Reading Quiz: Sept 9 2015

Reading Quiz: Sept 9 2015 • The Spacetime Interval is the special place where ___ and ___ meet. A. Calculated Time and Path Time B. Geometric Time and Standard Time C. Measured Time and Correct Time D. Coordinate Time and Proper Time

Reading Quiz: Sept 9 2015 • The Spacetime Interval is the special place where ___ and ___ meet. A. Calculated Time and Path Time B. Geometric Time and Standard Time C. Measured Time and Correct Time D. Coordinate Time and Proper Time Spacetime Interval

Reading Quiz: Sept 9 2015 • True or False: Two different inertial frames (traveling at different but constant velocities) will measure the same coordinate time. A. True B. False

Reading Quiz: Sept 9 2015 • True or False: Two different inertial frames (traveling at different but constant velocities) will measure the same coordinate time. A. True B. False Two different inertial frames will measure DIFFERENT coordinate times

Office Hours Revision Office: Wehr Physics #305 Normal Weeks: W/TH 2-3:30 PM (This week is an exception: TH 2-4 PM) Also by appointment on request.

Volume R, Chapter 3 The Nature of Time

Spacetime Diagrams • In SR units, c=1 so v≤1 • Slope of diagram = 1/v • (Remember v = d/t)

How do we measure time? • Coordinate time – 2 clocks method • Measured by synchronized clocks • Central clock emits EM pulse to left & right • Equidistant clocks receive the EM pulses • Measured in inertial reference frames • Both OF and HF have constant velocity! • Observers disagree about time and space intervals between two events

How do we measure time? • Coordinate time – radar method  use reflections • Measured using EM transceiver • Transceiver emits EM pulse toward object • EM pulse reflects off of object • Transceiver receives the reflected EM pulses • Measured in inertial reference frames • Both OF and HF have constant velocity! • Observers disagree about time and space intervals between two events

How do we measure time? • Analogs to space measurement • Coordinate Time = Δt • Interval between two events measured by between 1+ clocks in an inertialframe • Coordinate time is different in different inertial frames • Proper Time = Path Time = Δτ • Interval measured by one clock present at both events • All observers agree on proper time for a particular clock • Spacetime Interval = Δs • Interval measured by one inertialclock present at both events • Special case of being both proper time and coordinate time

How do we measure time?

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • According to an observer in this frame standing at x=0, what time does the left mirror reflect the light? • a) t = 0s b) t = 1s c) t = 2s t=2 t=1 t=0 x=0 x=-1 x=1

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • According to an observer in this frame standing at x=0, what time does the left mirror reflect the light? • a) t = 0s b) t = 1s c) t = 2s • Where is the synchronized clock that makes this measurement located? • a) x = -1s b) x = 0s c) x = 1s t=2 b) t = 1 second t=1 t=0 x=0 x=-1 x=1

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • According to an observer in this frame standing at x=0, what time does the left mirror reflect the light? • a) t = 0s b) t = 1s c) t = 2s • Where is the synchronized clock that makes this measurement located? • a) x = -1s b) x = 0s c) x = 1s • Does this clock measure: • Coordinate time • Proper time • Spacetime interval • a and b • a, b and c t=2 b) t = 1 second t=1 a) x = -1 (light) second t=0 x=0 x=-1 x=1

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • According to an observer in this frame standing at x=0, what time does the left mirror reflect the light? • a) t = 0s b) t = 1s c) t = 2s • Where is the synchronized clock that makes this measurement located? • a) x = -1s b) x = 0s c) x = 1s • Does this clock measure: • Coordinate time • Proper time • Spacetime interval • a and b • a, b and c t=2 b) t = 1 second t=1 a) x = -1 (light) second t=0 x=0 x=-1 x=1 a) Coordinate time Bonus question: How fast would a clock need to be traveling to measure the spacetime interval between the first event (light pulse) and the reflection event?

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • According to an observer in this frame standing at x=0, what time does the left mirror reflect the light? • a) t = 0s b) t = 1s c) t = 2s • Where is the synchronized clock that makes this measurement located? • a) x = -1s b) x = 0s c) x = 1s • Does this clock measure: • Coordinate time • Proper time • Spacetime interval • a and b • a, b and c t=2 b) t = 1 second t=1 a) x = -1 (light) second t=0 x=0 x=-1 x=1 a) Coordinate time Bonus question: How fast would a clock need to be traveling to measure the spacetime interval between the first event (light pulse) and the reflection event? The speed of light!

