Special. Relativity. Todd Huffman. Steve

Transcription

1 Special Steve Relativity Todd Huffman

2 Einstein s Two Postulates of Special Relativity: I. The laws of physics are identical in all inertial frames II. Light propagates in vacuum rectilinearly, with the same speed at all times, in all directions and in all inertial frames

3 Suppose velocities just added up: (Michelson & Morely 1987) 1 L d v t 1 2 c speed relative to mirrors c-v c speed relative to mirrors c+ v 2 v v v v v v v ct 1 = 2d round trip Mirror 1 c 2 t 2 1 = 4d 2 = 4 ( L 2 + v 2 t 12 /4) t 2 1 = 4(L/c) 2 + (v/c) 2 t 2 1 2L/c t 1 = 1 - v 2 /c 2 t 2 = t 2 = t 2 = L + c-v 2Lc c 2 -v 2 2L/c 1 - v 2 /c 2 L c+v

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6 1/8th predicted displacement!! data

7 lead-glass scintillator calorimetric Cherenkov measurement (Eg > 6 GeV) prompt timing signal thin lead converter Detection points spaced according to bunch structure (105ns x c) charged particle veto collimate beam Absorb swept particles p 0 2 g sweep charged particle again from grazing interactions proton collision with Be target to make pions Magnets sweep out charged particles

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10 Astrophysics, abstract astro-ph/ A time varying speed of light as a solution to cosmological puzzles Authors: Andreas Albrecht, Joao Magueijo Comments: To be published in Physical Review D. Note added referring to John Moffat's early work on VSL theories Journal-ref: Phys.Rev. D59 (1999) We consider the cosmological implications of light travelling faster in the early Universe. We propose a prescription for deriving corrections to the cosmological evolution equations while the speed of light c is changing. We then show how the horizon, flatness, and cosmological constant problems may be solved. We also study cosmological perturbations in this scenario and show how one may solve the homogeneity and isotropy problems. As it stands, our scenario appears to most easily produce extreme homogeneity, requiring structure to be produced in the Standard Big Bang epoch. Producing significant perturbations during the earlier epoch would require a rather careful design of the function c(t). The large entropy inside the horizon nowadays can also be accounted for in this scenario.

11 G. & V. Sokolov, 2007: Orbital Experiment with a Femtosecond Laser for Testing Light Speed Invariance Iman Joudaki, 2007: Test of Special Relativity Using Nano Technology

12 Einstein s Two Postulates of Special Relativity: I. The laws of physics are identical in all inertial frames II. Light propagates in vacuum rectilinearly, with the same speed at all times, in all directions and in all inertial frames

13 Nomenclature x, y, z, t x, y, z, t coordinates measured in the laboratory frame of reference coordinates measured in the moving frame of reference Dx Dt relative difference between 2 positions in a given frame relative difference between 2 times in a given frame

14 Time Dilation: d Dt v c = 2d Dt Dt v v v v v v v d vdt g 1 = Dt = g Dt b v/c where and = 1 - b 2 Your observation of the frame that seems to be moving Moving clocks have longer ticks (run slower)!

15 Length Contraction: 1 2 Dx Dt v c = 2Dx Dt Dt v v v v Dx + vdt 1 Dx - vdt 2 Dx g g 1 = Dx = b v/c where and = 1 - b 2 Your observation of the frame that seems to be moving Objects are shorter along their direction of motion!

16 ''p In The Sky" p p 0 typical v ~ 99.5% of speed of light (b = 0.995) p Blam! p d = v Dt = (0.995)(3x10 8 m/s) x (2x10-6 s) ~ 600m g 1 = 1 - b 2 = 10 Dt = 2x10-6 s Dt = g Dt = 2x10-5 s d = v Dt = (0.995)(3x10 8 m/s) x (2x10-5 s) ~ 6000m e e

17 ''Lorentz-Fitzgerald Contraction ''Aether Drag George Francis Fitzgerald Maxwell s Equations Hendrik Antoon Lorentz

18 Lab Frame v + I F (pure magnetic) In Frame of Test Charge F (pure electrostatic) +q +q B Electricity & Magnetism are identically the same force, just viewed from different reference frames UNIFICATION!! (thanks to relativity) Lorentz expanded Lorentz contracted

19 Special Steve Relativity Todd Huffman

20 Einstein s The 2 Postulates of Special Relativity: I. The laws of physics are identical in all inertial frames II. Light propagates in vacuum rectilinearly, with the same speed at all times, in all directions and in all inertial frames

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24 Planck s recommendation for Einstein s nomination to the Prussian Academy in 1913: In summary, one can say that there is hardly one among the great problems in which modern physics is so rich to which Einstein has not made a remarkable contribution. That he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light quanta, cannot really be held against him, for it is not possible to introduce really new ideas even in the most exact sciences without sometimes taking a risk.

