Dark Matter

Contrary to what you might think, astronomers are not interested in how much a telescope can magnify an object. In most cases, the objects we are viewing are so far away that we wouldn't be able to see them even if we magnified them thousands of times. The strength of a telescope is how much light it can collect in a given amount of time. The governing factor for this characteristic is the diameter of the mirror used in the telescope. The Keck telescopes in Hawaii have 10m mirrors which enable them to see objects in the sky that are literally thousands or even tens of thousands of times dimmer than you can see with the naked eye. If it is giving off even the slightest bit of light, Keck can see it.

But there's a problem with the Keck observatory, and with all the other telescopes in the world (and those floating above it). To understand it, first we need to imagine a few everyday occurrences.

First, imagine that you are stirring a glass of ice water with a straw. As you spin it faster and faster, a whirlpool begins to form in the middle of the glass. In the very center, the ice cubes are spinning around very quickly while on the outside, they spin much slower. This is a phenomenon known as differential rotation: the further from from the center, the smaller the rotational speed.

Second, imagine a record on a turntable (if you can even remember what they looked like). Let's say that it's a record you aren't particularly fond of, so you don't mind putting a few thumbtacks into it. You put one directly in the center, one halfway between the center and the edge, and one on the very edge of the record. When the record turns, which thumbtack is moving the fastest? Since the every point on the record is connected (i.e. it's solid), every single point makes one revolution in the same amount of time. The thumbtack on the edge has to travel the furthest (it has the largest circle to go around), but it has the same amount of time to do it as the other thumbtacks with smaller distances to go. Thus, the further out from the center of rotation, the faster the object is moving.

Lastly, imagine the Milky Way galaxy. You are probably imagining a big, spinning, spiral cloud of stars like this one here (though this is the Andromeda galaxy, ours probably looks very similar). How do you think it spins: like a record or like a glass of water with ice?

The answer, confusingly enough, is neither. At first, we thought that the galaxy would exhibit differential rotation. But the further out to the edge of the galaxy we observed, the more surprised we became to find that most stars are moving at the same speed. This means that no star orbits the center of the galaxy in the same amount of time (much like ice in a glass of water), but each has the same velocity (which is like nothing we've ever seen before).

So... why?

The frustrating answer is that we have absolutely no idea. The simplest explanation would be to say that the galaxy is much more massive than we originally thought. If the outer edges of the galaxy were permeated with an extremely large amount of mass, the physics works out to predict the so-called flat rotation curve. But therein lies another problem. We can't see anything out there. The Keck sees nothing, Hubble sees nothing. All we see is the stars with nothing (or next to nothing) in between. The stars we see make up only 20% of the mass that our calculations tell us need to be there! The billions of stars out there in our own galaxy, each weighing in at a trillion billion billion kilograms, make up only one-fifth of the total mass of the Milky Way. The rest is stuff we can only call Dark Matter.

Frankly, we don't have the slightest idea what it is. One theory talks about MACHOs (massive compact halo objects) and another, perhaps inevitably, about WIMPs (weakly-interacting massive particles). But all our speculation is just that. It's an almost frightening thought that 80% of everything that's out there has never been seen even by the most powerful telescopes in the world. We know so very little about the universe, about its composition and its behavior. The only thing we seem to really know for sure is that we're missing out on most of it.

Relativity

We've already discussed how units of time differ in importance depending on who is observing what and when they're observing it. However, more than relative perception, time is, in very fact, relative to the observer. That is, the speed at which a clock ticks depends on who is watching it. The overarching theory being described is called special relativity and was introduced in 1905 by Albert Einstein (while he was working as a patent clerk, no less).

Imagine that you invent a machine that, when sitting on a pitcher's mound, could throw a baseball at exactly 100mph every time. If you put that machine on top of a car traveling at 60mph and then shot a baseball, the ball would be moving at 160mph as a police officer would calculate from a parked car on the side of the road. However, to the person in the car, the ball still looks like it is traveling at 100mph away from him. In other words, the velocity of the baseball depends on who is watching it move. Specifically, it depends on how fast the observer is moving.

We call this principle Galilean Relativity since it was first described by Galileo. There was something that Galileo missed, however, which has to do with the speed of light. It's not his fault, really. He tried to measure the speed of light by sending an assistant to a nearby hilltop. The idea was that he would uncover a lamp and that his assistant would uncover his own lamp when he saw the light from Galileo's. The distance between the two scientists divided by the time between the unveiling of the two lamps would yield the speed of light. However, since light can circumnavigate the earth seven times in a second, he was grossly outmatched. Galileo's conclusion was that light goes really really fast ("if not instantaneous, it is extraordinarily rapid"). Little did he know the fire he was playing with.

