1. Modern Physics (PC301) Class #4 Moore - Chapter R5 – Proper time
Chapter R6 – Coordinate Transformation

2. Don’t forget:
Hand in homework Tomorrow by 10 am (8 am for webassign) and Sim2 on Friday
1) Length Contraction
Trip to Alpha Centuri revisited.
2) Drawing Two-Observer Spacetime Diagrams
time contraction
length contraction
Lorentz transformation equations
Review with some homework problems
Revisit length contraction with the diagram
3) Revisit length contraction and simultaneity with the conveyor belt painters and the barn/pole problem.

3. Homework Questions Due Wed by 8 am (Tomorrow!)
Problem Set #2
SR cool – use visualizations
Apply transformation equations
R1B.2, R1B.4, R1S.5 (events 125m apart on tracks), R1S.7 (particles flying apart), R1A.1 (elevator down)
Due Wed by 8 am (Tomorrow!)
Also Sim 2 due on Friday
First test in two weeks

4. 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 )
Previously worked in spacetime - need to use proper time.

5. Alpha Centauri Worldline
Twin Paradox t
Alpha Centauri Worldline
Earth Worldline
Ds=? C
13y B
Clocks really are running at different speeds -> correct interpretation is brother assumes his frame is inertial and can apply inverse argument. A
4.3y x
DISCUSSION

6. Proper Time - Shortest Possible TimeA B I NI
For inertial (I) Clock ->
For non-inertial (NI) clock ->

7. Different Views: Read Them This is FUN
Tipler: pages 50-53
Ohanian: pages 57-58
Epstein: 85-86
Feynman (6 ideas): 77-79

8. Binomial Expansion

9. Evidence
Hafele & Keating (1971)

10. Flying to Australia 10360 miles =16,672,803.84m 630 m/hr - 282m/s
What did I not take into consideration =: Earth Movement
10360 miles
=16,672,803.84m
630 m/hr
- 282m/s
Dt=16,4hrs
2.6*10-8s
Computer Clock Precision is about 1ns
EXTENSION

11. NIST ATOMIC CLOCKS (1949) NIST-1 Accurate to one part in 1,0*10-11s
(1999) NIST-F1
accurate to one part in 1,7*10-15 s

12. (which is most probable).
 Leptons
The leptons are perhaps the simplest of the elementary particles. They appear to be pointlike and seem to be truly elementary. Thus far there has been no plausible suggestion they are formed from some more fundamental particles. There are only six leptons ( displayed in Table 14.3) , plus their six antiparticles. We have already discussed the electron and muon. Each of the charged particles has an associated neutrino, named after its charged partner (for example, muon neutrino). The electron and all the neutrinos are stable. The muon decays into an electron, and the tau can decay into an electron, a muon, or even hadrons
(which is most probable).
From p of Thornton and Rex

13. Good reading for next two weeks
Read and summarize (type please) Chapter 1.
Read chapter 2 for greater understanding.
Located on P drive or borrow the book from me.
Essay be Isaac Asimov
Speed of Light

14. Length Definition
"In an inertial frame, an objects length is defined as the distance between two simultaneous events that occur at its ends."
Frame Dependent Quantity
My way - find events that occur on t’ axis (i.e. x’=0):Ds2=t’2=t2-x2=t2-(bt)2 =
Derive equation - Dsn2=t’2-x’2. @ x’, t’=nd=Dsn2=t2-x2=t2-(bt)2

15. Visualizing Length Contraction

17. Two Observer Spacetime Diagram: Time
t=t’ O t’ x t
Slope=1/b
@ x’=0, t’=nd
-> nd = t2 - x2
x=bt
My way - find events that occur on t’ axis (i.e. x’=0):Ds2=t’2=t2-x2=t2-(bt)2 =
Derive equation - Dsn2=t’2-x’2. @ x’, t’=nd=Dsn2=t2-x2=t2-(bt)2
Moore confusing -> d = separation between marks on t & t’ axis

18. Two Observer Spacetime Diagram: Lengthx t t’
Length Contraction
Slope=b x’ O

19. Two Observer Spacetime Diagram: Hyperbola Relationshipx t t’
Dt2-Dx2=Ds2 x’ O
At ds=1, x-0 -> t varies depending on speed
1/x2

22. From Moore p.108

23. Lorentz TransformationsQ tQ
tQ’
Inverse Lorentz Transformations
tPQ=gt’OQ
Normal Lorentz Transformations P x’
xQ’
bxOP
Generalized Normal Lorentz Transformations O xQ x
xOP=gx’OQ
btPQ

26. The Barn and Pole Paradox: Home Frame
Pole Rest Length (L0) = 10ns
Home Frame:
Pole moving at b = 3/5 -> L=8ns
Barn Length (L0) = 8ns
An instant in time when the pole is entirely in barn with doors shut.
Seems to Make Sense

27. The Barn and Pole Paradox: Other Frame
Barn moving at b = -3/5 -> L=6.4ns
Pole Length (L0) = 10ns
How can the pole 10ns long fit into a 6.4ns barn?
The runner with the pole does not observe that the pole is enclosed in the barn.
Front of pole reaches end of -6ns
End of pole reaches front of 0ns when pole has already left

28. The Barn and Pole Paradox Resolution

29. Geometric Analogy