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- 1. The Significance of the Speed of Light relating to Einstein’s Special theory of Relativity Kenneth A. Hansen December 14th, 2013 Abstract This paper explores the values and properties of the natural phenomenon known as “light” or electromagnetic radiation and its relationship to several other physical laws since the discoveries made by Albert Einstein. Topics such as light waves, particle theory, space, time dilation, the force of gravity, subatomic particles, and Energy are discussed. The goal is to lead the reader to the conclusion that light waves/particles and its universal constant speed has a specific value which is directly linked to mass, gravity, time, velocity, wave amplitude, space, momentum, intensity, frequency, wavelength, subatomic particles, and Energy. The implication being that the nature of the universe is deeply intertwined with this universal constant.
- 2. Table of Contents Introduction Einstein’s Special Theory of Relativity What is Light Wave or Particle? Properties of Light Classical vs. Quantum Particle Model Wave Model Interactions with Matter Planck’s Constant, de Broglie Wavelength, and Tachyons Speed of Gravity Neutrinos Lorentz Contraction Time Dilation Conclusion Bibliography
- 3. Einstein’s Special Theory of Relativity and the Speed of Light Mankind's understanding of the universe has made great strides in the near past. Today we have primarily Newtonian Mechanics, Relativity Theory, and Quantum Theory. Newtons laws describe the physics of forces acting upon bodies. Newton’s laws, however, lose accuracy at close to light speeds. Since an object gains mass as its velocity approaches the speed of light, the formula F=ma is strictly non-relativistic and becomes inaccurate. Special Relativity Theory corrects classical mechanics to handle situations involving motions nearing the speed of light making it the most accurate model of motion at any speed. Quantum theory deals with the atomic and subatomic spacetime and permits only probable or statistical calculation of the observed features of subatomic particles. My interest is primarily with Einstein’s Special Relativity and particularly, Light. The discoveries of Light and its properties have greatly contributed to the progress of scientific knowledge and should be studied more as light waves/particles are phenomena created by nature and widely affect the nature of the universe. The purpose of this paper is to show the importance of the universal constant of light. The fundamental laws of the universe are deeply intertwined with the its properties. It was Albert Einstein was the first to shed light on this fact with the Special Theory of Relativity in 1905. It is the accepted physical theory regarding the relationship between space and time. It is based on two postulates: that the laws of physics are identical in all inertial systems; and that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. The inconsistency of classical mechanics with Maxwell’s equations of electromagnetism led to the development of special relativity, which corrects classical mechanics to handle situations involving motions nearing the speed of light. Special relativity implies a wide range of consequences, which have been experimentally verified, including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit, and relativity of simultaneity. It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = mc2 , where c is the speed of light in vacuum. Relativistic Mass - In special relativity, an object that has nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of
- 4. light, the object's energy and momentum increase without bound. As the objects velocity approaches the speed of light its mass drastically increases requiring more energy to further accelerate the object. It would require infinite energy to bring an object with even the smallest mass to the full speed of light. A defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics with the Lorentz transformations. Time and space cannot be defined separately from one another. Rather space and time are interwoven into a single continuum known as spacetime. Events that occur at the same time for one observer could occur at different times for another. In special relativity space and time are so closely related that mathematically, it can be useful not to have to specify whether a variable represents a distance or a time.The theory is called "special" because it applied the principle of relativity only to the special case of inertial reference frames. What is light? Light refers to electromagnetic radiation of any wavelength, whether visible or not and may be viewed in one of two complementary ways: as a wave in an abstract electromagnetic field, or as a stream of massless particles called photons. Depending on the wavelength, light can be in the form of radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, x-rays, and gamma radiation. The speed of light is a universal constant measured to be 299,792,458 meters per second. The first successful measurement of c was made by Olaus Roemer in 1676. He noticed that, depending on the Earth–Sun–Jupiter geometry, there could be a difference of up to 1,000 seconds between the predicted times of the eclipses of Jupiter's moons, and the actual times that these eclipses were observed. He correctly surmised that this is due to the varying length of time it takes for light to travel from Jupiter to Earth as the distance between these two planets varies. He obtained a value of c equivalent to 214,000 km/s, which was very approximate because planetary distances were not accurately known at that time. One of the most recent experiments done to measure the speed of light was when Physicists measured the energy required to change the speed of electrons as they hopped from one orbital to another inside atoms of dysprosium, all while Earth rotated over a 12-hour period. This allowed the scientists to measure that the maximum speed of an electron, which, according to special relativity should be the speed of light, is the same in all directions to within 17 nanometers per second. This measurement was 10 times more precise than previous tests of electrons' maximum speed.
