Modern PhysicsModern Physics(PC300)(PC300)

Class #3 Class #3

Moore - Chapter R3 - TimeMoore - Chapter R3 - Time

Chapter R4 - Metric EquationChapter R4 - Metric Equation

Chapter R5 – Proper timeChapter R5 – Proper time

Chapter R6 – Coordinate Chapter R6 – Coordinate TransformationsTransformations

Homework QuestionsHomework Questions

New Homework New Homework assignment! assignment!

See online and pdrive.See online and pdrive.

Due Wed.Due Wed.

And Sim due tomorrow!And Sim due tomorrow!

2 2 2 2 2( )s t x y z

AB2

AB Δtβ1Δ τ

Time -- After a year of physics we better define how to measure it!Coordinate time intervalProper time intervalSpace time interval

The Metric Equationa) Derive the metric equation, the consequence of having a frame independent speed of light, c=1.

b) Example problems that use the metric equation

Measuring the proper time (path time) vs. time in another frame.

Derivation starting with the metric equation

Newton & Einsteins view of timeNewton & Einsteins view of timeIsaac Newton was right about some of his ideas about time but he was wrong about others. For instance, he said that time is absolute. His theory for this was that if a pulse of light is sent from one place to another, different observers would agree on the time it took for the light to get from one place to the next (since time is absolute), but the two observers would not always agree on the distance the light traveled (since space is not absolute). Since the speed of light is simply the distance divided by time, different observers would measure different speeds of light.

This is where Einstein disagreed with Newton, because in Einstein's relativity all observers must agree on the speed of light because it never changes. In Einstein's theory, since the two observers don't agree on the distance the light has traveled, they must disagree on the time it took for the light to go between the two places. The time taken is the distance the light traveled, which the observers don't agree on, divided by the speed of light, which they do agree on. In other words, Einstein put an end to the idea that time is absolute. Since time is relative, space must be relative too.

From Newton to EinsteinFrom Newton to Einstein

Newton: Time is absolute. Two people will measure the same time between events, but disagree on distance and thus velocity.

Einstein: Time is NOT absolute. Two people will measure different times of light moving from one place to another, and disagree on the distance traveled BUT would agree on velocity.

Concept of TimeConcept of TimeTime -- After a year of physics we Time -- After a year of physics we

better define how to measure it!better define how to measure it!

Coordinate Time Coordinate Time ((t)t)

Proper Time (Proper Time ())

Proper Time (Proper Time ())

“Path Dependent"The clock is present at both events and follows some path. The measurements depends on what path the clock takes, i.e. depends on clock worldline.

Experiment to Compare TimesExperiment to Compare Times

Hafele & Keating Tests; Did They Prove Anything? A. G. Kelly PhD*

Extension Project?

Concept of TimeConcept of TimeTime -- After a year of physics we Time -- After a year of physics we

better define how to measure it!better define how to measure it!

Coordinate Time Coordinate Time ((t)t)

Proper Time (Proper Time ())

Spacetime Spacetime Interval (Interval (s)s)

Spacetime Interval (Spacetime Interval (s)s)

Same as Proper Time but withconstant velocity between events

t'

O

Coordinate Time (Coordinate Time (t)t)Synchronizing ClocksSynchronizing Clocks

x'

A B t'A=t'B

leftclock right

clockcenterclock

Coordinate Time (Coordinate Time (t)t)Synchronizing ClocksSynchronizing Clocks

x

t

O

A

B tA ≠ tB

Concept of TimeConcept of Time

Coordinate Time (Coordinate Time (t)t)Time between events in given Time between events in given

inertial frame (frame dependent)inertial frame (frame dependent)

Proper Time (Proper Time ())One clock present at both One clock present at both

events (path dependent, but frame events (path dependent, but frame independent)independent)

Spacetime Interval (Spacetime Interval (s)s) One clock present at both One clock present at both events whose worldline is inertial events whose worldline is inertial (frame independent)(frame independent)

1. Proper Time - Brian & Alice2. Spacetime - Brian3. Coordinate Time – Brian,Cara &Dave

The Metric EquationThe Metric EquationRelationship linking coordinate differences t and d with spacetime s

Ls 2

OTHER FRAME

The Metric EquationThe Metric EquationTotal distance (DAB) light travels (using Pythagoras Theorem):

22)2( dLDAB

Synchronized => c=1: t=DAB

HOME FRAME

22)2( dLt

222 zyxd

222 dts

Metric Equation VisualizationsMetric Equation Visualizations

Tipler

Serway

)t-(t2

1x ABE

)t(t2

1t ABE

x

t

Earthworldline

0

9

The Twin ParadoxThe Twin Paradox

"If we placed a living organism in a box…one could arrange that the organism, after an arbitrary lengthy flight, could be returned to its original spot in a scarcely altered condition, while corresponding organisms which had remained in their original positions had long since given way to new generations." (Einsteins original statement of paradox - 1911)

Twin ParadoxTwin Paradox

x

t

A

C

B

Alpha Centauri Worldline

Earth Worldline

4.3y

13y

s=?

DISCUSSION

Different Views: Read ThemDifferent Views: Read ThemThis is FUNThis is FUN

Tipler: pages 50-53Ohanian: pages 104-106Epstein: 85-86Feynman (6 ideas): 77-79