman (on the character of physical law) is a treat to watch:

Tuesday, January 17, 2012

First Words on the Gramophone

The HMV Company had once published a pamphlet giving the history of the gramophone record. The gramophone was invented by Thomas Alva Edison in the 19th century. Edison, who had invented many other gadgets like the electric bulb and the motion picture camera, had become a legend even in his own time.

When he invented the gramophone record, which could record human voice for posterity, he wanted to record the voice of an eminent scholar on his first piece. For that he chose Prof. Max Muller of Germany, another great personality of the 19th century. He wrote to Max Muller saying, "I want to meet you and record your voice. When should I come?" Max Muller who had great respect for Edison asked him to come at a suitable time when most of the scholars of Europe would be gathering in England.

Accordingly, Edison took a ship and went to England. He was introduced to the audience. All cheered Edison’s presence. Later at the request of Edison, Max Muller came on the stage and spoke in front of the instrument. Then Edison went back to his laboratory and by afternoon came back with a disc. He played the gramophone disc from his instrument. The audience was thrilled to hear the voice of Max Muller from the instrument. They were glad that voices of great persons like Max Muller could be stored for the benefit of posterity.

After several rounds of applause and congratulations to Thomas Alva Edison, Max Muller came to the stage and addressed the scholars and asked them, "You heard my original voice in the morning. Then you heard the same voice coming out from this instrument in the afternoon. Did you understand what I said in the morning or what you heard this afternoon?"

The audience fell silent because they could not understand the language in which Max Muller had spoken. It was `Greek and Latin' to them as they say. But had it been Greek or Latin, they would have definitely understood, because they were from various parts of Europe. It was in a language which the European scholars had never heard.

Max Muller then explained what he had spoken. He said that the language he spoke was Sanskrit and it was the first sloka of the Rig-Ved, which says "Agni Meele Purohitam". This was the first recorded public version on the gramophone plate.

Why did Max Muller choose this? Addressing the audience he said, "Vedas are the oldest text of the human race. And Agni Meele Purohitam is the first verse of Rig Veda. In the most primordial time, when people did not know how even to cover their bodies, and lived by hunting and housed in caves, Indians had attained high civilization and they gave the world universal philosophies in the form of the Vedas".

Such is the illustrious legacy of India.

When “Agni Meele Purohitam” was replayed the entire audience stood up in silence as a mark of respect for the ancient Hindu sages.

This verse means:

Oh Agni, You who gleam in the darkness, 
To You we come day by day,
with devotion and bearing homage.
So be of easy access to us, Agni, 
as a father to his son, abide with us for our well being.

***  ***

Why did even Carl Sagan quote from the Rig-Ved? The sloka (verse) below is one of the reasons: 
Who knows for certain? 
Who shall here declare it? 
Whence was it born, whence came creation? 
No one knows whence creation arose; 
and whether god has or has not made it. 
He who surveys it from the lofty skies, 
only he knows - or perhaps he knows not.

Saturday, January 14, 2012

10. Relativity Matters

Mu mesons (or muons) are unstable particles, produced when protons from the Sun are absorbed in the atmosphere. They travel typically at ~99% the speed of light: v = 0.99 c. A muon has a certain lifetime, after which it disintegrates into something else. One may think that the lifetime should be something fixed and unique to the particle. It is so, provided the observer measuring the lifetime is moving with the muon. Otherwise it depends on its velocity relative to that of the observer. Observers at rest w.r.t. the muons measure the average lifetime to be ~2.2 milliseconds (ms). But observers on Earth measure the lifetime of the moving muon to be ~15.6 ms. Strange but true. Einstein's SPECIAL THEORY OF RELATIVITY explains such results.

Newton laid the foundations of classical mechanics in the 17th century. His monumental Principia enunciated simple laws of motion. These laws, when augmented by Newton's law of gravitation, dominated physics for the next 200 years. He assumed the existence of absolute space; space that is immovable and similar everywhere and at all times. He also presumed that gravitational interaction between any two bodies is instantaneous; that is, its speed of travel is infinite.

