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# SPECIAL THEORY OF RELATIVITY PDF

Tuesday, November 12, 2019

THE SPECIAL THEORY OF RELATIVITY. Lecture Notes prepared by. J D Cresser. Department of Physics. Macquarie University. July 31, GENERAL I ARTICLE. The Special Theory of Relativity. Vasant Natarajan and Diptiman Sen. Vasant Natarajan is at the. Department of Physics,. liSe, Bangalore. SPECIAL RELATIVITY. (Einstein From the two principles of special relativity, some important . SUMMARY OF THE PREDICTIONS OF THE THEORY OF.

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PDF | Special Relativity Theory (SRT) has two postulates, one stating that the laws of physics are the same for all observers, and the other stating that the speed. General Results of the Theory. Experience and the Special Theory of Relativity. Minkowski's Four-dimensial Space. Part II: The General Theory of. In this document we discuss Einstein's Special Theory of Relativity. The treatment is The html version is here and the pdf version is here. Technical note: if.

In all reference frames, only those frames moving with constant velocity with respect to a given inertial frame are considered inertial frames Stachel In Galilean relativity, the sum of velocities is a simple matter. For example, if a ship is moving relative to the shore at velocity v, and a bird is moving with velocity u as measured on the ship. Then the velocity of the bird as measured on the shore, s, is simply as follows: 1 Ether or Aether: Is the term for the cosmological medium.

Draco is almost perpendicular to the ecliptic path which the Earth takes in its annual revolution around the sun, showing that the images of stars move in small ellipses Bradley This phenomenon was explained correctly as stellar aberration due to the Earth's motion around the sun. However, this is inconsistent with a simple model of light as waves in the ether that is dragged along by the Earth. It is however consistent with special relativity and probably one of the very first pre-validation observations.

## Electromagnets

He developed two enduring experiments to support his theory Young In once such experiment, he demonstrated that the idea of interference, using the double-slit apparatus, can be interpreted only within the context of a wave theory of light.

It is highly significant and would lead to more complete theories. He believed that variations in the refractive index of different substances, such as the air and the glass of a telescope, would provide a useful method for measuring the velocity of light Arago This idea was supported by the corpuscular theory.

He examined the expected change in focus of a refracting telescope due to Earth's motion around the sun, but Arago only observed ordinary stellar aberration. He extended the wave theory of light to a large class of optical phenomena and examined Arago's results within the context of a wave theory of light.

The concept was that light propagates as a transverse wave in an elastic medium referred to as the luminiferous aether. Fresnel believed that if light were transmitted as waves through the different refractive indexes; then, the waves should vary. The dragging was referred to as the aether drag.

It also introduced the concept of a largely stationary aether dragged by dense substances such as glass but not by air or less dense substances. A couple of years earlier in , Austrian physicist Christian Doppler, put forward a revolutionary idea. Namely, that the change in frequency of a wave for an observer moving relative to the source of the wave would result in a shift: the Doppler shift.

The received frequency would be higher [compared to the emitted frequency] during the approach while it would be identical at the instant of passing, and it would be lower during the recession. Interestingly, Hippolyte Fizeau independently discovered the same shift phenomenon in electromagnetic waves in The experiment was designed to evaluate the prediction by Fresnel.

Namely, that a moving dispersive medium should create a partial offset in the speed of any light moving through it, for the refractive index would be dependent on the entrainment of the luminiferous aether.

The errors were quite large yet Fizeau assumed the result was indeed experimental confirmation. The device was the first terrestrial experiment designed for measuring the speed of light, using a rotating mirror Morizot et al. This experiment has only one arm containing water Hoek , to utilize the speed of the Earth moving around the sun. Light passed through water in one arm and through air in the other. Light traveling in one direction around the interferometer propagated through the water parallel to the motion of the earth around the sun, while light traveling in the opposite direction propagated antiparallel to that motion.

Essentially a null result. Hoek calculated a function that would compensate for the velocity of the water through the stationary aether and thus explain the vanishing optical path difference between the light propagating in the two directions.

## How Einstein discovered the Special Theory of Relativity

Around the same time, in , James Clerk Maxwell had developed an accurate theory of electromagnetism by deriving a set of equations in electricity, magnetism and inductance, named: the Maxwell's equations.

He first proposed that light was in fact undulations, or electromagnetic radiation, in the same aetherial medium which is the cause of electric and magnetic phenomena; namely, an all- pervading plenum in the universe. Maxwell's theory was unsatisfactory regarding the optics of moving bodies.

