GED-314

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ASA University Bangladesh

REPORT ON

The Report presented to the Faculty of Business Administration in

Partial Fulfillment of the Requirements for the Degree of Bachelorof Business Administration

Submitted To:

Md. Ahsan ul Hasan

Lecturer

Faculty of business

ASA University Bangladesh (ASAUB)

Submitted By:Name Section ID

Hosnain Ahmed 7A 092-12-0002

Riyad Ahmed 7A 092-12-0003

MD. Mahmudul Hassan 7A 092-12-0006

Tasmia Kamal 7A 092-12-0017

Nafisa Halim 7A 092-12-0021

Miss. Jannatul Ferdus 7A 092-12-0110

Date: 16th July 2011

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REPORT ON

The theory of relativity E=mc2

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ASA University Bangladesh (ASAUB)ASA Tower , 23/3 Khilji Road, Shyamoli, Mohammadpur, Dhaka-1207

E-mail: [email protected] http://www.asaub.edu.bd

Date: july10, 2011

To

Md.Ahsan ul HasanCoordinator, Faculty of Business

ASA University Bangladesh

Subject: Submission of group report on the theory of relativity E=mc2

Dear Sir

Here is the term paper that we have prepared for our GED-314: Business English. The topic of

this report was the “The theory of relativity E=mc2” that you asked us to conduct last 16 th July2011. As you will see, our course pointed some specific rules for the system of studying

introduction to natural science. Following the procedure we agree to prepare an outline of theseneeds in a revised curriculum plan that will help us to correct the student’s information with its

system in aspect of students need.

It was an interesting research and we would like to take this opportunity to thank you for

allowing us to work on this topic and for your constant guidance and support.

Sincerely Yours

Hosnain Ahmed ………………………

Riyadh Ahmed ……………………...

Md. Mahmudul Hassan ………………………

Tasmia Kamal ………………………

Nafisa Halim ………………………

Miss. Jannatul Ferdus ………………………

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mailto:[email protected]

http://www.asaub.edu.bd/

mailto:[email protected]

http://www.asaub.edu.bd/

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Acknowledgement

Preparing this report on “The theory of relativity E=mc2” was a wonderful experience for us.

We would like to thank our faculty, Md. Ahsan ul Hasan, Lecturer, Faculty of Business, ASA

University Bangladesh for giving us this opportunity as well as for her constant guidance andsupport. Finally we would like to thank our family and almighty Allah for supporting us the

courage to carry on our work.

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Executive Summary

Every invention makes world more preferable and fulfilled. E=MC2 is one of

them. E = mc2 has sometimes been used as an explanation for the origin of

energy in nuclear processes, but mass–energy equivalence does not explainthe origin of such energies. Instead, this relationship merely indicates that

the large amounts of energy released in such reactions may exhibit enough

mass that the mass-loss may be measured, when the released energy (and

its mass) has been removed from the system.

Einstein was not the first to propose a mass–energy relationship (see the

History section), the formula equivalence was proposed and published in

1904 by the Italian scientist Olinto de Pretto in the minutes of the Royal

Science Institute of Venice, he first published it in the Atte magazine of Italy

in 1903.

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Table of Contents

Table of Contents ................................................ 6

Introduction ........................................................ 7

Biography ........................................................... 7

Einstein’s idea ..................................................... 9

Einstein’s theory of relativity ............................. 13

Solving the Basic Equation ................................. 13

The Components of the Equation ........................ 14

E = Energy ..................................................................................................15M = Mass ....................................................................................................17

C = the Speed of Light ...............................................................................17

"Proof" of E=mc2 ............................................... 19

The "Proof" of Special Relativity .................................................................20

What Does the Equation Mean? ..................................................................21

The Law of the Conservation of Energy ......................................................21

Invention of atomic bomb ...........................................................................22

Conclusion ........................................................ 24

References ........................................................ 25

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Introduction

Albert Einstein is perhaps the most famous scientist of this century. One of his most well-known accomplishments is the formula E=mc2. One of themost extraordinary things about Einstein’s energy-mass equation is itssimplicity. However, we still need to make sure we are using the correctunits when solving the equation, and that we understand the answer. Thepurpose of this page is to solve the equation as it is and give some idea of the huge amount of energy locked up in even the smallest amount of mass. The famous equation E=mc2 was established in 1905 by German-bornphysicist Albert Einstein (1879–1955). (A physicist is a scientist specializingin the interaction between matter and energy.) The equation is significant

because it contributed to the development of nuclear energy and the atomicbomb. In the formula E stands for energy, m stands for mass, and c2 is asymbol called a constant factor, in which c stands for the speed of light and2 means squared (the factor, or number, is multiplied by itself). Thisequation illustrates the relationship between energy and matter, as well astheir exchangeability. In the 1930s scientists used Einstein's formula anddiscovered that when the atom is split, part of the atom is transformed intoparticles but that some is also converted into energy.