Maxwell’s theory of classical electrodynamics, formulated in 1864, extended Newtonian classical mechanics to account for the motion of charged particles in electric and magnetic fields. Modern communication technology and information technology and much else is governed by the celebrated Maxwell equations.

The beginning of the 20th century saw the sharpening of challenges to the existing edifice of theoretical physics based on Newton’s laws and Maxwell’s equations. The first challenge was to the concept of ether, a hypothetical medium assumed to be necessary for the propagation of electromagnetic waves. From such a presumption it followed that, observed from the Earth, light from different extra-terrestrial sources must travel at different speeds. But Michelson’s famous interferometric experiment showed in 1887 that the observed speed of light does not depend on its direction with respect to the direction in which the Earth is moving. Thus the postulation of ether as a medium at rest in the universe did not serve any sensible purpose, and the idea was abandoned. Electromagnetic waves travel in empty space; there is no ether anywhere.

Einstein's special theory of relativity is based on two postulates:

1. The laws of physics are the same for all observers in uniform (i.e. constant-velocity) motion relative to one another; this is the PRINCIPLE OF RELATIVITY.

2. The speed of light in vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

The theory has some remarkable consequences, most of which have been confirmed by experiment:

RELATIVITY OF SIMULTANEITY: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.

TIME DILATION: Moving clocks are measured to tick more slowly than an observer's 'stationary' clock, as confirmed by the muon-lifetime experiment mentioned above. [For the same reason, GPS technology involves having to make substantial time corrections for coordinating the various clocks.]

LENGTH CONTRACTION: Objects get shortened in the direction they are moving w.r.t. the observer.

MASS-ENERGY EQUIVALENCE: E = mc2; thus energy (E) and mass (m) are interconvertible, related by the square of the speed of light in vacuum (c).

FINITENESS OF MAXIMUM POSSIBLE SPEED: No physical object, message or field can travel faster than the speed of light.

However, predictions of the theory become significant only for speeds comparable to the speed of light, which is ~3 x 108 meters/second.

Unlike the Newtonian concept of absolute time which does not change from one frame of reference to another, space and time cannot be distinguished in this theory, and must be treated as a unified spacetime. Two observers moving relative to one another at a constant velocity would observe the same laws of Nature in action. One of these observers, however, might record two events on distant stars as having occurred simultaneously, while the other observer would find that one had occurred before the other. Simultaneity does not exist for distant events. In other words, it is not possible to specify uniquely the time when an event occurs, without a frame of reference. The 'distance' or 'interval' between any two events can be described only by means of a combination of space and time, and not by either of them separately. The spacetime of four dimensions (three for space and one for time) in which all events occur is the spacetime continuum.

Relativity became the premier guiding force in twentieth-century thought and art also: No independent absolute value exists, but rather truth is meaningful or significant only in a given context and time. Ditto for moral decisions. The relativity idea had a profound effect on artists, authors and musicians, and many new styles of literature, art, and music emerged in the early twentieth century.

The above painting ('The Persistence of Memory') is by Salvador Dali. As Dawn Ades wrote about it: 'The soft watches are an unconscious symbol of the relativity of space and time, a Surrealist meditation on the collapse of our notions of a fixed cosmic order'. Time seems to have stopped; a time interval of, say, one second, will extend to infinity if an identical watch were traveling at the speed of light.

Thursday, January 12, 2012

Spoilt for Choice

Courtesy Michael B. Larson
(Please click on the flowchart for a larger view.)

Saturday, January 7, 2012

9. Symmetry is Supreme

The edifice of modern physics, which we humans can be justly proud of, would have been unthinkable, even impossible, without the help and insights the scientists got from recognizing the role played by symmetry (and broken symmetry) in shaping the fundamental laws of Nature.
Long before any science, man was fascinated by symmetry (Klaus Mainzer).
Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection (Hermann Weyl).
Fundamental symmetry principles dictate the basic laws of physics, control the structure of matter, and define the fundamental forces of Nature (Lederman & Hill).
As far as I see, all a priori statements in physics have their origin in symmetry (Hermann Weyl).

