December 1, 2003

Kathy Phelan

Math G

Final

 

 

 

Albert Einstein

Final Paper

 

 

 

Submitted:  December 1, 2003

 

by:

Kathy Phelan

 

“I vill a little t’ink.”

Banesh Hoffmann recounting the phrase Einstein used

when he needed more time to think about something;

quoted in French, Einstein:  A Centenary Volume, p. 153

 [from The Quotable Einstein, page 214)

     Most people have heard of Albert Einstein.  His face is recognizable on t-shirts, posters and coffee mugs.  His name is associated with the famous e=mc² formula, the Nobel Prize and his eccentricities.  Some people have called Einstein a genius, others have called him, “completely cuckoo”, J. Robert Oppenheimer, [from The Big Idea, page 95].  When Einstein arrived in America he was treated as a celebrity, a hero and a legend.  He was a complicated man that believed in simplicity.  This paper will help to introduce you to Einstein, but will also introduce you to the concept of how our own world views and perspectives include our perceptions.  Perhaps it will help you to see that to truly understand someone or something else, you must take a closer look at yourself.

     While you read this paper keep in mind that we have a hard time trying to know ourselves, let alone someone else.  So, how do we understand Einstein? (or anyone else for that matter?)  There have been people in my life whom I thought I knew, but then I realized they were not who I thought they were.  Yet, in other situations I have met strangers for the first time and felt like I had known them all my life.  I have no idea what the connection is – only that it is.  While reading and researching about Albert Einstein, I’m surprised by how much more I think I know him as a person…or do I?

 

Albert Einstein - The Person

     Ulm, Germany, where Einstein was born had a curious town motto:  “The people of Ulm are mathematicians.”  [from Understanding Einstein, page 126.] The town adopted this slogan during a period of prosperity.  Presumably, the people of Ulm had to do a lot of calculating to keep track of their income.  Albert Einstein was born on March 14, 1879. 

     His father, Hermann had struggled to make a living for many years.  A year after Albert was born his father’s electrical goods business failed, and the family moved to Munich to live with Hermann’s brother, Jakob.  Here Hermann and Jakob established an

electrical and engineering firm.  Albert’s childhood was unassuming.  He was a dreamy

child and seemed to learn rather slowly.  He attended a Catholic school, where he found

himself the only Jew in his class.  Most of his teachers prided themselves on behaving

like bossy, sergeant majors.  Albert was bored, learned little and developed a grudge

against authority which remained with him throughout his life.  His teachers felt that he

didn’t apply himself as much as he could.  He was also prone to temper tantrums until

he was almost seven years old.  At home his mother made him study the violin, which

he enjoyed and learned to play well – another attribute that remained with him for life.

The quality that drove Albert Einstein as a child was his innate curiosity and sense of

wonder.  Einstein never lost his sense of wonder.  One of the most profound moments

in Albert’s life was when his father brought home a compass to help him occupy his

time.  Albert was intrigued by the magnetic compass.  He needed to know what made

the compass needle swing.  There had to be some hidden force behind it, making it

move, he thought. 

     At the same time, Einstein’s Uncle, “Onkel Jakob” introduced him to algebra.  “It is a

merry science,” he explained.  “When the animal we are hunting cannot be caught, we

call it x temporarily and continue to hunt it until it is bagged.”  [from The Big Idea, page

13.]   Albert Einstein taught himself, paid little or no attention to his teachers and preferred to follow his own interests and do things his own way.  From that, the result was an exceptional depth of knowledge, but it was also accompanied by difficulty with even the most elementary exams.  Regardless, the rumor about Einstein not being good at math, isn’t true.  He was a child prodigy when it came to math and taught himself more about math by the age of 14 than he could ever learn in school.  This is one key to understanding Einstein.  Even at a young age, he felt that people can learn a lot about studying concepts and ideas, but to really understand them, people have to work out the concepts for themselves. 

