% !TEX root = ../_superfluous_book_3.tex
\setcounter{chapter}{13}

\chapter[Michelson]{\texorpdfstring{The Most Important Zero Ever:\\ \textsf{Albert Michelson} }{Michelson}}

\begin{myblock1}{Our story now takes a turn by merging our \textsf{MOTION} and \textsf{LIGHT} themes in a post-Maxwell environment. Our last experimental stop before we get to Einstein. \\ \\
We'll now consider one of the most important experiments in the last two
centuries, and certainly the most important measurement ever of
\textbf{zero} ever. It starts in the Wild West of gold and silver mining---literally, the Wild West---and passes through Stockholm and the Nobel
Prize. Let's talk about one of the more interesting physicists of all.
Albert Michelson, a complicated person notoriously stern and difficult
(although he was an accomplished artist, musician, and tennis and
billiards player). He once had an argument about an experiment with a
colleague in a hotel lobby that drew a crowd, maybe because they were
loud and maybe because Michelson was still in his pajamas. He won the
Nobel Prize in 1907, not for his most famous measurement of zero, but
for his exquisitely precise instruments and the collection of scientific
measurements that he made with them. }
\end{myblock1}

\section{A Little Bit of Michelson}

Faced with a difficult situation, he did what any 16 year old would do:
he boarded the brand new Transcontinental Railroad at Oakland Land Wharf
in San Francisco and went to Washington, D.C. to see the President.
Albert was nothing, if not persistent.

Albert Michelson was born in 1852 in Poland to Rosalie and Samuel
Michelson. Life for Jews in Prussia was untenable and so this small
family decided to emigrate in a big way, following Samuel's sister and
brother-in-law to the California Gold Rush. With two babies in tow,
Samuel and Rosalie left from Hamburg for New York, and then San
Francisco. Not to chase gold, but to sell dry goods to the miners. As a
merchant, that's what Samuel knew best.

Sailing around Cape Horn or traveling across the country in covered
wagons must have seemed too tame for this adventurous couple. From New
York they boarded a steamer for Panama, then by canoe, mule train, and a
brand new railway, made their way across the Isthmus of Panama to a
clipper ship and then on to San Francisco. It was a harrowing journey
during which they lacked water, fought exotic insects, faced danger from
outlaws, and avoided the desperately sick natives who were all around
them. It made an impression on three year old Albert that he never
forgot. In retrospect, covered wagons must have seemed like a better
alternative.

The last leg of their journey was by stagecoach from the city to
Murphy's Camp in the foothills of California's Sierra Nevada mountains.
After more than a year of dangerous travel, they settled alongside
Samuel's brother-in-law and set up shop with the goods needed by any
respectable prospector.

\begin{figure}
\centering
\includegraphics[width=0.8\linewidth]{./14_Michelson/images/murphy.png}
\caption{Murphy's Camp in 1852 (Kenneth M. Castro)}
\label{fig:murphy} 
\end{figure}

Tens of millions of dollars in gold was shipped from Murphy's Camp and
that kind of activity came equipped with hard edges. The town resembled
a bad cowboy movie: full of drunks, violence, and public hangings---and
lots of cash. It thrived in its own way until it all burned to the
ground in 1859 in less than an hour.

The town and the Michelsons rebuilt but by the time Albert was 12 years
old in 1864, Rosalie decided that he needed a more formal education than
available in Murphy's. She had tutored him, even insisting on violin
lessons. But Albert was sent with his aunt and uncle to San Francisco
for high school where he so impressed the principal, that he was taken
into his home and given special access to the school's science
lab\ldots and boxing lessons.

By this time Murphy's gold had dried up and the family moved to Virginia
City, Nevada\ldots where silver was all the rage and their new boom-town
swelled to 30,000 inhabitants. The family moved into a large house over
Samuel's new store where the business flourished. A father-son
enterprise was a possibility, but by this time Albert needed a different
path. A scientific one.

\subsection{The Navy}

Today, in order to enter a U.S. military academy, an 18 year old
requires a nomination by a state or federal elected representative. It's
a highly competitive process requiring superior academics and typically,
an athletic background. Albert's growing interest in science had led to
a favorably received paper on optics and he wanted to pursue this
subject. But how?

The U.S. Naval Academy at Annapolis, Maryland was then only 20 years old
when Albert graduated from high school in San Francisco and Samuel
learned that Nevada's Congressman Thomas Fitch was accepting nominations
for boys to the Academy. Albert applied, took the exams and tied with
two other applicants for first place. Fitch chose one of the other boys,
who immediately failed prompting Fitch to write to President Grant on
Albert's behalf. In what was to become a characteristic Albert-move, at
the age when today's U.S. kids are just getting their learner's permits,
he took matters into his own hands and did what his family did: he got
on the road. Hence, that solo teenage train ride across the rough North
American continent.

When he arrived in Washington, D.C. he presented himself at the White
House, and made his case to President Grant personally. At that time the
President was allotted 10 at-large appointments (now the Vice President
can nominate five) and Grant had used up that total. Not to be outdone,
Albert then took himself to Annapolis and sought an audience with the
Commandant where he was examined, did well, but told that there were no
openings.

As Albert's daughter described later (Dorothy Michelson Livingston wrote
the definitive (technically accurate and moving) biography of her
father:\citealt{dl21}), he was literally at Union Station boarding the
train to return to San Francisco when a messenger from the President
intercepted him to say the the President had decided to appoint 11
midshipmen that year (and later two more, for a total of 13). Michelson
always joked that he was probably illegally a student at the Naval
Academy. But it worked out. In 1869 at the age of 17, Albert joined the
Navy.

\begin{wrapfigure}{R}{.45\textwidth}  
  \begin{center}
    \includegraphics[width=.40\textwidth]{./14_Michelson/images/michelson_midshipman.png}  
    \captionsetup{style=figures}
    \caption{Albert Michelson as a cadet-officer.} 
    \label{fig:albertyoung} 
  \end{center}
\end{wrapfigure}

Albert was a popular and successful midshipman, not above the occasional
fight or prank. He graduated in 1873 at or near the top in experimental
and mathematical subjects---at the top in optics\ldots and near the
bottom in seamanship. He did his two-year obligatory training at sea off
the coast of South America and the Caribbean in a combined steam-sailing
ship, ending his sailing obligation in Norfolk as an Ensign. He decided
to stay in the Navy and in 1875 was assigned physics instructor duties
at the Academy under Lieutenant Commander William Sampson, the head of
the Department of Natural and Experimental Philosophy who was to become
a friend as well as mentor. Mrs.~Sampson's niece recently returned from
finishing school in Paris and Margaret Heminway was introduced to him at
a family event. She was the daughter of a wealthy and powerful lawyer
and investor in New York City. In spite of their age and class
differences, Albert and Margaret were married in 1877---a marriage
``up'' for Albert into a rarified atmosphere as compared to his
immigrant upbringings. After more cruises, Albert and Margaret had their
first son, Albert, in 1878.

\subsection{Light}

One of Albert's first tasks as an instructor was to create
demonstrations for the midshipmen in their physics classes and he chose
to take on a relatively new method for measuring the speed of light, now
an experiment done by physics students in hallways around the world.
Except he made it better and found a calling.

\subsubsection{It's Really Fast\}}

In Chapter~\ref{chap:young} we enumerated the many ways that the speed
of light was determined prior to Michelson's time. Recall that it was
Fizeau who did it best in 1848 by chopping the light up with a rotating
mirror and capturing its return as the mirror rotated in the meantime.

This was the technique that Michelson adopted for his midshipmen
students and by 1878 he had a handful of ideas to better engineer the
device. He lengthened the path length to 11 meters, he greatly improved
the various focussing lenses required for the beams, swapped Foucault's
concave far mirror for a finely ground plane mirror, and he delicately
engineered the rotating mirror assembly by driving it with a regulated,
hand-operated bellows to a constant speed of 130 turns per second. With
this first measurement, he obtained $c=300,140,000$ m/s with an
uncertainty of about 0.2\%. It cost him \$10 in 1878 dollars.

In the same year that he and Margaret had a second child, he obsessed
about getting a new apparatus to work. With a lot of support from the
Academy (he was, after all still in the Navy but with this unusual
research assignment), \$2000 (worth more than $\$50,000$ today) from his
father-in-law, and space at Annapolis along the waterfront, he was able
to retain services from first-class instrument and optical
manufacturers. Meanwhile, Congress had turned down a request of support
and awarded $\$5000$ to Simon Newcomb, a distinguished astronomer who
actually suggested improvements in the young man's plans and supported
him publicly. His new path-length was to be 609 meters and his rotating
mirror assembly was a delicately controlled 128 revolutions per second
(he'd already destroyed an assembly at high speed when its balance was
not perfect). He devised a tuning-fork with a small mirror attached.
When it vibrated at its precise frequency, and the rotating mirror was
in synch, stable images of the rotating mirror would show in the tuning
fork's mirror. The time of day was regulated, as the heat would change
dimensions of the apparatus. His result was $c=299,910,000 \pm 50,000$
m/s, or a precision of $\pm 0.017\%$.

Measurement of the speed of light became his life-long passion and he
was working on an audacious experiment in the hills of southern
California when he died. His previous 1924 measurement of
$c=299,796,000 \pm 0.001\%$ m/s stood for three decades as most precise.

\begin{quote}
May 14, 1879, in the Virginia City Evening Chronicle:

``THE VELOCITY OF LIGHT A YOUNG COMSTOCKER'S CONTRIBUTION TO THE WORLD
OF SCIENCE

``Ensign A. A. Michelson, a son of S. Michelson, the dry goods merchant
of this city, has aroused the attention of the scientific minds of the
country by his remarkable discoveries in measuring the velocity of
light.'' The New York Times says: `It would seem that the scientific
world of America is destined to be adorned with a new and brilliant
name. Ensign A. A. Michelson, a graduate of the Annapolis Naval Academy,
and not yet 27 years of age, has distinguished himself by studies in the
science of optics which promise the discovery of a method for measuring
the velocity of light with almost as much accuracy as the velocity of an
ordinary projectile\ldots{}'''
\end{quote}

Albert didn't want to go back to sea, which would have been his next
Navy assignment. He was partially spared another sea voyage when Newcomb
had enough influence to ``borrow'' Michelson from the Navy to work in
his laboratory in Washington D.C\ldots.where his job was to make his
friendly competitor's Congressionally funded experiment work.

That probably wasn't ideal. He was fully aware that his engineering
degree (until recently the service academies offered only engineering)
would not qualify him for a university faculty position, but no
institution in the United States offered a doctorate in
physics.\footnote{John's Hopkins University in Baltimore was about to offer Ph.D. degrees.}

Again, not shy, he requested and received a leave of absence from the
Navy in order to pursue a Ph.D.~and secured a position at Humbolt
University in Berlin to study under and work with Helmholtz, whom we
learned about in Chapter~\ref{chap:joule}. Off the four of them went to
Berlin, Margaret, two children, and Albert.

Helmholtz was an expert in optics, having revolutionized ophthalmology
with his invention of the ophthalmoscope and was extraordinarily
multidimensional. His mathematical codification of the conservation of
energy (see Chapter 12), development of the science of fluid dynamics,
studies in acoustics, and both mathematical and experimental
contributions to electromagnetism all marked his name in
textbooks\ldots in multiple fields. Not bad for a medical doctor.

Michelson had something on his mind that had come to him during their
first stop in Paris and he went to Berlin with a research target in his
mind: the ether.

\subsection{Where Is the Ether?}

As we saw in Chapter~\ref{chap:young} it was Thomas Young who upon
determining that light must be a wave, then postulated that there needed
to be a substance ``that waves.'' A very definition, if you will, of
what light must be: the undulations of a substance, that ether. As
preposterous is the properties of the ether are, we saw in
Chapter~\ref{chap:maxwell} that nobody questioned it and huge
experimental and theoretical efforts were expended in describing it and
searching for evidence of it.