He was able to present a complete mathematical model; he was not able to provide a coherent mechanical description of the aether Born However, it seemed possible to determine absolute motion relative to the aether and therefore disprove Galilean invariance. A few years later in Heinrich Hertz demonstrated the existence of electromagnetic waves, which consolidated academic acceptance of Maxwell's theory.

## Special relativity

In addition, Oliver Heaviside and Hertz further developed the theory and introduced modernized versions of Maxwell's equations. In his discussion, he did not mention whether he thought that the aether was partially dragged by moving bodies as proposed by Fresnel or completely dragged as proposed by Stokes.

A year later, in , Ed Ketteler performed an experiment on interference and polarization similar to Hoek. In it, two rays of an interferometer were sent in opposite directions through two mutually inclined tubes filled with water Kettler No change in the interference fringes occurred. It was designed to find a change of rotation of the polarization plane, in quartz, when the light rays had the direction of Earth's motion, and then in the opposite direction.

The experiment showed that the interference fringes of polarized light in calcite remained uninfluenced as well Mascart In that same period, Lord Rayleigh conducted similar experiments with improved accuracy and obtained a negative result also. The Michelson and Morley experiment Now we move to the crucial turning point in the search for the aether, with an experiment that was performed over a decade later in by Albert Michelson and Edward Morley. The Michelson- Morley experiment was designed to detect interference patterns in light caused by the drift in the luminiferous aether Michelson-Morley Michelson interferometerPhoto credit: Wiki Commons.

The Michelson interferometer was supposed to create alternating interference fringes on a detector caused by the anisotropy of the motion of the Earth relative to the aether drift, but the result was a static interference pattern. However it indirectly proved the constancy of the speed of light across different inertial reference frames, which removed the conceptual need for a luminiferous aether to provide a rest frame for light.

In a real sense, the null result of the Michelson-Morley experiment was, in fact, the first pre-validation of special relativity. It proved the speed of light was constant for all reference frames, but no one had realized it at the time.

Interestingly, this occurred when Albert Einstein was only eight years old. The experiment was a primitive version of the Trouton-Noble experiment, which was performed later in The Lorentz transformations Almost a decade later Dutch physicist Hendrik Lorentz extended Maxwell's theory of electricity and light, together with his electron theory, and the classical theory of electromagnetism obtained a complete form.

At the time, it was referred to as the Maxwell—Lorentz theory Berends Here we see the first form where the velocity of light in a vacuum, c, is considered constant within a reference frame with a given velocity, v. During Lorentz worked on describing electromagnetic phenomena Lorentz , namely the propagation of light in reference frames, in relation to moving electrons that moved relative to each other.

Lorentz attempted to explain the null result of the Michelson-Morley experiment to detect motion through the aether. He developed a theory based on an immobile aether by proposing that moving bodies contract in the direction of motion, later to be referred to as length contraction.

Lorentz was a firm advocate of the luminiferous aether and used his mathematics to describe the physical behavior of an aether; the experiment failed Schaffner Joseph Larmor Larmor also had, quite independently and separately, worked on the phenomena. However, it was Lorentz who realized that the transition from one reference frame to another could be expressed by using a new time variable which he referred to as local time.

Lorentz's publications of and Lorentz made use of the term local time without giving a physical interpretation of its relevance Schaffner He showed that the concept of local time, introduced by Lorentz, gave a simple physical interpretation.

This idea was very similar to the one later proposed by Einstein. This concept was in conflict with the spirit of the principle of special relativity that is supposed to treat all frames as equal. He derived this interpretation from Lorentz's theory of electrons, which also incorporated Maxwell's radiation pressure. During the same period, in , Walter Kaufmann began to experiment with custom cathode ray tube by applying electric and magnetic fields to measure the ratio of the charge and mass of electrons Kaufmann Since the charge and speed of the electrons did not change, any change of the ratio must be the result of a change of their mass.

He attained intellectual fruition at a moment when the dilemma of the behavior of light required a new interpretation, and all the mathematics and concepts were waiting ready. Time was ripe for a paradigm change. This change in thinking would lead to the special theory of relativity and later the general theory of relativity. It is not unlike the problem that surrounds physics today: the resolution of general relativity with quantum theory.

Alternatively, was this thinking simply a true conceptual understanding of all the experimental physics that had taken place some decades prior? This author believes it is the latter. Einstein radically reinterpreted Lorentzian electrodynamics by changing the concepts of space and time and abolishing the need for a physical aether.

Additionally, he derived the Lorentz transformation equations independently, using the principle of constancy of the velocity of light and the relativity principle.