     Although Albert’s parents were Jewish, they were very liberal about their beliefs.  They followed some Jewish customs, but were relaxed compared to the strict orthodox standards.  Albert was introduced to philosophy by a medical student friend.  Thank God Albert’s parents were liberal thinkers that supported anything that might help expand Albert’s knowledge about the world.  After studying the works of Kant and other philosophers, along with a 20-volume series on science for young people, Albert’s views on religion had changed…drastically.  He was convinced that most of the stories in the bible couldn’t possibly be true and believed that young people were being deliberately lied to by the state.  This conviction laid the groundwork for Albert to question the truth behind many widely held beliefs concerning religion, government, politics, and of course, science.  He became a free thinker in the strongest sense, a quality that would make him many friends and …enemies.  Einstein found many of the stories in the Old Testament to be inconsistent with science and reason, yet he also realized that many people considered the stories to be symbolic in nature rather than historical.  He knew that the important thing was (and is) to respect other people’s beliefs.  No one holds a monopoly on the truth.

     Upon turning his back on religion, Albert devoted himself to math and music.  He loved to play the violin.  In typical fashion, he gave up the regimented mastery of scales and boring musical pieces in favor of teaching himself the music that he liked. 

In 1894, when Einstein was 15 his father’s business failed.  His family moved to Milan, Italy, but Albert was left behind at a boarding house in Munich so he could receive his diploma.  Within six months Einstein had a nervous breakdown and was expelled because his presence in class was “disruptive and disturbs the other pupils.”  Einstein viewed the school as a combination of deceit, irrelevance and boredom.  He wanted nothing better to do than join his family in Italy.  He had never been happier.  He did not attend school, but he did write a paper about the relationship between electricity, magnetism and the ether (the invisible medium that transmitted electromagnetic waves).  On a professional level, his paper had nothing original to say, but it was a remarkable feat for a sixteen year old.  It also showed that he continued to think about magnetism and how it traveled through space (i.e., the earlier compass question). 

     Einstein was becoming aware of his gifted intellect, which outstripped all other students in math and physics, and this gave him a pronounced self assurance.  This, combined with a degree of immaturity, made him appear cocky, arrogant and insolent.

 

Albert Einstein - The Philosopher

“Whatever there is of God and goodness in the universe, it must work itself out and express itself through us.  We cannot stand aside and let God do it.”

From a conversation recorded by Algernon Black, Fall 1940; Einstein Archive 54-834 [from The Quotable Einstein, page 152.)

 

     About 25 centuries ago, a Greek philosopher stated that the only thing anyone requires to be a good philosopher is the sense of wonder.  It is said that this is true for physicists as well - for ideas are the beginning of all physics and without the insatiable curiosity to know what lies behind the veil of nature, we would still be stuck on the evolutionary scale somewhere behind pine trees.

     As we’ve discussed earlier, Einstein had an innate curiosity and sense of wonder.

Almost all youngsters exhibit this child-like quality, but it seems to disappear in most

people with age.  Einstein attributed much of his love for physics throughout his life to

this feeling of wonder, which he never lost.

     The word physics comes from the Greek word physika, meaning “natural things,” or

the study of nature.  It has come to mean a little more than that in the last 300 years, but

in the beginning physics was simply the study of nature.  Where do you start such a

study?  One way is by asking questions, (which is why most physicists are also good

philosophers.)  Physics begins with a question, followed by a long process of hunting

for solutions, some work, some don’t.  Long ago a group of philosophers began thinking

in a new way.  Instead of seeing the world as a playground, they began to apply

reason as a means to comprehend the ways of nature.  The most fundamental

question that was asked by these philosophers is really no different from the question

Albert Einstein asked years later:  “What is the underlying order that is hidden in

nature?”  The question lead to others, such as, “What is the most basic substance of the

universe?” and “Is the structure of nature based on mathematics, processes or

substances?” Physics begins with ideas.  Ideas are based on reason and logic and, in

almost all cases, follow observations of the natural world.  However, instead of relying

only on observation and reason to come to a conclusion, modern science utilitizes

experimentation and mathematics to establish proofs of the ideas.  One could say that

mathematics is the language of physics.

     Einstein believed that ideas can be understood in many ways.  The use of

analogies are one way to comprehend difficult concepts.  Two other ways are through

the use of reason and intuition.  Aristotle embodied the use of reason and logic.

