Einstein ’ s Theory of Relativity

1. Einstein’s Theory of Relativity • Is there a maximum velocity in nature ? • If no, then one can travel or convey information over infinite distances in infinitesimally short time – Action at a distance as presupposed by Newton • But, do not observe instantaneous action implying infinite speed • But if yes, then what is the limiting velocity?

2. The Two Postulates of Relativity 1. Speed of light is the maximum speed in nature, and is constant regardless of the speed of the source or the observer 2. All physical laws are the same everywhere, and should have the same form (equations) when describing the same phenomenon (first proposed by Galileo)  Principle of Relativity Changes our concept of space and time

3. Consequences of Relativity • Special Theory of relativity  constant velocities • Can not simply add velocities v1 + v2 v = (v1 + v2) / (1 + v1v2 / c2) • E = m c2  Energy and mass are equivalent (example: atomic energy, A- and H-bombs) • No object with mass can attain the speed of light; its inertial mass becomes infinite m = m(rest) / (1 – v2/c2)1/2 • Light is bent by gravity of a massive object such as the Sun

4. Relativity (Contd.) • General Theory of Relativity  Accelerating objects and gravity • Why are astronauts in the orbiting space shuttle weightless ? • They are continuously falling towards the Earth at the same rate as the floor of the space shuttle (e.g. like a freely falling elevator) • Gravity   Acceleration (equivalent) • Basic idea: F = ma  W = mg

5. Relativity (Contd.) • Space and time are equivalent (simultaneity is relative, not absolute) • Example: Two observers, one on a moving train and the other stationary on the ground observe “simultaneous” flashes of light at different times  difference in space due to motion is “converted” to difference in time • Time ‘flows’ slower in a moving frame of reference (astronauts live slightly longer!), or near a massive object such as a black hole

6. Time Dilation and Space Contraction • A time interval in a moving frame of reference (platform moving with velocity v) gets longer as t’ = t / [ 1 – (v/c)2]1/2 • Clocks run slower in an astronauts timeframe • But the space interval gets shorter as x’ = x [ 1 – (v/c)2]1/2 • A moving meter stick will appear shorter

7. Light and Matter • Light is electromagnetic energy, due to interaction of electrical charges • Matter is made of atoms – equal number of positive and negative particles • An atom is the smallest particle of an element; natural element H to U • Atom  Nucleus (protons + neutrons), with ‘orbiting’ electrons • No. of protons in nucleus = Atomic Number • Science of light  Spectroscopy

9. Why is the sky blue ? The atmosphere scatters the blue light more than red light

10. Prisms disperse light into its component colors: Red-Violet White Light Spectrum Prism

11. Light is electromagnetic wave; Does not require a medium to propagate, unlike water or sound Wavelength is the distance between successive crests or troughs

12. WAVES: Frequency, Wavelength, Speed Frequency (f) (# waves/second) Wavelength () Speed (c) Frequency ‘ ‘f’ ’ is the number of waves passing a point per second c =   f Speed = wavelength x frequency  

13. Visible Light • Forms a narrow band within the electromagnetic spectrum ranging from gamma rays to radio waves • Human eye is most sensitive to which color? • Yellow. Why?

14. Units of wavelength and frequency • Frequency is the number of cycles per second • Since speed of light is constant, higher the frequency the shorter the wavelength and vice- versa • Wavelengths are measured in Angstroms: 1A = 1/100,000,000 cm = 1/10 nanometer (nm) • The higher the frequency the more energetic the wave • Wavelength (or frequency) defines radiation or color

15. Visible light spectrum: Each color is defined by its wavelength, frequency or energy Red - Blue  ( 1 nm = 10 A, 1 A = 10-8 cm) Blue light is more energetic than red light  7000 - 4000 Angstroms Light also behaves like ‘ ‘particles’ ’ called photons Photon energy, frequency, wavelength: E = h f = hc/l Planck’ ’s Law (‘h’ is a number known as Planck’s constant)

16. Spectroscopy: Science of Light Analysis of the color of light from a source

17. Light: Electromagnetic Spectrum From Gamma Rays to Radio Waves Gamma X-Ray UV Visible Gamma rays are the most energetic (highest frequency, shortest wavelength), Radio waves are the least energetic.