We speak of symmetry in any situation in which we can rearrange things (positions in space, values of quantities in time or direction, etc.) and still get the same answer for any physical question we may ask about the rearranged system. In the picture above, the flower has '5-fold rotational symmetry': If we rotate it by 2π/5 or 72o, we cannot tell whether the rotation was indeed performed or not. The flower is 'invariant' under this 'symmetry operation'.

Take the law of conservation of energy. It says that the total energy cannot be enhanced or diminished. What that means is that if you measure the total energy today, and then again measure it tomorrow, you get the same value. The total energy remains INVARIANT as time progresses. So this is time-symmetry of total energy. There is a deep connection between conservation laws and symmetry.

We see so much symmetry in Nature, so the question arises: Why is that so? In my recent book Latent, Manifest, and Broken Symmetry (2011) I have argued at length that the basic underlying cause of this is simply the second law of thermodynamics ('minimization of free energy'). I shall not repeat the argument here in this short post.
But we also see so much BROKEN SYMMETRY (or reduced symmetry) around us. It is the second law again. If a system can lower its free energy further by making a phase transition to a lower-symmetry phase or state, it would do so. The familiar example is liquid water freezing to crystals of ice on cooling to 0oC. Liquid water is highly symmetric: It looks the same from any direction, meaning that it is invariant to any rotation around any axis of rotation; it is isotropic. By contrast, a crystal of ice has a far lower degree of rotational symmetry; it is anisotropic.

The figure above (called the 'Mexican-hat potential') is an illustration of spontaneous breaking of symmetry. The ball could have rolled down along any direction, but once a random choice has been made spontaneously, the final state has a lower ('broken') symmetry. This figure also illustrates ‘unstable equilibrium’. The top position has zero slope, and therefore corresponds to equilibrium. But this is unstable equilibrium because it is not robust against even a minor displacement away from equilibrium. Unstable equilibrium can lead to spontaneous breaking of symmetry as the system seeks a state of stable equilibrium.

The moment of the Big Bang (cf. Part 2) was the moment of highest symmetry: No structure, no preferred direction, no inhomogeneity. Then a very brief interlude of cosmic inflation occurred (cf. Part 8),  during which even the tiniest of quantum fluctuations got amplified hugely; this created gradients. The emergence of matter from the earlier radiation field was a symmetry-breaking phase transition. The radiation field was translation-invariant, and the appearance of matter broke, among other things, the translational symmetry. A field called the Higgs field has been postulated in cosmology to understand these phenomena. This field breaks the symmetries of the interactions among the elementary particles, and gives the particles their mass.

Nature abhors gradients because they embody states away from equilibrium, meaning that there is scope for lowering the free energy. Phase transitions occur to lower the free energy, and there is usually a concomitant lowering or 'breaking' of symmetry.


[Sometimes it is not very appropriate to use the term 'phase transition'; a better description is 'bifurcation in phase space', but that is only a technicality.]

When objects interact with one another, only four types of interaction can be possibly involved: the gravitational interaction; the electromagnetic interaction; the weak nuclear interaction; and the strong nuclear interaction. But at the moment of the Big Bang there was only one 'unified' interaction. It is only because of the cooling of the universe that the four interactions known to us today emerged one by one, engendered by symmetry-breaking phase transitions.

Broken-symmetry-considerations occupy centre-stage in theoretical physics. Particularly in particle physics, progress often means postulating, and then discovering, a new broken symmetry. Why only a broken (or ‘hidden’) new symmetry? Because an unbroken symmetry would have been manifest already, and would thus be old symmetry rather than new symmetry. Broken symmetries in Nature are not always very obvious; one has to go looking for them.
Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop (C. N. Yang, Nobel laureate).

Thou hast no faults, or I no faults can spy;
Thou art all beauty, or all blindness I (Christopher Codrington).

'Diatoms are single-celled organisms found in oceans all over the world. There are estimated to be 100,000 species of these micron-sized creatures in existence, and they play a crucial role as one of the main food sources for marine organisms, including fish, molluscs and tunicates, such as sea squirts'