In addition, it’s always important to question any theory – you never know where that

questioning might lead.  One philosopher, Plato, examined how we acquire knowledge

about the world in which we live.  He felt that the first task of a philosopher is to

determine the reality or truth behind the way things appear.  The goal of discovering

reality is still one of the major goals of physics.

     Remember that the basis for the study of the universe begins with asking questions.

When you develop a system of thought that answers these questions, you’re on your

way to a greater degree of understanding.  Whether this system survives depends on

how well it works.  We use what works and discard it when we find something that

seems to work better.  Belief systems are intertwined with philosophical ideas and

scientific models, so even if a thinker developed mathematics that helped to explain

the physical mechanics of how something operated, he/she would run into trouble if the

explanation was in conflict with the belief system that went along with it.  Einstein said,

“the beliefs we hold come from our life experiences.  We consider these beliefs to be

true, but are they the truth?”  Philosophers have argued that many beliefs are relative in

nature and change according to our experiences.  The opposite is also true.  If you

change your belief; you also change how you experience the world. 

     Einstein believed that one of the basic premises is that philosophy and physics are very closely linked in terms of the types of questions they ask.  Each of these areas of study also can affect the development of the other.  Physics and philosophy continue to feed off each other.

 

Albert Einstein –Theorist and Physicist

After moving to Milan, Italy with his family, Albert resumed his academic studies.  He

wanted to enter the famous Polytechnic Institute in Zurich, Switzerland.  Albert had to

take the entrance exam that proved to be a rude awakening.  Although he was

recognized as a prodigy in mathematics, the rest of his scores in liberal arts were

not so good.  He had to return to another school nearby to finish his last year before

attending the Institute in Zurich.

     Photos from this period of time show Einstein as a handsome young man with dark

curly hair, a moustache and a confident air.  He had a lively and self-confident social

manner, with a definite edge, and he enjoyed laughing noisily.

     While attending the Institute, Einstein would rarely show up for lectures.  He was

dismissive toward his professors and refused to obey instructions, preferring his own

more up to date methods.  For the most part Einstein spent his time reading avidly,

working his way through the latest advances in physics.  In between reading and

research, Einstein would meet his university friends at a Café where students hung out. 

He started smoking a pipe and his favorite drink was iced coffee.  Einstein had a small

circle of friends.  All of them were bright, studying math or physics and obsessed with

the ultimate questions of science. 

     In 1900 Einstein borrowed lecture notes from a friend and took his final exams.  He

soon began applying for jobs.  He spent a lot of time job hunting when he first

graduated.  His father’s business in Italy had serious financial difficulties, and his

family needed money.  He wrote letters to every physics department in Europe inquiring

about a position.  He didn’t get one response.  His father even wrote a few letters,

almost begging his former instructors to give his son a position.  No luck.  Einstein

was off to a rough start.  He did finally manage to land a few substitute teaching

positions that helped out a bit.  His attitude toward discipline ensured that he was a

popular, though ineffectual teacher.  During his free time he continued with his

research, which had now begun to focus on the possibility of a link between molecular

forces and the force of gravity that acted over vast distances. 

     Einstein was 23 and desperately poor by the time he buried himself in his scientific

research.  When the going got tough, Einstein would escape into his abstract world.

During this period he produced a number of scientific papers.  It is considered the

miracle year in physics.  In 1905 Einstein sent four papers to the Annalen der Physik,

the foremost physics journal in Germany. 

     The first paper was entitled, “On a Heuristic Viewpoint Concerning the Production and Transformation of Light.”  Heuristic is a term commonly used in computer programming, referring to new ways for computer systems to learn.  The meaning of the word comes from German and simply means “helping to discover or learn.”  Einstein developed the theory of the photoelectric effect.  What Einstein proposed is that light energy came in chunks, or quanta (comes from the Latin word meaning “how much”), energy.  The wave acted as the carrier of these chunks or quanta of energy.  These special quanta of light came to be called photons (a particle of light).  The energy contained in each photon depended on its color, or frequency.  Einstein said that the energy of a photon (E) is equal to Planck’s constant (a mathematical constant, it relates energy’s particle nature to its wave nature.  6.626 divided by 10 million, divided by one billion, divided by one billion, and again, divided by one billion.  Or, 6.626 x 10 to the negative 34th power) (h) times the frequency (f). 

