Sunday, 19 December 2010

Brownian Motion - Atoms are Real afterall!

Even at the end of the 19th Century, scientists couldn't decide if atoms were real or just a convenient way to be able to calculate bulk properties of matter. Good amount of debate was going on - to the chemists it looked that atoms are real but the science of thermodynamics did not need atoms and thermodynamics was the queen of sciences at the end of the 19th Century with the Industrial Revolution providing the means of creating wealth and creating the feel-good factor in plenty.

How Einstein demonstrated the reality of atoms and counted them is fascinating.

I have published the slides of my talk on Einstein and the Theory of Relativity in the following to demonstrate how Einstein worked it out... (Click on the image for a full screen view)

Saturday, 18 December 2010

Specific Heat of Solids... Another problem with Classical Physics!

Towards the end of the 19th Century, classical physics had serious difficulties in explaing many observations. Einstein provided a solution of the specific heat of metals problem by assuming that energy absorption is quantised and is not continuous. This was a radical departure from the way physics was done in the 19th Century and demonstrates yet again the bold and visionary nature of Einstein's genius.
In the following I have published my slides from the talks on Einstein and the Theory of Relativity...

The Scientific Method - How Scientific Theories Get Accepted...

Many a times people ask me if Einstein's General Relativity has been proved wrong.

Probably, what they are reading is some article in popular press about some data which is not totally explained by General Relativity - sort of information requiring dark energy/dark matter etc.
In the following I want to address the way a scientific theory becomes accepted as a good description of nature but only until some new data contradicts the predictions of the theory in a fundamental way. Then scientists try to formulate a new theory, either extension of the old theory or something radically different, which has to pass the usual tests - this is what I want to discuss in the following. I have reproduced some slides from my talks on Einstein and The Theory of Realtivity:

This is a painting (refer to Wiki) showing the general belief during the 19th century that horses legs are splayed when they gallop. New evidence from Muybridge in 1887 shows that the legs are actually gathered together and are not splayed.


The usual process of constructing a scientific theory is best illustrated through a flow chart - a series of steps:
1. Define/Identify the problem
2. Form a hypothesis/Theory
3. Make observations to test the predictions of the Theory
OR Conduct some experiments to test the hypothesis
4. Data collected from 3. is analysed and results obtained
5. Do experiments and data support the hypothesis/theory?
5A: IF YES Then the theory is good and you can publish the results
5B: IF NO Then you must first check if the experiment has any faults which might be affecting the results. If the experiment is faulty then correct it. If experiment is good then
6. Discard the Theory and start again by formulating a new Theory (Go to Step 2)

Sunday, 12 December 2010

Einstein Rides a Light Wave...

This is a thought experiment Einstein might have done (not necessarily in the way I have described but the idea is interesting)
A light wave is an electromagnetic wave (EM Wave) which has oscillating electric and magnetic fields. Suppose Einstein travels with the wave at the speed of light! What will he see?
He will see a constant electric field - this will not generate any oscillating magnetic field which in turn cannot generate an electric field. There will be no oscillating electric and magnetic fields that typify an EM wave. It would seem that no wave would appear to exist.
This is the interesting part - if you travel with the speed of light then you can not transmit or receive information: there are no EM waves.This encouraged Einstein to postulate that speed of light is the maximum speed allowed and nothing can move with a speed greater than the speed of light.

Not tremendously convincing but the idea is interesting.

Friday, 10 December 2010

On the Nature of Light: Wave-Particle Duality

Three fundamental quantities that help us to perceive the world around us

Space 3-D space - We can use a ruler to measure this
Time - Use a clock - atomic clocks can be accurate to 1 sec in a billion years
Means of transmitting information – LIGHT or EM waves in general…..

The speed of light is the fastest speed at which information/energy can travel
Speed of light is 300,000 km per second
The finite speed of light means that the time we receive the signal is later than the time the signal left the source (we are observing what happened in the past). This situation may be different for different observers and can create some bizarre effects.
Light plays a fundamental role in the theory of relativity.