Sir Oliver Lodge was passionate (and relentless) on the subject, even
after it was ultimately clear that he was wrong. He spoke for almost all
of the now exhausted physics community:

\begin{quote}
``\ldots{} it is absurd to imagine one piece of matter acting
mechanically on another at a distance, whether that distance be large or
small, without some intervening mechanism or connecting link\ldots{}''
\end{quote}

So in addition to the chaos in the theory camp, there was a
corresponding chaotic situation among experiments going back many
decades: some results demanded that the ether was stationary and that
the Earth (somehow) moved through it and some experiments demanded that
the ether was dragged along---wholly or partially---by the orbiting
Earth. Chaos in both theory and experiment, an imperfect situation.

The ether's job description included two assignments, solving two
problems: First, it could function as Newton's absolutely at-rest
structure anchoring and even defining space and it second, it supported
light's wave propagation as convincingly suggested by Maxwell.

Always imaginative, Maxwell wondered about exactly that and during the
last year of his life---the year before Michelson went to Europe---he
suggested that it might be possible to measure the speed of the Earth
relative to the fixed ether---the ``breeze.'' However, he worked out
that the experimental accuracy of his scheme was depressingly
impossible: it must distinguish speeds relative to the ether of about
$0.0000000001\%$.

Michelson must have heard of Maxwell's idea around the time that he was
headed to Berlin and what was an impossibility to Maxwell, was a
challenge to him to him. After all, precision optics seemed to be his
game.

\subsubsection{Moving Through The Ether}

What was Maxwell's idea? A naval analogy that Michelson later described
to his children gives a good feeling for his plan. Let's look at Figure
Box\textasciitilde{}\underline{\ref{river}} on the next page.
\faHandORight  

And then come back here \faHandODown  $\text{ }$ to continue
\setword{reading}{reading} \ldots{}

Now suppose we make the following substitutions in our nautical race:

\begin{itemize}
\tightlist
\item
  instead of boats$\to$ we'll use light beams;
\item
  instead of the bank$\to$ we'll imagine the Earth; and
\item
  instead of a river$\to$ we'll imagine an ether ``current'' passing by
  it.
\end{itemize}

\subsection{The Michelson Interferometer}

The instrument Michelson invented and spent a decade of his life
perfecting is called the \emph{Michelson Interferometer} and it's a
standard tool in today's optics laboratories, industrial manufacturing,
telecommunications, and even in astronomy.

Remember our discussion of Thomas Young's experiment with light where he
demonstrated that light aimed at two holes or slits caused an
interference pattern to emerge on a far screen which can only happen if
light is a wave. When two waves go up or down together, they add and if
they are exactly out of phase, one with the other, the subtract to zero.
No wave. Dark. It's the principle behind your noise-cancelling
headphones if those waves are sound waves.

Sometimes the waves interfere between total cancellation and total
addition and the result is a new wave that can have a funny-looking
shape.

%----------------------------------------
\begin{minipage}[t]{.95\textwidth}
\noindent  \rule[-0.in]{0.35\textwidth}{0.001in} {\sffamily FIGURE BOX~\ref{river}}
 \rule[-0.in]{0.35\textwidth}{0.001in}\
    \begin{wrapfigure}{l}{0.5\textwidth}
        \includegraphics[width=0.5\textwidth]{./14_Michelson/images/river_400_side_V.png}
        \captionof{figure}{CAPTION.}
        \label{river}
    \end{wrapfigure}%\hfill 

{\color{mygray}{\sffamily \small As shown on the left in Figure~\ref{river}~(A), suppose Bob and Doris and are to race in a river. They each plan to pilot their identical
motor boats the same distances starting at a the same point on the south shore (P1) and ending up back at that same location. Bob goes across the
river north to the opposite shore (P2), and then returns south to P1. Doris pilots her boat to the east to P3 and then back to P1. In this
race, the river is still---no current. Who wins if both boats can move through the water at the same speed? \setlength\parskip\baselineskip

Obviously, since they're both traveling at the same speed over the same
distance and if the water is perfectly calm, their round trip race would
result in a tie. That's too easy.  \setlength\parskip\baselineskip

Now suppose that the river has a strong current from east to west, as
suggested in Figure~\ref{river}~(B). Same boats, same relative speeds
through the water, and the same trips, north then south for Bob and east
and return west for Doris. Both travel the to the same points as before,
relative to the shore. Who wins now? \setlength\parskip\baselineskip

Since the river is flowing to the west, Doris has to fight the current
to go the required distance to the east, but on her return, the current
helps. Meanwhile, in order to get directly across the river, Bob has to
aim to the east of his intended point so that the current pulls him back
to the north shore directly opposite his starting position. Coming back,
he must do the same sort of maneuver.  \setlength\parskip\baselineskip

Who wins? Bob or Doris? \setlength\parskip\baselineskip

It turns out that the round trip across the river and back will be
quicker than the trip to the right and to the left. (See Appendix 13 for
the calculation.) So Bob wins.

Now go back to  \underline{\ref{reading} } \faHandOLeft

 \setlength\parskip\baselineskip
}}
\vspace{5mm}
\end{minipage}\quad\hfill
\rule{\textwidth}{0.2mm}
%----------------------------------------

Light has wavelengths that are around 500 nanometers. That's 0.000000500
meters (for comparison, sound in a dry room at normal temperature, say
Middle C, has a wavelength of about 4 feet.) That means that detecting a
small difference between two light waves by separately comparing them
side by side would have been impossibly difficult, but unraveling their
\emph{interference} is much easier to observe. So if an experimenter has
a device that can measure the interference of two waves, then they know
that the waves arrived out of, or in, phase. If out, then one of them
led and the other followed.

Let's imagine a slightly different analogy where water is not involved.
Suppose we have two marchers,side by side. Gladys on the left walks
beside Clyde on the right and they're both the same height and practice
marching so thoroughly that when they walk beside on another, they are
in phase: when Glady's right foot goes down, so does Clyde's. Every
stride is the same.

Let's suppose that they enter an school stadium side by side and when
they reach the oval running track they separate\ldots Gladys goes left
and Clyde marches right. They circle around the track and meet at the
other end. When they meet Clyde's right foot lands, at the same instant,
so does Gladys' right foot. And they bump into one another. They're
still in phase, and dazed.

Now do it again, at a different school on a different track. This one
was laid out by a sloppy designer and the side that Clyde usually
travels is slightly longer than the other side. So when Gladys reaches
the opposite end, she marches in place. Clyde's not there yet and when
it does arrive, his cadence may not match hers. That different path
length made them go from originally being in phase, to out of phase.

If your job is to determine whether the sides are the same length, you
could just measure them with a tape measure (that's what I'd
do)\ldots or you could employ Gladys and Clyde to perform their routine
in front of you. If they get to the end and are not in phase, then you
know you've got a badly designed track on your hands.

Or let's suppose that on Glady's side of the track, the long stretch has
been replaced by a airport moving sidewalk going in her original
direction. While Clyde encounters an identical moving sidewalk that's
going in the other direction. Strange, right? So she's helped along and
ahd he's hindered and she obviously gets to the end before Clyde. Again,
they would be out of phase since she got the benefit of a moving medium
in which she would travel and his forward progress was hindered by that
medium.

That's a way to imagine the Michelson Interferometer. It's a device to
take a light beam and cause it to travel two different paths and then to
see whether they are still in phase when they are brought together.

So they could be out of phase because the paths they travel (the
\emph{optical path}, OP) are different and/or because the medium that
they travel in (the ether) helps one of them along because of the
interferometer's motion relative to that medium (the moving sidwalk).

Back to Bob and Doris: In the Michelson's Interferometer, the Bob-wave
is made to travel perpendicular to the motion of the Earth through space
and the Doris-wave is made to travel with, and against that motion.
Michelson would measure precisely a finite speed for the Earth relative
to the ether, by observing how out of phase the two paths are and he
could do it with a precision that he'd know from understanding his
instrument.

That was the plan, but the engineering and instrumentation was
formidable and while Humboldt University was prepared to give Michelson
a downtown Berlin laboratory in the basement, there was very little
funding for the equipment.

\subsubsection{With The Phone Guy's Help}

Simon Newcomb came to the rescue again. He seemed to know everyone and
of course that included his friend Alexander Graham Bell who came
through with sufficient financial support to allow Michelson to
collaborate with a German optical company to construct his first
interferometer. So in 1881 Michelson built an exquisitely precise device
which combined waves in exactly as the river analogy required.
Figure~\ref{fig:mmstill} is a sketch of how the apparatus works as
viewed from the Earth itself. Let's look carefully at it.

%----------------------------------------
\begin{minipage}[t]{.95\textwidth}
\rule{\textwidth}{0.2mm} 
    \begin{wrapfigure}{l}{0.5\textwidth}
        \includegraphics[width=0.5\textwidth]{./14_Michelson/images/MM_apparatus_still_400.png}
        \captionof{figure}{The stationary apparatus.}
        \label{fig:mmstill}
    \end{wrapfigure}%\hfill 

{\color{mygray}{\sffamily \small This is a simplified plan view of the Michelson Interferometer as seen from the Earth, without any ether.  The element in the center at A is called a
Beam Splitter (BS) or ``half-silvered mirror'' (think of a
teleprompter). It takes a beam of light and separates it into two
perpendicular, identical rays, one passing through and one directed
perpendicularly. Let's follow the paths: \setlength\parskip\baselineskip \setlength\parskip\baselineskip

Path 1: Light from the source, S, is separated into the two paths at A
by the BS oriented at $45^{\circ}$. Half of the light from S passes on
through the BS to the right at C. The other half is diverted into a vertical beam directed at a plane mirror, M1 at B (dashed rays). The
distance from A to B is $L_2$ That beam
reflects from M1 back through the BS where again, half is transmitted
down and half goes in the direction of the source (and ignored). The
half that continues down stops at the detector, D. The distance from A
to B is $L_1$. \setlength\parskip\baselineskip \setlength\parskip\baselineskip

Path 2: The light that went right through the BS to the right (now the
dotted rays) is reflected at another mirror, M2 at C, as close to being
perpendicular to M1 as can be arranged. It then passes back through BS,
and yes, half of it then reflects down toward the detector at D. The
distance from A to C is $L_2$. Michelson strove to make $L_1$ be as
close to $L_2$ as possible.}}
\vspace{5mm}
\end{minipage}\quad\hfill
\rule{\textwidth}{0.2mm}
%----------------------------------------

The magic is in the path between A and the detector, D. Each beam
started out as a partner of the other (Gladys and Clyde), and so they
are initially coherent and they mix on that short path to D. If they are
now slightly out of phase, the image at the detector will register that.
How?

Well, back to Gladys and Clyde who are now in demand and decided to add
to their act. Now there are 10 marchers. Ten marchers enter the track
together, five on the left and five on the right. They split up like
when it was just the two of them and take their paths---each of the 10
marchers never adjusts their pace. But wait. The marchers in the inside
of the track travel a shorter distance than the marchers on the outside
of the track. So the outside people travel further and are later than
the inside people to travel less and get their faster. The middle
marchers will meet exactly at the same opposite point, but the inside
marchers will get there earlier and the outside marchers later. There
will be phase-chaos when they meet. They will interfere with one another
in different ways, the two opposite sets of five.

The same thing happens in the interferometer. The beams are not
infinitesimal lines of light, they're broad (even made so with an unseen
lens just after S) so the result is a bullseye pattern at the detector
with the center being bright and then a dark-light-dark-light
progression from the center. These are called ``fringes'' and where the
light-dark regions are on the screen depends critically on the OP
lengths that the beams travel\ldots or their relative motion in the
medium through which they traveled.

Now, what could make those two beams be out of phase? Any number of
circumstances: the experiment could be misaligned (remember that
accuracy requirement) or the Earth's motion in the ether can be
determined:

\begin{itemize}
\tightlist
\item
  If $L_1 \ne L_2$ then they will arrive at different times and so be
  out of phase when they combine.
\item
  If either or both M1 or M2 are not perfectly perpendicular to the
  impinging light source, that will create a distortion.
\item
  If there is a temperature difference in the air between the two arms,
  even that would affect the beams' differently.
\item
  Or\ldots suppose that we're back in the river and the medium that is
  doing the waving---the river or the ether---is moving relative to the
  setup, then from our simple Doris-Bob race, the two combined beams
  will appear to be out of phase because the perpendicular, dashed path,
  will win.
\end{itemize}

The first three ways to get interference are under Michelson's control:
he must build the apparatus with great precision. The last
way\ldots Nature will determine that.