E = hf. 

This formula is pretty simple.  One of the great things about almost all of Einstein’s

formulas are that they were simple and easy to understand.  The brilliance of Einstein’s

mathematics was that he was able to derive simple equations from a lot of work. 

Einstein’s revolutionary idea was that light waves were streams of individual particles. 

But, how could light be made of these small particles?  Light was a wave and waves

aren’t made up of tiny particles.

     Einstein was in a situation, it worked but it didn’t fit with the accepted idea of reality. 

Even Einstein’s equation contained elements of both qualities of light.  Frequency (f) is

associated with waves, Planck’s constant (h) relates to particles.  So the formula itself

contained aspects of both the wave and particle natures of light.

     Albert spent the next 20 years trying to resolve this dual nature of light.  Much of his

work on the subject was never published, but it reflected his drive to find a single theory

that would encompass both the wave and particle natures of light. 

In 1951, Einstein wrote a letter to his long time friend Michele Besso.  In it, he said:

“All these 50 years of conscious brooding have brought me no nearer to the question:  What are light quanta?  Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken.” [from Understanding Einstein, page 159.]

 

That is as true now as it was then.  No one really knows exactly what light is.  All

we know is that it can be both a particle and wave.  And that’s the paradox.  How many

things do you know of that can be two different things at exactly the same time?

     “A new Determination of the Size of Molecules” is Einstein’s second paper to appear in the famous Annalen der Physik.  This paper is probably one of the easiest to

understand.  Einstein’s paper conclusively proved that molecules exist.  He worked from

the assumption that molecules existed, and by combining that with what were known of

Brownian motion, (Brownian motion, named after Robert Brown, refers to the motion of

particles suspended in a liquid.  These particles, which appear to just jiggle around

randomly, are being moved by a huge number of molecules that make up the liquid and

collide with the particles in suspension), he added the powerful statistical mathematical

methods he had mastered in his earlier papers.  He showed that he could estimate the

number of molecules per cubic centimeter of liquid, as well as the size of the individual

molecules.  Einstein’s mathematical description of Brownian motion is known today as

“the random walk,” because his formula works not only for molecular collisions, but can

also be used to describe the path of a drunk as he staggers down the street.  In other

words, when you have one too many drinks, your movement down the street as you

bounce off lampposts, parking meters and other people can be accurately described

with a scientific forumula. 

     Einstein’s third paper was published without reference to any previous sources.  This was unheard of, because all proper scientific papers always referred to previous

contributions and theories by other scientists in the field.  But no one had ever written

anything on the ideas that Einstein put forth in this paper.  It was unique and stood on

its own.  “On the Electrodynamics of Moving Bodies”, the paper was a radically new

idea and few people could understand the concepts he had developed.  The paper

contained very little math, which was not typical and it contained the thought

experiments that Einstein used as the basis for explaining how his theories worked. 

Einstein mathematically derived a formula involving different speeds, the speed of light,

and how they relate to each other.  He called it his relativity factor.  If you’re on board a

spaceship traveling at half the speed of light, according to the relativity factor your time

interval between events would be 15 percent shorter than the time interval between

events for someone at rest on Earth.  For on hour of time that passes on board your

ship, one hour and nine minutes pass by on Earth.  That’s because 115 percent of 60

minutes is 69 minutes.  It’s important to realize that this is not a perceived change in

time.  This is actual time for both individuals.  Time passes slower at speeds

approaching the speed of light. 

     Einstein was very disappointed by the reaction to his paper on relativity.  Quite a few years passed before it achieved the recognition he felt it deserved.  Einstein was perceived as cocky, but his work came from a position of confidence and self-assurance rather than from arrogance.  He felt that his theories could be explained so simply that they had to be right.  For the rest of his life in physics, Einstein’s ideas about what worked and what didn’t work always proved to be extremely accurate.  Einstein knew intuitively which experiments were correct and which ones weren’t. 

     The relativity of time and the constant speed of light are at the core of Einstein’s theory of relativity.  Two of the most important implications of the relativity theory are that time stops at the speed of light and that the length of an object becomes zero to the observer when it reaches the speed of light.

