STAV Supporting Slides VCE Physics – Study Design 2016-2021 Special Relativity

: from reference frame of platform World-Map : from reference frame of platform All “orange” clocks showing same time – synchronised

t0 t World-Map : from reference frame of platform t > t0 One clock is “proper time” t0 Two clocks (more clocks) measure larger time interval. This is what was “MEASURED” t t > t0 Time interval measured from platform frame is longer This is “Time Dilation”

: what is “seen” by the girl World-Picture : what is “seen” by the girl This is what I “saw”!

t0 t World-Picture : what is “seen” by the girl t0 > t This is what girl “SAW” t0 > t t0 So, time on train “is faster”! Approaching clocks LOOK like they are FAST. This is what I “saw”! t Similarly - receding clocks LOOK like they are SLOW. Time dilation equation does NOT tell us what time will LOOK like.

The time dilation equation relates to “measurements” NOT what we “see”.

Motion is relative… …shouldn’t time dilation be symmetrical? Experimenters in platform-frame measure time dilation of train-frame Train-frame should be able to measure time dilation of platform-frame… …how? Let’s take a look…

: from reference frame of train World-Map : from reference frame of train All “blue” clocks showing same time – synchronised

t t0 World-Map : from reference frame of train t > t0 One clock is “proper time” (this time on platform) Two clocks (this time on train) more clocks = larger interval This is what was “MEASURED” t > t0 t0 Time interval measured from train frame is longer Time dilation again!... but this time other way around

Time Dilation (definition) “proper time interval” (single clock) measured as larger (dilated) from a relatively moving frame of reference (by two clocks).

People do NOT “feel” any different – they do not experience time moving faster or slower.

𝑡= 𝑡 0 𝛾 𝑡 0 = 𝑡 𝛾 dilated time interval proper time interval two clocks larger 𝑡= 𝑡 0 𝛾 proper time interval one clock smaller 𝑡 0 = 𝑡 𝛾

Key Skill Identifying which time interval is the proper time / shorter time, so that we know whether to multiple or divide by gamma.

Summary Time dilation = Single clock measurement = “proper time” increase (dilation) of the measurement of a time interval. what we measure, NOT what we see. is a symmetrical effect BUT any particular measurement is not symmetrical. Single clock measurement = “proper time” less clocks = smaller time interval Two clock measurement (a relatively moving frame) = “dilated time” more clocks = larger time interval Time will seem to move faster (approaching) or slower (receding) mainly due to finite speed of light (+/- smaller SR effects). What time “looks like” is NOT covered by Study Design – “should be” no exam questions on this.

Muons – application of time dilation Lets look at exam question from sample exam:

determined by the scientists. fraction Expected answer = 22 μs Actual answer = 2.2 μs Nice 1960’s YouTube video: www.youtube.com/watch?v=tbsdrHlLfVQ determined by the scientists.

Muons – alternative to sample question Students get given the half-life determined by the scientists measuring numbers at top and bottom of mountain and have to provide the “proper” half-life of the muon. Would then divide by “gamma” i.e. 22 μs /10 = 2.2 μs

How to park a stretched limo in a short garage! Length Contraction How to park a stretched limo in a short garage!

How do you measure the length of an object? Use a ruler / tape measure Proper length, L0 = length measured in frame of rest of object

How do you measure the length of a moving object?

World Map v = 𝐿 0 𝛾 𝐿

World Picture : what she saw v

World Map : train frame v

World Map : train frame v 𝐿= 𝐿 𝛾

Key Skill Identifying which time interval is the proper length / longer length, so that we know whether to multiple or divide by gamma.

Summary Proper length = length measured by observer at rest relative to object Length contraction = decrease (contraction) of the measurement of a length. what we measure, NOT what we see. is a symmetrical effect BUT any particular measurement is not symmetrical. Length of object will appear to be longer (approaching) or shorter (receding) mainly due to finite speed of light (+/- smaller SR effects). Object is also distorted, colour is changed etc. What objects “look like” is NOT covered by Study Design – “should be” no exam questions on this.

Twin “Paradox” If time permits ;-)

If time dilation is all about “measurements” is Time Dilation “real”?

Is it real? Real impacts e.g. GPS Thought Experiment – Twin Paradox

clock at either end of platform one-clock on another train Clocks and trains one-clock on train X X A B clock at either end of platform Y Y one-clock on another train total X + Y time is less than same interval measured on platform

Space ships and planets one-clock on spaceship X X A clock on each planet B Y Y one-clock on another spaceship total X + Y time is less than same interval measured by planets

Re-using the same clock one-clock on spaceship X X A clock on each planet B X X same spaceship total X time is less than same interval measured by planets

Twins One twin on spaceship X X One twin on planet A A B X X Twin returns Twin on spaceship is younger on return!

Objection / Paradox Motion is relative: Look at it from reference frame of Twin on spaceship Twin on planet ages less!

Twins One twin on spaceship X One twin on planet A A Twin on planet is younger on return?

Resolution Situation is not symmetrical Cannot construct one-clock / two clock in same way Twin on spaceship changes reference frame (accelerates at turnaround)

CAREFUL Acceleration is NOT “central”: if the spaceship just accelerated out and back without the long journey there would not be much ageing ageing is approximately just the one-clock two-clock ageing calculate difference in age with time-dilation equation (+/- “insignificant bits”) Twin paradox “resolved” as situation is NOT symmetrical One twin remains in same frame of reference Other twin changes frame of reference OK… so this requires an acceleration but can be “minimised” and is “not the cause” of the ageing (though “cause” depends on interpretation)

Clearing up misconceptions SR CAN deal with accelerations and CAN deal with Twin Paradox Even the +/- little bit… calculus GR is NOT required to “resolve” Twin Paradox GR is NOT SR + acceleration GR = SR + Gravity Nice discussion (Scientific American): How does relativity theory resolve the Twin Paradox? Good detailed / technical discussion: Physics FAQ (Baez) – Twin Paradox

Actual Twin Experiment Hafele-Keating Atomic clocks sent around the world on airliners Does require GR correction, gravitational field – low vs high altitude.