PH 301

Dr. Cecilia VogelLecture 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

time place Event

0 0 takeoff (both are 20)

20 12

0

landing (I am 40, Nick is 36)

20landing celebration (I am 40, Nick is 36)

Nick’s Timeline x=0 is ship

time place Event

0 0 takeoff (both are 20)

16 0

-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, ttravel=d/v?

Did the light flashes arrive at the same time? (tarrive)

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, ttravel=d/v?

Did the light flashes arrive at the same time? (tarrive)

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, ttravel=d/v?

Did the light flashes arrive at the same time? (tarrive)

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 × 109, 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

0 0 departure (both are 20)

20 12

0

arrival (I am 40, Ryan is 36)

20landing celebration (I am 40, Ryan is 36)

Fill in Table Ryan’s frame. x=0 is ship

time (yr)place (c-

yr)Event

0 0 departure (both are 20)

__ __

__

arrival (I am 36, Vera is ___)

__ landing celebration (I am ___, Vera is __)