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- The Great Scientists Theory of Relativity
- The Great Scientists:
The Great Scientists Theory of Relativity
-by Chirantan Deb
ARCHIMEDES
He introduced many new ideas in other fields as well. He also invented the science of Hydrostatics, which is the study of fluid dynamics. He had proved that when a solid is weighed in air, and then in liquid, the loss of weight is equal to the weight of liquid displaced. One of his most important mechanical inventions was the Archimedean screw or the helical screw to lift water from one level to another.
When the Roman attacked Syracuse in 214 BC, Archimedes designed a number of defense weapons. One was a magnifying glass which directed the sun’s rays on to an object and set it alight. He also devised a system of levers for moving heavy loads with little effort.
Archimedes, born in Syracuse on the island of Sicily, is one of the greatest mathematician, physicist, astronomer and engineers of all times. He studied science under the Canon of Samos at the University of Alexandria, a hub of learning at that time. He devised many basic theorems regarding the geometry of various shapes like cones, circles, planes and parabola and they form the building blocks of mathematics.
Amazing:
Archimedes used mirrors to reflect sun rays and burn the approaching ships enemies. This phenomenon, also called ‘Archimedes ray’, was used to repel an attack by Roman forces during the siege of Syracuse.
ARYABHATA
Aryabhata is the author of several treatises on the mathematics and astronomy. His greatest work is Aryabhatiya, which he wrote in 499 AD. It is a scholarly treatise on mathematics and astronomy. The book deals with various topics like geometrical figure and their properties, arithmetic progression, simple and quadratic equations as well. It also gives rules and methods of trigonometric sine tables in which sine and cosine are known as jya and koti-jya.
Aryabhata formulated the rules for calculating the square and cube roots by the arithmetical method which are used even today. He gave an accurate approximation for pi. (3.14) The knowledge of zero was implicit in Aryabhata’s place-value system. He even stated that the earth is spherical and rotates about its axis. In fact, Aryabhatiya was extensively referred to in the Indian mathematical literature, and has survived to modern times.
Aryabhata was an Indian astronomer and mathematician of the 5th century AD. According to some scholars he was the Kulapathy (Vice-Chancellor) of the Nalanda University.
First Indian Satellite
The first Indian Satellite was named Aryabhata in honour of the Indian astronomer. The Satellite, primarily an experimental was made with the help of Soviet Union, and conducted experiments on atmospheric research.
EUCLID
The principles of Euclidean geometry are deduced from a small set of initial assumptions. His ‘Elements’ is the most successful textbook in the history of mathematics. Euclid also wrote works on perspective, spherical geometry, and possibly quadric surfaces. His book contains not only the geometrical results, but also many theories related to numbers. He wrote about the connection of perfect numbers and Mersenne primes, the infinitude of prime numbers and an algorithm for finding the greatest common divisor of two numbers. He also contributed a lot to poetry and wrote many tragedies as well. He is even considered to be one of the five great play- wrights of his time!
Euclid, a Greek mathematician of Hellenistic period is known as ‘The Father of Geometry’. He lived in Alexandria and taught scientific subjects at the new university set up there by Alexander the Great. He worked out his theorems, added some of the already existing ones, and put them all together in 13 books, titled, ‘The Elements’.
The influence of Euclid
The influence of Euclid is obvious on other scientists as well. Sir Isaac Newton wrote his great book , the Principia Mathematica, in a ‘geometric’ form, similar to that of the Elements.
PYTHAGORAS
Known as ‘the father of numbers’, Pythagoras believed that everything was related to mathematics and, through mathematics, everything could be predicted and measured in rhythmic patterns or cycles. He was very interested in music as well and discovered that musical notes could be translated into mathematical equations.
Pythagoras was the first man to call himself a philosopher, and his ideas had a marked influence on Plato.
Who are the Mathematikoi?
Pythagoras, a brilliant thinker, was born on Samos, a Greek island. Later, he settled in the Greek colony of Croton in Italy in about 530 BC. Here, he formed an elite circle of followers around himself called Pythagoreans. He made influential contributions to philosophy and religious teaching in the late 6th century BC. But, he is best known for the Pythagorean Theorem which bears his name. According to his theorem, if a triangle is right-angled then the square of the hypotenuse is equal to the sum of the square of the base and altitude. Pythagoras opened his school to male and female students alike. Those who joined the inner circle of Pythagoras’ society called themselves the Mathematikoi. They lived at the school, owned no personal possessions and were required to assume a mainly vegetarian diet. ‘Pythagorean diet’ was a common name for the abstention from eating meat and fish, until the coining of ‘vegetarian’ in the 19th century.