Biography

Albert Einstein was born at Ulm, in Württemberg, Germany, on March 14,1879. Six weeks later the family moved to Munich, where he later on beganhis schooling at the Luitpold Gymnasium. Later, they moved to Italy andAlbert continued his education at Aarau, Switzerland and in 1896 he enteredthe Swiss Federal Polytechnic School in Zurich to be trained as a teacher inphysics and mathematics. In 1901, the year he gained his diploma, heacquired Swiss citizenship and, as he was unable to find a teaching post, heaccepted a position as technical assistant in the Swiss Patent Office. In 1905he obtained his doctor's degree.

During his stay at the Patent Office, and in his spare time, he produced muchof his remarkable work and in 1908 he was appointed Privatdozent in Berne.In 1909 he became Professor Extraordinary at Zurich, in 1911 Professor of Theoretical Physics at Prague, returning to Zurich in the following year to filla similar post. In 1914 he was appointed Director of the Kaiser WilhelmPhysical Institute and Professor in the University of Berlin. He became aGerman citizen in 1914 and remained in Berlin until 1933 when he

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renounced his citizenship for political reasons and immigrated to America totake the position of Professor of Theoretical Physics at Princeton. He becamea United States citizen in 1940 and retired from his post in 1945.

After World War II, Einstein was a leading figure in the World GovernmentMovement, he was offered the Presidency of the State of Israel, which hedeclined, and he collaborated with Dr. Chaim Weizmann in establishing theHebrew University of Jerusalem.

Einstein always appeared to have a clear view of the problems of physicsand the determination to solve them. He had a strategy of his own and wasable to visualize the main stages on the way to his goal. He regarded hismajor achievements as mere stepping-stones for the next advance.

At the start of his scientific work, Einstein realized the inadequacies of

Newtonian mechanics and his special theory of relativity stemmed from anattempt to reconcile the laws of mechanics with the laws of theelectromagnetic field. He dealt with classical problems of statisticalmechanics and problems in which they were merged with quantum theory:this led to an explanation of the Brownian movement of molecules. Heinvestigated the thermal properties of light with a low radiation density andhis observations laid the foundation of the photon theory of light.

In his early days in Berlin, Einstein postulated that the correct interpretationof the special theory of relativity must also furnish a theory of gravitationand in 1916 he published his paper on the general theory of relativity. During

this time he also contributed to the problems of the theory of radiation andstatistical mechanics.

In the 1920's, Einstein embarked on the construction of unified field theories,although he continued to work on the probabilistic interpretation of quantumtheory, and he persevered with this work in America. He contributed tostatistical mechanics by his development of the quantum theory of amonatomic gas and he has also accomplished valuable work in connectionwith atomic transition probabilities and relativistic cosmology.

After his retirement he continued to work towards the unification of the basic

concepts of physics, taking the opposite approach, geometrisation, to themajority of physicists.

Einstein's researches are, of course, well chronicled and his more importantworks include Special Theory of Relativity (1905), Relativity (Englishtranslations, 1920 and 1950), General Theory of Relativity (1916),Investigations on Theory of Brownian Movement (1926), and The Evolution of Physics (1938). Among his non-scientific works, About Zionism (1930), Why

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War? (1933), My Philosophy (1934), and Out of My Later Years (1950) areperhaps the most important.

Albert Einstein received honorary doctorate degrees in science, medicineand philosophy from many European and American universities. During the

1920's he lectured in Europe, America and the Far East and he was awardedFellowships or Memberships of all the leading scientific academiesthroughout the world. He gained numerous awards in recognition of his work,including the Copley Medal of the Royal Society of London in 1925, and theFranklin Medal of the Franklin Institute in 1935.

Einstein's gifts inevitably resulted in his dwelling much in intellectual solitude

and, for relaxation; music played an important part in his life. He marriedMileva Maric in 1903 and they had a daughter and two sons; their marriagewas dissolved in 1919 and in the same year he married his cousin, ElsaLöwenthal, who died in 1936. He died on April 18, 1955 at Princeton, New Jersey.