He was the first to argue that those principles, together other basic assumptions about the homogeneity and isotropy of space, were sufficient to derive the theory. Moreover, as a result, this theory was initially referred to as the Lorentz-Einstein theory. Einstein was the first one to give up the idea of singling out a reference frame at rest relative to the aether. This paradigm shift enabled him to construct a simple logical structure based on the two basic postulates of relativity.

Consequently, he was the first one to arrive at the exact transformation equations relating two inertial frames of reference. Einstein had abandoned the luminiferous aether concept and talked of a new aether, pointing out that no substance and no state of motion can be attributed to that new aether. The new aether found little support in physics and was later abandoned by physicists.

Einstein wrote that he view the Fizeau experiment as a determination of the correct relativistic formula for the addition of velocities, and that showed that the simple Galilean addition law for velocities was incorrect. It was a crucial test in favor of the theory of relativity. The notion of simultaneity in the direction of motion becomes altered. Hence, the addition law for velocities changed.

This change is not noticeable at low velocities but as the velocity becomes relativistic it becomes important. The addition law is also called a composition law for velocities. However, the formula did not appear in the special relativity paper of Einstein Einstein was awarded the Nobel Prize for his work on the photoelectric effect Einstein c , not relativity. Many consider the latter the greatest intellectual achievement of all time as we shall see in part 2 Ashtekar Moreover, that Einstein had little to contribute in terms of originality.

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The statement is the essence of the relativity priority dispute which has contentiously resurfaced since the time of Einstein. Today many scholars still believe that Einstein was a plagiarist. They ignore the fact that Einstein has published several other very important papers, for a plagiarist is not someone who can develop groundbreaking theories in several areas of physics at the same time.

The term reference frame as used here is an observational perspective in space which is not undergoing any change in motion acceleration , from which a position can be measured along 3 spatial axes so, at rest or constant velocity. In addition, a reference frame has the ability to determine measurements of the time of events using a 'clock' any reference device with uniform periodicity. An event is an occurrence that can be assigned a single unique moment and location in space relative to a reference frame: it is a "point" in spacetime.

Since the speed of light is constant in relativity irrespective of reference frame, pulses of light can be used to unambiguously measure distances and refer back the times that events occurred to the clock, even though light takes time to reach the clock after the event has transpired. For example, the explosion of a firecracker may be considered to be an "event".

We can completely specify an event by its four spacetime coordinates: The time of occurrence and its 3-dimensional spatial location define a reference point. Let's call this reference frame S. In relativity theory, we often want to calculate the coordinates of an event from differing reference frames. The equations that relate measurements made in different frames are called transformation equations.

Standard configuration[ edit ] To gain insight in how the spacetime coordinates measured by observers in different reference frames compare with each other, it is useful to work with a simplified setup with frames in a standard configuration. In Fig. Since there is no absolute reference frame in relativity theory, a concept of 'moving' doesn't strictly exist, as everything may be moving with respect to some other reference frame.

Instead, any two frames that move at the same speed in the same direction are said to be comoving. Lack of an absolute reference frame[ edit ] The principle of relativity , which states that physical laws have the same form in each inertial reference frame , dates back to Galileo , and was incorporated into Newtonian physics.

However, in the late 19th century, the existence of electromagnetic waves led some physicists to suggest that the universe was filled with a substance that they called " aether ", which, they postulated, would act as the medium through which these waves, or vibrations, propagated in many respects similar to the way sound propagates through air.

The aether was thought to be an absolute reference frame against which all speeds could be measured, and could be considered fixed and motionless relative to Earth or some other fixed reference point. The aether supposedly possessed some wonderful properties: it was sufficiently elastic to support electromagnetic waves, and those waves could interact with matter, yet it offered no resistance to bodies passing through it its one property was that it allowed electromagnetic waves to propagate.

The results of various experiments, including the Michelson—Morley experiment in subsequently verified with more accurate and innovative experiments , led to the theory of special relativity, by showing that the aether did not exist.For example, this can be seen in the spin of moving particles , where Thomas precession is a relativistic correction that applies to the spin of an elementary particle or the rotation of a macroscopic gyroscope , relating the angular velocity of the spin of a particle following a curvilinear orbit to the angular velocity of the orbital motion.

Theoretical Phenomenology Computational Experimental Applied. For example, a receding object would appear contracted, an approaching object would appear elongated, and a passing object would have a skew appearance that has been likened to a rotation.

The frames are actually equivalent. The aether was formerly the plenum and had originated in the Hellenistic period in ancient Greece. It is not unlike the problem that surrounds physics today: the resolution of general relativity with quantum theory. Norton, John D. Serway, R. Kettler, E.