SPECIAL THEORY OF RELATIVITY

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1 SPECIAL THEORY OF RELATIVITY 1. Basi information author Albert Einstein phenomena obsered when TWO frames of referene moe relatie to eah other with speed lose to the speed of light speial theory of relatiity (STR) the mutual speed of the frames is onstant 1915 general theory of relatiity (GTR) - the mutual speed of the frames is NOT onstant What will be obsered by an outer and inner obserer of the following experiment?. Postulates of STR I. The laws of physis are the same in all inertial frames of referene. II. The speed of light in a free spae (auum) has the same alue in all inertial frames of referene Mihelson Morley experiment What was the main idea of the experiment? Did the authors sueed? SPECIAL THEORY OF RELATIVITY

2 a) time dilation A moing lok tiks more slowly than a lok at rest t = ( ) = t = + 1 = t = inner obserer time interal on a moing lok = in its rest frame outer obserer time interal on a lok at rest = measured between the eents in a moing frame Questions: 1. Muon paradox (07 m e, harge +e or e): these partiles are reated at higher altitudes, their lifetime is about. µs. As they are deteted at sea leel, although this should not be possible een when their speed is almost. Resolution their own lifetime is the same but it differs for us, as they are so fast! Take = 0.9 and alulate what will be the lifetime of muons measured by us. + π. Mesons, m = 73 m e, lifetime.5x10-8 s, moe relatie to us at How far will they moe during this time in their frame of referene and relatie to us? - - SPECIAL THEORY OF RELATIVITY

3 b) length ontration Faster means shorter To measure the distane between the ends of a moing rod at the same instant is impossible what happens at the same time in one frame of referene does not do so in another moing frame of referene (see the first figure light pulse in a railway truk) for an obserer moing with the frame K the time taken to trael OZO is l0 t = for an obserer in frame K : OZ : t t + l 1 = 1 ZO : t = l t l l l total time t = t1 + t = + = t + time obeys relatiity, so: t = t hene 0 1 l = l rest frame outer obserer SPECIAL THEORY OF RELATIVITY

4 ) relatiity of mass and momentum Rest mass is least nd N.L.: F R = ma if m = onst Ek = W done by F R - the objet ould aelerate to infinity, but energy is onsered een at relatiity and when the speed of the objet rises, the fore needed to aelerate it rises too not possible to aelerate to reah m0 m = rest mass m kg mass for the outer obserer p = m een in relatiity m 0 p = d) adding speeds Maximum speed in any frame of referene is u? u for for : u = u + u + u = u 1+ derie what happens when u = : SPECIAL THEORY OF RELATIVITY

5 e) equialene of mass and energy When mass of objet hanges by m, it orresponds to the energy hange of E. E = m Example binding energy of a nuleus: The mass of any nuleus is always...than the sum of masses of separated nuleons. This is due to energy... in forming the nuleus. When we want to split the nuleus to get the nuleons again, we hae to... the same amount of energy. hoose: biggersmaller, suppliedreleased, supplyrelease 3. Summary no basi = rest frame of referene maximum speed with whih objets or information an pass, other quantities differ in eah frame! GENERAL RELATIVITY spae and time is formed by mass and energy distribution the shortest distane between objets need not be a straight line graity = aeleration graity affets time (GPS set up) essential for extreme onditions (blak holes,...) Questions: 3. Calulate the period and frequeny of the light lok of length 5 m in its a) rest frame, b) in a frame moing at = A spaeship moes at = 0.5 relatie to us. If a light pulse is produed in the spaeship, what will be the speed of light measured by us? Proe derie using the equation. L71-9, 1-13 Answers: 1. 5 µs. 7.4 m, 53 m s, Hz; s, Hz SPECIAL THEORY OF RELATIVITY