Puzzling behaviour of light: Sometimes light acts as a wave while at other times it behaves like a stream of particles (photons) - Light displays a dual nature

But first a brief history:
1675 - Isaac Newton thought that light was composed of corpuscles (particles of matter) which were emitted in all directions from a source. Newton Published Optiks in 1704
Despite some serious problems with this view, Newton’s reputation helped the particle theory of light to hold sway during the 18th century

Robert Hooke (1635 - 1703) proposed in 1660 a wave theory of light.
Christiaan Huygens (1629 - 1695)in 1690 suggested that light was emitted in all directions as a series of waves in a medium called the Luminiferous ether
Thomas Young (1773 – 1829) in 1801 performed the Double-slit Interference Experiment.
Some say that it is the most beautiful experiment in physics.

The observations of the double-slit experiment could only be explained if light behaved as waves...

In 1860s, Maxwell combined the fields of electricity, magnetism and light and predicted the existence of electromagnetic (EM) waves. In his brilliant and very successful theory, Maxwell showed that all EM waves travel at 300,000 km/s which was the same as the measured speed of light.
Light is the “visible” EM wave
EM waves span a wide spectrum from radio waves to nuclear gamma rays

It was thought that as a wave motion, light would require a medium to travel - such a medium was called ether which was supposed to pervade the whole universe and had some really bizarre properties like being extremely stiff to allow vibrations of very high frequencies, be extremely thin (rare) to allow unimpeded motion of planets and objetcs through it etc. Attempts were made to measure the speed of the Earth relative to the ether but even the most sensitive experiments failed to find any evidence of the expected relative motion.
This caused a big headache for physicists at the end of the 19th Century.

Thursday, 9 December 2010

Einstein suggestes quantum nature of Light - Photoelectric Effect

Photoelectric Effect - Another Problem for Classical Physics
Photoelectric effect is the emission of electrons from a metal surface by gaining energy from light.
First observed by Heinrich Hertz (1857 – 94) in 1887
Studied in detail by Philipp Lenard(1862 – 1947) in 1902
Lenard was awarded Nobel Prize in 1905

According to classical physics, the metal surface simply soaked up light energy and sooner or later, depending on the intensity of the light, it would accumulate enough energy to cause emission of electrons.
Experiments did not verify this and cast doubt on the validity of the wave theory of light – a cornerstone of Maxwell’s theory of electromagnetic waves

Experimental results were:
1. If the light is below a certain frequency f0 , then no electrons would be produced however long we shine it on the metal surface.
2. For light frequency above f0 electrons would be produced immediately, with no time delay even for extremely weak light intensities

In 1900, to explain a problem with black-body radiation spectrum Planck had made an ad hoc assumption that emission and absorption of energy can occur only in discrete amounts.
Einstein made the bold assumption that light consists of a stream of particles; the energy of individual particles or quanta is determined by the frequency of light. Einstein’s light quanta are now called photons
Energy of a photon is E = h x f where h is the Planck’s constant.

According to Einstein, in photoelectric emission, a light photon penetrates the metal and knocks an electron loose. A minimum energy is required to knock off an electron from the metal. Hence photons below a certain frequency f0 do not have sufficient energy (= hf0) to release electrons. Increasing the intensity of the light increases the number of photons and hence the number of electrons emitted would increase.

Einstein’s theory raises a fundamental question:
Is light a wave, or a stream of photons?

Wednesday, 8 December 2010

Black Body Radiation - Planck's Solution

(Planck’s assumption of) ...the atomistic (quantum) structure to energy, governed by the universal constant h ... became the basis of all twentieth-century research in physics and has almost entirely conditioned its development ever since. ... Albert Einstein 1950

Every body radiates energy over a range of wavelengths.
How much energy is emitted at each wavelength (shape of the curves) is predicted by the classical theory. Well established theories of Thermodynamics, Statistical mechanics and Electromagnetism
form the basis of such predictions.

In 1900 Planck suggested that physics should abandon the assumption that energy is continuous and wavelike. Instead, if energy can only be absorbed and emitted in discrete packets (or quanta now called photons ), theory can be made to fit observations exactly.

Energy of a quantum = h x its frequency

Planck’s suggestion was ad hoc and had no theoretical basis This troubled a lot of people including Planck. Planck believed in the wave nature of light (energy) and insisted that it might be in the way individual matter atoms interact with radiation that gives rise to the quantum aspects in the emission of radiation. It was Einstien who in 1905 first suggested that light (energy) is actually quantised following Planck's equation.

Planck was awarded Nobel Prize for his work in 1918. Planck and Einstein became good friends. Planck supported Einstein during the turbulent period when Jews were being prosecuted in Germany.