But he was really clever and even the first three ways of getting out of
phase won't matter!

Here's the genius part: Michelson constructed his apparatus so that the
whole thing could be rotated by $90^{\circ}$ about a vertical axis. When
that happens, then the two beams trade places and the original fringe
pattern shifts\ldots the spot where light was bright and where it was
dark, changes between the rotated and un-rotated positions. So he marked
where the bright spots were and then rotated, and looked to see where
they moved to.

That rotation not only cancels instrumental effects, but it also doubles
the fringe shifting from nominal. Appendix~\ref{app:river} shows you how
this comes about. The expected shift of the fringes comes from the
path-length difference that would result from the speed of the Earth
through the ether of $v$, the speed of light, $c$, and the two arms'
lengths: \% $$\delta L = \dfrac{v^2}{c^2}(L_1+L_2).$$ \% The speed of
the Earth in its orbit is about 30,000 m/s and the speed of light is
about 300,000,000 m/s\ldots so the shift is a tiny amount of \%
$$\delta L \approx 0.00000001(L_1+L_2)!$$ \% The question is whether
tiny instrumental effects might either mask a positive result, or signal
a false positive result.

\begin{figure}[htp]
\centering
\includegraphics[width= \linewidth]{./14_Michelson/images/potsdam_fringe.png}
\caption{(A) On the left is a perspective engineering drawing of Michelson's prototype where I've labeled it like the sketch above. (B) On the right is a fringe pattern resulting from the apparatus (by the author).}
\label{fig:engineering} 
\end{figure}

His first prototype instrument had arms about a meter long and was
finicky and delicate. Horse-drawn traffic outside of the lab building
was so disruptive that the fringe pattern was unstable. So, he made the
measurements in the middle of the night, but that was not sufficient .
That was still unstable and so he subsequently moved it to a new lab at
rural Potsdam, and then a second lab in the basement of that same
facility. This was quieter but delicate still.In his publication later
he noted that even stomping on the ground 100 meters away from the
building would cause the interference patterns to disappear! So, taking
data was exhausting. Figure~\ref{fig:engineering} is a perspective
engineering drawing from Michelson's Potsdam apparatus and also a
candidate Michelson Interferometer fringe pattern is shown.

After more than six months of painstaking work, he published his results
and wrote to his benefactor:

\begin{quote}
Heidelberg, Baden, Germany

April 17th, 1881

My dear Mr.~Bell,

The experiments concerning the relative motion of the Earth with respect
to the ether have just been brought to a successful termination. The
result was however negative\ldots{}

At this season of the year the supposed motion of the solar system
coincides approximately with the motion of the Earth around the Sun, so
that the effect to be oserve {[}sic{]} was at its maximum, and
accordingly if the ether were at rest, the motion of the Earth through
it should produce a displacement of the interference fringes, of at
least one tenth the distance between the fringes; a quantity easily
measurable. The actual displacement was about one one hundredth, and
this, assignable to the errors of experiment.

Thus the question is solved in the negative, showing that the ether in
the vicinity of the Earth is moving with the Earth; a result in direct
variance with the generally received theory of aberration\ldots{}

N.B. Thanks for your pamphlet on the photophone.
\end{quote}

The speed of the ether relative to the Earth seemed to be zero. He
believed it to be a failure, the first in his so-far, distinguished
career as the young King of Optics.

\subsection{Getting Serious: The Michelson Meets Morley}

\begin{wrapfigure}{R}{.45\textwidth}  
  \begin{center}
    \includegraphics[width=.40\textwidth]{./14_Michelson/images/M_youngish_1887.png}  
    \captionsetup{style=figures}
    \caption{Michelson in 1887, around the time of the Michelson-Morley experiment.} 
  \end{center}
\end{wrapfigure}

The work in Potsdam was exhausting and discouraging and so after his
experiment was done, he and Margaret and (now three) young children
explored the German countryside with Albert watercoloring and studying.
They spent some time in Heidelberg where he worked in another lab and
improved his ability to produce half-silvered mirrors. After a pleasant
summer, they went back to Paris (Margaret's stomping ground from her
youth) and Albert spent time in the École Polytechnique where the legacy
of Foucault lived on. The next fall and winter Albert repeatedly failed
to show his skeptical French colleagues that his interferometer worked!
Eventually, he succeeded with relief\ldots which was short-lived. One of
them showed him that he'd made an arithmetic mistake in his ether
publication's analysis which served to reduce the fringe shift. About
that same time, Hendrik Antoon Lorentz (1853-1928,
Chapter~\ref{chap:lorentz}) found the same mistake. That raised the
stakes as we will see, Lorentz was the first to begin to think seriously
about what an actual null result might mean.

\subsubsection{Cleveland}

The most significant thing to happen in Cleveland, Ohio before the
installation of the Rock and Roll Hall of Fame was Albert Michelson's
arrival.

When Michelson's time in Europe was complete, his future was uncertain
and so he was delighted to discover that colleagues had interceded on
his behalf to offer him a faculty position at the brand new Case School
of Applied Science in Cleveland, Ohio. (This is now the very fine Case
Western Reserve University.) With a salary of \$2000 per year and \$7500
for equipment, and his graduate education under Helmholtz, he readily
accepted the position, resigned from the Navy, and in 1881
re-established his light-speed measurement work in Cleveland. A
structure was erected for his lab and he reassembled as much of his
Annapolis equipment as he could find. As his daughter pointed out,
``Michelson's experiments had a way of costing far more than had been
originally expected.'' He ran out of money and was assisted
by\ldots Newcomb, again. His eventual result of $299,853,000$ meters per
second ($0.02\%)$ precision) stood as the standard for four decades.

\begin{wrapfigure}{R}{.45\textwidth}  
  \begin{center}
    \includegraphics[width=.40\textwidth]{./14_Michelson/images/morley.png}  
    \captionsetup{style=figures}
    \caption{Edward Morley (1838-1923)} 
    \label{fig:morley} 
  \end{center}
\end{wrapfigure}

In 1884 while on a trip to Montreal to attend a scientific conference,
he met Edward Morley (1838-1923) on the train---a senior Western Reserve
University chemistry professor who was good with his hands in a lab.
They struck up a friendship and determined to work together upon their
return. Michelson had the pleasure of hearing his results discussed in
lectures at the conference and Simon Newcomb made sure to introduce him
to all of the attendees of note. As a result he found himself becoming
friends with John William Strutt, 3rd Baron Rayleigh---future Nobel
Laureate and another king of physics who invited him to Baltimore for a
marathon 20 lectures on physics at Johns Hopkins to be delivered by Sir
William Thomson, the future Lord Kelvin. One of Kelvin's emphases was
the elastic properties that the ether must have for the planets to move
it aside as they pass. Thomson paid no attention to Maxwell's
electromagnetic theory as Hertz was still three years away from his
experimental confirmation in Helmholtz' lab.

Michelson had given up on the ether measurement, believing it to be a
failure but in Baltimore Rayleigh persuaded him to try again and he and
Morley resolved to do that experiment together and to use an
interferometer as the device in Main Hall on the Case campus. With
modifications designed to mitigate the problems of the Potsdam effort,
surely, that would yield a positive result.

As a warm-up they decided to try to repeat Fizeau's 1851 experiment that
suggested that the ether is dragged, but with better engineering than 30
years before. (We'll look at Fizeau's work in
Chapter~\ref{chap:lorentz}.) They nearly got the experiment assembled
and ready for data when the first of a series of events happened.

Events that launched a three year period of triumph and disaster.

Morley wrote:

\begin{quote}
``I can only guess at the stresses which brought about his illness.
Overwork---and the ruthless discipline with which he drove himself to a
task he felt must be done with such perfection that it could never again
be called into question.''
\end{quote}

Michelson wasn't sleeping, nor eating. He'd been a tennis champion on
campus, but now only worked. Eventually he collapsed and on September
19, 1885 at the age of only 33, Margaret had him committed to a nerve
specialist in New York. Again, from Morley:

\begin{quote}
\ldots{} Mr.~Michelson of the Case School left week ago yesterday. He
shows some symptoms which point to softening of the brain; he goes for a
year's rest, but it is very doubtful whether he will ever be able to do
any more work. He had begun some experiments in my laboratory, which he
asked me to finish, and which I consented to carry on.
\end{quote}

What happened next is astonishing. He recovered in two months and wrote
to Morley to inquire as to the experiment and learned that Case
University had hired his replacement! It gets worse.

His doctor wrote:

\begin{quote}
\ldots{} his {[}Michelson's{]} wife has urged me to shut him up in an
asylum which I promptly refused to do. Mr.~Michelson is one of the
brightest men of this country if not of the world in his chosen study.
He is an accomplished man, very popular with those who know him\ldots{}
Professor Michelson's most temperamental fault is a tendency to
emotional acting, but I cannot say that it is unduly expressed, or that
he ever acts without proper and adequate stimulus\ldots{}
\end{quote}

Fortunately, he recovered by December and returned to try to piece
together his career and his marriage. He struggled with the knowledge
that Margaret tried to commit him to an asylum against his will and as a
result their marriage was troubled until it ended 13 years later. Upon
returning to Cleveland, Michelson moved himself into his own quarters in
their large house and by many accounts, his personality seemed to change
after these two betrayals: by his wife and his university.

While healthy and ready to resume his research, the Case Board of
Trustees hadn't done their worst: They indicated that they would be
happy for him to return to the faculty, but he'd have to take a
considerable cut in his salary since they had hired his replacement for
the year. Michelson had to pay for his own stand-in.

In any case, after another desperate infusion of funds, he and Morley
completed their first experiment and confirmed the Fizeau result: the
ether seems to be dragged along with the Earth. He was urged by many
then to repeat the Potsdam experiment with better precision as the
ether-chaos was unbearable for the community. Life settled down for
Michelson. Still bruised, he and Margaret worked towards some measure of
reconciliation. He played tennis and painted and thought about how to do
Potsdam better. But the Universe was not done challenging him yet.

Sometime between midnight and 2AM on October 27, 1886 Main Hall on
campus spectacularly exploded. In the aftermath, Michelson and Morley
were able to salvage much of their apparatus and they reconstructed it
in Morley's, now cramped, Western Reserve chemistry lab. That's when it
got serious. They set out to reduce as many of the systematic
uncertainties that the Potsdam experiment encountered and succeeded.

\subsection{The ``Michelson Morley Experiment''}

What followed during the summer of 1887 is arguably one of the most
important experiments in the history of physics, the ``Michelson-Morley
Experiment.'' The issue was to repeat the Potsdam work, but improve the
accuracy by mitigating the drawbacks of Michelson's original design.
They tried to damp the vibrations that plagued the earlier measurement
by building the new apparatus on a huge, heavy sandstone slab that
floated in a donut-shaped channel of mercury---a dangerous environment,
not allowable today. This isolated it vibrationally and allowed the
experimenters to keep the whole instrument in constant, smooth rotation,
slowly, so that the directions of the arms are constantly and uniformly
changing with respect to the ether direction. Now all they needed to do
was observe \emph{any} shift in the fringe positions. That would
eliminate any potential bias and it relieved him from the disruption
that rotating his Potsdam apparatus by $90^\circ$ might have caused.

\begin{figure}[htp]
\centering
\includegraphics[width= \linewidth]{./14_Michelson/images/MM_photo.png}
\caption{The Michelson-Morley apparatus on its huge concrete, rotating slab.}
\label{fig:MMphoto} 
\end{figure}

Furthermore with high quality mirrors the two $L_1$ and $L_2$ light
paths were increased by reflecting them back and forth to an effective
overall length of 11 meters---more than a factor of 10 longer than
Potsdam---greatly improving the precision as well. Remember that the
tiny shift in optical length is proportional to the sum of the lengths
of the two arms, so that factor of 10 is significant.

\begin{figure}[htp]
\centering
\includegraphics[width= 0.8\linewidth]{./14_Michelson/images/MM_Case.png}
\caption{Plan and perspective engineering drawings }
\label{fig:MM} 
\end{figure}

So on six days in July of 1887 they did their experiment walking around
the circle looking into the eyepiece all the while in 30 minute shifts
each. Figure~\ref{fig:fringe} shows their results:

\begin{figure}[htp]
\centering
\includegraphics[width= 0.5\linewidth]{./14_Michelson/images/fringes.png}
\caption{As they rotated the interferometer, if the speed of the Earth relative to a stationary ether were real, then they would expect to see the result shown as the dashe curve. The broken solid lines is what their results showed. }
\label{fig:fringe} 
\end{figure}

The vertical axis is the amount of fringe shift in fractions of the
wavelength of the light. The sine-wave curve is what they would expect
to see as the apparatus rotated through a circle based on the Earth's
speed and a stationary ether, \emph{but they drew it in the plot reduced
by a factor of
eight}.\footnote{This is not always appreciated when Figure\ \ref{fig:fringe} is reproduced.}
The sort of sad, flat curve is what they actually measured. By reducing
the expected curve, the dramatic difference with the expectaion---and
the tiny flatness of their result---isn't as prominent as it should be.
This really is zero: no effect is seen. It's the most important
measurement of zero, well, ever.