From Nobel Lectures , Physics 1901-1921, Elsevier Publishing Company, Amsterdam, 1967

Einstein’s idea

As mentioned Bodanis claims that before Einstain mass and energy werebelieved to be separate domains. In the equation e=mc2 Einstein unitesthese two domains by claiming that if we could transform mass into energy,we could get mc2 units of energy out it the process. This is a startling claimbecause it implies that within 1 kg of mass lies hidden about 25 billionkilowatt units of energy (if we somehow could convert the mass into energy). The reason such small amount of materials contains so much energy isbecause of the large value of c – the speed of light. Light travels 300 000 km

in one second (a fact first discovered by the Danish scientist Ole Rømer in1676). Einstein says that to find the energy of mass it should be multipliedby this large number no only once, but twice. That is, to find the energy of some material we multiply its mass first by 300 000 and then we multiplythis again by 300 000. No wonder we get such a large number in the endeven with a small starting point! In effect, then, the equation says that massis the purest form of concentrated energy and it raises the possibility thatmass can be transformed to energy and vice versa.

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http://nobelprize.org/nobel_organizations/nobelfoundation/publications/lectures/index.html

http://nobelprize.org/nobel_organizations/nobelfoundation/publications/lectures/index.html

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How did Einstein get this idea? Even before Einstein it was known thatenergy was most conveniently measured by the its mass times the square of its velocity. Bodanis presents this, as always, in a fascinating story where thehero is a rich, beautiful and very intelligent woman named Emilie du Chãtelet(a modern day equivalent, Bodanis says, is Geena Davies!). The background

was as follows. Newton had suggested that energy should be measured bythe mass of something times it velocity. The problem with this was that itopened up the possibility for energy to disappear, as when two objectscollide and come to rest. The energy from one seems to cancel the other andthe result is a loss of energy. And, if collisions caused a loss of energy, theword should gradually come to a standstill since all objects occasionallycollide and loose energy.

For Newton, however, this was not a problem. In fact, Newton believed thathis theory demonstrated the existence of God. If you believe his theory thenthe world should come to a halt, but the fact that it does not shows that

there must be a God who is continually supplying energy to the world.Leibniz disagreed with this and argued that surely God would have beensmart enough to create a self-sustaining world where energy did notdisappear. Hence, instead of Newton’s suggestion that energy should bemeasured by mass time’s velocity, Leibniz claimed that energy should bemeasured by velocity squared times mass. This had the advantage that theenergy from to colliding object would not be zero. What was needed, then,was knowledge of experimental evidence that could determine the matter.

Due Chãtelet herself did not conduct such an experiment, but she knewabout an experiment conducted by Williem s’Gravesande. He had discovered

that if you double the speed of a bullet it will not go twice as far into a layerof mud or clay, but four times as far. Triple its speed and it goes nine timesas deep. It is the same with cars, double the speed of a car and the distanceit takes to stop becomes four times as long (2 squared). The samephenomenon is observed in many other processes and one may speculatethat it expresses some kind of fundamental law derived from a deepermathematical symmetry or unity in nature. In any case, the point is thateven before Einstein it was established that energy should be measured asmass times velocity squared.

I found the story above very fascinating, if nothing else because it reveals

what today must seem like quite quaint arguments about the existence of God was used to support or reject a theory about how to measure energy. Iwas, however, also slightly confused. First, measuring energy in terms of thesquare of the velocity does not seem to prevent energy from being lost. If both objects reduce their velocity to zero after the collision, the energy islost even if it measured by velocity squared since zero times something elseis zero. Also the story seems to contradict the argument that Einstein wasthe first to connect energy and mass together. That had been done by

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Newton, Leibniz, du Chãtelet and many others. Indeed, it was even alreadyknown that the mass of electrons increased when their velocity approachedthe speed of light (Hendrik Antoon Lorentz's theory of electrons). What wasnew and revolutionary, however, was the idea that the potential energy insome mass was not only the square of its velocity, but the square of the

speed of light. In this perspective even an object standing still contained a lotof energy. Thus, the question becomes not so much why Einstein connectedmass and energy, but why he used the speed of light as the factor of conversion.

To explain this Bodanis adapts an analogy used by Einstein himself. Imagineyou are flying a very fast space-ship and that you try to go faster than thespeed of light (300 000 km/s). What happens when you are flying at 299 999km/s and tries to go even faster? The answer, according to Einstein, is thatthe space shuttle will not go faster, but the energy used in trying to go fasterwill result in larger mass: the space-ship will become larger and heavier!

Today we can prove this experimentally. Using the particle acceleratorsoutside Chicago and in CERN, it has been found that a proton (a very smallthing) running at a velocity that is 99,9997% of the speed of light becomes430 times bigger than it was originally. In short, since nothing can go fasterthan the speed of light the extra energy will instead become mass, notspeed.

