Talking Points for “Relatively Einstein” PowerPoint

Slide 1: Relatively Einstein

In 1905, Albert Einstein wrote his legendary articles which provided the basis of three fundamental fields in physics:

1)      The theory of relativity

2)     Quantum theory

3)     The theory of Brownian motion 

Ten years later, he published his General Theory of Relativity, reconciling gravity with the modern perspective.

Note the symbol chosen for the World Year of Physics – its origin will become apparent later (Slide 3).

Note that Einstein did not receive the Nobel Prize for his work in relativity.  At the time, it was controversial and not as appreciated as his work on the photoelectric effect.

Slide 2: Special Relativity (SR, 1905)

Note that the phrase “the speed of light is constant” does not mean that light never changes speed!  What it does mean is that two independent observers (even two that are traveling at different velocities) will measure the same speed for all beams of light.  This is one of the few measurements they will actually agree on.

An inertial frame is one that is not accelerating.  Thinking about the more generalized case of accelerating frames of reference led Einstein to his General Theory of Relativity years later.

Suggested Question:  Ask the students how fast they are traveling right now.  Students should realize that almost any answer is acceptable as long as they have specified their speed relative to something specific, e.g., the floor of the room, the center of the earth, the sun, the center of our galaxy, a car on the highway, etc.

Slide 3: What does this mean? 

The graphic is an example of a light cone in a space-time diagram.  Time is the z-axis, and the three spatial coordinates have been collapsed into x and y.  The yellow cone contains all the possible future events and past events for someone at the center.  The rest of space-time can have no effect nor can be affected by the person at the center.  Note that an event in this diagram is at a specific place and time.  In relativity, our universe is four dimensional (x , y, z, t)

Demo:  If you are connected to the web, this link will take you to an applet that shows a single light source propagating outwards from the center.  From the cart’s point of view (and yours), the light reaches both ends simultaneously.  However, once the cart is in motion (click on the bar in the middle), you will no longer agree that the events are simultaneous.  However, the person on the cart will still see the same thing as before, since light travels at the same speed relative to him as it does to you.

Slide 4: Defining Relativity 

Suggested Question:  What happens to gamma in the limit of v much less than c (v << c)?  What about v very close to c (v » c)?

This question is meant to bring up the issue of correspondence:  new theories should give us the classical results in the classical limit.  If v << c, then gamma is basically one and there is no time dilation or length contraction.  At the limit of   v = c, time stops and length along the velocity direction disappears.  (Note that the other two directions perpendicular to the velocity vector are unaffected.)

Suggested Question:  What happens to gamma if v > c?  (Gamma becomes an imaginary number; thus, this case is not physically possible.)

Slide 5: Defining Relativity 

Note that L0 and T0 are called the “rest length” and “rest time” (or “proper length” and “proper time”) since these are the lengths and times as measured in the object’s own inertial reference frame.

Slide 6: Defining Relativity

For advanced students, a quick illustration of the binomial theorem on the denominator will illustrate explicitly that the first two terms in the expansion are the rest energy (or mass energy) and the classical kinetic energy:

Slide 7: That’s crazy talk! Can you prove it? 

“Extraordinary claims require extraordinary proofs.” – Carl Sagan

Relativity Theory is better tested than Newtonian Mechanics precisely because it is so counter-intuitive. 

Although the Michelson-Morley experiment predates SR and is cited as the definitive proof for dispelling the notion of the “ether” (the mysterious medium pervading the universe in which light waves are a disturbance), it can now be seen as proof that the speed of light is independent of its source.  The interferometer was the most accurate way to measure the speed of light at the time, and by orienting the device in different directions on Earth, one would obtain the speed of light to be constant (despite the known fact that the Earth has its own motion relative to the universe).  The interferometer allows the experimenter to count the interference fringes that go by as the path length of one of the paths L is changed by a known amount.  Given the frequency of the source light and calculating the exact wavelength (path length change divided by the number of interference fringes), one can determine the velocity of light.

