Chapter 26 Lorentz Transform Michelson/Morley Experiment

Hint: Be able to do the homework (both the problems to turn in AND the recommended ones) you’ll do fine on the exam! Monday, May 10, :30am - 11:20am Chs. 20, 26, and 27 You may bring one 3”X5” index card (hand-written on both sides), a pencil or pen, and a scientific calculator with you. Same format!

Hint: Review notes from my review lectures! Try to do some of the old homework recommended homework, and exam problems. Monday, May 10, :30am - 12:30pm everything we’ve covered You may bring one 8.5”X11” sheet (hand-written on both sides), a pencil or pen, and a scientific calculator with you.

Monday, December 15, :30am - 12:30pm everything we’ve covered Format: 5 problems, pick 4. 1 problem on each of the following topics: ElectrostaticsCircuitsMagnetism Optics Modern

An electron is accelerated across an electrical potential of 100 million volts. What is the final speed of the electron? PE = qV = (1.6 X C)(10 8 V) Initially, the electron’s energy is all potential energy... = 1.6 X J electron

When the electron reaches the opposite plate, all the energy will be kinetic electron KE = 1/2 mv 2 = 1.6 X J m = 9.1 X kg v = 5.9 X 10 9 m/s = 19.7c !!!!

Classical theory has let us down again! Which led to a flood of work trying to reconcile classical theory with observation!

At first, many thought that Maxwell’s equations must be wrong. After all they were but 20 years old at the time while Newton’s and Galileo’s had been around hundreds of years! H.A. Lorentz found that Maxwell’s equations were invariant (i.e., of the same form) under the following transformation:

Provided a means by which to reconcile the electromagnetic observations with Maxwell’s equations in a variety of reference frames.

Well, shortly after Lorentz’s work, Henri Poincare suggested that the laws of mechanics should also remain invariant under a Lorentz transformation. Einstein took on the task of rewriting the old laws of mechanics in a new form that would satisfy Poincare’s proposal.

In tackling this task, Einstein put forth two postulates, from which the entirety of special relativity can be derived: 1) absolute, uniform motion cannot be detected (your book says, “The laws of physics are the same in all inertial reference frames,” which isn’t quite as good of a statement…) 2) the speed of light is always measured to be 3 X 10 8 m/s in vacuum independent of the motion of the source or of the observer.

And the correction to Newton’s laws proceeded along the following lines: Newton’s second law implicitly assumed that the mass of a body is a constant, independent of the body’s velocity.

If we dispose of this classical limitation and instead allow mass to vary with velocity, then Newton’s second law says instead And, of course, Einstein derived the relationship between mass and velocity...

where m o is called the “rest mass” of the body and is defined to be the mass of the body in the frame in which it is at rest! Notice that as the velocity v of the body increases toward c, the mass increases toward infinity!

Now we can understand why our experiment with the electron and the capacitor could never produce an electron travelling at or greater than the speed of light: electron If the mass of the electron increases to infinity, then it’s kinetic energy must also increase toward infinity: KE = 1/2 mv 2

electron And that kinetic energy must come from the initial potential energy the electron had before it started moving across the potential gap. Potential Energy = e V So we must increase V to infinity!

This “little” adjustment to the mass term throughout Newtonian mechanics results in a consistent set of physical laws that remain invariant under Lorentz transformations. And the work that went into proving these new laws of mechanics were correct created a legendary man known as….

What is the mass of an electron moving 0.999c? m = 2.0 X kg

The greatest experiment to produce a null result in the history of physics! We have to go back in time 18 years before Einstein’s theory of relativity…to Scientists were trying to understand Maxwell’s theory that light propagated like a wave...

Well, sound waves travel in air. But they do not travel in vacuum (that’s why the astronauts need microphones when out on their space walks)! Water waves also fall apart when they get to shore, transferring some of their momentum and energy to objects on shore. The waves they knew about had one thing in common: They all propagated in some medium or other!

So, light must travel in a medium as well, they concluded. The medium was called A very strange medium that allowed light waves to propagate, but had no mass itself and no effect upon the planets orbits or the motion of any other matter! The Michelson-Morely Experiment was designed to detect this ether.

bulb mirrors partially silvered mirror detector L L The distances to the mirrors for the two paths are identical.

L L So if the device is at rest relative to the ether, we will see constructive interference at our detector. On the contrary, if the device is actually passing through the ether...

L L …then we expect that light will require different amounts of time to travel the two different paths. At some velocity relative to the ether, we should observe destructive interference. Let’s consider a more classical example to better understand why...

Let’s look at a boat (it represents the light in the Michelson-Morley Experiment) travelling across a river (that represents the ether). v L L Both boats travel at the speed c.

v L L How long does it take the brown boat to travel down river a distance L and back again? c+v c-v

Brown boat

v L L What about the red boat? In order for the red boat to sail straight across the river, it must aim its bow slightly upriver. c v

v L L c v The same will be true as the red boat sails back across the river...

v L L So, the total time for the red boat to cross the river both was is: Red boat

Clearly these times are NOT the same! Red boat Brown boat

The Michelson-Morley Experiment is completely analogous to our boating expeditions! Instead of boats and a river, we have light and ether. Despite valiant efforts, interference of the two light beams was NEVER observed. Conclusions: 1) there is no ether 2) light travels the same speed in all reference frames (EINSTEIN)

Swallowing the second of those two conclusions requires a bit of faith... Accepting it, however, completely changes the Universe in which we live! Not only does mass change with the velocity at which we move, but so do apparent distances and times!