- 5. Properties of Light Scientists have observed that light energy can behave like a wave as it moves through space, or it can behave like a discrete particle with energy that can be absorbed and emitted. Atoms emit radiation when their electrons return from an excited state back to their original level. They will absorb energy from light if the frequency of the light oscillation and the frequency of the electron or molecular "transition motion" match. This "transition motion" frequency is related to the frequencies of motion in the higher and lower energy states. Particle Model (Quantum) The particle-like or “quantum view” of light is as a particle-like wave packet. Each wave packet is called a photon. A photon has no mass and no charge. It is a carrier of electromagnetic energy and interacts with other discrete particles (e.g., electrons, atoms, and molecules). A beam of light is modeled as a stream of photons, each carrying a well-defined energy that is dependent upon the wavelength of the light. Quantum Theory dictates the probabilities of subatomic particles and can be calculated with wave functions and Schrödinger's equations. A wave function is the most complete description that can be given to a physical system. Solutions to equation describe not only molecular, atomic, and subatomic systems, but also macroscopic systems, possibly even the whole universe. Wave Model (Classical) The propagation of light or electromagnetic energy through space can also be described in terms of a traveling wave motion. The wave moves energy, without moving mass, from one place to another at a speed independent of its intensity or wavelength. This wave nature of light is the basis of physical optics and describes the interaction of light with media. Many of these processes require calculus to describe them rigorously. Light exhibits certain behaviors that are characteristic of any wave and would be difficult to explain with a purely particle-view. For example: The light from a point light source spreads out uniformly in all directions. Waves carry energy, and the amplitude of a wave is generally a measure of how much energy the wave carries. The amplitude of light is the number of photons hitting a spot per time interval rather than the amplitude of a single photon. The energy is relative to amplitude squared. E α A² The frequency and wavelength are directly proportional to the speed of light by the equation c = λ f. Shorter wavelengths carry more energy than longer wavelengths.The limit for long wavelengths is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length, although in principle the spectrum is infinite and continuous. Intensity is similar to brightness, and is measured as the rate at which light energy is delivered to a unit
- 6. of surface, or energy per unit time per unit area. Light scattering can be thought of as the deflection of a ray from a straight path. Electromagnetic waves share six properties with all forms of wave motion: Superposition - For many kinds of waves, including electromagnetic, two or more waves can traverse the same space at the same time independently of one another. This means that the electric field at any point in space is simply the vector sum of the electric fields that the individual waves alone produce at the point. Both the electric and magnetic fields of an electromagnetic wave satisfy the superposition principle. Thus, given multiple waves, the field at any given point can be calculated by summing each of the individual wave vectors. Interference - The first definitive demonstration of the wavelike nature of light was the classical two-slit experiment performed by Thomas Young in 1801. The two slits are very small compared to their separation distance. Thus, each slit produces diffracted spherical waves that overlap as they expand into the space to the right of the barrier. When they overlap, they interfere with each other, producing regions of mutually reinforcing waves. Polarization - Polarization arises from the direction of the E-field vector with respect to the direction of the light’s propagation. Since a light wave’s electric field vibrates in a direction perpendicular to its propagation motion, it is called a transverse wave and is polarizable. Diffraction - Conclusive evidence of the correctness of a wave model came with the explanation of observed diffraction and interference. This property of light that causes it to spread out as it travels by sharp edges or through tiny holes can be explained by light having wavelike properties. Diffraction is predicted from Huygens’ principle which states: Every point of a wave front may be considered the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the waves. Refraction - When a ray of light passes from one medium to another, it changes direction at the interface because of the difference in speed of the wave in the media. The ratio of this speed difference is called the index of refraction (n) according to Snell’s Law. Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media.