Special relativity is founded on the principle that light travels at 3.00×10^{8 m}⁄_s (we'll call it c from now on) for all observers. Unlike the baseball, if you are in a spaceship traveling at half that speed (^c⁄₂) and you shoot a beam of light at a "stationary ship", the ship would see the beam of light approaching at c (not at c + ^c⁄₂ as you might expect).

That may seem like an inconsequential—albeit strange—fact, but it ends up being extremely important. That means for someone traveling at 99% of the speed of light who shoots a beam at a "stationary" observer, both the moving and the stationary observer perceive the beam of light traveling at c. If you think about that fact in such an extreme case, some discrepancies seem to arise.

Consider the perspective of the moving ship. If the beam of light is really moving away from it at c, it will pass the stationary observer at some time in the future (we'll call that time t₁). In that amount of time, the beam of light will be some distance away from the moving ship (which we'll call x₁). Since light travels very quickly, you can imagine that the distance between the moving ship and the light beam at t₁ is pretty big (even if it only took a second, the light would be 186,000 miles away).

Now consider the perspective of the stationary observer. He sees the light traveling toward him at c and the ship traveling toward him at 99% of that speed. From his perspective, because the two velocities are so close, the distance between the moving ship and the light beam (in his perspective, x₂) will appear to be significantly less than x₁.

In the car/baseball example, this is like saying that when the machine shoots the ball, the person in the car sees it moving away from him at 100mph while he is traveling 60mph, but the police officer also thinks the baseball is traveling at 100mph (not 160mph). In his perspective the ball is only moving 40mph faster than the car. So when it hits the police car, the baseball has spent the same amount of time traveling away from the moving car at 100mph in one perspective as it has traveling away from the car at 40mph in the other perspective. The two distances, x₁ and x₂, aren't the same!

That sounds ridiculous for a car and a baseball, but that's exactly what happens with light. The problem is that only one thing happens. That is, the light beam only hits the stationary ship one time, and the moving ship would only pass the stationary ship once. But if the distance between the beam and the moving ship is different, it seems like the moving ship would pass the stationary ship twice (once in one perspective then later in the other). Obviously that's impossible. At the end of the day, the ship and the light can only pass the stationary observer once. So when does it happen, and where?

This is the problem that relativity solves. When talking about relativity to my students in their introductory physics lab, I discovered that they couldn't answer a simple yet important question: In relativity, what is relative? For instance, in Galilean relativity, we could say something like, "Relative to the police car, the baseball is traveling 160mph; velocity is relative." So, in special relativity, what is relative?

The answer is the genius of Einstein's theory and is two-fold. It's pretty clear that distance, or space, is relative since each ship perceives the separation between the moving ship and the beam of light to be different. If that's true, then for the light to pass the stationary ship exactly once without repeating itself, then each ship must perceive the passage of time differently. That is, for the stationary ship, the distance between the moving ship and the beam of light is small, so the light and the ship pass him in some small amount of time (for the sake of argument, let's say that the clock on the observer's ship ticks away one second between the time that the beam of light hits him and the time that the ship passes him). But in the perspective of the moving ship, the distance between itself and the beam is much larger, which means that it will take much longer than a second to get to the observer once the beam of light hits him.

Remember that two different things cannot happen. If the stationary observer saw exactly one second tick away on his clock, the moving observer absolutely must see only and exactly one second tick on the same clock. The only way that's possible is if the clock ticks slower for the moving observer so that the pendulum swings only once in what must be for him an amount of time greater than one second. In other words, time is relative also.

And that's the answer to the question I posed earlier. In special relativity, what is relative? Time and space. Depending on how fast you are moving and what you are looking at, the distance between two fixed places and the time it takes to get there at a constant velocity is different. For the moving ship in our example, he sees the stationary clock tick away only one second, but he would see an identical clock on his moving ship tick away several seconds. For either observer, the distance between the beam and the ship that we've called the "moving" ship (that's relative, too) is different.

We are so accustomed to thinking that space is constant. If I drive 10 miles to work today, then when I go back home by the same route, I will travel 10 miles. A second is a second is a second, right? Well, not exactly. Time and space are as changeable and as capricious as the velocity of the baseball. It's 160mph to the stationary police officer, 100 mph to the guy in the car, and an infinite number of other velocities to the various people on the road traveling at different speeds.