BHASKARA II
Bhaskaracharya became head of the astronomical observatory at Ujjain, the leading mathematical centre in India at that time. Outstanding mathematicians such as Varamihira and Brahmagupta had worked there, built up a strong school of mathematical astronomy. Bhaskaracharya achieved an understanding of calculus, astronomy, the number systems, and solving equations, which was not to be equaled anywhere in the world for several centuries.
Bhaskaracharya’s main works were the ‘Lilavati’, ‘Bijganita’, and ‘Siddhanta Shiromani.’ Some scholars have suggested that Bhaskaracharya’s work influenced later developments in the Middle East and Europe. The Mughal emperor Akbar commissioned a famous Persian translation of the ‘Lilavati’ in 1587.
A story about Bhaskara
Lilavati was the name of the daughter of Bhaskaracharya. From her horoscope, Bhaskaracharya had discovered the only possible hour for her wedding. He placed a cup with a hole at the bottom, in a vessel filled with water, so that the cup would sink at the beginning of that particular hour. But out of curiosity, Lilavati bent over the vessel, and a pearl fell that into the cup from her dress, blocked the hole in it. The lucky hour passed without the cup sinking. So, Lilavati could never get married. Bhaskaracharya wrote a manual of mathematics naming it Lilavati, to console his dejected daughter.
Bhaskara II (1114-1185) was an Indian mathematician and astronomer born near Bijapur in Karnataka. He was known as ‘Bhaskaracharya’ meaning ‘Bhaskara the teacher’.
Theory of Relativity - The Basics
-by Rounak Chakraborty
The Theory of Relativity, proposed by the Jewish physicist Albert Einstein (1879-1955) in the early part of the 20th century, is one of the most significant scientific advances of our time. Although the concept of relativity was not introduced by Einstein, his major contribution was the recognition that the speed of light in a vacuum is constant and an absolute physical boundary for motion. This does not have a major impact on a person's day to day life since we travel at speeds much slower than light speed. For objects traveling near light speed, however, the theory of relativity states that objects will move slower and shorten in length from the point of view of an observer on Earth. Einstein also derived the famous equation, E = mc2, which reveals the equivalence of mass and energy. When Einstein applied his theory to gravitational fields, he derived the "curved space-time continuum" which depicts the dimensions of space and time as a two-dimensional surface where massive objects create valleys and dips in the surface. This aspect of relativity explained the phenomena of light bending around the sun, predicted black holes as well as the background radiation left from the Big Bang. For his work on relativity, the photoelectric effect and blackbody radiation, Einstein received the Nobel Prize in 1921.
Theoretical Basis for Special Relativity
Einstein's theory of special relativity results from two statements -- the two basic postulates of special relativity:
- The speed of light is the same for all observers, no matter what their relative speeds.
- The laws of physics are the same in any inertial (that is, non-accelerated) frame of reference. This means that the laws of physics observed by a hypothetical observer traveling with a relativistic particle must be the same as those observed by an observer who is stationary in the laboratory.
Given these two statements, Einstein showed how definitions of momentum and energy must be refined and how quantities such as length and time must change from one observer to another in order to get consistent results for physical quantities such as particle half-life. To decide whether his postulates are a correct theory of nature, physicists test whether the predictions of Einstein's theory match observations. Indeed many such tests have been made -- and the answers Einstein gave are right every time!
Relativistic Definitions
Physicists call particles with v/c comparable to 1 "relativistic" particles. Particles with v/c << 1 (very much less than one) are "non-relativistic." At SLAC, we are almost always dealing with relativistic particles. Below we catalogue some essential differences between the relativistic quantities the more familiar non-relativistic or low-speed approximate definitions and behaviors.
Gamma( )
The measurable effects of relativity are based on gamma. Gamma depends only on the speed of a particle and is always larger than 1. By definition:
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c is the speed of light
v is the speed of the object in question
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For example, when an electron has traveled ten feet along the accelerator it has a speed of 0.99c, and the value of gamma at that speed is 7.09. When the electron reaches the end of the linac, its speed is 0.99999999995c where gamma equals 100,000.
What do these gamma values tell us about the relativistic effects detected at SLAC? Notice that when the speed of the object is very much less than the speed of light (v << c), gamma is approximately equal to 1. This is a non-relativistic situation (Newtonian).
