% !TEX root = ../_superfluous_book_3.tex \setcounter{chapter}{13} \chapter[Michelson]{\texorpdfstring{The Most Important Zero Ever:\\ \textsf{Albert Michelson} }{Michelson}} testing wrap \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.