The thing that is constant is something called "spacetime", a combination (as the name suggests) of "space" and "time", which were considered to be separate, into one single continuum. We have used spacetime to better understand the universe since it, for the first time, explains the behavior of gravity and light with relative (ha!) clarity.

Time

Time is a concept that's difficult to think about. We divide it into manageable pieces like seconds, minutes, and years, but those divisions are man made. Time itself, as an entity, really has no divisions; it's smooth (as opposed to the percussive passing of ticking seconds in a watch) and unending. Something that time isn't, however, is constant. For understandable reasons, most people assume that a second is a second is a second and that it will never change. Time seems to be the one thing we can count on to always be the same. But it's not true.

First of all, our perception of time, as well as the importance of a given unit of time, varies depending on the system being considered. To humans, a year is significant enough that we keep track of how many of them we've experienced. Years indicate our expected development and position. Yet, babies' ages are frequently counted in months. Their development is acute enough that simply saying "She's about a year old" isn't specific enough. Six months is not the same as nine for a baby, but no one takes note of the difference between a person who is 57 years and 6 months old and their "different" age three months later.

Even then, humans assign significance to different units of time depending on their circumstances. Seconds of age mean nothing, but seconds of a race make the difference between the winner and the loser. We count months of pregnancy, semesters remaining before graduation, decades of fashion and trends (the 60s, the 70s, etc.), hours of sleep, minutes to get ready, and years of experience. Each accepts a unit of time that makes sense.

Physics works in very much the same way. In particle physics, a second may as well be an eternity for particles which exist for millionths or billionths of seconds before decaying. Waiting for a second is allowing for so much change in a sub-atomic system that it would be like examining a 90-year-old man and trying to determine how heavy and tall he was at his birth.

When the universe was a "baby", smaller units of time had significantly more meaning than they do today. We recognize five major milestones in the development of matter before the first second of the universe transpired. In the same way that a month differs in the consideration of the life of an infant, billionths of seconds mattered in the beginning of the universe because even a billionth of a second could double its life. And yet today, not even a second means anything to the universe as a whole. For that matter, days, years, and even millennia are inconsequential moments in the universal perspective. In 100,000 years, 99.9% of all of the stars in the universe will be as identical as a man turning 57 is to himself a day after his birthday (even though they burn hundreds of billions of tons of hydrogen each second). Only when we start talking in millions (and in most cases, billions) of years do we begin to notice the first inklings of significant change.

So, certain lengths of time are only important if they correspond to the length of time it takes for something to change. Even then, in a single system (like that of the universe, as explained above), the important unit of time changes with the passage of time. It depends on who is measuring, when he's measuring, and why he's measuring.

And even then, there's more to the story. Perception and importance aside, a single unit of time differs depending on the observer. With absolutely no metaphor or figure of speech employed, the length of a second (or any other unit of time) depends upon the velocity of the person observing the thing experiencing the second. The principles behind this fact are all contained in Einstein's explanation of time and space which is known generally as (trumpet fanfare) relativity and will be discussed in the next installment.

Circumstellar Masers

The image above is called the Hertzsprung-Russell (H-R) Diagram. In a very simple synopsis, it relates the temperature (and thus, the color) of stars with the amount of light they put out. As you can see, the higher the temperature (and the bluer the color), the greater their total luminosity (energy output per unit time). The long, slightly bent line in the center is called the "main sequence" and is where we find stars in the middle of their life.

If you look at the top corner, though, you'll see two clusters: one a straight line labeled "supergiant" and the other a hockey-stick-shaped line labeled "giants." Both of these branches of the H-R diagram have to do with the death of stars. Everyone is generally familiar with super nova star deaths, where a star explodes in a violent output of energy and is no more. However, most are unfamiliar with the less extravagant, more common method of star death.

Small stars (all stars with a total mass less than about 8 times the mass of our sun) are too small to explode. Instead they swell up. At the end of their life, all of the hydrogen they were so used to fusing into helium is depleted. With no radiation pressure to keep it at the size it was, the star contracts due to its immense gravity, which crushes the helium at the center. Suddenly, the density becomes so great that the helium core starts to fuse the helium into carbon. An enormous amount of energy is released, pushing the edge of the star to an unprecedented radius. In fact, when our sun starts to swell into a red giant, its radius will extend until its surface is at about where the earth is now (about 93 million miles)! The so-called giant branch on the H-R diagram shows us that as stars leave the main sequence in this manner, their luminosity increases by several orders of magnitude (as a result of the brightly burning helium). The star gets so big that its outer layers star to peel off and expand into space, leaving a very hot chuck of carbon ash in the middle (called a white dwarf star) and forming what we call a planetary nebula (an example of which you can see here).