In August, 1887, Michelson wrote to Lord Rayleigh who had encouraged him
to return to the ether experiment:

\begin{quote}
``The Experiments on relative motion of Earth and ether have been
completed and the result is decidedly negative. The expected deviation
of the interference fringes from the zero should have been 0.40 of a
fringe --- the maximum displacement was 0.02 and the average much less
than 0.01---and then not in the right place.

``As displacement is proportional to squares of the relative velocities
it follows that if the ether does slip past {[}the Earth{]} the relative
velocity is less than one sixth of the Earth's velocity.''
\end{quote}

For Michelson it was a failure. Either the ether moves with the Earth or
there is no ether. Or something else. Neither Michelson nor anyone could
imagine that the ether didn't exist. And even after Einstein's dismissal
of the ether on different grounds, Michelson couldn't get rid of it
during the rest of his life.

After their result became public, the physics world began to pay anxious
attention. An explanation was needed. But he never liked that result and
was discouraged enough to abandon their original run-plan to do the
measurement at different times of the year, and presumably different
angles with the ether.

He was done and he never returned to this experiment again.

\subsection{Michelson and Chicago}

By 1888 Michelson had become unhappy at Case---his illness, Case's
response, the fire and the refusal to rebuild his lab, and trouble at
home weighed on him. But that still malicious universe wasn't yet done
with Michelson. The family was to suffer through two more calamities in
1887. A cook actually robbed them of their jewelry and other valuables
(which were recovered in another town). And, in later in that same year
a maid accused Michelson of sexual assault actually leading to his
arrest at home with headlines in the paper! Blackmail had been demanded
and Michelson, Morley, a lawyer, and the Cleveland police actually set
up a sting operation to get the perpetrator to expose her plot
exonerating Michelson. Quite another year in Cleveland.

So he was ripe for the picking. When Clark University was formed in
Worcester, Massachusetts and started recruiting scientists in 1889,
Michelson jumped at the chance to restart his program as the first Chair
of Physics with finally adequate financial and technical support. In
retrospect, Case had made a terrible mistake.

Off they went to the New England countryside. But after a promising
start, it wasn't a match made in heaven for any of the talented faculty
recruited to Clark. By 1892, Michelson and 12 of the 16 scientists on
Clark's faculty resigned in unison because of an unbearable meddling by
the university president who was on an entirely different course from
the founder and financial benefactor, Jonas Clark. It was a mess. Today,
Clark University is a thriving institution. But another one owning the
distinction of losing Michelson. This time to the new University of
Chicago in 1892, along with the 11 others from Clark. The University of
Chicago promised big and delivered.

\subsubsection{A Meter}

Michelson's arrival in Chicago was delayed. The International Bureau of
Weights and Measures in Paris recruited him for an important job:
determining the most precise length of the standard meter. The French
metric system relied on a platinum bar housed in Paris which defined 1
meter according to the original 1791 definition: 1 m = one 10-millionth
of the distance from the north pole to the equator on a meridian passing
through Paris. More precision was needed since the Earth is a
non-spherical, geologically active object---it's not great as the basis
for a standard length. And, even though there was a ``standard''
platinum bar kept at a controlled temperature in Paris, each nation,
even cities, had their own copies of the original standard meter. So
there were lots and lots of
``meters''!\footnote{Also, there was real concern that were a war to break out that the unique platinum bar could be destroyed.}
Sir Humphrey Davy and Maxwell suggested a standard which could be
independently replicated using a natural phenomenon of some sort: the
wavelength (for length) and frequency (for time) of light.

One of the outgrowths of the Michelson-Morley experiment at Case
(Western!) was the realization that the interferometer could be used for
other purposes. For example, by making one of the arms moveable and with
a careful micrometer measurement of just how far it moves, one could
watch the interference fringes change place, a half-wavelength at at
time. By marking where one peak was, changing the distance of the
movable mirror would march the peak across the eyepiece and when a
trailing peak lined up at the origin spot again, the lengthening would
correspond to one half of a wavelength. So, one could precisely
determine the wavelength of spectral lines of various light sources. In
1887 they proposed using interferometry as the tool for precisely
measuring the meter and proposed that the spectral lines of Sodium light
might serve as the source. (Sodium vapor emits a bright pair of yellow
emission lines.) Then they decided Mercury's green line would be
suitable, but discovered that Mercury's line was actually quite
complicated---many lines. So they actually made a discovery about the
element Mercury! Of course they could then measure the spectral lines of
other elements an important addition to the nascent science of
spectroscopy.\footnote{They and others became less interested in the interferometer for this purpose and it went out of style. Only to be resurrected in the 1950's as "Fourier transform spectroscopy."}
They kept at it and found that the red Cadmium spectral line
($\lambda = 6,438\; \AA$ where an Angstrom is $10^{-10}$ meters) was
singular and could become a calibration point.

That's what the International Bureau of Weights and Measures wanted.
They invited Michelson to come to Paris and find an emission-line
standard for a meter. This he did with characteristic precision and
accuracy with a result that lasted for four decades. After being
repeated in 1905, two years later the standard meter became
1,553,163.5.180 wavelengths of that Cadmium red line's wavelength with
an uncertainty of 0.08 parts per million. This measurement was
referenced as a part of the justification for Michelson's Nobel Prize in
1907.

When his work was done, he reported to duty at the new University of
Chicago. Margaret bought a house on the East Coast and his family didn't
join him for a while.

\subsubsection{University of Chicago}

The University of Chicago's was born out of the commitment of a handful
of private (wealthy) citizens with a vision of a world-class research
university. The United States' university system, and so its scientific
expertise and training, was rudimentary compared to that of Europe's and
Marshall Field and other Chicago businessmen were determined to compete.
The new Ryerson Physical Laboratory was completed in 1894 and Michelson
and others moved in. Students who could pass the difficult entrance
examinations came from all over the world. It must have been a heady
time as the new faculty knew that they were participating in something
special in the Unites States. He was to spend the next 40 years there.

The next couple of years were replete with honors: the Société Française
de Physique, the Royal Astronomical Society, the Cambridge Philosophical
Society, and the Société Hollandaise des Sciences. But they were not
without heartache as well.

In 1897, the Michelson's shocked the tight-knit faculty when Albert
moved to a hotel. Margaret sued for divorce and he agreed to support his
three children (Albert Heminway, Truman, and Elsa) with \$10,000. The
court proceedings were humiliating as the children had been trained to
describe cruelty at his hands in their upbringings and he vowed to never
see them again.

While his divorce was still pending, Michelson met Edna Stanton, the
daughter of a former diplomat to Russia (she lived there for 12 years)
and a German mother. She was radical and a free-spirit\ldots and 20
years Albert's junior. Nonetheless, they courted, married in 1899, and
subsequently had three children. (One of those daughters was Dorothy
Michelson Livingston, the biographer of her father \citealt{dl21})

\begin{wrapfigure}{R}{.45\textwidth}  
  \begin{center}
    \includegraphics[width=.40\textwidth]{./14_Michelson/images/michelson_nobel.png}  
    \captionsetup{style=figures}
    \caption{Michelson around the time of his Nobel Prize.} 
  \end{center}
\end{wrapfigure}

His time at Chicago was nonetheless productive and pleasant. His
students enjoyed him. He played tennis regularly and had a professional
and well-staffed laboratory and was able to watch his new family grow
up. He was in demand around the country and the world and took on new
and engaging experiments with enthusiasm and his characteristic talent
for precision optics. The projects he took on included:

\begin{itemize}
\tightlist
\item
  The measurement of the radius of a star---initially the red giant,
  Betelgeuse using interferometry---essentially capturing light with two
  telescopes and letting them interfere. In effect this increases the
  resolving power (or effective size) of any single telescope by a
  considerable factor. This is a standard technique especially in radio
  astronomy today.
\item
  He continued his speed of light measurements and was engaged in a
  long-baseline experiment in California when he passed away.
\item
  He created and perfected the creation of very precise diffraction
  gratings with an engineered instrument in the basement of the physics
  building. They were the best in the world and required weeks of
  patient, delicate fabrication.
\end{itemize}

Oh. And he won the Nobel Prize in 1907, the first American to do so and
the first Jew to win the physics prize. The award was not for the ether
experiment, as Special Relativity was still only a year or so old and
Einstein was still unknown. Michelson's award reads: ``For his optical
precision instruments and the spectroscopic and meterological
investigations carried out with their aid.''

Michelson died in 1931 at the age of 79 in Pasadena, California where he
was engaged in a multiple experiments to improve the precision of the
determination of the speed of light. He and Edna had retired from the
University of Chicago and moved the previous year so he could focus on
the culmination of nearly a half century of steadily improving this
measurement. He had had multiple operations for prostate and intestinal
disease with multiple infections (before the time of antibiotics), often
writing and working from a bed. This final experiment involved the
construction of an evacuated tube about a mile long in the mountains of
Irvine Ranch near Santa Ana, California. With multiple reflections, the
path length was effectively more than 8 miles. His biggest hurdle? The
whole Earth. By the time he ended his life's work, his precision battle
was against tiny geological shudders in the crust of a major mountain.

Today the determination of the speed of light is exquisitely precise
using lasers: and for many years the technique is still essentially the
same one that Michelson pioneered while he was in the Navy. That's
changed in the last 50 years as is described in
Section~\ref{interferometer} in Section~\ref{more_Michelson}. Likewise,
his original notion of measuring the size of a star using two small, but
widely spaced optical receivers and letting the interfering pattern
determine the angular size of the star is now the standard technique of
optical and radio astronomy for huge telescopes around the world. Again,
find this story in Section~\ref{michelson_astronomy}. Finally, not onl
is the Michelson Interferometer a standard bench instrument in optics
labs everywhere it is the principle deployed in the LIGO experiment that
has recently discovered Gravitational Radiation and has initiated a
whole new branch of astronomy by studying the collisions of neutron
stars and black holes. More below.

A nice side-story to the Nobel award was in the crowd who surround him
after his Nobel lecture in Copenhagen. A young man approached him to
say, ``You don't know me. I am your son.'' The bitterness of the divorce
from Margaret left Albert estranged from his two sons and daughter 11
years previously. Young Albert had graduated from Harvard and at 29 was
the American consular agent at Charleroi, Belgium. He'd been in Italy at
a meeting, saw that his father had won the Prize and was bound for
Stockholm and so Albert Junior traveled north to meet his father.
Michelson abandoned his ceremonial and social plans and spent time with
his first-born son.