Problems with Classical Physics around the year 2000

Some selected pioneers in the development of Physics

Leucippus (first half of 5th century BC) first proposed atomism
Archimedes (287 BC – 212 BC) derived many correct quantitative descriptions of mechanics, statics, hydrostatics, levers etc.
Of the modern physicists, the most famous is Isaac Newton (1642 - 1727) who built on the works of Galileo Galilei (1564 - 1642) and Johannes Kepler (1571 - 1630)
James Clerk Maxwell’s (1831 – 1879) theory of electromagnetism unified the fields of electricity, magnetism and optics
The work of Albert Einstein (1879 – 1955) marked a new direction in physics that continues to the present day.

Between 1600-1900 AD, great progress was made in explaining the way the world is organised. Classical physics was largely based on observations at macroscopic scale and at modest values of velocities - the laws of physics were very successful in explaining a large body of empirical data.
However, the world operates on the atomic/molecular level.
Speeds at which electrons and other particles move are comparable to the speed of light. Physics works differently for these conditions.

Quantum Physics and Relativity provide the theoretical basis to understand the new physics. The results of quantum physics and relativity reproduce those of classical physics for macroscopic systems and for low velocities.

By the end of the nineteenth century, the general belief was that science and technology are fully developed. In 1897 Charles H. Duell, Director of the US Patent Office, advised President McKinley to close down the Patent Office, because it no longer serves a purpose since:
“Everything that could ever be invented had already been invented”!

but physicists were worried...

Serious cracks had begun to appear in Classical Physics!

By the year 1900, Classical Physics started to have serious difficulties with the experimental results from black-body radiation, photoelectric effect etc.
Results were in contradiction with the fundamental laws that had served well for the past two centuries.

Additionally, the nature of light and of the newly discovered X-rays and nuclear radiation just did not make sense. Probably most serious of all, physics could not define a reference frame with respect to which laws could be stated – the whole framework on which physics was based was in doubt!

Tuesday, 7 December 2010

Albert Einstein Early Life 1879 to 1905

In the following and later blogs (to come in due course) I have published some outlines from my talks on
Albert Eistein and the Theory of Relativity
I am truly a ‘lone traveller’ and have never belonged to my country, my home, my friends, or even my immediate family, with my whole heart... --- Albert Einstein 1930

In 1905, Albert Einstein published his famous Special Theory of Relativity and overthrew commonsense assumptions about space and time. Relative to the observer, both are altered near the speed of light: lengths appear to contract; clocks tick more slowly.

A decade and a year later, Einstein further challenged conventional wisdom by describing gravity as the warping of spacetime, not a force acting at a distance.
Since then, Einstein's revolutionary insights have largely stood the test of time. One by one, his predictions have been borne out by experiments.
Paul Dirac called General Relativity probably the greatest scientific discovery ever made
Max Born called it the greatest feat of human thinking about nature

In 1999, an opinion poll of 100 leading physicists ranked Einstein the "greatest physicist ever"
In many ways, Einstein has become a mythical figure
He has been the subject of or inspiration for many novels, films, plays, and works of music.
His expressive face and distinctive hairstyle have been widely copied and exaggerated.
He is frequently depicted as an absent-minded professor -
"a cartoonist's dream come true".
While Einstein is best known for his theory of relativity, he had contributed many other groundbreaking ideas

Einstein – Early Life 1879-1905
Einstein was born on 14 March 1879 in Ulm, in Württemberg, Germany
1880 – Parents moved to Munich to set up a company to manufacture electrical equipment. Parents were non-observant Jews.
Einstein attended a catholic school until age 10
1894 – Parents moved to Pavia, Italy. Einstein stayed in Munich to finish his studies at the Luitpold Gymnasium
Einstein clashed with authorities and resented the school's rules and teaching method. He later wrote that the spirit of learning and creative thought were lost in strict rote learning.
1895, he convinced the school to let him go by using a doctor's note and joined his family in Pavia
Einstein's youth could be summarized as rebellious and subversive of authority
1896: renounced his citizenship in the German Kingdom of Württemberg to avoid 3 years of compulsory military service. Einstein became stateless
1901: became a Swiss citizen
1896: After a failed attempt, enrolled in ETH in Zurich, Switzerland, ETH is ranked among the top universities in the world with more than 20 of its graduates winning Nobel Prize.
Both at the Gymnasium and at ETH, Einstein found it difficult to adjust and was hugely disliked by his teachers. He did not regularly attend lectures at ETH and borrowed notes from Grossman.
‘Your mere presence here undermines the class’s respect for me’ -- Gymnasium Teacher 1894
Hermann Minkowski referred him as a "lazy dog".