Some stars, however, don't quite make it to that stage without a fight. They get so big that the helium fusion at the center shuts down. As before, with no outward radiation pressure, the star contracts and crushes the helium core until it starts fusing again. This cycle repeats and repeats in a process known simply as "variability." The star increases in luminosity and decreases again in a matter of days or years (depending on the star) but with such regularity that we can spot them a mile away (ok, more).

Even then, a few layers of gas on the very outer edge of the star manage to escape and expand in a sphere around the star. As you would expect, heavier molecules expand slower and lighter ones move faster; we soon see a separation of individual gases. The fascinating thing about these expanding envelopes is that they quite naturally form lasers.

All of the lasers on earth are man-made. A study of the Einstein coefficients and some fancy math told us that they were possible and we gave it a shot. Eventually we created the right conditions to make a concentrated beam of stimulated emission. Looking into space, however, we can see gigantic (some can be almost 5 billion miles wide!) stellar lasers (which we call masers because the photons coming from them are microwaves) which are continually fueled by the variable star in the center.

These huge masers emit in all directions, which means that when we look at variable stars, we commonly see maser emissions (if we're looking for the right wavelength with our telescope). In other words, all over space there are absolutely enormous laser pointers shining directly at the earth. Just another proof that the universe is way cooler and more complicated than you thought before.

The Foucault Pendulum

Have you ever seen one of those pendulums that swings back and forth but over the course of a day or so makes a complete circle? It's called a Foucault Pendulum (and please, people, it's pronounced /Foo-coh/ not /Fow-cult/). I'm going to tell you how it works.

Get some thread and tie a relatively heavy object (a ring, for example) to one end to make a pendulum. Suspend it from your car's rear-view mirror on the windshield. Before you make a 90° turn, start the pendulum swinging so that it swings directly toward and away from the windshield. Execute 90° turn. The pendulum is now swinging side to side towards the passenger- and driver-side windows. BAM. Foucault pendulum.

No, seriously. This is exactly the same idea, but the thing that's turning is the earth. If you get a really heavy pendulum and have it swing with no friction, it's rotational inertial is very high (i.e. it is very hard to get it to start travelling in a circle). So when the earth rotates, it tends to swing in the same absolute plane as when it started. In the car example, if the windshield-rear-window plane is North-South, then when your car turns, the pendulum is still swinging N-S but the plane of oscillation relative to the car has rotated 90°. The car has, in effect, turned around, above, and underneath the pendulum which is still swinging in its original plane.

Interestingly enough, the time it takes for a Foucault pendulum to complete a full revolution in the relative frame (i.e. when it looks like it's swinging the way it started out to observers on earth), varies depending on latitude because of the Coriolis "force" (just a side note here. Please never ever refer to the Coriolis "force" as the thing that makes toilets flush in the opposite direction south of the equator. Hearing that drives me crazy). Simply stated, if you stand on the north (or south) pole, you turn in a full circle once a day (just like everywhere else), but your linear velocity is zero (you just spin around in a circle because you're standing on the axis of rotation). Standing on the equator, you still make one full revolution per day, but now you're 6000 km away from the axis of rotation (thus, your linear velocity is huge. Think of how the middle of a spinning record and the edge of a spinning record both go around at the same frequency. For this to happen, the outside point must be moving much faster than the inside point. Same idea as a marching gate turn (for parades); the inside guy just rotates in place, but the outside guy tears a hole in his pants taking long strides to keep the line straight).

In other words, there is a velocity gradient between the poles and the equator, meaning that as you get closer to the poles, your linear velocity decreases. We don't notice it because frictional forces (our feet on the ground) keep us in the same relative position. A free-swinging pendulum, however, swings above an earth with faster linear velocity at (minutely) lower latitudes and into slower linear velocity at higher latitudes. The earth is travelling faster under the pendulum when it is further to the north. So, think of how a tank turns. If both treads move at the same speed, it goes straight, but if one tread moves faster than the other, it turns. So with the pendulum, when the earth under the pendulum at its northern-most swinging point moves slower than the earth under the pendulum's southern-most point, it appears to turn in place (but we know it's really the earth doing the turning). Now on the equator, the pendulum feels a Coriolis "force" when it swings north, but then the exact opposite "force" when it swings south, so it stays in the same plane. At my latitude (40° N), the pendulum takes a little more than 37 hours to make a full revolution relative to an observer. At the north pole, it takes exactly 24 hours.