\% !TEX root = ../\_superfluous\_book\_3.tex \setcounter{chapter}{13}

\chapter[Michelson]{\texorpdfstring{The Most Important Zero Ever:\\ \textsf{Albert Michelson} }{Michelson}}

\begin{myblock1}{Our story now takes a turn by merging our \textsf{MOTION} and \textsf{LIGHT} themes in a post-Maxwell environment. Our last experimental stop before we get to Einstein. \\ \\
We'll now consider one of the most important experiments in the last two
centuries, and certainly the most important measurement ever of
\textbf{zero} ever. It starts in the Wild West of gold and silver mining---literally, the Wild West---and passes through Stockholm and the Nobel
Prize. Let's talk about one of the more interesting physicists of all.
Albert Michelson, a complicated person notoriously stern and difficult
(although he was an accomplished artist, musician, and tennis and
billiards player). He once had an argument about an experiment with a
colleague in a hotel lobby that drew a crowd, maybe because they were
loud and maybe because Michelson was still in his pajamas. He won the
Nobel Prize in 1907, not for his most famous measurement of zero, but
for his exquisitely precise instruments and the collection of scientific
measurements that he made with them. }
\end{myblock1}

\section{A Little Bit of Michelson}

Faced with a difficult situation, he did what any 16 year old would do:
he boarded the brand new Transcontinental Railroad at Oakland Land Wharf
in San Francisco and went to Washington, D.C. to see the President.
Albert was nothing, if not persistent.

Albert Michelson was born in 1852 in Poland to Rosalie and Samuel
Michelson. Life for Jews in Prussia was untenable and so this small
family decided to emigrate in a big way, following Samuel's sister and
brother-in-law to the California Gold Rush. With two babies in tow,
Samuel and Rosalie left from Hamburg for New York, and then San
Francisco. Not to chase gold, but to sell dry goods to the miners. As a
merchant, that's what Samuel knew best.

Sailing around Cape Horn or traveling across the country in covered
wagons must have seemed too tame for this adventurous couple. From New
York they boarded a steamer for Panama, then by canoe, mule train, and a
brand new railway, made their way across the Isthmus of Panama to a
clipper ship and then on to San Francisco. It was a harrowing journey
during which they lacked water, fought exotic insects, faced danger from
outlaws, and avoided the desperately sick natives who were all around
them. It made an impression on three year old Albert that he never
forgot. In retrospect, covered wagons must have seemed like a better
alternative.

The last leg of their journey was by stagecoach from the city to
Murphy's Camp in the foothills of California's Sierra Nevada mountains.
After more than a year of dangerous travel, they settled alongside
Samuel's brother-in-law and set up shop with the goods needed by any
respectable prospector.

\begin{figure}
\centering
\includegraphics[width=0.8\linewidth]{./14_Michelson/images/murphy.png}
\caption{Murphy's Camp in 1852 (Kenneth M. Castro)}
\label{fig:murphy} 
\end{figure}

Tens of millions of dollars in gold was shipped from Murphy's Camp and
that kind of activity came equipped with hard edges. The town resembled
a bad cowboy movie: full of drunks, violence, and public hangings---and
lots of cash. It thrived in its own way until it all burned to the
ground in 1859 in less than an hour.

The town and the Michelsons rebuilt but by the time Albert was 12 years
old in 1864, Rosalie decided that he needed a more formal education than
available in Murphy's. She had tutored him, even insisting on violin
lessons. But Albert was sent with his aunt and uncle to San Francisco
for high school where he so impressed the principal, that he was taken
into his home and given special access to the school's science
lab\ldots and boxing lessons.

By this time Murphy's gold had dried up and the family moved to Virginia
City, Nevada\ldots where silver was all the rage and their new boom-town
swelled to 30,000 inhabitants. The family moved into a large house over
Samuel's new store where the business flourished. A father-son
enterprise was a possibility, but by this time Albert needed a different
path. A scientific one.

\subsection{The Navy}

Today, in order to enter a U.S. military academy, an 18 year old
requires a nomination by a state or federal elected representative. It's
a highly competitive process requiring superior academics and typically,
an athletic background. Albert's growing interest in science had led to
a favorably received paper on optics and he wanted to pursue this
subject. But how?

The U.S. Naval Academy at Annapolis, Maryland was then only 20 years old
when Albert graduated from high school in San Francisco and Samuel
learned that Nevada's Congressman Thomas Fitch was accepting nominations
for boys to the Academy. Albert applied, took the exams and tied with
two other applicants for first place. Fitch chose one of the other boys,
who immediately failed prompting Fitch to write to President Grant on
Albert's behalf. In what was to become a characteristic Albert-move, at
the age when today's U.S. kids are just getting their learner's permits,
he took matters into his own hands and did what his family did: he got
on the road. Hence, that solo teenage train ride across the rough North
American continent.

When he arrived in Washington, D.C. he presented himself at the White
House, and made his case to President Grant personally. At that time the
President was allotted 10 at-large appointments (now the Vice President
can nominate five) and Grant had used up that total. Not to be outdone,
Albert then took himself to Annapolis and sought an audience with the
Commandant where he was examined, did well, but told that there were no
openings.

As Albert's daughter described later (Dorothy Michelson Livingston wrote
the definitive (technically accurate and moving) biography of her
father:\citealt{dl21}), he was literally at Union Station boarding the
train to return to San Francisco when a messenger from the President
intercepted him to say the the President had decided to appoint 11
midshipmen that year (and later two more, for a total of 13). Michelson
always joked that he was probably illegally a student at the Naval
Academy. But it worked out. In 1869 at the age of 17, Albert joined the
Navy.

\begin{wrapfigure}{R}{.45\textwidth}  
  \begin{center}
    \includegraphics[width=.40\textwidth]{./14_Michelson/images/michelson_midshipman.png}  
    \captionsetup{style=figures}
    \caption{Albert Michelson as a cadet-officer.} 
    \label{fig:albertyoung} 
  \end{center}
\end{wrapfigure}

Albert was a popular and successful midshipman, not above the occasional
fight or prank. He graduated in 1873 at or near the top in experimental
and mathematical subjects---at the top in optics\ldots and near the
bottom in seamanship. He did his two-year obligatory training at sea off
the coast of South America and the Caribbean in a combined steam-sailing
ship, ending his sailing obligation in Norfolk as an Ensign. He decided
to stay in the Navy and in 1875 was assigned physics instructor duties
at the Academy under Lieutenant Commander William Sampson, the head of
the Department of Natural and Experimental Philosophy who was to become
a friend as well as mentor. Mrs.\textasciitilde Sampson's niece recently
returned from finishing school in Paris and Margaret Heminway was
introduced to him at a family event. She was the daughter of a wealthy
and powerful lawyer and investor in New York City. In spite of their age
and class differences, Albert and Margaret were married in 1877---a
marriage ``up'\,' for Albert into a rarified atmosphere as compared to
his immigrant upbringings. After more cruises, Albert and Margaret had
their first son, Albert, in 1878.

\subsection{Light}

One of Albert's first tasks as an instructor was to create
demonstrations for the midshipmen in their physics classes and he chose
to take on a relatively new method for measuring the speed of light, now
an experiment done by physics students in hallways around the world.
Except he made it better and found a calling.

\subsubsection{It's Really Fast\}}

In Chapter\textasciitilde{}\ref{chap:young} we enumerated the many ways
that the speed of light was determined prior to Michelson's time. Recall
that it was Fizeau who did it best in 1848 by chopping the light up with
a rotating mirror and capturing its return as the mirror rotated in the
meantime.

This was the technique that Michelson adopted for his midshipmen
students and by 1878 he had a handful of ideas to better engineer the
device. He lengthened the path length to 11 meters, he greatly improved
the various focussing lenses required for the beams, swapped Foucault's
concave far mirror for a finely ground plane mirror, and he delicately
engineered the rotating mirror assembly by driving it with a regulated,
hand-operated bellows to a constant speed of 130 turns per second. With
this first measurement, he obtained $c=300,140,000$ m/s with an
uncertainty of about 0.2\%. It cost him \$10 in 1878 dollars.

In the same year that he and Margaret had a second child, he obsessed
about getting a new apparatus to work. With a lot of support from the
Academy (he was, after all still in the Navy but with this unusual
research assignment), \$2000 (worth more than $\$50,000$ today) from his
father-in-law, and space at Annapolis along the waterfront, he was able
to retain services from first-class instrument and optical
manufacturers. Meanwhile, Congress had turned down a request of support
and awarded $\$5000$ to Simon Newcomb, a distinguished astronomer who
actually suggested improvements in the young man's plans and supported
him publicly. His new path-length was to be 609 meters and his rotating
mirror assembly was a delicately controlled 128 revolutions per second
(he'd already destroyed an assembly at high speed when its balance was
not perfect). He devised a tuning-fork with a small mirror attached.
When it vibrated at its precise frequency, and the rotating mirror was
in synch, stable images of the rotating mirror would show in the tuning
fork's mirror. The time of day was regulated, as the heat would change
dimensions of the apparatus. His result was $c=299,910,000 \pm 50,000$
m/s, or a precision of $\pm 0.017\%$.

Measurement of the speed of light became his life-long passion and he
was working on an audacious experiment in the hills of southern
California when he died. His previous 1924 measurement of
$c=299,796,000 \pm 0.001\%$ m/s stood for three decades as most precise.

\begin{quote}
May 14, 1879, in the Virginia City Evening Chronicle:

``THE VELOCITY OF LIGHT A YOUNG COMSTOCKER'S CONTRIBUTION TO THE WORLD
OF SCIENCE

``Ensign A. A. Michelson, a son of S. Michelson, the dry goods merchant
of this city, has aroused the attention of the scientific minds of the
country by his remarkable discoveries in measuring the velocity of
light.'' The New York Times says: `It would seem that the scientific
world of America is destined to be adorned with a new and brilliant
name. Ensign A. A. Michelson, a graduate of the Annapolis Naval Academy,
and not yet 27 years of age, has distinguished himself by studies in the
science of optics which promise the discovery of a method for measuring
the velocity of light with almost as much accuracy as the velocity of an
ordinary projectile\ldots{}'''
\end{quote}

Albert didn't want to go back to sea, which would have been his next
Navy assignment. He was partially spared another sea voyage when Newcomb
had enough influence to ``borrow'\,' Michelson from the Navy to work in
his laboratory in Washington D.C\ldots.where his job was to make his
friendly competitor's Congressionally funded experiment work.

That probably wasn't ideal. He was fully aware that his engineering
degree (until recently the service academies offered only engineering)
would not qualify him for a university faculty position, but no
institution in the United States offered a doctorate in
physics.\footnote{John's Hopkins University in Baltimore was about to offer Ph.D. degrees.}

Again, not shy, he requested and received a leave of absence from the
Navy in order to pursue a Ph.D.\textasciitilde and secured a position at
Humbolt University in Berlin to study under and work with Helmholtz,
whom we learned about in Chapter\textasciitilde{}\ref{chap:joule}. Off
the four of them went to Berlin, Margaret, two children, and Albert.

Helmholtz was an expert in optics, having revolutionized ophthalmology
with his invention of the ophthalmoscope and was extraordinarily
multidimensional. His mathematical codification of the conservation of
energy (see Chapter 12), development of the science of fluid dynamics,
studies in acoustics, and both mathematical and experimental
contributions to electromagnetism all marked his name in
textbooks\ldots in multiple fields. Not bad for a medical doctor.

Michelson had something on his mind that had come to him during their
first stop in Paris and he went to Berlin with a research target in his
mind: the ether.

\subsection{Where Is the Ether?}

As we saw in Chapter\textasciitilde{}\ref{chap:young} it was Thomas
Young who upon determining that light must be a wave, then postulated
that there needed to be a substance ``that waves.'\,' A very definition,
if you will, of what light must be: the undulations of a substance, that
ether. As preposterous is the properties of the ether are, we saw in
Chapter\textasciitilde{}\ref{chap:maxwell} that nobody questioned it and
huge experimental and theoretical efforts were expended in describing it
and searching for evidence of it.