The analogy, however, does not explain exactly why nothing can go fasterthan light, or, indeed, why the phenomenon is gradual and not discrete. Totake the latter first: You do not need to approach the speed of light to beforethe energy is increasing the mass. The analogy may make people believe

that only the “extra” energy that is used trying to go beyond the speed of light will be used to increase in mass, but in fact the phenomenon can beobserved at all speeds – although the effect is much larger when the speed ishigh.

Second, why is the speed of light an absolute “speed-limit” in the universe?Bodanis has a go at this question. He first introduces us to absolute limits innature. For instance, nothing can become colder than -274 degrees Celsiusbecause at that point the atoms stop vibrating. It is impossible to vibrate lessthan “no vibration” and since “no vibration” occurs at -274 degrees then thisis the “absolute zero” – nothing can be colder by vibrating less! This shows

that “absolute” limits exist in nature, but it does not show why nothing cango faster than the speed of light.

To go further Bodanis tries to explain how light moves. The starting point of the story is James Clark Maxwell’s discovery that light is a physical processinvolving “jumps” and squeezes. Light is, briefly, a jump made by an electricfield from a magnetic field. Out of this magnetic field jumps an electric fieldand so the process goes on. This is only make things slightly more

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understandable. The explanation in terms of “jumps” is very general and itdoes not add much to my knowledge except, maybe, to make me believethat light is a physical process and as such it has an inherent “speed” bywhich it can move. It does not, however, say exactly why this is the speedlimit for all kinds of movement.

A third step in the argument tries to make this last argument more explicit,but I am unsure about how convincing it is. In brief, the argument is thatsince light IS movement, then there will be no light if you go faster than lightitself. This I understand, but I still do not know why things cannot movefaster than light (even if they then will be “in the dark” or onlyseeing/catching up “old light”). This is not to say that I believe things can gofaster than light, only to say that I do not fully understand why. I basicallyaccept the velocity of light as an empirically established “speed limit” innature, although I do have some problems even with this based onexperiments from quantum physics where things seem to “communicate” or

“react” faster than can be explained by the speed of light (but mycompetence here is far too thin to be convincing). In short, Bodanis’arguments, analogies, and examples did bring me closer to anunderstanding, but I did not reach the point where I felt “everything” fell intoplace.

How did Einstein arrive at his revolutionary equation? Bodanis suggest that itwas a combination of several factors. First of all Einstein disliked authority,so he was always eager to challenge the established physical laws. Hence,the “old” laws that total mass is constant and total energy is constant werenot – for Einstein – unquestionable truths and in fact, his equation implies

that the laws are wrong. Since energy can be transformed into mass andmass into energy then sum of each is not constant, but it is the sum of energy and mass together that is constant. Why was Einstein so critical of authority? Building on an argument from Thorstein Veblen, Bodanis suggeststhat religion played a role here. The argument is that if you as a child istaught to believe in a religious world view, you might later develop a deepsuspicion of authority when you discover that some of these teachingsseems to be wrong. Second, Bodanis suggests that not having a job inresearch was important since such a job could have promoted a tendency tosuperficial research. Third – and slightly in conflict with the first argument,there was the importance of being supported and encouraged by his family

to challenge established truths even from childhood. There are also severalother arguments and although some of them are plausible, I think it is a fieldill-suited for generalization. All kinds of people with all kinds of differentbackgrounds seem to make important discoveries and although there mightbe some common tendencies in their background, I am not sure what theyare.

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Einstein’s theory of relativity

The title of Bodanis’ book is e=mc2, not the theory of relativity. This isprobably a good thing since the term “relativity” is often misunderstood tomean “everything is possible” or “nothing is true” or “no precise results arepossible.” In fact, as Bodanis explains very well, the special theory of relativity is best understood by Einstein’s equation combined with anassumption that the speed of light is 50 km/hour. This would imply that a carwould change its mass as it went faster. Things would appear differentdepending from where I was watching the cars. If I were sitting in a car goingat a certain speed things would appear to be different than if I were standingstill, or going slightly faster. Mass and so on would be relative and since noposition can be defined as the “true” perspective, things could be calledrelative (although Einstein himself did not like the expression). The generaltheory of relativity, takes this a bit further and tries to unite not only massand energy, but time and space as well as mass and energy, but this is thetopic of a whole new subject and Bodanis ends his story of e=mc2 beforegoing into the general theory of relativity.

Solving the Basic Equation

Now, we have everything in order. Let’s have a go at solving the equation.