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30 Einstein s Box : E = h (Planck) = hc/l p = h/l (De Broglie) E = pc absorber p=e/c emitter E/c = Mv recoil p=mv motion stops distance travelled d = vdt = v (L/(c+v)) But no external forces, so CM cannot change! Must have done the equivalent of shifting some mass m to other side, such that Md = ml M {EL/(Mc 2 +E)} = m L

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32 Space-Time: ct + y - x + x -y

33 ct returns to point of origin moves with constant velocity (b) until t 2 ct 2 slope = (ct 2 - ct 1 )/(x 2 -x 1 ) = cdt/dx = c/v = 1/b object stationary until time t 1 ct 1 - x x 1 x 2 + x

34 light sent backwards ct tanq = x/ct = v/c = b v = c q v = c tanq max = 1 q max = x + x

35 ct absolute elsewhere absolute future ct 1 no message sent from the origin can be received by observers at x 1 until time t 1 - x x 1 + x absolute past there is no causal contact until they are inside the light cone

36 Spacetime Showdown ct - x + x

37 Twin paradox C. Darwin, Nature 180, 976 (1957). On New Year s day 2030 an astronaut (A) sets out from Earth at speed 0.8c to travel to the nearest star Centauri, about 4 light-years away (as measured in the Earth frame of reference). On reaching the star A immediately turns around and returns to Earth arriving back on New Year s day 2040 (Earth time). A has a sibling B who remains on Earth and they agree to send each other greetings by radio every New Year s day until A returns.

38 Twin paradox C. Darwin, Nature 180, 976 (1957). On New Year s day 2030 an astronaut (A) sets out from Earth at speed 0.8c to travel to the nearest star Centauri, about 4 light-years away (as measured in the Earth frame of reference). On reaching the star A immediately turns around and returns to Earth arriving back on New Year s day 2040 (Earth time). A has a sibling B who remains on Earth and they agree to send each other greetings by radio every New Year s day until A returns. ct star x

39 Twin paradox C. Darwin, Nature 180, 976 (1957). On New Year s day 2030 an astronaut (A) sets out from Earth at speed 0.8c to travel to the nearest star Centauri, about 4 light-years away (as measured in the Earth frame of reference). On reaching the star A immediately turns around and returns to Earth arriving back on New Year s day 2040 (Earth time). A has a sibling B who remains on Earth and they agree to send each other greetings by radio every New Year s day until A returns. ct star signals sent to ship x

40 Twin paradox C. Darwin, Nature 180, 976 (1957). On New Year s day 2030 an astronaut (A) sets out from Earth at speed 0.8c to travel to the nearest star Centauri, about 4 light-years away (as measured in the Earth frame of reference). On reaching the star A immediately turns around and returns to Earth arriving back on New Year s day 2040 (Earth time). A has a sibling B who remains on Earth and they agree to send each other greetings by radio every New Year s day until A returns. ct star signals sent from ship x

41 Twin paradox C. Darwin, Nature 180, 976 (1957). On New Year s day 2030 an astronaut (A) sets out from Earth at speed 0.8c to travel to the nearest star Centauri, about 4 light-years away (as measured in the Earth frame of reference). On reaching the star A immediately turns around and returns to Earth arriving back on New Year s day 2040 (Earth time). A has a sibling B who remains on Earth and they agree to send each other greetings by radio every New Year s day until A returns. ct star signals sent from ship x

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43 Relativity The nearest potentially inhabitable planet observed so far orbits the star Gliese 581, at a distance of 20 lightyears (i.e. 20 times the distance light travels in one year) from earth. The fastest spaceship ever launched is the New Horizons probe that flew past Pluto, which has achieved a speed in excess of km/hr using a boost from Jupiter's gravity. How long would it take such a rocket to reach this star? As part of their summer programme, one team of physics students invents a new propulsion system capable of travelling at 90% the speed of light. Another team of students builds the rocket, which is 100m in length, while a third team offers to fly it to Gliese 581 in the hope of finding better financial support for students elsewhere in the Universe. According to observers on Earth: How long will it take the spacecraft to reach the star? What is the length of the rocket while it is travelling there? According to the students in the rocket: How long will it take them to reach the star? How do they explain this given their speed? A future group of concerned students back on earth (concerned because they are still paying higher tuition fees!) build a huge telescope to point towards the star. When should they look through it to see the spaceship arrive at its destination?