IB Physics – Relativity Relativity Lesson 4 General Relativity (without the maths) 1.The equivalence principle 2.Spacetime 3.Gravitational redshift 4.Black holes

IB Physics – Relativity The Nature of Mass Gravitational Mass m g = W/g Inertial Mass m i = F/a I do not think so! These are completely different

IB Physics – Relativity Einstein’s Happiest Thought Sitting in a chair in the Patent office at Berne (in 1907), a sudden thought occurred to me. " If a person falls freely he will not feel his own weight”. I was startled and this simple thought made a deep impression on me. It impelled me towards a theory of gravitation. It was the happiest thought in my life. I realised that for an observer falling freely from the roof of a house there exists – at least in his immediate surroundings – no gravitational field. The observer therefore has the right to interpret his state as at rest or in uniform motion McEvoy & Zarate, 1995, p32

IB Physics – Relativity The equivalence principal a Planet 1.An object inside an accelerating rocket in outer space will “fall”. 2.An object in a stationary rocket inside a gravitational field will fall So both situations are equivalent Path of “falling” objects

IB Physics – Relativity and similarly Planet v 1. An object inside a rocket in outer space moving at constant velocity is weightless. 2. An object inside a rocket accelerating due to a gravitational field feels weightless Again both situations are equivalent Equivalence animations ?????

IB Physics – Relativity Einstein’s elevator

IB Physics – Relativity The path of light v Observer inside rocket Inertial observer outside rocket xyx y1y1

IB Physics – Relativity The bending of light a xyx y1y1 y2y2 y2y2 Observer inside rocket Inertial observer outside rocket

IB Physics – Relativity But according to the equivalence principle a xy y2y2 Is equivalent to Planet x y y2y2 So gravity bends light towards the planet

IB Physics – Relativity Space time Einstein viewed space time like a rubber sheet extending into the x, y, z and t dimensions Space time is “curved” by mass. An object moves along the path of least resistance. This means they take the shortest path between two points in curved space time. Flat space time. Objects move in a “straight line” McEvoy & Zarate, 1995, p32

IB Physics – Relativity General relativity Model of a planet in orbit An object is “just” captured by the depression. Model of a meteorite crashing into the Earth. McEvoy & Zarate, 1995, p32

IB Physics – Relativity Space-time movie

IB Physics – Relativity So what’s so great about general relativity? Matter tells space how to curve and then space tells matter how to move The beauty of this simple model is.... we don’t need forces. “objects move in a straight line in curved space-time”

IB Physics – Relativity More on space-time Events can be given an x, y, z and t coordinate in space-time to describe where and when they occurred. ct x space-time diagram 45 o a b c 1.Why is the time axis multiplied by c? 2.What is the gradient of a line on this axis? 3.What is the velocity of lines a, b and c? 4.What is wrong with d? d Think?

IB Physics – Relativity Gradient of a space-time diagram or now try the questions on the previous slide

IB Physics – Relativity Even light bends in space time General relativity predicts that the path of light is deviated by curved space-time. “There was to be a total eclipse of the Sun on 29 May 1919, smack in the middle of a bright field of stars in the cluster Hyades.” Arthur Eddington led an expedition to the island of Principe off the coast of Africa to photograph the eclipse. Eddington found that the position of the stars appeared different from pictures taken at a different time. He concluded that the light had curved around the sun by the exact amount that Einstein had predicted. hyperphysics.com, 2006 McEvoy & Zarate, 1995, p32

IB Physics – Relativity Gravitational lensing Light from objects (e.g.quasars) which are very far away can be bent round massive galaxies to produce multiple images; the galaxy behaves like a lens. Researchers at Caltech have used the gravitational lensing afforded by the Abell 2218 cluster of galaxies to detect the most distant galaxy known (Feb, 15 th 2004) through imaging with the Hubble Telescope. Spot the multiple images Wikiepedia.org, 2006 Kirk, 2003, p155

IB Physics – Relativity Black Holes When a star uses up its nuclear fuel it collapses. If the remnant mass of the star is greater than 3 x the sun’s mass there is no mechanism to stop it collapsing to a singularity. The curvature of space-time near a singularity is so extreme that even light cannot escape. Escape velocity For a photon

IB Physics – Relativity Schwarzchild Radius; R Sch At a distance, R Sch, from a singularity the escape velocity is the speed of light. At a distance less than R Sch from a singularity; escape velocity > C  Light cannot escape R Sch is also called the event horizon. Everything trapped within the event horizon is not observable in our universe.