- 7. Reflection -When a ray of light reflects off a surface (such as a mirror), its new direction depends on only the angle of incidence. The law of reflection states that the angle of incidence on a reflecting basic surface is equal to the angle of reflection. Interactions of Light with Matter As light travels through different materials, it scatters off of the molecules in the material and is slowed down. The important interactions are absorption and scattering. Absorption is a transfer of energy from the electromagnetic wave to the atoms or molecules of the medium. Energy transferred to an atom can excite electrons to higher energy states. Energy transferred to a molecule can excite vibrations or rotations. The wavelengths of light that can excite these energy states depend on the energy-level structures and therefore on the types of atoms and molecules contained in the medium. The spectrum of the light after passing through a medium appears to have certain wavelengths removed because they have been absorbed. This is called an absorption spectrum. Selective absorption is also the basis for objects having color. A red apple is red because it absorbs the other colors of the visible spectrum and reflects only red light. Light scattering is the deflection of a ray from a straight path. Ordinary transparent media like water, glass and crystal slow light slightly. In 1999 Dr. Lene Vestergaard Hau slowed light to about 38 miles an hour (17 m/s) in a system involving beams of light shone through a chilled sodium gas. More recently, two independent teams of physicists have brought a light beam to a full stop, one led by Dr. Lene Vestergaard Hau of Harvard University and the Rowland Institute for Science in Cambridge, Mass., and the other by Dr. Ronald L. Walsworth and Dr. Mikhail D. Lukin of the Harvard-Smithsonian Center for Astrophysics. Using a distantly related but much more powerful effect, the Walsworth-Lukin team first slowed and then stopped the light in a medium that consisted of specially prepared containers of gas. In this medium, the light became fainter and fainter as it slowed and then stopped. By flashing a second light through the gas, the team could essentially revive the original beam. The beam then left the chamber carrying nearly the same shape, intensity and other properties it had when it entered. We have used laser light with fiber optic cables (silica glass) and until recently the light traveled 31% slower than in a vacuum. Soon we will be able to transfer data at 99.7% of the speed of light thanks to researchers at the University of Southampton in England.
- 8. Planck’s Constant, The de Broglie Wavelength, and Tachyons The Planck constant was first described as the proportionality constant between the energy (E) of a charged atomic oscillator in the wall of a black body, and the frequency (ν) of its associated electromagnetic wave. This relation between the energy and frequency is called the Planck relation: The Planck relation describes the energy of each photon in terms of the photon's frequency. Since the frequency , wavelength λ, and speed of light c are related by λν = c, the Planck relation for a photon can also be expressed as The planck constant , which governs the strength of quantum effects, and the intrinsic weakness of the gravitational force team up to yield the planck length, which is small almost beyond imagination: a millionth of a billionth of a billionth of a billionth of a centimeter (10^-33 cm.). If we were to magnify an atom to the size of the known universe, the Planck length would barely expand to the size of a tree. The above equation leads to another relationship involving the Planck constant. Given p for the linear momentum of a particle (not only a photon, but other particles as well), the de Broglie wavelength λ of the particle is given by The de Broglie wavelength relations show that the wavelength is inversely proportional to the momentum of a particle. Also the frequency of matter waves, as deduced by de Broglie, is directly proportional to the total energy of a particle. Some theoretical physicists have speculated on the possible existence of particles which always travel faster than light, avoiding the complications of acceleration past the cosmic speed limit. Physicist Gerald Feinberg even gave them a name, tachyons. If they existed tachyons would be really, really bizarre things, for example they would always be moving faster than light, dropping to less than 300,000 km/s would be as impossible for them as exceeding this speed is to us. In 1973 two Australian researchers, Roger Clay and Philip Crouch, claimed successful detection of a tachyon but no one has ever been able to duplicate this result, and Clay has subsequently concluded “No positive evidence has been found using conventional scintillation detectors for producing a tachyon signal”. Experiments to create tachyons in collisions with particle accelerators at Amhearst College and Brookhaven National Laboratory (both in the USA) had negative results.