     Einstein’s fourth paper, entitled, “Does an Object’s Inertia Depend on Its Energy Content?” was presented much like his other three.  It contained hardly any math and presented a few good experiments.  Contained in just three short pages of

his paper was the equation that would become his most well known:  E = mc².  In English, this formula states that mass (m) equals energy (E) divided by the speed of light (c) squared (²).

     That’s all there is to it.  The formula says that all objects with mass have an equivalent amount of energy of mass, which equals the object’s mass times the square of the speed of light, which is an extremely large number.  In other words, even the smallest amount of matter contains an incredible amount of energy.  If your mass is around 150 pounds, you contain enough energy of mass to power a small city for a week, if only you could convert it.  In almost all cases, this energy is unavailable for use, which is one of the reasons why no one discovered it before Einstein did.  It couldn’t be converted into other forms of energy such as heat, electricity, or light.  However, almost 40 years after the famous formula was published, the first nuclear bomb converted the energy of the mass of a small amount of uranium into kinetic energy, demonstrating that it was in fact possible to convert matter into energy.  Einstein’s equation is not the formula for the atomic bomb.  It only gives the description of the relationship between mass and energy.  It did, however, lead to the physics that made the development of the bomb possible.  Einstein hated his association with it.

     I think it’s important to point out that generally physicists fall into two main categories:  those who experiment and those who theorize.  This division is the source of many disagreements, because sometimes theory says something should work that experimentation contradicts.  Einstein always preferred theory to experiment.

 

 

 

Albert Einstein – The Teacher

     Albert Einstein is often remembered as the absent minded, kindly old professor.  He became a much wiser and more insightful man, who had learned important truths about human nature in his later years.  But the young Albert was a less perceptive man who was not as aware of the needs of others, and this lack of awareness was a deliberate choice he made.  After the publication of Einstein’s papers, the world of physics slowly began to recognize his achievements.  Einstein knew that a whole new world of possibilities lay before him and he figured that one day soon the universities would come looking for him.  Turns out, they were slow in coming.

     In June 1907 Einstein applied for a position as a private teacher at the University of Bern.  He was rejected for not turning in a thesis specifically written for the department to which he was applying.  At the same time Einstein was approached to write an article on his theory of relativity.  The administration at the University of Bern decided they could afford to bend the rules a little bit to allow someone of Einstein’s caliber to teach for them.  Einstein had three students in his class in his first semester.  The following year he had only one student, so he canceled the class altogether. 

     In 1909 the Einstein’s moved back to Zurich, where Einstein took up an associate professorship.  The students were at first perplexed by the sight of this scruffy young man, whose trousers were too short and whose hair was too long, holding lecture notes, that he ignored because he preferred to follow his own train of thought.  Einstein was not fond of giving formal lectures, nor did he really like people.  Albert’s ambition to full professorship was not to seek more and more prominent positions in the academic world.  What he sought were jobs in which he could pursue his research and teaching, and of course receive a little more money. 

     In 1911 Einstein was offered a full professorship at the German University in Prague.  In 1914 Einstein was made director of physics at the Kaiser Wilhelm Institute in Berlin.  He was thirty five years old and academically he had at last arrived.  He could continue his research undisturbed and only required to give the occasional lecture. 

     It was during this period of time that Einstein realized that he would not compromise his love of physics for his love of his wife, Mileva.  The search for the meaning of gravity became his sole obsession.  For him, physics would always come first, it’s not that he didn’t care about people – he was very concerned with humanity as a whole.  But on a personal level, his passion and conscious focus was on the hidden workings of nature and not with individual relationships.  He decided to end his marriage with Mileva.

 

Albert Einstein – The Genius

     You would think that Einstein would have received numerous Nobel prizes for physics.  But as it turns out, he was awarded only one.  The committees at the time were very wary of awarding prizes for speculative theories.  Most Nobel prizes were given for experimental rather than theoretical physics.  In November 1921, which was when Einstein received his prize for the discovery of light quanta, the special theory of relativity was considered too speculative.  All in all, Einstein would be nominated for Nobel prizes five times, but he never made a particularly concerted effort to win them. 

