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Review of Special Theory of Relativity Special Theory of Relativity Part I Prof. Awni B. Hallak Department of Physics The Hashemite University Zarqa 13115, JORDAN Prof. Awni B. Hallak Theory of Relativity Albert Einstein (1879 – 1955) : Nobel Prize, 1921 2 Prof. Awni B. Hallak Einstein’s Most Important Accomplishments Albet Einstein (1879–1955) was a renowned theoretical physicist of the 20th century, best known for his theories of special relativity and general relativity. He also made important contributions to statistical mechanics, especially his treatment of Brownian motion, his resolution of the paradox of specific heats, and his connection of fluctuations and dissipation. Despite his reservations about its interpretation, Einstein also made influential contributions to quantum mechanics and, indirectly, quantum field theory, primarily through his theoretical studies of the photon. 3 Prof. Awni B. Hallak Einstein’s Publications Scientific Papers Published by Einstein 30 Publications Number 25 25 Scientific Papers 271 Book Chapters 31 20 17 Books 16 14 Authorized Translations 24 15 12 10 10 9 9 9 10 8 8 8 . 7 7 7 7 6 6 6 6 6 5 55 55 4 4 5 3 3 3 2 2 2 2 2 2 2 22 2 Number of Publications 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1901 1903 1905 1907 1909 1911 1913 1915 1917 1919 1921 1923 1925 1927 1929 1931 1933 1935 1937 1939 1941 1943 1945 1947 1949 1951 1953 1955 Year 4 Prof. Awni B. Hallak Review of Pre-Einstein Physics . Newtonian Mechanics . Electricity and Magnetism . Electromagnetism . Quantum Mechanics 5 Prof. Awni B. Hallak Newtonian Mechanics (1) 1 . Kinetic Energy: K mv2 2 . Potential Energy: U m g h (In a gravitational field) . Linear Momentum: p mv . Mechanical Energy: E K U . Mechanical Energy is conserved for conservative forces. (Example: Collisions) . Linear Momentum is conserved (Example: Collisions) dp . F (Newton Laws) dt 6 Prof. Awni B. Hallak Newtonian Mechanics (2) . dU (One dimension) Fx dx f f Fxdx dU W U K i i or f f f f dv 1 2 2 W Fxdx madx m dx m vdv m[vf vi ] i i i dt i 2 K K K f i . Work-Energy Theorem W = ΔK . Angular Momentum r p . Angular Momentum is conserved 7 Prof. Awni B. Hallak Electricity and Magnetism (1) 1 q1q2 . Coulomb force: F 2 4 r 1 q q . Potential Energy: U 1 2 4 r 1 q due to a point charge at distance r: . E E 2 4 r (In the raidal direction) I . Electric current I in a loop of radius r B 2r (At the center of the loop and perpendicular to it) . εo= permittivity of empty space . μo= permeability of empty space 8 Prof. Awni B. Hallak Electricity and Magnetism (2) . Magnetic Moment : I A (A=area of the loop, is perpendicular to the plane of the loop) . Torque: B ext Potential Energy: . U Bext . Electromagnetic waves . EM waves travel at c = λ ν , c = velocity of light, λ is the wavelength, ν is the frequency. 1 . c = constant = 2.99792458 x 108 m/s (Predicted by Maxwell) 9 Prof. Awni B. Hallak Electromagnetism (1) . Maxwell Equations: - Integral Form: qin Gauss’s Law: E d s (1) S Gauss’s Law of magnetism: B d s 0 (2) S B Faraday’s Law if Induction: E d d s (3) S t E Ampere’s Law: (4) B d I oo ds S t 10 Prof. Awni B. Hallak Electromagnetism (2) . Maxwell Equations: - Differential Form: Gauss’s Law: E (1) Gauss’s Law of magnetism: B 0 (2) B Faraday’s Law if Induction: E (3) t E Ampere’s Law: B J (4) o o t 11 Prof. Awni B. Hallak Electromagnetism (3) . Maxwell Equations: - Gaussian Units Form: Gauss’s Law: E 4 (1) Gauss’s Law of magnetism: B 0 (2) 1 B Faraday’s Law if Induction: E (3) c t 4 1 E Ampere’s Law: B J (4) c c t 12 Prof. Awni B. Hallak Solution to Maxwell’s Equations (1) B . In free space (J=0, ρ=0): 1. E t - Take 1, curl it, getting 2. B 2. E t - Substitute 3, identity 4, and 5 E - Obtain result 3. B 0 0 t 2 2 2 E 4. E E E E 0 0 t 2 5. E 0 - Result is a wave equation, saying electric field can propagate at speed c where: 1 c 0 0 13 Prof. Awni B. Hallak Solution to Maxwell’s Equations (2) . Similarly, 2E 2B . Both 2 E and 2B 0 0 t 2 0 0 t 2 are equations of a wave traveling at the speed 1 c 299 792 458 m/s 0 0 . Matches speed of light! – Based on this, Maxwell predicted that light is an electromagnetic wave. 14 Prof. Awni B. Hallak Consequences of Maxwell Equations . Electromagnetic waves travel at . Does not depend on speed of emitter! 