PH 301 Dr. Cecilia Vogel Lecture 4

Review Outline  Lorentz transformation  simultaneity  twin paradox  Consequences of Einstein’s postulates  length contraction  Relativistic Doppler Effect

Recall Trip Example  John saw Nick’s trip to take 20 years, so John aged 20 yrs.  Nick saw the trip to take 16 years, so Nick aged 16 yrs.  Moving clocks run slowly, moving bodies age slowly, …  Nick ages slowly from John’s point of view.

Symmetry  From Nick’s reference frame.  Nick is at rest  John is moving  If moving bodies age slowly, then John should age slowly, as seen by Nick.

John’s Timeline  x=0 is Earth timeplaceEvent 00takeoff (both are 20) landing (I am 40, Nick is 36) 20 landing celebration (I am 40, Nick is 36)

Nick’s Timeline  x=0 is ship timeplaceEvent 00takeoff (both are 20) 160 -x landing (I am 36, John is 32.8) 25 landing celebration (I am 45, John is 40)

Twin Paradox  If John sees Nick aging slowly, and Nick sees John aging slowly,  what happens if Nick comes back to Earth and they see each other face-to-face?  Who has actually aged less?

Not Actually Symmetric  On way there, each sees the other age slowly,  On way back, each sees the other age slowly.  both are inertial reference frames  so time dilation holds  While Nick is turning around  Nick is not in inertial reference frame  He knows it – acceleration can be felt/detected  He sees John age quickly, catch up, and get ahead  Enough so that he agrees, John has aged more in the end.

Simultaneity  Can we at least agree on what things happen at the same time (simultaneous)?  No.  Example – John said he celebrated Nick’s arrival at the same time as Nick’s arrival happened  In Nick’s frame the celebration happened 9 years later!  If events happen at different places, one observer might see them as simultaneous, another not.  If they happen at same place & same time  all agree  often physical consequences

Simultaneity  If events 1 & 2 happen at different places and some reference frames measure them to be simultaneous  others measure event 1 to happen first  still others measure event 2 to happen first  However….  If the earlier event causes later event  all agree on order  often physical consequences

Simultaneous?  Pretend the last part of the demo was done with light flashes rather than erasers. If any answer is no, say which is larger.  In your frame:  Did the light flashes travel the same distance?  Did the light flashes travel at the same speed?  Did the light flashes travel for the same amount of time, t travel =d/v?  Did the light flashes arrive at the same time? (t arrive )  Did the light flashes actually occur at the same time?

Simultaneous?  Pretend the last part of the demo was done with light flashes rather than erasers. If any answer is no, say which is larger.  In my frame:  Did the light flashes travel the same distance?  Did the light flashes travel at the same speed?  Did the light flashes travel for the same amount of time, t travel =d/v?  Did the light flashes arrive at the same time? (t arrive )  Did the light flashes actually occur at the same time?

Simultaneous?  Pretend the last part of the demo was done with light flashes rather than erasers. If any answer is no, say which is larger.  In my frame:  Did the light flashes travel the same distance?  Did the light flashes travel at the same speed?  Did the light flashes travel for the same amount of time, t travel =d/v?  Did the light flashes arrive at the same time? (t arrive )  Did the light flashes actually occur at the same time?

PAL – part 1  Hitler born 20 April 1889 in Germany.  Call that x1=0, t1=0, x1'=0, t1'=0  Suppose history book published in New York on 20 April 2010,  t2 = 121 yr= 3.8 × 10 9, x2=6800 km.  How fast would observer need to go to observe events in opposite order, t2'<0?  Answer should describe all velocities that work, and should be in units of c.

PAL – part 2  Vera’s Frame. x=0 is Earth time (yr)place (c-yr)Event 00departure (both are 20) arrival (I am 40, Ryan is 36) 20 landing celebration (I am 40, Ryan is 36)

Fill in Table  Ryan’s frame. x=0 is ship time (yr)place (c-yr)Event 00departure (both are 20) __ arrival (I am 36, Vera is ___) __ landing celebration (I am ___, Vera is __)