1. Announcements
Apologies: Karen Mertz and Prof. Szarmes sent in an order for the PHYS274 text book over three months ago. The Hawaii representative of Pearson moved to a different textbook company, Cengage, during the intervening period. However the information and order was not properly transferred.
10 copies of the textbook, Young and Freedman, including volume 3 are now available at the UH bookstore.
There are other online options (e.g. Amazon) as well. This edition is out of print.
The full textbook is available as part of the Mastering Physics package

2. Wunderjahr
Question: What was the “annus mirabilis” for Albert Einstein ?
1905: While working at the Swiss Patent office, he wrote four seminal papers that changed the course of history
Photoelectric effect
Brownian motion
Special relativity
Equivalence of mass and energy.

3. Goals for Chapter 37
To understand the two postulates of relativity and their motivation
To see why two observers can disagree on simultaneity
To learn why moving clocks run slow
To see how motion affects length
To understand why velocity depends on the frame of reference
To calculate relativistic momentum and kinetic energy
To explore the key concepts of general relativity

4. Introduction
How do particles behave if they reach 99.99% the speed of light?
What are the basic postulates behind special relativity?
Far-reaching and mind-blowing implications of relativity, such as the effect of motion on time and length. The breakdown of simultaneity.
Momentum and kinetic energy must be redefined.
Electrons (7 GeV) and (4 GeV) positrons moving close to the speed of light around a 3.1 km circumference tunnel at KEK in Tsukuba, Japan.
The accelerator is “SuperKEKB”
What do I mean by the breakdown of simultaneity ?

5. Electricity and Magnetism (Phys272) gives us hints

6. Einstein’s first postulate
Einstein’s first postulate, known as the principle of relativity, states that the laws of physics are the same in every inertial reference frame. (For example, remember magnetic induction from PHYS272.)

7. Michelson-Morley Experiment to detect ether wind
Without Ether wind
With Ether wind
Not clear if Einstein know about this result in 1905.
Conclusion: no interference effect observed by Michelson-Morley in 1881

8. Einstein’s second postulate
Einstein’s second postulate is that the speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source. X
Common sense breaks down. Need to follow logic and mathematics.

9. One more consequence It is impossible for an inertial observer to
travel at c, the speed of light in the vacuum.
Consider v(S’/S) = c in the spacecraft and earth frame

10. Einstein’s second postulate
Einstein’s second postulate is that the speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source.
As a consequence, it is impossible for an inertial observer to travel at c, the speed of light in the vacuum.

11. Galilean coordinate transformations have to be modified
Review what are Galilean coordinate transformations ?
(these work well at low relative velocities e.g. everyday life but not for GPS or particle accelerators)
(x,y,z,t) are Earth coordinates; (x’,y’,z’,t’) are spacecraft coordinates. The spacecraft is moving at constant velocity u with respect to Earth.
“obvious”

12. Galilean velocity transformations have to be modified
(x,y,z,t) are Earth coordinates; (x’,y’,z’,t’) are spacecraft coordinates. The spacecraft is moving at velocity u with respect to Earth.
“obvious”
Now differentiate with respect to time t
First worked this out in Chapter 3 of Young and Freedman !
But this does not work for u=c ! Violates Einstein’s second postulate

13. Galilean velocity transformations have to be modified
But this does not work for u=c ! Violates Einstein’s second postulate. (speed of light is the same in all frames).
Question: How can we fix this ?
Something was wrong in the derivation. But what ?
Ans: The assumption t=t’ is flawed. Need to introduce 4-dimensional spacetime (x,y, z, t) and (x’,y’,z’, t’)

14. Special Relativity Example
Example: As a high speed spaceship flies past you, it fires a strobe light that sends out a pulse of light in all directions. An observer aboard the spaceship measures a spherical wave front that speeds away from the spaceship at speed c in all directions.
What do you measure ?
1)Ellipsoidal with the long axis along the direction of the spaceship motion
2) Spherical
3) Ellipsoidal with the short axis along the direction of the spaceship’s motion
4) not enough information given to decide
Ans: Spherical. the speed of light is the same in all reference frames ! Hence 2)

15. Special Relativity Example (cont’d)
Example: As a high speed spaceship flies past you, it fires a strobe light that sends out a pulse of light in all directions. An observer aboard the spaceship measures a spherical wave front that speeds away from the spaceship at speed c in all directions.
Is the spherical wavefront centered on the spaceship ?
Ans: No. It is not centered on the current center of the spaceship but rather on the location of the spaceship where the light was emitted.
Further explanation: If the spaceship is moving at c/3 and time t has elapsed since the pulse was emitted, the wavefront is a sphere of radius ct centered on P and the spaceship is now a distance of ct/3 away from P

16. Breakdown of Simultaneity Example
Lightening bolts appear to be simultaneous to Stanley.
What does Mavis see ?

17. Breakdown of Simultaneity Example
Note that both sets of wavefronts from A’ and B’ (as well as from A and B) are moving at c

18. Breakdown of Simultaneity Example
N.B. that both sets of wavefronts from A’ and B’ are moving at c in Mavis’ frame of reference. The first wavefront reaches Mavis early
Mavis says that the lightening hit the front of the train first and the back of the train later. The two events are not simultaneous.

19. Breakdown of Simultaneity Example
Stanley says that the lightening hit the front of the train and the back of the train at the same time (simultaneously).
Stanley and Mavis do not agreesimultaneity has broken down (depends on frame of reference)