Slide 8: Proving It 

There are two classic experiments that first demonstrated time dilation.  In the first, two atomic clocks were flows around the world in opposite directions and compared to one left on the ground.  Although they were previously synchronized, the clocks in motion were behind the stationary one by an amount predicted by the relativity theories.  The experiment was dependent on the invention of atomic clocks precise enough to show the small amounts of time dilation predicted by the theories.

In the second demonstration: muons are unstable subatomic particle that decay quickly into other particles.  When a cosmic shower strikes the Earth’s atmosphere, extremely fast muons are created, and their half-lives were shown to be longer (red line) than that of laboratory muons (green line) by exactly the Special Relativistic time dilation factor gamma.

Slide 9: SR in Radio Astronomy

Last slide on SR.  Synchrotron radiation happens whenever a charged particle travels in a magnetic field.  The magnetic field causes the charged particle to spiral.  In radio astronomy, specifically oriented, regular flashes of light are frequently seen due to near-light-speed electrons spiraling in large cosmic magnetic fields.

Note that the classical spherical radiative pattern on the left (slow electron) is distorted by the length contraction and time dilation indicated on the right (fast electron). 

Slide 10: General Relativity (GR, 1916) 

Try rephrasing this notion using the question, “What experiment could you do inside of a windowless lab to tell the difference between the picture on the left and the one on the right?”  Einstein’s answer: no such experiment exists.  (In this case, we are ignoring the rotation of the Earth, which of course can be detected; we are concerned with the downward pull of gravity only.)

Slide 11: Light

Almost everyone will see that Observer A will find that the light hits lower on the opposite wall due to the box accelerating up while the light travels in a “straight line path”.   The same must be true for Observer B since they are equivalent, and the GR explanation is that the Earth has bent the space-time lines such that the light is still following a ‘straight’ path according to the warped space lines; we, however, see the light as bent because space itself is bent.

Slide 12: Gravity 

Why is the bending caused by both “mass and energy”?  From SR, Einstein showed E=mc2 demonstrating that mass and energy are two forms of the same thing.  Therefore, energy has all the same space-time distorting effects that mass has!

Looking at the bottom graph, imagine the sun is sitting at the center of the depression.  Now imagine the Earth being a ball that is rolled towards the depression, but not directly towards it.  The circular motion of the ball going around and around is the orbit of the Earth.

Slide 13: More crazy talk! Can you prove it?  

  1. Newtonian gravitation does predict some precession of the perihelion (the rate at which the elliptical orbit itself rotates around the sun), but not enough.  Although Einstein’s GR successfully accounted for the difference, this was not considered definitive proof of GR.
  2. This is the famous result gathered on an expedition by Eddington that turned Einstein into an overnight international celebrity.  This effect of gravity bending light towards the mass is also known as “gravitational lensing”.

Slide 14: More crazy talk! Can you prove it

  1. Sending gamma rays up a stairwell in the physics building (74 feet tall), Pound and Rebka at Harvard demonstrated a tiny effect of GR.
  2. By bouncing a radio signal off of Venus and Mercury while the beam traveled close to the sun, a team of scientists led by Shapiro verified that the round trip time in flight of the radio wave was longer than expected by exactly the prediction of GR. Clicking on the link will take you to a separate power point presentation on the fourth test – see additional notes on that talk in a separate note.

Suggested Question:  Why was the signal strength reduced by 1/D4 for the fourth test when radiation usually falls off as 1/D2 ?  (There is a 1/D2 loss going out to the planet times a 1/D2 loss coming back to Earth.)

Slide 15: So, are there any practical uses for this stuff?

Suggested Question:  Are the satellite clocks running too slow or too fast according to SR and GR?  (Due to SR, they are running slow.  Due to GR, they are running fast.  Combining the two, the net result is that they are running 38 microseconds faster per day.)