1. STAV Supporting Slides
VCE Physics – Study Design
Special Relativity

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

3. 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”

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

5. 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.

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

7. 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…

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

9. 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

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

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

12. 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

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

14. 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.

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

16. determined by the scientists.
fraction
Expected answer = 22 μs
Actual answer = 2.2 μs
Nice 1960’s YouTube video:
determined by the scientists.

17. 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

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

19. 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

20. How do you measure the length of a moving object?

21. World Map v
= 𝐿 0 𝛾 𝐿

22. World Picture : what she sawv

23. World Map : train frame v

24. World Map : train frame v
𝐿= 𝐿 𝛾

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

27. 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.

28. Twin “Paradox”
If time permits ;-)

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

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

31. 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

32. 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

33. 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

34. 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!

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

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

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

38. 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)

39. 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

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