1 c 0 0 15 Prof. Awni B. Hallak Quantum Theory (1) . Old Quantum Theory of Planck and Bohr . Quantum Mechanics of Schrödinger . Quantum Field Theory - Quantum Electrodynamics - Relativistic Field Theory . Quantum Gravity General Relativity . Quantum Optics Quantum Electronics (Lasers) . Quantum Theory developed in parallel with Relativity 16 Prof. Awni B. Hallak Timeline of Development of Quantum Theory 1922: 1925: 1940: •Heisenberg 1905: •Neils Bohr Pauli proves developed the won Nobel Spin-Statistic •Albert Einstein wrote Heisenberg Prize in Theorem the paper, "On a Uncertainty physics Heuristic Viewpoint principle 1936: •Stern- Publishes Concerning the •Wolfgang 1932: Gerlach paper on 1944: Production and 1918: Pauli •Werner Experiment Wave Transformation of developed the Heisenberg •Wolfgang •Max Planck won (Verified the Mechanics Light“; proposed the fourth quantum won Nobel Pauli won Nobel prize in space and idea of energy number- the Prize in Nobel Prize in physics quantization Schrödinger's quanta dealing with spin number physics physics the photoelectric theory) Equation effect. 1924: 1921: •Louis De Broglie 1929: 1933: 1943: Louis De •Otto Stern published his •Otto Stern 1900: 1913: •Einstein Won Broglie won measures the doctoral thesis, receives Nobel the Nobel Prize the Nobel magnetic •Max Planck •Neils Bohr “Recherches sur la prize in Physics in Physics for his Prize in moment of the proposed theory proposed théorie des about black- discovery and quanta”, which Physics for proton atomic explanation of hypothesis. •Schrodinger body radiation structure theory introduced his the law of the theory of electron wins Nobel photoelectric waves. prize for his effect. Schrodinger 17 Prof. Awni B. Hallak Equation Erwin Schrödinger . In 1926, at the University of Zurich, published a series of 4 papers – Wave Mechanics & Schrödinger’s Equation – Solved Quantum Harmonic Oscillation, the Rigid rotor, diatomic molecules and rederived his equation – Compared his approaches to Heisenberg – Showed how to work with time 18 Prof. Awni B. Hallak Schrödinger’s Equation . While this appears to be a rather complicated equation, it is . means at time t . i is the square root of –1 . Planck’s constant divided by 2π . Derivative with respect to time . ψ(t) = Wave Function . H(t) = Quantum Hamiltonian 19 Prof. Awni B. Hallak Otto Stern & Walter Gerlach . Otto Stern and Walter Gerlach are famous for their Stern-Gerlach experiment, in which they shot a beam of silver atoms through a non- uniform magnetic field, showing that the atomic levels split into only 2 bands . This verified the space quantization theory, and tested whether particles had intrinsic angular momentum 20 Prof. Awni B. Hallak Stern-Gerlach Experiment Classical Silver What was Prediction atoms actually observed Furnace Inhomogeneous magnetic field 21 Prof. Awni B. Hallak More on Otto Stern • Developed Molecular Ray Method • Demonstrated the wave nature of atoms and molecules • Measured atomic magnetic moments • Corrected the proton’s magnetic moment • Nobel Prize in Physics in 1943 22 Prof. Awni B. Hallak Werner Heisenberg . Won Nobel Prize in 1932 in Physics "for the creation of quantum mechanics, the application of which has led to the discovery of all isotopic forms of hydrogen". Heisenberg pointed out that it is impossible to know both the exact position and the exact momentum of an object at the same time. This concept is called Heisenberg Uncertainty principle. Any electron that is subjected to photons will have its momentum and position affected. 23 Prof. Awni B. Hallak Wolfgang Ernst Pauli . Nobel Prize in Physics in 1945. The exclusion principle (No two electrons exist in the same quantum state) provided the reason for electrons in atoms being arranged in shells with the maximum number of electrons being 2, 8, 18, 32… etc, from the first to the nth shell. This principle explains why matter occupies space exclusively for itself and does not allow other material objects to pass through it and at the same time allowing lights and radiations to pass. It states that no two identical fermions may occupy the same quantum state simultaneously. 24 Prof. Awni B. Hallak Max Planck and Black Body Radiation . Emission of light from hot objects (objects appear black before heating) . How does the intensity of the electromagnetic radiation emitted by a black body depend on the frequency of the radiation and the temperature of the body? . Interpolated between the laws of Wien and Rayleigh-Jeans . Assumed that energy exists in individual units (discrete bundles) 25 Prof. Awni B. Hallak Planck’s Contributions . Formula predicts the spectral intensity of electromagnetic radiation at all wavelengths from a black body at temperature T . h is Planck’s constant which is measured to be 6.63x 10-34 J.s . Energy is always emitted or absorbed as a whole number multiple of h (2hv, 3hv…) 26 Prof.
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