Momentum
Notice that this equation tells you that for any particle with a non-zero mass, the momentum gets larger and larger as the speed gets closer to the speed of light. Such a particle would have infinite momentum if it could reach the speed of light. Since it would take an infinite amount of force (or a finite force acting over an infinite amount of time) to accelerate a particle to infinite momentum, we are forced to conclude that a massive particle always travels at speeds less than the speed of light.
For non-relativistic objects Newton defined momentum, given the symbol p, as the product of mass and velocity -- p = m v. When speed becomes relativistic, we have to modify this definition -- p = gamma (mv)
Energy
Probably the most famous scientific equation of all time, first derived by Einstein is the relationship E = mc2.
Einstein also showed that the correct relativistic expression for the energy of a particle of mass m with momentum p is E2 = m2c4 + p2c2. This is a key equation for any real particle, giving the relationship between its energy (E), momentum ( p), and its rest mass (m).
If we substitute the equation for p into the equation for E above, with a little algebra, we get E = gamma mc2, so energy is gamma times rest energy. (Notice again that if we call the quantity M =gamma m the mass of the particle then E = Mc2 applies for any particle, but remember, particle physicists don't do that.)
This tells us the energy corresponding to a mass m at rest. What this means is that when mass disappears, for example in a nuclear fission process, this amount of energy must appear in some other form. It also tells us the total energy of a particle of mass m sitting at rest.
Another interesting fact about the expression that relates E and p above (E2 = m2c4 + p2c2), is that it is also true for the case where a particle has no mass (m=0). In this case, the particle always travels at a speed c, the speed of light. You can regard this equation as a definition of momentum for such a mass-less particle. Photons have kinetic energy and momentum, but no mass!
The energy E is the total energy of a freely moving particle. We can define it to be the rest energy plus kinetic energy (E = KE + mc2) which then defines a relativistic form for kinetic energy. Just as the equation for momentum has to be altered, so does the low-speed equation for kinetic energy (KE = (1/2)mv2). Let's make a guess based on what we saw for momentum and energy and say that relativistically KE = gamma(1/2)mv2. A good guess, perhaps, but it's wrong.
In the case of an atomic explosion, mass energy is released as kinetic energy of the resulting material, which has slightly less mass than the original material.
In any particle decay process, some of the initial mass energy becomes kinetic energy of the products.
Even in chemical processes there are tiny changes in mass which correspond to the energy released or absorbed in a process. When chemists talk about conservation of mass, they mean that the sum of the masses of the atoms involved does not change. However, the masses of molecules are slightly smaller than the sum of the masses of the atoms they contain (which is why molecules do not just fall apart into atoms). If we look at the actual molecular masses, we find tiny mass changes do occur in any chemical reaction.
At SLAC, and in any particle physics facility, we also see the reverse effect -- energy producing new matter. In the presence of charged particles a photon (which only has kinetic energy) can change into a massive particle and its matching massive antiparticle. The extra charged particle has to be there to absorb a little energy and more momentum, otherwise such a process could not conserve both energy and momentum. This process is one more confirmation of Einstein's special theory of relativity. It also is the process by which antimatter (for example the positrons accelerated at SLAC) is produced.
Theory of Relativity - Abused and Misused
In addition to being misrepresented as an undeniable fact, the Theory of Relativity has been misapplied to areas beyond gravitational phenomena even in the scientific community. Concerning the origin of the universe, Einstein's Theory of Relativity is the basis for the Big Bang Theory, a theory postulating on the origin of the universe. Likewise, Darwin's Theory of Evolution is a theory focused on the origin of species and, ultimately, the origin of man. Yet, these two theories are often discussed as though they are two ends of a larger unified theory. In reality, they are not theories on a continuum, but separate theories describing two completely different physical phenomena.
Additionally, Einstein's Theory is intended to describe physical laws of the universe alone, not philosophy or religion or God. For instance, the Theory of Relativity and the philosophical belief of moral relativism have nothing in common except for the term relative, yet some believe them to have common meanings. Some might argue that moral relativity - the belief that truth and lies, good and evil, God or other gods are determined and validated by an individual's personality, genetics, and environmental upbringing - is a consequence of Einstein's work.
In fact Einstein's relationship tells us more, it says
Energy and mass are interchangeable. Or, better said, rest mass is just one form of energy. For a compound object, the mass of the composite is not just the sum of the masses of the constituents but the sum of their energies, including kinetic, potential, and mass energy. The equation E=mc2 shows how to convert between energy units and mass units. Even a small mass corresponds to a significant amount of energy.
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