So how do they make a pendulum swing without friction? Well, they don't. However, they can counteract the force of friction using a (patented Newton's first law) equal and opposite force (Ok, I know that using the words equal and opposite sounds like the third law, but the law that's really in effect here is that if the net force on something is zero, it doesn't accelerate—first law). At the top of our Foucault pendulum at BYU there is a metal disc (Radius ≅ 3 in) that swings into an electromagnet once per oscillation. At the peak of the swing, the magnet turns on momentarily, turning the disc and undoing the frictional force from the swing. So, we can't really make a frictionless pendulum, but we can make it act like one. In any case, the electromagnet doesn't cause any acceleration, it prevents (or counteracts, rather) negative acceleration.

You may be wondering why I keep putting quotes around the word force when it's next to the word Coriolis. I'll tell you. It is not a force. It just looks like one. Imagine if you sat in a room with a flat floor with no windows. The room is actually on a turntable and spins around in circles (but so slowly that you can't feel it). To you it seems like a normal room, but if you set a ball on the perfectly flat floor, it would start to roll towards whichever wall it was closest to. In your Newtonian-trained mind, you would think "Hey, the ball accelerated. There must be a force on it." But you would be wrong because you are now in a non-inertial (accelerating) reference frame where Newtonian physics doesn't apply. The thing that's feeling the force is the frame of reference itself. The ball rolls because the floor is turning (accelerating by changing direction, not speed) underneath it. Hey! That sounds like a Foucault pendulum. Yep. The "rotating room" we are in is the planet earth. It's so big that we don't notice it spinning (except for the sun, moon, and stars) but sometimes we find things that seem to violate physics. They don't. Trust me.

Kepler's Laws

Astronomy has come a long way in the last several thousand years. We are able to locate celestial bodies with unprecedented precision and the light that we analyze from these sources tells us more information about them then we could have ever expected. However, when considering the most talented astronomers in history, the originals make a fairly convincing argument without even considering the immense effect of their studies on future astronomers. Tycho Brahe made the most accurate measurements in history with extremely rudimentary instruments. More amazingly, his assistant Johannes Kepler used these instruments and stated three laws of planetary motion that still stand. It's important to realize that these laws came not from any mathematical treatment as most do; rather they are a product of extraordinarily accurate measurements and deduction.

Kepler's First Law

The orbit of every planet is an ellipse with the Sun at a focus

Before Kepler, it was thought that planets traveled around the Sun in a perfect circle. Instead, the Sun resides at one of two foci. The discovery of elliptical orbits helped to explain the motion of and interaction between planets as well as comets and asteroids.

Kepler's Second Law

The line joining a planet and the Sun sweeps out equal areas during equal intervals of time

This law is a little more difficult to understand at first glance. It is generally believed that the Earth travels at the same speed all the time, but this is a misconception. Because the planet orbits the Sun in the shape of an ellipse it is not always the same distance from the Sun. And the closer it is to the Sun, the faster it goes. The picture above depicts two different periods of equal time in the path of a planet. Though the Earth moves farther in a given time when closer to the Sun, the area it sweeps out when a line is drawn between it and the Sun remains constant for that given time. In other words, the two shaded areas are exactly equal. This may seem like a small thing, but it helps us to understand the variable motion of the planet which aids us in calculating what the real time is (which allows us to calculate leap days, leap minutes, leap seconds, etc. which keep Spring on the 21^st day of March).

Kepler's Third Law

The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit

In simpler terms, the only thing that determines the length of a year of a given planet it its distance from the star it orbits. In other words, if the positions of Jupiter and the Earth were switched, they would also switch years. Jupiter would have a year of 365.25 days and Earth would orbit the Sun every 4,331.6 days.

Again, these laws may seem inconsequential, but they are both influential and incredible when you consider their source. It wasn't until Isaac Newton invented calculus that he was able to prove these laws. They were all stated by Kepler from very accurate observation with what we would consider rudimentary instruments. Further, such accuracy has furthered the science of Astronomy in every way (just because knowing the correct behavior of a system yields further discovery). For example, even after applying all of Kepler's laws to the orbit of Mercury, we were still unable to predict the exact position of the planet; we were off by a few fractions of a degree. This was later accounted for by Einstein and presented as a proof of the variability of time for moving bodies in a paper on relativity. So we see yet another example of a small observation later affecting a hugely important physical discovery.

