Hence light World Lines of moving bodies always make an angle of less than 45 to the ct-axes.

Transcription

1 For = second c=30 8 m and ligh ravels 30 8 m. c Hence ligh World Lines always make an angle of 45 o he c-aes. For = second c=30 8 m and for observer ravelling a v<c disance ravelled = v < 30 8 m. Hence ligh World Lines of moving bodies always make an angle of less han 45 o he c-aes.

2 SIMULTANEITY c S c c S A C c C A C c A A B C A B C A, B & C a res in frame S. A & C are simulaneous A, B & C moving in S. A & C are NOT simulaneous

3 z v r y P(,y,z) z r P(,y,z ) y

4 Lorenz Transformaions v y z z y v c Inverse: v y z y z v c where v c and v is he velociy of S as measured in S

5 c v v c v c v v v

6 Wha Would You See? A res v = 0.5 c v = 0.95 c v = 0.99 c Compuer generaed graphics show he visual appearance of a hree-dimensional laice of rods and balls moving owards you a various speeds. The laice only becomes disored as v approaches c.

7 Wha Would You See? A view of a bo a res and a view of he bo phoographed by a single observer shows a disored shape. (a) The appearance of a rain a res as seen in a phoograph. (b) The appearance of ha rain as i moves a 0.9c pas a camera.

8 HENCE WE HAVE TWO CONTRACTIONS (i) FITZGERALD-LORENTZ TO EXPLAIN MICHELSON- MORLEY EXPERIMENT (ii) EINSTEIN ARISING FROM THE INVARIANCE OF c THESE ARE EXACTLY THE SAME IN MAGNITUDE BUT VERY DIFFERENT IN ORIGIN.

9 FITZGERALD-LORENTZ ARISES FROM GALILEAN TRANSFORMATIONS IS A REAL CONTRACTION OF ALL BODIES MOVING THROUGH THE ETHER v IS THE VELOCITY OF THE BODY RELATIVE TO THE ETHER

10 EINSTEIN CALLED IT THE LORENTZ-CONTRACTION ONLY REFERS TO THE MEASURED VALUE OF THE LENGTH OF AN OBJECT IN RELATIVE MOTION TO THE OBSERVER ARISES FOR THE INVARIANCE OF c v IS THE VELOCITY OF THE BODY RELATIVE TO THE OBSERVER CONTRACTION IS DIFFERENT FOR DIFFERENT OBSERVERS IN RELATIVE MOTION EINSTEIN SPOTTED THE CORRECT EXPLANATION!

11 RELATIVTY IS TRULY RELATIVE SUPPOSE WE HAVE TWO IDENTICAL METER STICKS IN REALTIVE MOTION ALONG THE DIRECTION OF THEIR LENGTH IF IS RIDING WITH ONE OF THE STICKS HE SHALL MEASURE THE LENGTH OF THE OTHER STICK TO BE LESS THAN m. HE INCORRECTLY THINKS THAT HIS STICK MUST APPEAR LONGER TO AN OBSERVER IN THE REST FRAME OF THE OTHER STICK.

12 YOU NEED NEVER BE PERPLEXED BY SUCH A QUESTION IF YOU ONCE REALISE THAT EACH INERTIAL FRAME MUST SPEAK FOR ITSELF! THE OBSERVATIONS THAT LEAD TO SAY THAT S STICK HAS SHRUNK ARE S OBSERVATIONS! CAN MAKE HIS OWN OBSERVATIONS OF S STICK AND CONCLUDE THAT SHRUNK! S STICK HAS

13 BOTH ARE CORRECT THERE IS NO CONTRADICTION BECAUSE IT IS PHYSICALLY IMPOSSIBLE FOR BOTH SETS OF OBSERVATIONS TO REFER TO ONE AND THE SAME FRAME

14 TIME DILATION BEWARE WHEN IT COMES TO TIME OUR INTUITIONS CAN LET US DOWN! THERE IS NO SUCH THING AS THE TIME

15 Is Space Travel Possible? Suppose you ook a rip across he Universe in a spaceship, acceleraing all he ime a one Earh graviy g. How far would you ravel in how much ime? See hp://casa.colorado.edu/~ajsh Time elapsed on spaceship in years Time elapsed on Earh in years Disance ravelled in ligh years To Earh (saring poin) Proima Cenauri Vega Pleiades Cenre of Milky Way Andromeda galay Virgo cluser Coma cluser Edge of observable Universe

16 Around he World wih Aomic Clocks Hafele & Keaing, Science 77, 67, 97 gh R v v c c 0 0 Graviaional red shif Earh s roaion Time dilaion Where is clock a res on Earh; v is he ground speed of he aircraf Resuls (ns) Eas Wes 44 ± 4 79 ± 8 Graviy Prediced relaivisic ime gain for a flying clock afer a non-sop equaorial circumnavigaion of he earh a various aliudes. The area wihin he hached lines is below deecion hresholds wih a porable Cs clock. Predicion Measuremen -84 ± 8-40 ± 3-59 ± 0 96 ± 0 75 ± 73 ± 7 Roaion/ Kinemaic Ne

17 Frame s has a speed v 0. 6c relaive o s. Clocks are adjused so ha a 0 0 Two evens occur y z y z 0 v v c v c Have shown how o calculae he separaion in posiion or ime of wo arbirary and uncorrelaed evens! v c

18 Time Inerval measured in he frame ha has a velociy v relaive o he paricle v c Proper Time Inerval Inerval Measured in he Res Frame of he paricle

19 Relaivisic Doppler Effec Saionary observer sees waves redshifed Saionary observer sees waves blue shifed 3 4 u S S S3 S4 Source moving o righ while emiing waves u

20 Relaivisic Doppler Shif 0 f f 0 f f (Observer moving away from source) (Observer moving owards source)

21 Hubble s Law Hubble (99) noiced ha disan galaies always showed a RED SHIFT. They are moving AWAY from us, hose furher away move faser. Hubble s Law: u = DH Edwin Hubble Velociy is proporional o disance Hubble s original daa Curren acceped value = 67 kms - Mpc -

22 Measuring Red Shifs Disance ( 0 6 l.yrs.) H = u / D H =. 0-8 s