We will use a mass of 1kg to keep things simple and I will show all of theworkings of the equation. So, with 1kg of mass (around 2.2 pounds) we get:

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Note how the units were dealt with and that kg m2 s-2 is the same as joules (arigorous proof of this is outside the scope of these pages).

So from 1kg of matter, any matter, we can get out 9 x 1016 joules of energy.Writing that out fully we get:

90,000,000,000,000,000 joules

That is a lot of energy! For example, if we converted 1 kg of mass intoenergy and used it all to power a 100 watt light bulb how long could we keepit lit for? The first thing to do is divide the result by watts (remember that 1watt is 1 joule per second):

9 x 1016 J / 100W = 9 x 1014 seconds

How long is that in years? A year (365.25 days) is 31,557,600 seconds, so weget:

9 x 1014 seconds / 31,557,600 seconds = 28,519,279 years

That is a very long time!

Of course, converting mass into energy is not quite that simple, and apartfrom with some tiny particles in experimental situations has never beencarried out with 100% efficiency. Perhaps that’s just as well.

The Components of the Equation

If we break the equation E = mc2 into its components and write out the termsfully we get:

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• E = energy (measured in joules)• m = mass (measured in kilograms)• c = the speed of light (186,000 miles per second, or 3 x 108 ms-1)

We will now examine each of the terms in a little more detail.

E = Energy

The word "energy" is actually quite new. Its modern use dates from aroundthe middle of the nineteenth century, when it was beginning to be realizedthat the power that drove many different processes could be explained bythe concept of energy being transferred from one system and form toanother. For example, the trains of the day were powered by coal. The coalwas burned under a water-filled boiler to produce steam, which in turnpushed pistons attached to the wheels of the train, the wheels turned andthe train was set in motion. In this example we start with locked up ("latent")

chemical energy in the coal. The chemical energy is turned into heat energy(sometimes called "thermal" energy) by burning the coal and boiling thewater. Finally, the thermal energy is turned into the energy of movement("kinetic energy") by forcing the steam into pistons to drive the wheels.

A moving steam train.

Chemical energy - thermal energy - kinetic energy

There are many other forms of energy, such as electrical, gravitational,nuclear, and strain energy. However, as different as all these types of energyseem they can all be measured in the same way and thought of as the samething. The unit that we use to measure energy, from whatever energysource, is the joule (J). Two ways in which we use this unit in everyday termsare:

• The total amount of energy in a system.

An example is a lump of coal, which when burned will release a certainnumber of joules of energy. Another example is food. A calorie (moreformally called the small or gram calorie) contains almost 4.2 joules of

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energy, so if we eat a piece of chocolate that has 100 calories we can expectto get around 420 joules of energy from it.

Note: The labeling on food products in Europe shows kJ meaning kilo (1thousand) joules, and kcal meaning 1000 calories, while in the U.S.A. the

labeling on food products shows either "calories" or "Calories", with bothtaken to mean kilocalories. To add further confusion, "Calories" can also tobe taken to mean kilocalories in Europe.

• Energy used up over time.

Most electrical devices have their power consumption rated in watts. A wattis a rate of energy consumption of one joule per second. So, if you have alight bulb in your room that is rated at 100W it is using energy at a rate of

100 joules every second. To go back to the example in the previous bulletpoint, a piece of chocolate with 100 calories isn’t very big but could easilyruin a planned daily diet. However, if we turned the chemical energy in ourpiece of chocolate into electrical energy (a process that can be done) itwould only have enough energy to keep our light bulb shining for 4.2seconds. Personally, I’d rather eat the chocolate.

So, to summaries, energy comes in many forms, and it can be transferredfrom one system to another. The basic unit of measurement for energy is the joule.

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M = Mass

Mass is strictly defined as a measure of a body’s inertia, i.e. its resistance toacceleration. Another and simpler way of defining mass is to say that it is thetotal amount of matter in an object. This latter definition isn’t strictly true,

but is good enough for our purposes here. Mass is measured in kilograms(kg).

Note that mass isn’t the same as weight, although it is often thought to be.Weight is actually a measure of the gravitational force (pull) felt by a bodyand is measured in Newton (N) (note that scientific units that are namedafter people are almost always in lower case when spelled out fully, hencenewtons and not Newtons). For example, an astronaut walking on thesurface of the Moon has the same mass as he or she does on the Earth but

only weighs one sixth what they would do back home. The reason for this isthat while the mass of the astronaut hasn’t changed, the pull of the Moon’sgravity is only one sixth of what the Earth’s gravitational pull is.