Einstein, later said at at ETH, he seems to have been written off as virtually unemployable,"a pariah, discounted and little loved”

At ETH, Einstein made good friends with Michelangelo Besso, a somewhat eccentric but brilliant electric engineer and Marcel Grossmann, a gifted mathematician.
In June 1902, Grossman’s father arranged Einstein to be interviewed for a position as technical expert in the Swiss Patent Office. He accepted the position of rank 3rd class – not a very high ranking.
Away from the coercive environment of academia, Einstein could once again start to think about science, and resumed his self-directed studies
The work at the Patent Office was undemanding and left Einstein time to develop the momentous ideas that his mind had already started churning.
In 1905 he completed his doctoral thesis.
In 1905 Einstein published four groundbreaking papers in the prestigious journal Annalen der Physik which revolutionised the way physical theories are formulated
These papers not only explained some of the difficulties that physics at the turn of the century was confronted with, but also formed the basis of the development of modern physics on which much of the industrial innovation is now based

The papers brought Einstein to the attention of the scientific world and soon he became one of the most respected physicist of his times
One also notes how the scientific establishment has changed. It will be difficult to imagine a reputed journal publishing papers from an unknown scientist

Einstein met Mileva Maric, a fellow student at ETH
They married in 1903 and had two sons Hans (1904) and Eduardo (1910)
The couple divorced in 1919.
They had negotiated a settlement whereby the Nobel Prize money that Einstein anticipated he would soon receive was to be placed in trust for their two boys, while Marić would be able to draw on the interest, but have no authority over the capital without Einstein's permission

Saturday, 4 December 2010

Nobel Prizes related to Relativity...Nobel Prizes in Relativity

Much of modern physics is founded on Quantum Physics and Einstein's Theories of Relativity - this is evidenced by a large number of Nobel Prizes related to the development and testing of the predictions of Special and General Relativity.

I give a brief description of the important ones: More detailed information is available in the website of the Nobel Prize Organisation.

I shall put a list of Nobel Prizes for work in Quatum Physics to coincide with my talks on Quantum Mechanics sometime in 2011. Watch this space.

1921 - Albert Einstein
Ironically, while relativity has led to so many Nobel prizes, it only played a minor role in Einstein's own. The Nobel committee's brief prize announcement refers to Einstein's "services to Theoretical Physics" with explicit mention given only to his finding the law of the photoelectric effect.

1933 - Paul Dirac
Dirac's prize was the first of many given for work on the connection between special relativity and quantum theory.
Dirac was the pioneer of relativistic quantum mechanics and formulated the Dirac equation, the first equation for the quantum behaviour of relativistic matter particles. He discovered a fundamental relativistic quantum phenomenon: for every species of relativistic particle, there must be a kind of mirror image, a species of corresponding antiparticles. In a world in which electrons exist, which carry negative electric charge, Dirac's equation demands the existence of anti-electrons, particles with the same mass as electrons, but a positive electric charge.

1936 - Carl D. Anderson
What, at first sight, appeared to be a stumbling stone for Dirac's theory - where were those anti-electrons he postulated? - later turned into a triumph. Among the particles of cosmic rays, a highly energetic particle radiation reaching the earth's surface from space, Carl Anderson discovered traces of anti-electrons. Diracs anti-particles, with the same mass as electrons but the opposite electric charge, really do exist! Anti-electrons are now called positrons.

1949 - Hideki Yukawa
The force that bonds protons and neutrons together to form atomic nuclei has a strictly limited range: of the order of a trillionth of a metre. Yukawa found an explanation for the short-range nuclear force that is directly linked to the fact that the carrier particle of nuclear force has a non-zero (rest) mass. He derived this directly from a relativistic quantum equation for massive particles.