     Einstein never doubted the importance of his work or that one day his work would be recognized and rewarded.  He was well aware of the ludicrous aspect of his celebrity.  As a form of self-protection he played up his eccentricity.  Although creatively he was a genius.  He had remarkable insight and the ability to look at the same issue from a number of different views.  He was not attached to any one particular interpretation, which reflected his personal desire to understand, rather than to invest his ego in any one perspective.   

     Before Einstein was cremated, an autopsy was performed to learn the exact cause of death.  His brain was removed and carefully examined under a microscope to see if anything could be discovered that might give a physical clue to his genius.

 

 

Albert Einstein – The Pacifist

“I am not only a pacifist but a militant pacifist.  I am willing to fight for peace…Is it not better for a man to die for a cause in which he believes, such as peace, than to suffer for a cause in which he does not believe, such as war?”

From an interview on a visit to the United States, 1931; quoted in Alfred Lief, ed., The Fight against War

(New York:  John Day, 1933) [from The Quotable Einstein, page 116.)

 

     Einstein’s pacifist beliefs were a major part of who he was.  From an early age, he disliked authoritarian behavior, the military mentality and any groups, religious or political, that held themselves to be superior to others.  Einstein’s beliefs demonstrated the perspective from which he saw the world.   

     Einstein lobbied long and hard for international disarmament and did all he could to counter the growing tide of anti-Semitism in Germany.

 

Kathy Phelan – The Student

     There is so much more I could write about Albert Einstein.  I have deliberately left out what seems to be a handful of important events in Einstein’s life.  For instance, his job at the patent office seemed to take on great importance throughout my research, and his marriage to his cousin also seemed to be important.  To me, they were not any more (or less) important than the other events I shared in this paper.  All of the books, web sites and papers I’ve found in my research are essentially the same - they were just told in different story formats.  Some of my resources were inconsistent in regard to dates, or the titles of papers that Einstein published.  I also have found inconsistencies with the year he received the Nobel prize, why he divorced his first wife, Mileva, how he felt about his children and other supposed facts about his life.  None were so inconsistent that it really mattered (to me), though. 

     Regardless, the message I received from working on this paper is to be free, be an independent thinker, be curious and ask questions, use one’s intuition and be guided by one’s conscious while looking at the bigger picture and seeing outside of the individual. For me, that’s “what it’s all about.”

     I am not a genius, but I know I have genius qualities.  Whether society and its rules and regulations have converted me into a follower, I’ll never know – but I hope not.  I do know that I have an innate sense of curiosity and I’ve always asked questions.  As I’ve grown older I feel a stronger sense of doing great things for the “good of the group.”  It isn’t what Albert Einstein discovered, researched or theorized that impressed me about his life.  Rather, learning who he was and what he believed – that he remained true to himself throughout his life is what motivates and inspires me.  

     In closing, it amazes me how many books, etc., have published quotes and sayings from Albert Einstein.  It really makes one wonder if it’s all true.  I’ll close with this quote:

“In the past it never occurred to me that every casual remark of mine would be snatched up and recorded.  Otherwise I would have crept further into my shell.”

“Einstein to his biographer Carl Seelig, October 25, 1953 [from The Quotable Einstein, Preface and Acknowledgements.]  

 

 

Sources

 

The Big Idea Einstein and Relativity – Paul Strathern, 1997 Doubleday

Einstein’s Brainchild Relativity Made Relatively Easy! – Barry Parker, 2000 Prometheus Books

Albert Einstein The Incorrigible Plagiarist – Christopher Jon Bjerknes, 2002 XTX, Inc. 

The Complete Idiot’s Guide to Understanding Einstein - Gary Moring, M.A., 2002 alpha books Macmillan USA, Inc.

Einstein’s Dreams – Alan Lightman, 1993 Warner Books

The Quotable Einstein – Collected and Edited by Alice Calaprice, 1996 The Hebrew University of Jerusalem and Princeton University Press

http://www-groups.dcs.st-and.ac.uk/~history/mathematicians/einstein.html, viewed on November 20, 2003 at 9:00 p.m. and again on November 23, 2003 at 2:40 p.m.

http://www.aip.org/history/einstein/, viewed on November 15, 2003 at 4:00 p.m.