18. Decreasing Wavelength OR Increasing Frequency

19. Matter and Particles of Light: Quantum Theory • Light (energy) and matter in motion behave both as waves and particles • Wave-Particle Duality - Quantum Theory • Particles of light are called photons: E = hf = hc/l • Photons of a specific wavelength l may be absorbed or emitted by atoms in matter • Matter is made of different natural elements: lightest Hydrogen (1 proton), heaviest Uranium (92 protons) • Smallest particle of an element is atom, made up of a nucleus (protons and neutrons), and orbiting electrons • Electrons and protons attract as opposite electrical charges, NOT gravitationally like planets and Sun

20. The simplest atom: Ordinary Hydrogen Resemblance to planets orbiting the Sun is superficial ! Electrons also move both as particles and waves p – positively charged e – negatively “ “ One proton in the center (nucleus) and one electron in orbits of definite energy; Ordinary H has no neutrons, but ‘ ‘heavy hydrogen’ ’ has one neutron in the nucleus

21. Energy, Frequency, Wavelength • Light particles ‘photons’ have a unique wavelength • The more ‘energetic’ a wave, the higher its frequency, or lower its wavelength • Planck’s Law: Photon energy (‘quantum’) is E = h f = h /  ‘h’ is the Planck’s constant This ‘quantum’ of energy must be equal to the difference in energies between two electron orbits, for either absorption or emission by an atom 

22. Absorption and emission of photons by H-atom An electron may absorb or emit light photons at specific wavelength Wavelength (n = 3   n = 2): 6562 Angstroms (RED Color) Energy of the photon must be exactly equal to the energy difference between the two ‘ ‘orbits’ ’

23. file:///E:/Univ7e/content/ch05/0503002.html

24. Energy Level Diagram of 1H Continuum n= n=5 n=4 n=3 (2ndexcited state) n=2 (1stexcited state) n=1 (Ground State)

25. 2625 24 n=23 n=6 n=5 n=4 n=3 (2ndexcited state) n=2 (1stexcited state) Photons of all other energies (wavelengths) are ignored and pass on by unabsorbed. n=1 (Ground State)

26. 6252 42 n=32 n=6 n=5 n=4 n=3 (2ndexcited state) n=2 (1stexcited state) Larger Jump = More Energy = Bluer Wavelength n=1 (Ground State)

27. Series of spectral lines of Hydrogen

28. Wavelengths of series of lines from Hydrogen

29. Spectrum of a Fluorescent Light Mercury

30. Characteristic spectra of elements Each element has a unique set of spectral lines, thus enabling its identification in the source. Observations of spectra of different elements in a source (planet, star, galaxy etc.) yields its chemical composition

31. Continuous, Absorption, and Emission spectra of a source Continuous spectrum covers wavelengths in a given range; absorption or emission spectrum consists of dark or bright lines respectively at definite wavelengths

32. Color Indicates Temperature and Energy of the Source Blackbody: Perfect absorber and emitter Of radiation at a given Temperature T Surface T (Sun) = 5600 K “ “ (Mercury) = 800 K Objects generally emit radiation at all wavelengths, but mostly at one peak Wavelength depending on their temperature (e.g. blue – hot, red – cool)

33. TEMPERATURE SCALES Astronomers usually use the Kelvin Scale Room Temp = 300 K = 27 C = 81 F K = C + 273 C = (F - 32) x 5/9 ~ (F - 30) / 2 F = (C x 9/5) + 32 ~ C x 2 + 30

34. Brightness decreases inversely as the square of the distance d=1 B=1 d=2 B=1/4 d=3 B=1/9 B ~ 1/d2

35. Brightness and Temperature • Brightness is related to the total energy emitted, or the luminosity of an object • The energy emitted is related to the temperature of the object • B = s T4 (s is a constant) Stefan-Boltzmann Law

36. The Doppler Effect • Why does the “pitch” of a police siren differ when, say, a police car is approaching you, or when you are running away from the police (not recommended) ? • The frequency (the number of sound waves per second) is higher when approaching, and smaller when receding from the source

37. Doppler Effect in Sound Low Pitch (long waves) High Pitch (short waves)

38. The Doppler Effect Velocity c = frequency (f) x wavelength () )

39. Doppler Shift of Wavelengths • What about the wavelength? • What about light? • Shorter wavelength  Blue-shift, • Longer wavelength  Red-shift • We can determine the velocity of astronomical objects, moving away or towards the Earth, by measuring the wavelength of light from the object • Observed red-shift of galaxies all over the sky shows that galaxies are moving away from one another  the Universe is expanding (Hubble’ ’s Law)