1951 - John Cockcroft and Ernest T. S. Walton
Cockcroft and Walton bombarded atomic nuclei of the element Lithium with fast protons, thus creating helium nuclei in the first controlled transmutation of one species of nucleus to another. Summing up the energies before and after the transmutation, they tested directly the equivalence of mass and energy postulated by Einstein: the helium nuclei that result have a slightly lower mass than that of proton and lithium nucleus combined, and this difference in mass leads to a kinetic energy of the resulting nuclei that is higher than expected by non-relativistic physics, exactly following Einstein's prediction.

1955 - Willis Eugene Lamb and Polykarp Kusch
Lamb and Kusch performed precision measurements, establishing the reality of two effects: called the Lamb shift and the electron's magnetic properties that Dirac's equation could not correctly predict. These measurements contributed to the eventual development of relativistic quantum feld theories: of quantum electrodynamics, the relativistic quantum theory of the electromagnetic field.

1959 - Emilio Segrè and Owen Chamberlain
In relativistic quantum theories, for every species of particle, there is a species of antiparticles. Segrè and Chamberlain received their prize for the discovery of anti-protons, the antiparticles of protons.

1963 - Eugene Wigner
The relativity principle states that observers that are in motion relative to each other are on equal footing; the physical laws are exactly the same for each of them. In physics, such equality is called a symmetry. Whether or not a physical theory, be it a model of electromagnetic phenomena, fluid dynamics or a theory of heat, is consistent with the relativity principle can be examined in a general framework that analyzes the theory's symmetries. Wigner was the first to apply this framework to quantum theory, and laid the foundation of modern relativistic quantum feld theories.

1965 - Shin-Itiro Tomonaga, Julian Schwinger, Richard P. Feynman
In quantum field theories, not only the matter particles, but also the forces acting between them follow quantum laws. The distinction between matter and forces becomes blurred: The action of a force is represented by the exchange of particles - the carrier particles.
Tomonaga, Schwinger and Feynman formulated a theory of relativistic quantum forces for the simplest case, that of the electromagnetic force, creating what is known as quantum electrodynamics.
This was the starting point leading to the formulation of the more general quantum field theories of the standard model of particle physics.

1974 - Antony Hewish
The discovery that won Hewish his prize, although not a consequence of relativity, is nonetheless an important step for relativistic astrophysics.
Together with his graduate student Jocelyn Bell-Burnell, Hewish discovered the first pulsar, opening up the field of observational astronomy of neutron stars.

1978 - Arno Penzias and Robert Wilson
Penzias and Wilson won their Nobel prize for the first detection of the cosmic background radiation, an afterglow from the early, hot days of the universe. With their discovery, they confirmed a prediction made by Ralph Alpher and Robert Herman in 1948 on the basis of the relativistic big bang models.

1983 - Subramanyan Chandrasekhar and William A. Fowler
The Chandrasekhar mass is the maximal mass for which the inner pressure of the White Dwarf can resist further collaps. For remnants with higher mass the collapse continues, forming a neutron star or even a black hole.
Fowler won the prize for his research on the origin of the chemical elements in the universe. Part of that work concerned another prediction of the big bang models of relativistic cosmology, namely that of the formation of light elements in the early universe.

1993 - Russell A. Hulse and Joseph H. Taylor
Hulse and Taylor discovered the first binary pulsar: a binary in which a pulsar and a companion neutron star orbit each other. Their observations of this binary pulsar, called PSR1913+16, led to the first indirect detection of gravitational waves and provided some sensitive tests of the General theory of Relativity.

2002 - Riccardo Giacconi
Giacconi won the prize for his pioneering work in X-ray astronomy, in part for the first detection of objects tha are now widely believed to be black holes.

2006 - John C. Mather and George F. Smoot
With the COBE satellite, Mather and Smoot made precise measurements of the black body nature of the cosmic background radiation, confirming an important prediction of the big bang models. The tiny fluctuations observed in the background microwave radiation are the first seeds for the large scale structure in the Universe.

Friday, 26 November 2010

Einstein's Credo

Einstein was not only a brilliant scientist but also a great thinker. He had profound views about religon, politics and society in general.


In August 1932 Einstein wrote "My Credo" in Caputh (Einstein’s summer house in Potsdam, Germany) and read it for a recording by order and to the benefit of the German League of Human Rights.