- 9. Speed of force of Gravity The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, c. Within the theory of special relativity, the constant c is not exclusively about light; instead it is the highest possible speed for any physical interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and/or gravity. Thus, the speed of "light" is also the speed of gravitational waves and any other massless particle. Such particles include the gluon (carrier of the strong force), the photons that light waves consist of, neutrinos, and the theoretical gravitons (quantum particles) which make up the associated field particles of gravity. The strength of gravity and the intensity of light both abide by the inverse-square law, which states that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. Newton's law of universal gravitation follows an inverse- square law, as do the effects of electric, magnetic, light, sound, and radiation phenomena. In equation form: Speed of Neutrinos The speed of Neutrinos has also been found to travel at the speed of light. CERN’s conclusion for the experiment published January 24, 2013 are as follows; “ The OPERA experiment after improving its timing system, has conﬁrmed the result, showing no signiﬁcant deviation of the muon neutrino velocity from the speed of light. Lorentz Contraction Length Contraction is the phenomenon of a decrease in length measured by an observer of objects which are traveling at any non-zero velocity relative to the observer. At extremely high speeds, space is warped to the point that the object's dimensions are altered. This contraction is usually only noticeable at a substantial fraction of the speed of light. As the magnitude of the velocity approaches the speed of light, the effect becomes dominant, as can be seen from the formula:
- 10. Time Dilation “It is one of the deepest insights into the nature of reality ever discovered” -Brian Greene Just as the frequency and wavelength are in a balance and always equal the speed of light, so it also goes with velocity and time. The velocity of an object/observer and the rate of time it experiences are proportional to the universal constant. This means that if a person is at rest, he/she is “travelling” through time at 100%. If the person has a velocity 50% the speed of light, he/she is travelling through time at half the rate. The faster you are moving, less time elapses. The big detail here is that light that is travelling through a vacuum is not travelling through the time dimension at all, it is timeless. Implications The implications that the speed of light has a direct correlation with Energy, Mass, Space, Time, Velocity, Momentum, Wavelength, Frequency, and the force of Gravity. The latest experiment to measure the speed of light confirmed that the formula E = mc2 is correct to an incredible accuracy of better than one part in a million, or six decimal places. One of the largest implications of Einstein’s work is that there are no absolute values, they have become relative. This makes constants like the speed of light an anchor in an ocean of math. Another implication is that mass can be converted to energy with E=mc^2. Time has also become relative. If you were to travel on a spaceship away from earth at half the speed of light for 10 “earth” years, you would only age five years. Space is also relative to velocity. If a meter stick was travelling half the speed of light, its length would appear to be only 86.6025404 centimeters long. The speed of the attractive force of Gravity and subatomic particles are also limited by the universal constant. The behavior of light waves alone has its own implications. It has been calculated that the sun emits approximately 1 x 10^45 photons/second. The radiation interacts with our planet in many ways, the ultraviolet rays reflect off of the ozone layer at the angle of incidence and continue through space. Other wavelengths make it through and refract through mediums such as gas, liquid, glass, and crystals. Other light waves diffract off of edges or through small openings changing their direction. When more than one light wave is travelling through the same space, they interfere with the crescents and peaks. More than one light wave can traverse the same space as others and the energy at any one location at any time can be calculated by the sum of several electric field’s produced by the electromagnetic waves with superpositioning. Simply put, light