As with energy, the idea that mass is common to all objects is relatively newand again dates back to around the nineteenth century. Before that time,different solids, liquids and gases were all thought to be only looselyconnected in conceptual terms. As with energy we now consider that mass isneither created or destroyed, but is merely changed from one form to

another, e.g. we can turn water from a solid (ice) into a gas (steam), but itstotal mass doesn’t change.

C = the Speed of Light

We use the letter c to represent the speed of light. The ‘c’ comes from theLatin word "celeritous", meaning swift, and it’s a very apt definition - there isnothing faster than light. In a vacuum, such as space, it travels at close to

186,300 miles per second (300,000 km per second). That’s about seventimes around the Earth every second.

The speed of light was first accurately estimated by the Danish astronomer,Ole Roemer (sometimes written as Rømer) during the 1670s. Up until thattime everyone assumed that the speed of light was infinite, i.e. that light

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arrived at its destination instantly. This isn’t such an unreasonableassumption given that when we look around us light does indeed appear toreach us instantly.

During the seventeenth century it was discovered that there was a problem

in calculating the orbital time of Io, the innermost moon of Jupiter. Itsometimes took "too long" to make an orbit of the planet and at other timeswas "too quick". It was thought that the problem must be due to a wobble inthe orbit of Io, but Roemer took a different, and very radical, view of thematter. He argued that light, instead of being everywhere instantly, had afinite speed and that this would explain the problem of Io. The Earth wasknown to travel around the Sun and this meant that sometimes the Earthwas closer to Jupiter and sometimes further away. Roemer realised thatwhen the Earth was on the opposite side of the Sun from Jupiter the lightfrom Io would take longer to reach us than when the two bodies were on thesame side.

This means that the light has to travel further and therefore takes longer,providing, of course, that light has a speed in the first place. During ameeting of the new Academy of Science in Paris in 1676 Roemerdemonstrated that the amassed observational data of the astronomerCassini indicated that Io would next appear at 5.25pm on November the 9thof that year. He himself predicted that it wouldn’t appear until 10 minutes

and 45 second later, using his theory that light had a finite speed. The daycame and virtually every major observatory in Europe was ready to test theprediction. At 5.25pm, the time predicted by Cassini, Io wasn’t visible. Evenat 5.35pm Io wasn’t visible. But at exactly 5.35pm and 45 second itappeared, just as Roemer said it would. From this it was possible to make thefirst accurate measurement of the speed of light and the calculated figurewas within one percent of what we know it to be today.

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You may think that that was the end of the matter and that Roemer wascelebrated as a scientific genius, showered with honours and given a securefuture. Sadly, that’s far from what happened. He was only 21 when he madehis discovery, while Cassini was a well-respected if egotistical elder scientist,who used his powerful friends to back him up to rubbish Roemer’s ideas.

Scientists, it seems, are human after all and this wasn’t the first, or sadly,the last time that an ego got in the way of a new discovery. Roemereventually gave up science completely and later became the director of theport of Copenhagen and then head of the state council of the realm. It wasn’tuntil 50 years later that further experiments convinced the scientificcommunity that Roemer had been right all along.

"Proof" of E=mc2

Before Einstein, it was known that a beam of light pushes against matter;

this is known as radiation pressure. This means the light has momentum. Abeam of light of energy E has momentum E/c. Einstein used this fact to showthat radiation (light) energy has an equivalent mass.

Consider a cylinder of mass M (see accompanying figure-"energy"). A pulseof light with energy E is emitted from the left side. The cylinder recoils to theleft with velocity v=E/(Mc). If the mass of the cylinder is large, it doesn'tmove far before the light reaches the other side. So, the light must travel adistance L, requiring time t=L/c. In this time, the cylinder travels a distancex=vt=[E/(Mc)](L/c).

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Einstein reasoned that the center of mass of an isolated system doesn't justmove on its own. So, the motion of the cylinder must be compensated by themotion of some other mass. Let's assume the light has mass m. Then,Mx=mL, since the cylinder moves x to the left and the light moves L to the

right. Substituting the expression for x given above, the equation can besimplified to E=mc2.

From the fact that light has momentum, Einstein showed that light energyhas the characteristics of mass also. In other words, energy has inertia. Itturns out that all energy has this feature. That's because one form of energycan be transformed into another. So, if one kind of energy has thischaracteristic, all forms of energy do.