My Credo
"It is a special blessing to belong among those who can and may devote their best energies to the contemplation and exploration of objective and timeless things. How happy and grateful I am for having been granted this blessing, which bestows upon one a large measure of independence from one's personal fate and from the attitude of one's contemporaries. Yet this independence must not inure us to the awareness of the duties that constantly bind us to the past, present and future of humankind at large. Our situation on this earth seems strange. Every one of us appears here, involuntarily and uninvited, for a short stay, without knowing the why and the wherefore. In our daily lives we feel only that man is here for the sake of others, for those whom we love and for many other beings whose fate is connected with our own.

I am often troubled by the thought that my life is based to such a large extent on the work of my fellow human beings, and I am aware of my great indebtedness to them.
I do not believe in free will. Schopenhauer's words: 'Man can do what he wants, but he cannot will what he wills,' accompany me in all situations throughout my life and reconcile me with the actions of others, even if they are rather painful to me. This awareness of the lack of free will keeps me from taking myself and my fellow men too seriously as acting and deciding individuals, and from losing my temper.

I have never coveted affluence and luxury and even despise them a good deal. My passion for social justice has often brought me into conflict with people, as has my aversion to any obligation and dependence I did not regard as absolutely necessary.

I have a high regard for the individual and an insuperable distaste for violence and fanaticism. All these motives have made me a passionate pacifist and antimilitarist. I am against any chauvinism, even in the guise of mere patriotism.

Privileges based on position and property have always seemed to me unjust and pernicious, as does any exaggerated personality cult. I am an adherent of the ideal of democracy, although I know well the weaknesses of the democratic form of government. Social equality and economic protection of the individual have always seemed to me the important communal aims of the state.

Although I am a typical loner in daily life, my consciousness of belonging to the invisible community of those who strive for truth, beauty, and justice keeps me from feeling isolated.
The most beautiful and deepest experience a man can have is the sense of the mysterious. It is the underlying principle of religion as well as of all serious endeavor in art and science. He who never had this experience seems to me, if not dead, then at least blind. To sense that behind anything that can be experienced there is a something that our minds cannot grasp, whose beauty and sublimity reaches us only indirectly: this is religiousness. In this sense I am religious. To me it suffices to wonder at these secrets and to attempt humbly to grasp with my mind a mere image of the lofty structure of all there is."

Courtesy of the Albert Einstein Archives, Hebrew University of Jerusalem, Israel.

Tuesday, 28 September 2010

Einstein and Relativity talks by Ravi Singhal start in October 2010

11 am to 12 noon on Saturdays
23, 30 October; 6, 13, 20 and 27 November 2010
James Watt Auditorium, E.K. Technology Park, G75 0QD
(Ample free parking on site)

Einstein is considered the greatest physicist of the 20th century. Einstein’s theory of relativity forever altered our understanding of the Universe. In this series of talks, we shall learn about Einstein’s life and how working in isolation he was able to resolve many of the serious difficulties that physics faced around 1900 AD and prepared the ground for the development of modern physics on which most industry is based.
Without using mathematics, we shall learn about the nature of gravity and make sense of some of the bizarre effects like the twin paradox, bending of light by stars that the theory of relativity predicts.

Speed of light plays a fundamental role in the theory of relativity. It is fascinating to learn how light appears to behave both as a wave and as a stream of particles.

Einstein is best remembered for his theory of relativity but it was his work regarding the nature of light that won him the Nobel Prize in 1921. Einstein resolved the longstanding question about the existence of atoms and molecules, and determined their sizes. Among other groundbreaking discoveries, theory of lasers was developed by Einstein more than 40 years before they were invented.

Talks are free to attend; e-mail to confirm interest. Please check for updates.

Friday, 29 January 2010

Why do we always see the same side of the Moon?...

This is due to the effect known as 'Gravitational Locking'. The Earth's gravitational field slowed the Moon's spin over time and now the Moon spins about its axis at a rate such that the time to rotate once on its axis is exactly equal to the time it takes to go round the Earth. The diagram (click on the figure to see it clearly) explains how this results in effectively the same side of the Moon facing the earth all the time.
Gravitational Locking is observed in the case of other planets as well whose satellite moons are locked in the same way as the Moon is locked to the Earth.

Sunday, 17 January 2010

Units in Cosmology...

In the study of cosmolgy, one encounters distances and masses which are extremely large compared with what we can easily comrehend.