Sir Oliver Lodge was passionate (and relentless) on the subject, even
after it was ultimately clear that he was wrong. He spoke for almost all
of the now exhausted physics community:

\begin{quote}
``\ldots{} it is absurd to imagine one piece of matter acting
mechanically on another at a distance, whether that distance be large or
small, without some intervening mechanism or connecting link\ldots{}''
\end{quote}

So in addition to the chaos in the theory camp, there was a
corresponding chaotic situation among experiments going back many
decades: some results demanded that the ether was stationary and that
the Earth (somehow) moved through it and some experiments demanded that
the ether was dragged along---wholly or partially---by the orbiting
Earth. Chaos in both theory and experiment, an imperfect situation.

The ether's job description included two assignments, solving two
problems: First, it could function as Newton's absolutely at-rest
structure anchoring and even defining space and it second, it supported
light's wave propagation as convincingly suggested by Maxwell.

Always imaginative, Maxwell wondered about exactly that and during the
last year of his life---the year before Michelson went to Europe---he
suggested that it might be possible to measure the speed of the Earth
relative to the fixed ether---the ``breeze.'\,' However, he worked out
that the experimental accuracy of his scheme was depressingly
impossible: it must distinguish speeds relative to the ether of about
$0.0000000001\%$.

Michelson must have heard of Maxwell's idea around the time that he was
headed to Berlin and what was an impossibility to Maxwell, was a
challenge to him to him. After all, precision optics seemed to be his
game.

\subsubsection{Moving Through The Ether}

What was Maxwell's idea? A naval analogy that Michelson later described
to his children gives a good feeling for his plan. Let's look at Figure
Box\textasciitilde{}\underline{\ref{river}} on the next page.
\faHandORight  

And then come back here \faHandODown  $\text{ }$ to continue
\setword{reading}{reading} \ldots{}

Now suppose we make the following substitutions in our nautical race:

\begin{itemize}
\tightlist
\item
  instead of boats$\to$ we'll use light beams;
\item
  instead of the bank$\to$ we'll imagine the Earth; and
\item
  instead of a river$\to$ we'll imagine an ether ``current'' passing by
  it.
\end{itemize}

\subsection{The Michelson Interferometer}

The instrument Michelson invented and spent a decade of his life
perfecting is called the \emph{Michelson Interferometer} and it's a
standard tool in today's optics laboratories, industrial manufacturing,
telecommunications, and even in astronomy.

Remember our discussion of Thomas Young's experiment with light where he
demonstrated that light aimed at two holes or slits caused an
interference pattern to emerge on a far screen which can only happen if
light is a wave. When two waves go up or down together, they add and if
they are exactly out of phase, one with the other, the subtract to zero.
No wave. Dark. It's the principle behind your noise-cancelling
headphones if those waves are sound waves.

Sometimes the waves interfere between total cancellation and total
addition and the result is a new wave that can have a funny-looking
shape.

\%----------------------------------------

\begin{minipage}[t]{.95\textwidth}
\noindent  \rule[-0.in]{0.35\textwidth}{0.001in} {\sffamily FIGURE BOX~\ref{river}}
 \rule[-0.in]{0.35\textwidth}{0.001in}\
    \begin{wrapfigure}{l}{0.5\textwidth}
        \includegraphics[width=0.5\textwidth]{./14_Michelson/images/river_400_side_V.png}
        \captionof{figure}{CAPTION.}
        \label{river}
    \end{wrapfigure}%\hfill 

{\color{mygray}{\sffamily \small As shown on the left in Figure~\ref{river}~(A), suppose Bob and Doris and are to race in a river. They each plan to pilot their identical
motor boats the same distances starting at a the same point on the south shore (P1) and ending up back at that same location. Bob goes across the
river north to the opposite shore (P2), and then returns south to P1. Doris pilots her boat to the east to P3 and then back to P1. In this
race, the river is still---no current. Who wins if both boats can move through the water at the same speed? \setlength\parskip\baselineskip

Obviously, since they're both traveling at the same speed over the same
distance and if the water is perfectly calm, their round trip race would
result in a tie. That's too easy.  \setlength\parskip\baselineskip

Now suppose that the river has a strong current from east to west, as
suggested in Figure~\ref{river}~(B). Same boats, same relative speeds
through the water, and the same trips, north then south for Bob and east
and return west for Doris. Both travel the to the same points as before,
relative to the shore. Who wins now? \setlength\parskip\baselineskip

Since the river is flowing to the west, Doris has to fight the current
to go the required distance to the east, but on her return, the current
helps. Meanwhile, in order to get directly across the river, Bob has to
aim to the east of his intended point so that the current pulls him back
to the north shore directly opposite his starting position. Coming back,
he must do the same sort of maneuver.  \setlength\parskip\baselineskip

Who wins? Bob or Doris? \setlength\parskip\baselineskip

It turns out that the round trip across the river and back will be
quicker than the trip to the right and to the left. (See Appendix 13 for
the calculation.) So Bob wins.

Now go back to  \underline{\ref{reading} } \faHandOLeft

 \setlength\parskip\baselineskip
}}
\vspace{5mm}
\end{minipage}

\textbackslash end\{minipage\}\quad\hfill

\rule{\textwidth}{0.2mm}

\%----------------------------------------

Light has wavelengths that are around 500 nanometers. That's 0.000000500
meters (for comparison, sound in a dry room at normal temperature, say
Middle C, has a wavelength of about 4 feet.) That means that detecting a
small difference between two light waves by separately comparing them
side by side would have been impossibly difficult, but unraveling their
\emph{interference} is much easier to observe. So if an experimenter has
a device that can measure the interference of two waves, then they know
that the waves arrived out of, or in, phase. If out, then one of them
led and the other followed.

Let's imagine a slightly different analogy where water is not involved.
Suppose we have two marchers,side by side. Gladys on the left walks
beside Clyde on the right and they're both the same height and practice
marching so thoroughly that when they walk beside on another, they are
in phase: when Glady's right foot goes down, so does Clyde's. Every
stride is the same.

Let's suppose that they enter an school stadium side by side and when
they reach the oval running track they separate\ldots Gladys goes left
and Clyde marches right. They circle around the track and meet at the
other end. When they meet Clyde's right foot lands, at the same instant,
so does Gladys' right foot. And they bump into one another. They're
still in phase, and dazed.

Now do it again, at a different school on a different track. This one
was laid out by a sloppy designer and the side that Clyde usually
travels is slightly longer than the other side. So when Gladys reaches
the opposite end, she marches in place. Clyde's not there yet and when
it does arrive, his cadence may not match hers. That different path
length made them go from originally being in phase, to out of phase.

If your job is to determine whether the sides are the same length, you
could just measure them with a tape measure (that's what I'd
do)\ldots or you could employ Gladys and Clyde to perform their routine
in front of you. If they get to the end and are not in phase, then you
know you've got a badly designed track on your hands.

Or let's suppose that on Glady's side of the track, the long stretch has
been replaced by a airport moving sidewalk going in her original
direction. While Clyde encounters an identical moving sidewalk that's
going in the other direction. Strange, right? So she's helped along and
ahd he's hindered and she obviously gets to the end before Clyde. Again,
they would be out of phase since she got the benefit of a moving medium
in which she would travel and his forward progress was hindered by that
medium.

That's a way to imagine the Michelson Interferometer. It's a device to
take a light beam and cause it to travel two different paths and then to
see whether they are still in phase when they are brought together.

So they could be out of phase because the paths they travel (the
\emph{optical path}, OP) are different and/or because the medium that
they travel in (the ether) helps one of them along because of the
interferometer's motion relative to that medium (the moving sidwalk).

Back to Bob and Doris: In the Michelson's Interferometer, the Bob-wave
is made to travel perpendicular to the motion of the Earth through space
and the Doris-wave is made to travel with, and against that motion.
Michelson would measure precisely a finite speed for the Earth relative
to the ether, by observing how out of phase the two paths are and he
could do it with a precision that he'd know from understanding his
instrument.

That was the plan, but the engineering and instrumentation was
formidable and while Humboldt University was prepared to give Michelson
a downtown Berlin laboratory in the basement, there was very little
funding for the equipment.

\subsubsection{With The Phone Guy's Help}

Simon Newcomb came to the rescue again. He seemed to know everyone and
of course that included his friend Alexander Graham Bell who came
through with sufficient financial support to allow Michelson to
collaborate with a German optical company to construct his first
interferometer. So in 1881 Michelson built an exquisitely precise device
which combined waves in exactly as the river analogy required.
Figure\textasciitilde{}\ref{fig:mmstill} is a sketch of how the
apparatus works as viewed from the Earth itself. Let's look carefully at
it.

\%----------------------------------------

\begin{minipage}[t]{.95\textwidth}
\rule{\textwidth}{0.2mm} 
    \begin{wrapfigure}{l}{0.5\textwidth}
        \includegraphics[width=0.5\textwidth]{./14_Michelson/images/MM_apparatus_still_400.png}
        \captionof{figure}{The stationary apparatus.}
        \label{fig:mmstill}
    \end{wrapfigure}%\hfill 

{\color{mygray}{\sffamily \small This is a simplified plan view of the Michelson Interferometer as seen from the Earth, without any ether.  The element in the center at A is called a
Beam Splitter (BS) or ``half-silvered mirror'' (think of a
teleprompter). It takes a beam of light and separates it into two
perpendicular, identical rays, one passing through and one directed
perpendicularly. Let's follow the paths: \setlength\parskip\baselineskip \setlength\parskip\baselineskip

Path 1: Light from the source, S, is separated into the two paths at A
by the BS oriented at $45^{\circ}$. Half of the light from S passes on
through the BS to the right at C. The other half is diverted into a vertical beam directed at a plane mirror, M1 at B (dashed rays). The
distance from A to B is $L_2$ That beam
reflects from M1 back through the BS where again, half is transmitted
down and half goes in the direction of the source (and ignored). The
half that continues down stops at the detector, D. The distance from A
to B is $L_1$. \setlength\parskip\baselineskip \setlength\parskip\baselineskip

Path 2: The light that went right through the BS to the right (now the
dotted rays) is reflected at another mirror, M2 at C, as close to being
perpendicular to M1 as can be arranged. It then passes back through BS,
and yes, half of it then reflects down toward the detector at D. The
distance from A to C is $L_2$. Michelson strove to make $L_1$ be as
close to $L_2$ as possible.}}
\vspace{5mm}
\end{minipage}\quad\hfill
\rule{\textwidth}{0.2mm}

\%----------------------------------------

The magic is in the path between A and the detector, D. Each beam
started out as a partner of the other (Gladys and Clyde), and so they
are initially coherent and they mix on that short path to D. If they are
now slightly out of phase, the image at the detector will register that.
How?

Well, back to Gladys and Clyde who are now in demand and decided to add
to their act. Now there are 10 marchers. Ten marchers enter the track
together, five on the left and five on the right. They split up like
when it was just the two of them and take their paths---each of the 10
marchers never adjusts their pace. But wait. The marchers in the inside
of the track travel a shorter distance than the marchers on the outside
of the track. So the outside people travel further and are later than
the inside people to travel less and get their faster. The middle
marchers will meet exactly at the same opposite point, but the inside
marchers will get there earlier and the outside marchers later. There
will be phase-chaos when they meet. They will interfere with one another
in different ways, the two opposite sets of five.

The same thing happens in the interferometer. The beams are not
infinitesimal lines of light, they're broad (even made so with an unseen
lens just after S) so the result is a bullseye pattern at the detector
with the center being bright and then a dark-light-dark-light
progression from the center. These are called ``fringes'\,' and where
the light-dark regions are on the screen depends critically on the OP
lengths that the beams travel\ldots or their relative motion in the
medium through which they traveled.

Now, what could make those two beams be out of phase? Any number of
circumstances: the experiment could be misaligned (remember that
accuracy requirement) or the Earth's motion in the ether can be
determined:

\begin{itemize}
\tightlist
\item
  If $L_1 \ne L_2$ then they will arrive at different times and so be
  out of phase when they combine.
\item
  If either or both M1 or M2 are not perfectly perpendicular to the
  impinging light source, that will create a distortion.
\item
  If there is a temperature difference in the air between the two arms,
  even that would affect the beams' differently.
\item
  Or\ldots suppose that we're back in the river and the medium that is
  doing the waving---the river or the ether---is moving relative to the
  setup, then from our simple Doris-Bob race, the two combined beams
  will appear to be out of phase because the perpendicular, dashed path,
  will win.
\end{itemize}

The first three ways to get interference are under Michelson's control:
he must build the apparatus with great precision. The last
way\ldots Nature will determine that.

