Special Relativity (Physics 11)

Special Relativity (Physics 11)

Some extraordinary claims

• Time slows down in a moving reference frame.

• Lengths contract in the direction of motion.

• Simultaneous events in one reference frame may not be simultaneous in another reference frame.

Electromagnetism and light

How are balloons, circuits, and magnets related to light?

Electrostatics: Coulomb's Law

 $F=\frac{kq_1q_2}{r^2}=\frac{1}{4\pi\epsilon_0}\cdot\frac{q_1q_2}{r^2}$  

 $\epsilon_0=8.854\times10^{-12}\$   $A^2\cdot kg^{-1}\cdot m^{-3}\cdot s^4$  

Magnetostatics: Ampere Force Law

 $F=\frac{\mu_0L}{2\pi}\cdot\frac{I_1I_2}{r}$  

 $\mu_0=1.257\ \times10^{-6}\ A^{-2}\cdot kg\cdot m\cdot s^{-2}$  

Multiple Select

Select all that apply.
 $\epsilon_0=8.854\times10^{-12}\ A^2\cdot kg^{-1}\cdot m^{-3}\cdot s^4$ 

 $\mu_0=1.257\times10^{-6}\ A^{-2}\cdot kg\cdot m\cdot s^{-2}$  
 $\frac{1}{\sqrt{\epsilon_0\mu_0}}=$  

• The speed of light

•  $2.998\times10^8$  m/s

A few new questions

• What is light waving through? (i.e. What is the medium?)

• In which reference frame does light travel at its characteristic speed?

The ether hypothesis

Light travels through a substance called the ether. It travels at its characteristic speed only in the frame of reference of the ether.

Multiple Choice

A tennis ball is falling straight down and you run towards it trying to catch it in a tube. Should you point the tube straight up or tilt it in some direction?

• Point straight up

• Tilt in the direction of motion

• Tilt opposite the direction of motion

Aberration of star light

Astronomers have to tilt their telescopes in the direction of the Earths motion.

Multiple Choice

What does the aberration of star light imply about our speed relative to the ether?

• We are moving relative to the ether.

• We are at rest relative to the ether.

Fill in the Blanks

Fill in the Blanks

Michelson-Morley Experiment

The experiment attempted to measure the difference in the speed of light upstream/downstream vs cross-stream. No difference was detected.

Multiple Choice

What does the null result of the Michelson-Morley experiment imply about our speed relative to the ether?

• We are moving relative to the ether.

• We are at rest relative to the ether.

Einstein's Postulates

• Absolute uniform motion cannot be detected.

• The velocity of light does not depend upon the velocity of its source.

Time dilation

Time slows down in a moving reference frame.

The Light Clock

Multiple Choice

For a stationary light clock, what is the time between ticks?

• $\Delta t=\frac{D}{c}$

• $\Delta t=\frac{2D}{c}$

• $\Delta t=cD$

• $\Delta t=2cD$

Multiple Choice

For a light clock moving at speed v, the light still travels at speed c, but now it travels at an angle. Using the vertical component of the velocity, what is the time between ticks?

•  $\Delta t=\frac{2D}{c}$  

•  $\Delta t=\frac{2D}{v}$  

•  $\Delta t=\frac{2D}{c-v}$  

•  $\Delta t=\frac{2D}{\sqrt{c^2-v^2}}$  

Multiple Choice

What would happen to other types of clocks such as mechanical clocks, biological clocks, atomic clocks, etc.?

• They would all slow down as well.

• They would all speed up.

• They would neither slow down nor speed up.

Time dilation

Time slows down in a moving reference frame.

The Lorentz Factor

Comparing the two tick times:

 $\Delta t_{stationary}=\frac{2D}{c}$   $\Delta t_{moving}=\frac{2D}{\sqrt{c^2-v^2}}=\frac{2D}{c}\cdot\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$  
 $\Delta t_{moving}=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\Delta t_{stationary}=\gamma\Delta t_{stationary}$  

The Lorentz Factor

 $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$  

Summary of important consequences

• Time dilation: time passes more slowly in a moving reference frame.

• Length contraction: distances are shorter in the direction of motion

• Relativity of simultaneity: Events that are simultaneous in one reference frame may not be simultaneous in another reference frame.

Some free resources

• https://youtu.be/AInCqm5nCzw

• https://www.feynmanlectures.caltech.edu/I_15.html