Albert Einstein

b. 14 March 1879
d. 18 April 1955

I will not attempt to explain the contributions that Einstein made to physics in this little biographical sketch. For one thing, I don't understand the majority of what he wrote. For another, I would like to focus instead on his character and life as an interesting and important glimpse into his mind.

Though born in Germany, Einstein did not die a citizen thereof. In fact, he renounced his citizenship for the small price of three German marks and became a naturalized citizen of Switzerland five years later, paying twenty francs. The price of his citizenship notwithstanding, national affiliation was extremely important to him. He both detested and rejected the nationalistic and militaristic government of Germany and embraced the peaceful attitude of Switzerland. To the end of his life, Einstein remained a pacifist, conceding only that military force should be used to combat institutions which "pursue the destruction of life as an end in itself."

He further hated the German educational system which consisted of rote studies and a particular deference to authority. Though it is often stated that Einstein was a poor student, the more accurate statement is that he did not thrive in the stifling classroom being forced into a discipline in which he was not naturally engaged.

In fact, after being rejected from the Zürich Polytechnic Institute, Einstein spent a year in Aarau, Switzerland where he succeeded in a flexible education with a casual teacher who allowed Einstein a liberty of thought that was necessary for his future discoveries. About the necessity of such liberty he wrote that "it is, in fact, nothing short of a miracle that the modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry; for this delicate little plant, aside from stimulation, stands mainly in need of freedom."

His ability to thrive in a self-determined schedule accounts for his eventual success at the Zürich Poly (having been accepted after a second application). He largely ignored his classes, showing up only for the exams which he passed due to the copious notes of his studious friend Marcel Grossmann. After graduation, Einstein found his desired freedom in an unlikely place. He was refused a position as an assistant at the Zürich Poly (perhaps due to some underhanded manipulation by a professor who disliked him) and accepted a job at the Bern Patent Office in 1902 where he was assigned to read and approve patent applications. The job proved useful, however, in that it was not difficult. He spent his spare time theorizing and conducting gedankenexperiemnts (literally: thought experiments) which are designed to prove a principle without actually having to conduct the experiment physically.

Einstein was so successful in this free environment that he published three papers in the 1905 edition of Annalen der Physik each on a different subject. The first, for which he eventually won a Nobel Prize, explained the connection between the photoelectric effect and quantum mechanics. The second paper treated molecular behavior. The third was his inspired explanation of relativity which gave rise to spacetime. To restate for emphasis, during seven years working as a patent clerk, Einstein published—among others—a Nobel Prize winning paper and the foundational paper for the most (culturally) famous development in science.

Inevitably, Einstein was noticed by the scientific community. He subsequently worked in Berlin at the Prussian Ministry of Education with Max Planck (a great scientist in his own right who wrote of him, "All in all, one can say that among the great problems, so abundant in modern physics, there is hardly one to which Einstein has not brought some outstanding contributions.") and at Princeton. But the former was overrun with Nazis and the latter boring yet peaceful enough for him to, as he wrote to the Queen of Belgium with whom he had apparently frequent correspondence, "create for [himself] an atmosphere conducive to study . . . free from distraction."

He was married twice. And though the first marriage failed due probably to a lack of attention to his family in favor of scientific pursuits, he remained supportive of his first wife and children, sending them his prize money after receiving the Nobel Prize in 1921 (two years after his marriage to his second wife, Elsa). Elsa was described as "gentle, warm, motherly, and prototypically bourgeoisie." She enjoyed the fame of her husband's publications and tolerated his absence and distractions.

Notably, Einstein's genius was not happened upon, nor was it easy to obtain. Though none can deny his natural ability in theoretical physics, the secret to his success was work. Though some concepts eventually unfolded before him, others such as his Unified Field Theory never came to fruition. Yet he never ceased his work nor became discouraged. "After all," he wrote, "to despair makes even less sense than to strive for an unattainable goal." Three months before he died, Abraham Pais, one of Einstein's biographers, visited him at home and spoke with him for a half an hour. Einstein had been at his desk working when Pais entered and before Pais was able to leave (a journey of approximately five steps), Einstein was hunched over his desk "oblivious to his surroundings" yet again.

Now, fifty years after his death, Einstein remains one of the most well known names in scientific and even in common history. His developments in theoretical physics, along with those of Planck, de Broglie, Schrödinger and others, laid the groundwork for most if not all of the scientific developments that came thereafter.