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • According to an observer in this frame standing at x=0, what time does the light return to the detector? • a) t = 0s b) t = 1s c) t = 2s t=2 t=1 t=0 x=0 x=-1 x=1

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • According to an observer in this frame standing at x=0, what time does the light return to the detector? • a) t = 0s b) t = 1s c) t = 2s • Where is the synchronized clock that makes this measurement located? • a) x = -1s b) x = 0s c) x = 1s t=2 c) t = 2 seconds t=1 t=0 x=0 x=-1 x=1

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • According to an observer in this frame standing at x=0, what time does the light return to the detector? • a) t = 0s b) t = 1s c) t = 2s • Where is the synchronized clock that makes this measurement located? • a) x = -1s b) x = 0s c) x = 1s • Does this clock measure: • Coordinate time • Proper time • Spacetime interval • a and b • a, b and c t=2 c) t = 2 seconds t=1 b) x = 0 (light) second t=0 x=0 x=-1 x=1

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • According to an observer in this frame standing at x=0, what time does the light return to the detector? • a) t = 0s b) t = 1s c) t = 2s • Where is the synchronized clock that makes this measurement located? • a) x = -1s b) x = 0s c) x = 1s • Does this clock measure: • Coordinate time • Proper time • Spacetime interval • a and b • a, b and c t=2 c) t = 2 seconds t=1 b) x = 0 (light) second t=0 x=0 x=-1 x=1 a) Coordinate time c) Spacetime interval & b) Proper time of the detector.

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • An intergalactic dragonfly wearing a very high quality Swiss watch flies through our experiment along the new green trajectory. • Does her watch measure: • Coordinate time • Proper time • Spacetime interval t=2 t=1 t=0 x=0 x=-1 x=1

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • An intergalactic dragonfly wearing a very high quality Swiss watch flies through our experiment along the new green trajectory. • Does her watch measure: • Coordinate time • Proper time • Spacetime interval t=2 t=1 t=0 x=0 x=-1 x=1 b) Proper time of the dragonfly. • Does the dragonfly’s watch read exactly 2 seconds when the light is detected? • a) yes b) no

Remember: Coordinate time is measured by synchronized inertial clocks Proper time is measured by a clock present at both events Spacetime interval is measured by an inertial clock moving at just the right constant velocity to be present at both events. Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) • An intergalactic dragonfly wearing a very high quality Swiss watch flies through our experiment along the new green trajectory. • Does her watch measure: • Coordinate time • Proper time • Spacetime interval t=2 t=1 t=0 x=0 x=-1 x=1 b) Proper time of the dragonfly. • Does the dragonfly’s watch read exactly 2 seconds when the light is detected? • a) yes b) no b) no

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 What time is the left light beam reflected according to an observer in this new “Moving” frame? a) t = t0 b) t = t1 c) t = t2 d) t = t3

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 What time is the left light beam reflected according to an observer in this new “Moving” frame? a) t = t0 b) t = t1 c) t = t2 d) t = t3 b) t=t1 Is this time larger (a) or smaller (b) than 1 second?

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 What time is the left light beam reflected according to an observer in this new “Moving” frame? a) t = t0 b) t = t1 c) t = t2 d) t = t3 b) t=t1 b) smaller Is this time larger (a) or smaller (b) than 1 second?

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 What time is the right light beam reflected according to an observer in this new “Moving” frame? a) t = t0 b) t = t1 c) t = t2 d) t = t3

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 What time is the right light beam reflected according to an observer in this new “Moving” frame? a) t = t0 b) t = t1 c) t = t2 d) t = t3 c) t=t2 Is this time larger (a) or smaller (b) than 1 second?

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 What time is the right light beam reflected according to an observer in this new “Moving” frame? a) t = t0 b) t = t1 c) t = t2 d) t = t3 c) t=t2 a) larger Is this time larger (a) or smaller (b) than 1 second?