But he was really clever and even the first three ways of getting out of
phase won't matter!

Here's the genius part: Michelson constructed his apparatus so that the
whole thing could be rotated by $90^{\circ}$ about a vertical axis. When
that happens, then the two beams trade places and the original fringe
pattern shifts\ldots the spot where light was bright and where it was
dark, changes between the rotated and un-rotated positions. So he marked
where the bright spots were and then rotated, and looked to see where
they moved to.

That rotation not only cancels instrumental effects, but it also doubles
the fringe shifting from nominal.
Appendix\textasciitilde{}\ref{app:river} shows you how this comes about.
The expected shift of the fringes comes from the path-length difference
that would result from the speed of the Earth through the ether of $v$,
the speed of light, $c$, and the two arms' lengths: \%
$$\delta L = \dfrac{v^2}{c^2}(L_1+L_2).$$ \% The speed of the Earth in
its orbit is about 30,000 m/s and the speed of light is about
300,000,000 m/s\ldots so the shift is a tiny amount of \%
$$\delta L \approx 0.00000001(L_1+L_2)!$$ \% The question is whether
tiny instrumental effects might either mask a positive result, or signal
a false positive result.

\begin{figure}[htp]
\centering
\includegraphics[width= \linewidth]{./14_Michelson/images/potsdam_fringe.png}
\caption{(A) On the left is a perspective engineering drawing of Michelson's prototype where I've labeled it like the sketch above. (B) On the right is a fringe pattern resulting from the apparatus (by the author).}
\label{fig:engineering} 
\end{figure}

His first prototype instrument had arms about a meter long and was
finicky and delicate. Horse-drawn traffic outside of the lab building
was so disruptive that the fringe pattern was unstable. So, he made the
measurements in the middle of the night, but that was not sufficient .
That was still unstable and so he subsequently moved it to a new lab at
rural Potsdam, and then a second lab in the basement of that same
facility. This was quieter but delicate still.In his publication later
he noted that even stomping on the ground 100 meters away from the
building would cause the interference patterns to disappear! So, taking
data was exhausting. Figure\textasciitilde{}\ref{fig:engineering} is a
perspective engineering drawing from Michelson's Potsdam apparatus and
also a candidate Michelson Interferometer fringe pattern is shown.

After more than six months of painstaking work, he published his results
and wrote to his benefactor:

\begin{quote}
Heidelberg, Baden, Germany

April 17th, 1881

My dear Mr.~Bell,

The experiments concerning the relative motion of the Earth with respect
to the ether have just been brought to a successful termination. The
result was however negative\ldots{}

At this season of the year the supposed motion of the solar system
coincides approximately with the motion of the Earth around the Sun, so
that the effect to be oserve {[}sic{]} was at its maximum, and
accordingly if the ether were at rest, the motion of the Earth through
it should produce a displacement of the interference fringes, of at
least one tenth the distance between the fringes; a quantity easily
measurable. The actual displacement was about one one hundredth, and
this, assignable to the errors of experiment.

Thus the question is solved in the negative, showing that the ether in
the vicinity of the Earth is moving with the Earth; a result in direct
variance with the generally received theory of aberration\ldots{}

N.B. Thanks for your pamphlet on the photophone.
\end{quote}

The speed of the ether relative to the Earth seemed to be zero. He
believed it to be a failure, the first in his so-far, distinguished
career as the young King of Optics.

\subsection{Getting Serious: The Michelson Meets Morley}

\begin{wrapfigure}{R}{.45\textwidth}  
  \begin{center}
    \includegraphics[width=.40\textwidth]{./14_Michelson/images/M_youngish_1887.png}  
    \captionsetup{style=figures}
    \caption{Michelson in 1887, around the time of the Michelson-Morley experiment.} 
  \end{center}
\end{wrapfigure}

The work in Potsdam was exhausting and discouraging and so after his
experiment was done, he and Margaret and (now three) young children
explored the German countryside with Albert watercoloring and studying.
They spent some time in Heidelberg where he worked in another lab and
improved his ability to produce half-silvered mirrors. After a pleasant
summer, they went back to Paris (Margaret's stomping ground from her
youth) and Albert spent time in the École Polytechnique where the legacy
of Foucault lived on. The next fall and winter Albert repeatedly failed
to show his skeptical French colleagues that his interferometer worked!
Eventually, he succeeded with relief\ldots which was short-lived. One of
them showed him that he'd made an arithmetic mistake in his ether
publication's analysis which served to reduce the fringe shift. About
that same time, Hendrik Antoon Lorentz (1853-1928,
Chapter\textasciitilde{}\ref{chap:lorentz}) found the same mistake. That
raised the stakes as we will see, Lorentz was the first to begin to
think seriously about what an actual null result might mean.

\subsubsection{Cleveland}

The most significant thing to happen in Cleveland, Ohio before the
installation of the Rock and Roll Hall of Fame was Albert Michelson's
arrival.

When Michelson's time in Europe was complete, his future was uncertain
and so he was delighted to discover that colleagues had interceded on
his behalf to offer him a faculty position at the brand new Case School
of Applied Science in Cleveland, Ohio. (This is now the very fine Case
Western Reserve University.) With a salary of \$2000 per year and \$7500
for equipment, and his graduate education under Helmholtz, he readily
accepted the position, resigned from the Navy, and in 1881
re-established his light-speed measurement work in Cleveland. A
structure was erected for his lab and he reassembled as much of his
Annapolis equipment as he could find. As his daughter pointed out,
``Michelson's experiments had a way of costing far more than had been
originally expected.'\,' He ran out of money and was assisted
by\ldots Newcomb, again. His eventual result of $299,853,000$ meters per
second ($0.02\%)$ precision) stood as the standard for four decades.

\begin{wrapfigure}{R}{.45\textwidth}  
  \begin{center}
    \includegraphics[width=.40\textwidth]{./14_Michelson/images/morley.png}  
    \captionsetup{style=figures}
    \caption{Edward Morley (1838-1923)} 
    \label{fig:morley} 
  \end{center}
\end{wrapfigure}

In 1884 while on a trip to Montreal to attend a scientific conference,
he met Edward Morley (1838-1923) on the train---a senior Western Reserve
University chemistry professor who was good with his hands in a lab.
They struck up a friendship and determined to work together upon their
return. Michelson had the pleasure of hearing his results discussed in
lectures at the conference and Simon Newcomb made sure to introduce him
to all of the attendees of note. As a result he found himself becoming
friends with John William Strutt, 3rd Baron Rayleigh---future Nobel
Laureate and another king of physics who invited him to Baltimore for a
marathon 20 lectures on physics at Johns Hopkins to be delivered by Sir
William Thomson, the future Lord Kelvin. One of Kelvin's emphases was
the elastic properties that the ether must have for the planets to move
it aside as they pass. Thomson paid no attention to Maxwell's
electromagnetic theory as Hertz was still three years away from his
experimental confirmation in Helmholtz' lab.

Michelson had given up on the ether measurement, believing it to be a
failure but in Baltimore Rayleigh persuaded him to try again and he and
Morley resolved to do that experiment together and to use an
interferometer as the device in Main Hall on the Case campus. With
modifications designed to mitigate the problems of the Potsdam effort,
surely, that would yield a positive result.

As a warm-up they decided to try to repeat Fizeau's 1851 experiment that
suggested that the ether is dragged, but with better engineering than 30
years before. (We'll look at Fizeau's work in
Chapter\textasciitilde{}\ref{chap:lorentz}.) They nearly got the
experiment assembled and ready for data when the first of a series of
events happened.

Events that launched a three year period of triumph and disaster.

Morley wrote:

\begin{quote}
``I can only guess at the stresses which brought about his illness.
Overwork---and the ruthless discipline with which he drove himself to a
task he felt must be done with such perfection that it could never again
be called into question.''
\end{quote}

Michelson wasn't sleeping, nor eating. He'd been a tennis champion on
campus, but now only worked. Eventually he collapsed and on September
19, 1885 at the age of only 33, Margaret had him committed to a nerve
specialist in New York. Again, from Morley:

\begin{quote}
\ldots{} Mr.~Michelson of the Case School left week ago yesterday. He
shows some symptoms which point to softening of the brain; he goes for a
year's rest, but it is very doubtful whether he will ever be able to do
any more work. He had begun some experiments in my laboratory, which he
asked me to finish, and which I consented to carry on.
\end{quote}

What happened next is astonishing. He recovered in two months and wrote
to Morley to inquire as to the experiment and learned that Case
University had hired his replacement! It gets worse.

His doctor wrote:

\begin{quote}
\ldots{} his {[}Michelson's{]} wife has urged me to shut him up in an
asylum which I promptly refused to do. Mr.~Michelson is one of the
brightest men of this country if not of the world in his chosen study.
He is an accomplished man, very popular with those who know him\ldots{}
Professor Michelson's most temperamental fault is a tendency to
emotional acting, but I cannot say that it is unduly expressed, or that
he ever acts without proper and adequate stimulus\ldots{}
\end{quote}

Fortunately, he recovered by December and returned to try to piece
together his career and his marriage. He struggled with the knowledge
that Margaret tried to commit him to an asylum against his will and as a
result their marriage was troubled until it ended 13 years later. Upon
returning to Cleveland, Michelson moved himself into his own quarters in
their large house and by many accounts, his personality seemed to change
after these two betrayals: by his wife and his university.

While healthy and ready to resume his research, the Case Board of
Trustees hadn't done their worst: They indicated that they would be
happy for him to return to the faculty, but he'd have to take a
considerable cut in his salary since they had hired his replacement for
the year. Michelson had to pay for his own stand-in.

In any case, after another desperate infusion of funds, he and Morley
completed their first experiment and confirmed the Fizeau result: the
ether seems to be dragged along with the Earth. He was urged by many
then to repeat the Potsdam experiment with better precision as the
ether-chaos was unbearable for the community. Life settled down for
Michelson. Still bruised, he and Margaret worked towards some measure of
reconciliation. He played tennis and painted and thought about how to do
Potsdam better. But the Universe was not done challenging him yet.

Sometime between midnight and 2AM on October 27, 1886 Main Hall on
campus spectacularly exploded. In the aftermath, Michelson and Morley
were able to salvage much of their apparatus and they reconstructed it
in Morley's, now cramped, Western Reserve chemistry lab. That's when it
got serious. They set out to reduce as many of the systematic
uncertainties that the Potsdam experiment encountered and succeeded.

\subsection{The ``Michelson Morley Experiment''}

What followed during the summer of 1887 is arguably one of the most
important experiments in the history of physics, the ``Michelson-Morley
Experiment.'\,' The issue was to repeat the Potsdam work, but improve
the accuracy by mitigating the drawbacks of Michelson's original design.
They tried to damp the vibrations that plagued the earlier measurement
by building the new apparatus on a huge, heavy sandstone slab that
floated in a donut-shaped channel of mercury---a dangerous environment,
not allowable today. This isolated it vibrationally and allowed the
experimenters to keep the whole instrument in constant, smooth rotation,
slowly, so that the directions of the arms are constantly and uniformly
changing with respect to the ether direction. Now all they needed to do
was observe \emph{any} shift in the fringe positions. That would
eliminate any potential bias and it relieved him from the disruption
that rotating his Potsdam apparatus by $90^\circ$ might have caused.

\begin{figure}[htp]
\centering
\includegraphics[width= \linewidth]{./14_Michelson/images/MM_photo.png}
\caption{The Michelson-Morley apparatus on its huge concrete, rotating slab.}
\label{fig:MMphoto} 
\end{figure}

Furthermore with high quality mirrors the two $L_1$ and $L_2$ light
paths were increased by reflecting them back and forth to an effective
overall length of 11 meters---more than a factor of 10 longer than
Potsdam---greatly improving the precision as well. Remember that the
tiny shift in optical length is proportional to the sum of the lengths
of the two arms, so that factor of 10 is significant.

\begin{figure}[htp]
\centering
\includegraphics[width= 0.8\linewidth]{./14_Michelson/images/MM_Case.png}
\caption{Plan and perspective engineering drawings }
\label{fig:MM} 
\end{figure}

So on six days in July of 1887 they did their experiment walking around
the circle looking into the eyepiece all the while in 30 minute shifts
each. Figure\textasciitilde{}\ref{fig:fringe} shows their results:

\begin{figure}[htp]
\centering
\includegraphics[width= 0.5\linewidth]{./14_Michelson/images/fringes.png}
\caption{As they rotated the interferometer, if the speed of the Earth relative to a stationary ether were real, then they would expect to see the result shown as the dashe curve. The broken solid lines is what their results showed. }
\label{fig:fringe} 
\end{figure}

The vertical axis is the amount of fringe shift in fractions of the
wavelength of the light. The sine-wave curve is what they would expect
to see as the apparatus rotated through a circle based on the Earth's
speed and a stationary ether, \emph{but they drew it in the plot reduced
by a factor of
eight}.\footnote{This is not always appreciated when Figure\ \ref{fig:fringe} is reproduced.}
The sort of sad, flat curve is what they actually measured. By reducing
the expected curve, the dramatic difference with the expectaion---and
the tiny flatness of their result---isn't as prominent as it should be.
This really is zero: no effect is seen. It's the most important
measurement of zero, well, ever.