It would be fair to say we can judge numbers that are a few hundred times a billion. We hear of companies worth 100 billion pounds etc. and appear to be comfortable with such statements, but a million billion will be difficult to understand.

Average distance of the Sun from the Earth is 150 million km and the diameter of the Milky Way galaxy is about a million million million km.
Mass of the Sun is 2000 billion billion billion kg and the numbers get bigger as we study the galaxies.

Therefore in astronomy we talk about a different set of unit.

Unit of mass is one solar mass = 2000 billion billion billion kg
Rest of the heavenly bodies are weighed relative to the Sun.
The situation about length is not so simple. There are three different units used depending on the context. These are:

1. The astronomical unit or AU:
1 AU ~ 150 million km = 149,597,871 km
An Astronomical Unit is approximately the mean distance between the Earth & the Sun.
AU is used when discussing distances of planets and other objects in the Solar System.

2. The light Year or Ly:
A Ly = about 10 million million km
A light year is the distance traveled by light in vacuum in one year.
It takes light 8.32 minutes to travel from the Sun to the Earth.
Ly is a big unit, it is about 63,000 astronomical units.
Diameter of the Milky Way galaxy is about 100,000 Ly
and the size of the observable Universe is measured in billions of Lys!
Light Year is the most commonly used unit when one is talking about galaxies and the Universe. It is also starightforward to understand.

3. Parsec or pc:
One parsec = 31 million million km or 210260 AU or 3.26 Ly
Parsec is based on the change of angle in a star's position when viewed from the Earth as it revolves round the Sun. We shall not use this unit in our discussions.

Saturday, 16 January 2010

In Cosmology one deals with big numbers...

Writing numbers that are very big or very small ...
In science, you will encounter numbers that are very big or extremely small. These can be rather inconvenient to write out in the normal notation.
Powers of ten is a useful shorthand method of writing very large or very small numbers.

For example:
One thousand (1000) is 103 ; reads 'ten to the power 3' and is 1 followed by 3 zeros
One divided by 1000 is 0.001 or 10-3 ; reads 'ten to the power minus 3'

And that is it -

the positive power on ten tells us how many zeros are after 1.
negative powers of ten tell us the position of the 1 after the decimal point.

Distance of the Sun from the Earth is 150 million km or 150,000,000 km or 15 x 107 km.
Diameter of an atom is 0.0000000002 m or 2 x 10-10 m.

Multiplication and division of powers of ten numbers is very easy...

When you multiply two numbers powers add

When you divide two numebrs powers substract.

Example: Multiply 2 million by 4 million

Longhand: 2,000,000 x 4,000,000 = 8,000,000,000,000

Powers of ten: 2 x 106 x 4 x 106 = 8 x 1012

Exploring the Cosmos

Dr Ravi Singhal
Free Science Talks for Secondary Pupils & Adults
No Science Background Needed

11 am to 12 noon on Saturdays
30 January; 6, 13, 20 and 27 February 2010
James Watt Auditorium, E.K. Technology Park, G75 0QD

(Ample free parking on site)
In Partnership with: Glasgow University and Scottish Enterprise, Lanarkshire

The size and complexity of the Universe is truly astounding. The Sun is but one of more than 200 billion stars in the Milky Way galaxy and the observable Universe could contain 100 billion galaxies. It takes light a hundred thousand years to travel across the Milky Way. The Universe
is populated with strange and bizarre objects like the white dwarfs, neutron stars, black holes; the true nature of which we are now beginning to understand. Prodigious amount of energy is produced by the heavenly bodies – the Sun produces a million times more energy in one second than we consume globally in a year!

Human curiosity has always wondered about the nature of the Universe we live in and attempted to rationalise what could be observed. Our understanding has enormously improved due to technological advances of the last century. However, many questions remain unanswered…..

Have you ever wondered how the distance, size, motion, temperature, composition of a star are measured? How are stars formed and how do they die? A frequently asked question is - How do they know? Exploring the Cosmos is a programme of ten talks, five of which are being announced at this stage. Come along to the talks to find out.
The fifth talk will discuss the search for extraterrestrial life.

Talks are free to attend; e-mail to confirm interest. Please check for updates.

The Science for All programme is a community education initiative. The talks are aimed at the general audience and no prior background in science is assumed. The talks are also suitable for secondary school pupils. The presentation promises to be visually attractive and highly informative.