The "Proof" of Special Relativity

When Einstein first proposed his Special Theory of Relativity in 1905 fewpeople understood it and even fewer people believed it. It wasn't until 1919that the Special Theory was "proved by inference" from an experimentcarried out on his General Theory of Relativity. Physicists now routinely userelativity in many experiments all over the world every week of the year.However, these experiments are highly specialized and usually require agreat deal of knowledge and training in order to understand them. So whatevidence is there for the general public that special relativity is correct?Probably the most spectacular "proof" is nuclear weapons. These pages arenot about the morality of such weapons (but that is not to say the questionof their existence or use is not an important one). However, whether one"likes" nuclear weapons or not no one would deny that they exist.

Nuclear weapons (A- and H-bombs) are built on one principle; that mass canbe turned into energy, and the equation that exactly predicts that conversionis E = mc2. So what has that to do with Special Relativity? The answer is thatE = mc2 is derived directly from Special Relativity. If relativity is wrong, thennuclear weapons would simply not work. Any theory or point of view thatopposes Special Relativity must explain where E = mc2 comes from if notrelativity. Other models of relativity that contain E = mc2 exist but here weare concerned with the "standard" model as proposed by Einstein.

This page explains, with minimal mathematics, how E = mc2 is derived fromspecial relativity. In doing so it follows the same theoretical arguments thatEinstein used.

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What Does the Equation Mean?

The equation tells us that energy and mass are the same thing, and howmuch energy is contained in a given mass, or vice versa. In other words,mass is really very tightly packed energy. That energy and mass are really

the same thing is quite an extraordinary claim and seems to go against twolaws that had been established by scientists before Einstein came along:

The Law of the Conservation of Mass

As we have seen, mass can be thought of as the quantity of matter in anobject. The law of the conservation of mass states that mass is alwaysconserved. That is, whatever we do with matter in a closed system we willalways have the same amount of substance at the end. For example, if weburn a log, the wood gets lighter as the fuel in it is used up. However, if wegather together the ashes, all the tiny smoke particles and the water vapour

produced and then weigh everything we find that the mass is exactly equalto the mass of the log that was burned. Mass is just mass, or so it seems,and while it can be chemically altered, such as burned, the total amount inany system remains the same.

The Law of the Conservation of Energy

But what about the energy released in burning the log? The energy released

in the burning process is "chemical energy", i.e. the breaking and reformingof chemical bonds between particles. Burning the wood released thechemical energy locked up in it. No energy was created in the process andnone was destroyed, it was just changed from one sort of energy (chemicalbonds) to other forms of energy (heat and light). In other words the totalamount of energy, just like the total amount of mass, remained the same.

After many experiments, notably by the scientist for whom the unit of energyis named, James Prescott Joule (1818-1889), it was established that the totalamount of energy in a closed system always remains the same. This isknown as the law of the conservation of energy.

What Einstein showed via his now famous equation was that mass andenergy are in fact the same thing. Converting one into the other doesn’ttherefore violate either of the two conservation laws. Both quantities areconserved, although the state of the mass/energy may have changed. Eachatom of a substance can be thought of as a little ball of tightly packedenergy that can be released under certain circumstances. Likewise, we can

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take energy (such as particles of light, called photons) and turn it intomatter. This was first achieved in the 1930s.

Invention of atomic bomb The physicist Albert Einstein did not directly participate in the invention of the atomic bomb. But as we shall see, he was instrumental in facilitating itsdevelopment.

In 1905, as part of his Special Theory of Relativity, he made the intriguingpoint that a large amount of energy could be released from a small amountof matter. This was expressed by the equation E=mc2 (energy = mass timesthe speed of light squared). The atomic bomb would clearly illustrate thisprinciple.

But bombs were not what Einstein had in mind when he published thisequation. Indeed, he considered himself to be a pacifist. In 1929, he publiclydeclared that if a war broke out he would "unconditionally refuse to do warservice, direct or indirect... regardless of how the cause of the war should be judged." (Ronald Clark, "Einstein: The Life and Times", pg. 428). His positionwould change in 1933, as the result of Adolf Hitler's ascent to power inGermany. While still promoting peace, Einstein no longer fit his previous self-description of being an "absolute pacifist".