In August, 1887, Michelson wrote to Lord Rayleigh who had encouraged him
to return to the ether experiment:

\begin{quote}
``The Experiments on relative motion of Earth and ether have been
completed and the result is decidedly negative. The expected deviation
of the interference fringes from the zero should have been 0.40 of a
fringe --- the maximum displacement was 0.02 and the average much less
than 0.01---and then not in the right place.

``As displacement is proportional to squares of the relative velocities
it follows that if the ether does slip past {[}the Earth{]} the relative
velocity is less than one sixth of the Earth's velocity.''
\end{quote}

For Michelson it was a failure. Either the ether moves with the Earth or
there is no ether. Or something else. Neither Michelson nor anyone could
imagine that the ether didn't exist. And even after Einstein's dismissal
of the ether on different grounds, Michelson couldn't get rid of it
during the rest of his life.

After their result became public, the physics world began to pay anxious
attention. An explanation was needed. But he never liked that result and
was discouraged enough to abandon their original run-plan to do the
measurement at different times of the year, and presumably different
angles with the ether.

He was done and he never returned to this experiment again.

\subsection{Michelson and Chicago}

By 1888 Michelson had become unhappy at Case---his illness, Case's
response, the fire and the refusal to rebuild his lab, and trouble at
home weighed on him. But that still malicious universe wasn't yet done
with Michelson. The family was to suffer through two more calamities in
1887. A cook actually robbed them of their jewelry and other valuables
(which were recovered in another town). And, in later in that same year
a maid accused Michelson of sexual assault actually leading to his
arrest at home with headlines in the paper! Blackmail had been demanded
and Michelson, Morley, a lawyer, and the Cleveland police actually set
up a sting operation to get the perpetrator to expose her plot
exonerating Michelson. Quite another year in Cleveland.

So he was ripe for the picking. When Clark University was formed in
Worcester, Massachusetts and started recruiting scientists in 1889,
Michelson jumped at the chance to restart his program as the first Chair
of Physics with finally adequate financial and technical support. In
retrospect, Case had made a terrible mistake.

Off they went to the New England countryside. But after a promising
start, it wasn't a match made in heaven for any of the talented faculty
recruited to Clark. By 1892, Michelson and 12 of the 16 scientists on
Clark's faculty resigned in unison because of an unbearable meddling by
the university president who was on an entirely different course from
the founder and financial benefactor, Jonas Clark. It was a mess. Today,
Clark University is a thriving institution. But another one owning the
distinction of losing Michelson. This time to the new University of
Chicago in 1892, along with the 11 others from Clark. The University of
Chicago promised big and delivered.

\subsubsection{A Meter}

Michelson's arrival in Chicago was delayed. The International Bureau of
Weights and Measures in Paris recruited him for an important job:
determining the most precise length of the standard meter. The French
metric system relied on a platinum bar housed in Paris which defined 1
meter according to the original 1791 definition: 1 m = one 10-millionth
of the distance from the north pole to the equator on a meridian passing
through Paris. More precision was needed since the Earth is a
non-spherical, geologically active object---it's not great as the basis
for a standard length. And, even though there was a
\texttt{standard\textquotesingle{}\textquotesingle{}\ platinum\ bar\ kept\ at\ a\ controlled\ temperature\ in\ Paris,\ each\ nation,\ even\ cities,\ had\ their\ own\ copies\ of\ the\ original\ standard\ meter.\ So\ there\ were\ lots\ and\ lots\ of}meters'\,'!\footnote{Also, there was real concern that were a war to break out that the unique platinum bar could be destroyed.}
Sir Humphrey Davy and Maxwell suggested a standard which could be
independently replicated using a natural phenomenon of some sort: the
wavelength (for length) and frequency (for time) of light.

One of the outgrowths of the Michelson-Morley experiment at Case
(Western!) was the realization that the interferometer could be used for
other purposes. For example, by making one of the arms moveable and with
a careful micrometer measurement of just how far it moves, one could
watch the interference fringes change place, a half-wavelength at at
time. By marking where one peak was, changing the distance of the
movable mirror would march the peak across the eyepiece and when a
trailing peak lined up at the origin spot again, the lengthening would
correspond to one half of a wavelength. So, one could precisely
determine the wavelength of spectral lines of various light sources. In
1887 they proposed using interferometry as the tool for precisely
measuring the meter and proposed that the spectral lines of Sodium light
might serve as the source. (Sodium vapor emits a bright pair of yellow
emission lines.) Then they decided Mercury's green line would be
suitable, but discovered that Mercury's line was actually quite
complicated---many lines. So they actually made a discovery about the
element Mercury! Of course they could then measure the spectral lines of
other elements an important addition to the nascent science of
spectroscopy.\footnote{They and others became less interested in the interferometer for this purpose and it went out of style. Only to be resurrected in the 1950's as "Fourier transform spectroscopy."}
They kept at it and found that the red Cadmium spectral line
($\lambda = 6,438\; \AA$ where an Angstrom is $10^{-10}$ meters) was
singular and could become a calibration point.

That's what the International Bureau of Weights and Measures wanted.
They invited Michelson to come to Paris and find an emission-line
standard for a meter. This he did with characteristic precision and
accuracy with a result that lasted for four decades. After being
repeated in 1905, two years later the standard meter became
1,553,163.5.180 wavelengths of that Cadmium red line's wavelength with
an uncertainty of 0.08 parts per million. This measurement was
referenced as a part of the justification for Michelson's Nobel Prize in
1907.

When his work was done, he reported to duty at the new University of
Chicago. Margaret bought a house on the East Coast and his family didn't
join him for a while.

\subsubsection{University of Chicago}

The University of Chicago's was born out of the commitment of a handful
of private (wealthy) citizens with a vision of a world-class research
university. The United States' university system, and so its scientific
expertise and training, was rudimentary compared to that of Europe's and
Marshall Field and other Chicago businessmen were determined to compete.
The new Ryerson Physical Laboratory was completed in 1894 and Michelson
and others moved in. Students who could pass the difficult entrance
examinations came from all over the world. It must have been a heady
time as the new faculty knew that they were participating in something
special in the Unites States. He was to spend the next 40 years there.

The next couple of years were replete with honors: the Société Française
de Physique, the Royal Astronomical Society, the Cambridge Philosophical
Society, and the Société Hollandaise des Sciences. But they were not
without heartache as well.

In 1897, the Michelson's shocked the tight-knit faculty when Albert
moved to a hotel. Margaret sued for divorce and he agreed to support his
three children (Albert Heminway, Truman, and Elsa) with \$10,000. The
court proceedings were humiliating as the children had been trained to
describe cruelty at his hands in their upbringings and he vowed to never
see them again.

While his divorce was still pending, Michelson met Edna Stanton, the
daughter of a former diplomat to Russia (she lived there for 12 years)
and a German mother. She was radical and a free-spirit\ldots and 20
years Albert's junior. Nonetheless, they courted, married in 1899, and
subsequently had three children. (One of those daughters was Dorothy
Michelson Livingston, the biographer of her father \citealt{dl21})

\begin{wrapfigure}{R}{.45\textwidth}  
  \begin{center}
    \includegraphics[width=.40\textwidth]{./14_Michelson/images/michelson_nobel.png}  
    \captionsetup{style=figures}
    \caption{Michelson around the time of his Nobel Prize.} 
  \end{center}
\end{wrapfigure}

His time at Chicago was nonetheless productive and pleasant. His
students enjoyed him. He played tennis regularly and had a professional
and well-staffed laboratory and was able to watch his new family grow
up. He was in demand around the country and the world and took on new
and engaging experiments with enthusiasm and his characteristic talent
for precision optics. The projects he took on included:

\begin{itemize}
\tightlist
\item
  The measurement of the radius of a star---initially the red giant,
  Betelgeuse using interferometry---essentially capturing light with two
  telescopes and letting them interfere. In effect this increases the
  resolving power (or effective size) of any single telescope by a
  considerable factor. This is a standard technique especially in radio
  astronomy today.
\item
  He continued his speed of light measurements and was engaged in a
  long-baseline experiment in California when he passed away.
\item
  He created and perfected the creation of very precise diffraction
  gratings with an engineered instrument in the basement of the physics
  building. They were the best in the world and required weeks of
  patient, delicate fabrication.
\end{itemize}

Oh. And he won the Nobel Prize in 1907, the first American to do so and
the first Jew to win the physics prize. The award was not for the ether
experiment, as Special Relativity was still only a year or so old and
Einstein was still unknown. Michelson's award reads: ``For his optical
precision instruments and the spectroscopic and meterological
investigations carried out with their aid.'\,'

Michelson died in 1931 at the age of 79 in Pasadena, California where he
was engaged in a multiple experiments to improve the precision of the
determination of the speed of light. He and Edna had retired from the
University of Chicago and moved the previous year so he could focus on
the culmination of nearly a half century of steadily improving this
measurement. He had had multiple operations for prostate and intestinal
disease with multiple infections (before the time of antibiotics), often
writing and working from a bed. This final experiment involved the
construction of an evacuated tube about a mile long in the mountains of
Irvine Ranch near Santa Ana, California. With multiple reflections, the
path length was effectively more than 8 miles. His biggest hurdle? The
whole Earth. By the time he ended his life's work, his precision battle
was against tiny geological shudders in the crust of a major mountain.

Today the determination of the speed of light is exquisitely precise
using lasers: and for many years the technique is still essentially the
same one that Michelson pioneered while he was in the Navy. That's
changed in the last 50 years as is described in
Section\textasciitilde{}\ref{interferometer} in
Section\textasciitilde{}\ref{more_Michelson}. Likewise, his original
notion of measuring the size of a star using two small, but widely
spaced optical receivers and letting the interfering pattern determine
the angular size of the star is now the standard technique of optical
and radio astronomy for huge telescopes around the world. Again, find
this story in Section\textasciitilde{}\ref{michelson_astronomy}.
Finally, not onl is the Michelson Interferometer a standard bench
instrument in optics labs everywhere it is the principle deployed in the
LIGO experiment that has recently discovered Gravitational Radiation and
has initiated a whole new branch of astronomy by studying the collisions
of neutron stars and black holes. More below.

A nice side-story to the Nobel award was in the crowd who surround him
after his Nobel lecture in Copenhagen. A young man approached him to
say, ``You don't know me. I am your son.'\,' The bitterness of the
divorce from Margaret left Albert estranged from his two sons and
daughter 11 years previously. Young Albert had graduated from Harvard
and at 29 was the American consular agent at Charleroi, Belgium. He'd
been in Italy at a meeting, saw that his father had won the Prize and
was bound for Stockholm and so Albert Junior traveled north to meet his
father. Michelson abandoned his ceremonial and social plans and spent
time with his first-born son.