- 11. is constantly going through space, transporting energy, bouncing off of mediums, passing through mediums, interfering with other light, being absorbed and emitted by atoms, and continuously spanning over an increasingly large area. Light behaves similarly on a larger scale through space. Space between planets is mostly a vacuum, but not a complete vacuum. It is estimated that there is less than 1 hydrogen atoms per meter cubed. So most of the light travels uninterrupted over large distances. As the space around a large planet, star, or black hole is warped, the linear path of light follows a curved line, so the light can bend around and continue in a new path or even possibly return towards the light source. With all of these properties combined it would be safe to assume that there is energy in the vast majority of space at every moment in time. Light waves flowing through each-other, sometimes in every direction at any particular point in space. Even within matter, x-rays and (depending on the energy level) neutrinos can fit between the atoms with their extremely small wavelengths. Another characteristic of light is that it does not travel through time at all. This leads me to believe that its half-life is potentially infinite. It cannot decay because it is timeless. So as long as all of its energy is not absorbed, a particular beam of light can exist with energy for eternity. The intensity of light does decrease over distance. All of these properties, values, relationships, and effects of light lead me to the conclusion that it is strongly intertwined with the physical laws governing our universe. To conclude, the knowledge and understanding we now have regarding Electromagnetic radiation, when seen in this context, should be seen as a key piece of the puzzle of the Universe that we are tediously trying to put together.
- 12. Bibliography International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 112, ISBN 92-822-2213-6 Hartle, JB (2003). Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley. p. 332. ISBN 981-02-2749-3 Laplace, P.S.: (1805) "A Treatise in Celestial Mechanics", Volume IV, Book X, Chapter VII, translated by N. Bowditch (Chelsea, New York, 1966) OPERA collaboration, T. Adam et al., Measurement of the neutrino velocity with the OPERA detector in the CNGS beam, JHEP 10 (2012) 093. Resnick, R.; Eisberg, R. (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (2nd ed.). New York: John Wiley & Sons. ISBN 0-471- 87373-X. Albert Einstein (1905) "Zur Elektrodynamik bewegter Körper", Annalen der Physik 17: 891; English translation On the Electrodynamics of Moving Bodies by George Barker Jeffery and Wilfrid Perrett (1923); Another English translation On the Electrodynamics of Moving Bodies by Megh Nad Saha (1920). Tom Roberts and Siegmar Schleif (October 2007). "What is the experimental basis of Special Relativity?". Usenet Physics FAQ. Retrieved 2008-09-17 Albert Einstein (2001). Relativity: The Special and the General Theory (Reprint of 1920 translation by Robert W. Lawson ed.). Routledge. p. 48. ISBN 0-415- 25384-5 Richard Phillips Feynman (1998). Six Not-so-easy Pieces: Einstein's relativity, symmetry, and space–time (Reprint of 1995 ed.). Basic Books. p. 68. ISBN 0- 201-32842-9.
- 13. Taylor, Edwin F. and Wheeler, John Archibald, Spacetime Physics, 2nd edition, 1991, p. 12. Brian Greene ,The Elegant Universe, 1999, page 36. Schrödinger, E. (1926). "An Undulatory Theory of the Mechanics of Atoms and Molecules". Physical Review 28 (6): 1049–1070 Curtis Wilson (1989), "The Newtonian achievement in astronomy", ch.13 (pages 233–274) in "Planetary astronomy from the Renaissance to the rise of astrophysics: 2A: Tycho Brahe to Newton", CUP 1989. David C. Cassidy, Gerald James Holton, Floyd James Rutherford (2002).Understanding physics. Birkhäuser. pp. 339 ff. ISBN 0-387-98756-8 U. A. Bakshi, A. P. Godse (2009). Basic Electronics Engineering. Technical Publications. pp. 8–10. ISBN 978-81-8431-580-6. Retrieved 2011-10-16