Modern Physics (PC300) Class #3 Moore - Chapter R3 - Time Chapter R4 - Metric Equation Chapter R5 – Proper time Chapter R6 – Coordinate Transformations

Homework Questions New Homework assignment! See online and pdrive. Due Wed. And Sim due tomorrow!

Time -- After a year of physics we better define how to measure it! Coordinate time interval Proper time interval Space time interval The Metric Equation a) 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 time Isaac 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 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 Time Time -- After a year of physics we better define how to measure it! Coordinate Time (  t) 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 Times Hafele & Keating Tests; Did They Prove Anything? A. G. Kelly PhD* Extension Project?

Concept of Time Time -- After a year of physics we better define how to measure it! Coordinate Time (  t) Proper Time (  ) Spacetime Interval (  s)

Same as Proper Time but with constant velocity between events

t' O Coordinate Time (  t) Synchronizing Clocks x' A B t' A =t' B left clock right clock center clock

Coordinate Time (  t) Synchronizing Clocks x t O A Bt A ≠ t B

Concept of Time Coordinate Time (  t) Time between events in given inertial frame (frame dependent) Proper Time (  ) One clock present at both events (path dependent, but frame independent) Spacetime Interval (  s) One clock present at both events whose worldline is inertial (frame independent) One clock present at both events whose worldline is inertial (frame independent) 1. Proper Time - Brian & Alice 2. Spacetime - Brian 3. Coordinate Time – Brian, Cara & Dave

The Metric Equation Relationship linking coordinate differences  t and  d with spacetime  s OTHER FRAME

The Metric Equation Total distance (D AB ) light travels (using Pythagoras Theorem): Synchronized => c=1:  t=D AB HOME FRAME

Metric Equation Visualizations Tipler Serway

x t Earth worldline 0 9

The 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 )

Twin Paradox x t A C B Alpha Centauri Worldline Earth Worldline 4.3y 13y  s=? DISCUSSION

Different Views: Read Them This is FUN Tipler: pages Ohanian: pages Epstein: Feynman (6 ideas): 77-79