IB Physics – Relativity Try this 1. Calculate the Schwarzschild radius for a star of one solar mass; (M = 2 x Kg) Tsokos, 2005, p591

IB Physics – Relativity Time in gravitational fields General relativity predicts that time runs slower in places where the gravitational field strength is stronger. For example; the Earth’s field weakens as you go further away from the Earth’s surface. This means that time runs more slowly at the ground floor than at the top floor of a building.

IB Physics – Relativity Gravitational Red Shift Gravitational time dilation, or clocks running slower in strong gravitational fields, leads us directly to the prediction that the wavelength of a beam of light leaving the Earth’s surface will increase with height. or but Period

IB Physics – Relativity Red-shift Explained As the light gains height so time runs more quickly because the gravitational field weakens. So as time speeds up, the period increases and hence the wavelength also increases Planet Large wavelength Short wavelength

IB Physics – Relativity Calculating frequency shifts. Consider a photon of frequency f 0 leaving the surface of the Earth. It gains potential energy given by mg  h and the frequency is reduced to f. Photons do not have mass but have an effective mass given by; Conserving energy we get; Do not get h the Planck's constant confused with  h the height gain.

IB Physics – Relativity Blue shift Similarly, a beam of light directed from outer space towards the Earth is blue-shifted i.e. the wavelength decreases as the gravitational intensity increases. The same formula is used to calculate red-shift or blue-shift. Examples to try 1. A photon of energy 14.4 KeV is emitted from the top of a 30 m tall tower toward the ground. What shift of frequency is expected at the base of the tower? Ans;  f = 1.16 x 10 4 Hz Tsokos, 2005, p A UFO travels at such a speed to remain above one point on the Earth at a height of 200 Km above the Earth’s surface. A radio signal of frequency 110MHz is sent to the UFO. (i) What is the frequency received by the UFO? (ii) If the signal was reflected back to Earth, what would be the observed frequency of the return signal? Explain your answer. Ans; (i) f = 1.1 x 108 Hz (shift is v. small). (ii) return signal is the same frequency as the emitted signal Kirk, 2003, p153

IB Physics – Relativity Experimental support In 1960 a famous experiment called the Pound-Rebka experiment was carried out at Harvard University to verify gravitational blue/red-shift. The frequencies of gamma ray photons were measured at the bottom and top of the Jefferson Physical Laboratory tower. Very small frequency shifts were detected as predicted by the theory. Atomic clocks are very sensitive and precise. Atomic clocks sent to high altitudes in rockets have been shown to run faster than a similar clocks left on Earth

IB Physics – Relativity An alternative view of black holes The gravitational intensity near black holes is very strong and approaches infinite at the event horizon. Time effectively stops and any object falling into a black hole will appear to stop at the event horizon according to a far observer. Light emitted from a black hole will therefore be infinitely red- shifted; hence no light is emitted. RsRs x ct Space-time diagram of the formation of a black hole This photon is trapped in the black hole. This photon will escape

IB Physics – Relativity Beyond relativity!

IB Physics – Relativity Bibliography Kirk, T; Physics for the IB diploma, OUP, UK, 2003 McEvoy, J.P. & Zarate, O; Stephen Hawking for beginners, Icon Books, U.K., Tsokos, K.A.; IB Physics, Cambridge University press, U.K., hyperphysics.com, Mar 06 ©Neil Hodgson Sha Tin College

IB Physics – Relativity Videology 1.Postulates of special relativity 2.Speed of light is constant 3.Simultaneity 4.Time dilation 5.Atomic clocks prove time dilation