Special Relativity Einstein

Transcription

1 Speial Relatiity Einstein Published 5 papers in Annalen der Physik Photoeletri effet (led to Nobel Prize in 191) Brownian Motion (proed existene of atoms) Speial Relatiity Speial Relatiity (E=m ) Moleular dimensions (PhD) 3 were onsidered to be among the greatest in the history of physis Relatiity made simple But the greatest was yet to ome... Dr. Jan Skakle Uniersity of Aberdeen 1 Speial? The onept of relatiity had been well know sine the time of Galileo E=m Did not appear in Einstein s first relatiity paper. It was used by Newton, and Poinaré deeloped this idea. Jules Poinaré Einstein said that he thought of the idea whilst riding his biyle (On the Eletrodynamis of Moing Bodies) 3 4 Postulates of Speial Relatiity Einstein built the Speial Theory of Relatiity on two postulates: Inertial Referene Frames An inertial Frame of Referene is one in whih the basi laws of physis apply e.g. a train moing at a onstant eloity. In this, objets moe normally. The Relatiity Priniple: The laws of motion are the same in eery inertial frame of referene. Constany of the Speed of Light: The speed of light in a auum is the same independent of the speed of the soure or the obserer. This relates to objets obeying Newton s first law. Einstein in

2 Non-Inertial Frames Compare this with an aelerating or deelerating objet. During this period, you are in a non-inertial frame. Can be intuitie... Moing apart; what is the green ar s eloity relatie to your frame? Same if you are in a Ferris wheel you are always aelerating inwards so non-inertial. = 70 km h -1 V = 50 km h -1 Stritly speaking the Earth is a non-inertial frame, but it s lose enough so we onsider it inertial. We know the answer intuitiely (10 km h -1 ) but this also works in terms of Lorentz transformations (of ourse!) 7 8 Same idea, but with light: The luminiferous ether The ether, or æther, was the basis of understanding After all, if the speed of light is, what is that relatie to? = 3 x 10 8 ms -1 = 3 x 10 8 ms -1 From the examples aboe, we would expet the relatie eloity to be = 6 x 10 8 ms -1. This is in fat wrong! The ether was tranparent had zero density was eerywhere was the substane whih allowed light to propagate Speed of light - Fizeau First suessful earthbound measurement Maxwell Had alulated that the speed of light was 3 x 10 8 ms -1 A. H. L. Fizeau ( ) This was assumed to be with respet to the ether Maxwell in 1878 suggested how to make the measurement, but said that no method would be able to detet the subtle differene inoled. Obtained alue of 3.1 x 10 8 ms -1 Refined to.98 x 10 8 ms -1 by Foualt Leon Foualt ( ) 11 1

3 Enter Mihelson... Apparatus Born 185 on German/Polish border Moed to US in California Gained free plae at US Naal Aademy, learned Maths & Physis amongst other things Professor in Cleeland, Ohio Albert Mihelson Years of experiments to find speed of the ether The interferometer Mihelson-Morley Experiment Instrumentation by Mihelson inluding nerous breakdown Found speed of light (in a auum) is always the same Most famous negatie result in the history of Physis (William H. Cropper) Paper Bak to Einstein... Some questions... Can you ath up with light? What would happen if I rode a light beam? If you were traelling at the speed of light and looked in a mirror - would you see your refletion? Questions keep me awake at night. If you were in your ehile traelling at the speed of light and you turn your headlights on, what would they do? OK, what s the speed of dark? Stephen Wright 17 18

4 Seond postulate Gedanken The speed of light in a auum is absolute = 3 x 10 8 ms -1 no matter the speed of the obserer. Consistent with Mihelson-Morley Reoniles Maxwell s equations with mehanis What time dilation means... Graph Usually written t = γ t 0 1 where γ = 1 t 0 is alled the proper time interal Moing loks are measured to run slowly. Valid when proper time refers to eents ouring at same point Time is an illusion. Lunhtime doubly so. Hith-hikers Guide to the Galaxy Douglas Adams Eidene? Atomi loks flown on ommerial jets for about 45 hours then ompared with ground-based loks. Elementary partiles measurement of muons at the earth's surfae. should hae deayed in the atmosphere Example. Example A muon at rest has lifetime. x 10-6 s. In a partile aelerator, it moes at Find: (a) how long it lasts at this speed and (b) how far it traels before it deays. (a) t = t o / [1 - ( / )] = (. x 10-6 ) / [ ] = 16 x 10-6 s (b) Distane traelled = t = 4.6 x 10 3 m 3 4

5 The Twin Paradox The Twin Paradox As before t = t o / [1 - ( / )] = 9/ [1 - (0.96 ) ] t = 9/ [0.08] = 9/0.8 = 3 years One twin traels to Alpha Centauri (4.3 light years away) at a speed of The other stays on Earth. Compare the time interals. So one twin ages by 9 years, the other by 3 years! Light takes 4.3 years to get to Alpha Centauri. At 0.96 it takes 4.5 years (4.3/0.96). There and bak thus take 9 year - this is t o. 5 6 The Paradox The aboe seems fine EXCEPT the speial theory states that no referene frame is better than another. Who is moing? If we onsider the spaeship to be stationary Earth moes by 0.96 in opposite diretion This time it is the opposite twin who ages more!? Length ontration L = L o 1 So this time the proper length is ontrated as the speed inreases. Contration in diretion of motion If the spaeship omes bak, it will hae had to deelerate & aelerate and this makes it non-inertial general relatiity. Einstein at rest Einstein at =.6 x 10 6 ms Distortion Mass is also relatie. Mass m = m 0 1 This has been obsered for elementary partiles If we moe past building at to the right, then onsider ourseles at rest the building moes to the left at Howeer we should beware of isualising anything getting bigger. The building gets out of the way of the light from the side. 9 30

6 Mass inrease So, as speed inreases, the mass inreases, until at the speed of light.? We annot aelerate anything up to the speed of light. Consequenes If we try to aelerate something lose to then the mass inreases but we an t speed it up any more. Energy (the work we are doing) onerts to mass E = m 1 For a partile at rest, =0 so E o (rest energy) = m 31 3 E=m?? Examples Atomi bomb Partile physis deay of partiles The sun The mass of the sun is 1.99 x kg. If it were all onerted to energy this would gie M = L / V 1.99 x x (3 x 10 8 ) = 1.79 x J. We an also do some other alulations The sun The sun radiates energy at 3.9 x 10 6 W 1 W = 1 J/s so sun loses 3.9 x 10 6 J eery seond This means it will last 1.79 x / 3.9 x 10 6 Čerenko radiation Soni boom happens when you pass through the sound barrier (330 ms -1 ) In dense media, light an be oertaken too Best desribed as a soni boom for light = 4.57 x 10 0 seonds = 1.5 x years! (15 million million years) Also if it loses 3.9 x 10 6 J eery seond: m = E/ = 3.9 x 10 6 / (3 x 10 8 ) = 4.4 x 10 9 kg eery seond!! Pael Čerenko

7 Slowing down light Lene Hau (Harard) Tiny loud of ultraold sodium atoms (0.9 µk) Very low pressure Light slowed to 8 ms -1 Stopped for se Diisions 1) Things that trael below the speed of light (tardions). These are normal things known to us with mass. ) Things that trael at the speed of light. Partiles with zero mass, e.g. photons. 3) Things that trael aboe the speed of light (tahyons) Imaginary mass 37 38