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 According to an observer in the “stationary” frame, are the left and right beams reflected simultaneously? a) yes b) no

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 According to an observer in the “stationary” frame, are the left and right beams reflected simultaneously? a) yes b) no Yes Same question for the “moving” frame:

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 According to an observer in the “stationary” frame, are the left and right beams reflected simultaneously? a) yes b) no Yes No! Same question for the “moving” frame:

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 According to an observer in the “stationary” frame, do the left and right beams return to the detector simultaneously? a) yes b) no

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 According to an observer in the “stationary” frame, do the left and right beams return to the detector simultaneously? a) yes b) no Yes Same question for the “moving” frame:

Spacetime Diagram 1: “Stationary” frame (frame of the laser and detector apparatus) Spacetime Diagram 2: “Moving” frame (frame moving at 0.5c relative to the laser and detector apparatus) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=-1 x=1 According to an observer in the “stationary” frame, do the left and right beams return to the detector simultaneously? a) yes b) no Yes Yes! Same question for the “moving” frame:

Spacetime Diagram 2: “Moving” frame according to Einstein (frame moving at 0.5c relative to the laser and detector apparatus) Spacetime Diagram 3: “Moving” frame according to Newton (Not correct!) t=t3 t=2 t=t2 t=1 t=t1 t=0 t=0 x=0 x=1 x=-1 x=0 x=1 x=-1 These beams move at 0.5c These beams move at 1.5c! The speed of light is a constant and is strictly enforced. Simultaneity is strictly enforced. The timing is required to be the same as in the “Stationary” frame.

R3T.1 • Coordinate time could be frame-independent if the Newtonian concept of time were true. • True • False

R3T.1 • Coordinate time could be frame-independent if the Newtonian concept of time were true. • True • False (Because in Newtonian time, the speed of light would be different for different observers in two inertial frames.)

R3T.3 • A person riding a merry-go-round passes very close to a person standing on the ground once (event A) and then again (event B). Which person’s watch measures the proper time between these two event? Assume that the ground is an inertial frame and that the merry-go-round rider moves at a constant speed.) • the rider in the merry-go-round. • the person standing on the ground. • Both. • Neither.

R3T.4 • A person riding a merry-go-round passes very close to a person standing on the ground once (event A) and then again (event B). Which person’s watch (if any) measures the spacetime interval between these two event? (Assume that the ground is an inertial frame and that the merry-go-round rider moves at a constant speed.) • the rider in the merry-go-round. • the person standing on the ground. • Both. • Neither.

R3T.4 • A person riding a merry-go-round passes very close to a person standing on the ground once (event A) and then again (event B). Which person’s watch (if any) measures the spacetime interval between these two event? (Assume that the ground is an inertial frame and that the merry-go-round rider moves at a constant speed.) • the rider in the merry-go-round. • the person standing on the ground. • Both. • Neither. (clock must be in an inertial frame—the merry-go-round rider is changing direction non-inertial frame)

R3T.5 • A person riding a merry-go-round passes very close to a person standing on the ground once (event A) and then again (event B). Which person’s watch (if any) measures the coordinate time between these two event? (Assume that the ground is an inertial frame and that the merry-go-round rider moves at a constant speed.) • the rider in the merry-go-round. • the person standing on the ground. • Both. • Neither.

R3T.5 • A person riding a merry-go-round passes very close to a person standing on the ground once (event A) and then again (event B). Which person’s watch (if any) measures the coordinate time between these two event? (Assume that the ground is an inertial frame and that the merry-go-round rider moves at a constant speed.) • the rider in the merry-go-round. • the person standing on the ground. • Both. • Neither. (clock must be in an inertial frame—the merry-go-round rider is changing direction non-inertial frame)

R3T.6 • A spaceship departs from the solar system (event A) and travels at a constant velocity to a distant star. It then returns at a constant velocity, finally returning to the solar system (event B). A clock on the space-ship registers which of the following kinds of time between these events? • Proper time • Coordinate time • Spacetime Interval • A and C • A, B and C

R3T.6 • A spaceship departs from the solar system (event A) and travels at a constant velocity to a distant star. It then returns at a constant velocity, finally returning to the solar system (event B). A clock on the space-ship registers which of the following kinds of time between these events? • Proper time • Coordinate time • Spacetime Interval • A and C • A, B and C (Only for proper time is a non-inertial reference frame ok. Spaceship frame is non-inertial because it returns.)

Example • The tortoise and the hare are having a race from one end to the other of the sidewalk running from LaLumier to Raynor Library as shown in the diagram. Two snails watch the race and serve as timekeepers for the campus reference frame. The tortoise and the hare each have their own reference frames. Both leave A at the same moment and reach B at the same moment as seen by the snails. (The rabbit is showing off…) • Which frames are inertial? • Which frames measure coordinate time? • Which frames measure proper time (path time)? • Do any frames measure a spacetime interval between A and B? If so, which one(s)?

Reading Quiz: Sept 9 2015