Einstein’s Theory of Relativity

1. 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? Einstein’s Theory of Relativity

2. The Two Postulates of Relativity • Speed of light is the maximum speed in nature, and is constant regardless of the speed of the source or the observer • 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 • But the space interval gets shorter as x’ = x [ 1 – (v/c)2]1/2

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

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

12. 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

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

14. Visible light spectrum: Each color is defined by its wavelength, frequency or energy Red - Blue 7000 - 4000 Angstroms ( 1 nm = 10 A, 1 A = 10-8 cm) Blue light is more energetic than red light 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)

15. Spectroscopy: Science of LightAnalysisof the color of light from a source

16. Decreasing Wavelength OR Increasing Frequency

17. Light: Electromagnetic SpectrumFrom 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. 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?

19. 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)

20. 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

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

22. 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

23. 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

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

25. The Doppler Effect Velocity c = frequency (f) x wavelength (l)

26. 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)