Einstein's greatest role in the invention of the atomic bomb was signing a

letter to President Franklin Roosevelt urging that the bomb be built. Thesplitting of the uranium atom in Germany in December 1938 plus continuedGerman aggression led some physicists to fear that Germany might beworking on an atomic bomb. Among those concerned were physicists LeoSzilard and Eugene Wigner. But Szilard and Wigner had no influence withthose in power. So in July 1939 they explained the problem to someone whodid: Albert Einstein. According to Szilard, Einstein said the possibility of achain reaction "never occurred to me", altho Einstein was quick tounderstand the concept (Clark, pg. 669+; Spencer Weart & Gertrud WeissSzilard, eds., "Leo Szilard: His Version of the Facts", pg. 83). After consultingwith Einstein, in August 1939 Szilard wrote a letter to President Roosevelt

with Einstein's signature on it. The letter was delivered to Roosevelt inOctober 1939 by Alexander Sachs, a friend of the President. Germany hadinvaded Poland the previous month; the time was ripe for action. ThatOctober the Briggs Committee was appointed to study uranium chainreactions.

But the Briggs Committee moved very slowly, prompting Einstein, Szilard,and Sachs to write to FDR in March 1940, pointing again to German progress

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in uranium research (Weart & Szilard, pg. 119+). In April 1940 an Einsteinletter, ghost-written by Szilard, pressed Briggs Committee chairman LymanBriggs on the need for "greater speed"

(Weart & Szilard, pg. 125+; Clark, pg. 680).

Research still proceeded slowly, because the invention of the atomic bombseemed distant and unlikely, rather than a weapon that might be used in thecurrent war. It was not until after the British MAUD Report was presented toFDR in October 1941 that a more accelerated pace was taken. This Britishdocument stated that an atomic bomb could be built and that it might beready for use by late 1943, in time for use during the war.

(Richard Rhodes, "The Making of the Atomic Bomb", pg. 377+).

Einstein biographer Ronald Clark has observed that the atomic bomb wouldhave been invented without Einstein's letters, but that without the early U.S.work that resulted from the letters, the a-bombs might not have been readyin time to use during the war on Japan.

(Clark, pg. 682-683).

The atomic bomb related work that Einstein did was very limited and hecompleted it in two days during December 1941. Vannevar Bush, who wascoordinating the scientific work on the a-bomb at that time, asked Einstein'sadvice on a theoretical problem involved in separating fissionable materialby gaseous diffusion. But Bush and other leaders in the atomic bomb projectexcluded Einstein from any other a-bomb related work. Bush didn't trustEinstein to keep the project a secret: "I am not at all sure... [Einstein] wouldnot discuss it in a way that it should not be discussed."

(Clark, pg. 684-685; G. Pascal Zachary, "Endless Frontier: Vannevar Bush,Engineer of the American Century", pg. 204).

As the realization of nuclear weapons grew near, Einstein looked beyond thecurrent war to future problems that such weapons could bring. He wrote tophysicist Niels Bohr in December 1944, "when the war is over, then there willbe in all countries a pursuit of secret war preparations with technologicalmeans which will lead inevitably to preventative wars and to destruction

even more terrible than the present destruction of life."

(Clark, pg. 698).

The atomic bombings of Japan occurred three months after the surrender of Germany, whose potential for creating a Nazi a-bomb had led Einstein topush for the development of an a-bomb for the Allies. Einstein withheldpublic comment on the atomic bombing of Japan until a year afterward. A

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short article on the front page of the New York Times contained his view:"Prof. Albert Einstein... said that he was sure that President Roosevelt wouldhave forbidden the atomic bombing of Hiroshima had he been alive and thatit was probably carried out to end the Pacific war before Russia couldparticipate." ("Einstein Deplores Use of Atom Bomb", New York Times,

8/19/46, pg. 1). Einstein later wrote, "I have always condemned the use of the atomic bomb against Japan."

(Otto Nathan & Heinz Norden, editors, "Einstein on Peace", pg. 589).

In November 1954, five months before his death, Einstein summarized hisfeelings about his role in the creation of the atomic bomb: "I made one greatmistake in my life... when I signed the letter to President Rooseveltrecommending that atom bombs be made; but there was some justification -the danger that the Germans would make them."

(Clark, pg. 752).

Conclusion

The subject of this page is quite difficult to understand, even though much of the more difficult mathematics has been left to one side. The conceptual jump from the two postulates of special relativity to the equivalence of massand energy is certainly not obvious, and it is extraordinary that Einsteinproposed it long before there were any experimental results to indicate thetrue nature of the relationship between mass and energy.

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The results of Einstein's work in this area are far more widespread than isusually thought and affects everyone on the planet. As with all science wecan use the results for "good" and "bad". The reason the words "good" and"bad" are in quotes is because it all depends on your point of view. Forexample, you may think that nuclear power

Stations (which use E = mc2 directly) are either a good or a bad thing.Likewise, depending on your point of view, nuclear weapons are either agood or a bad thing; they either stopped one war or prevented another, orthey are immoral and are bound to fall into the "wrong" hands sooner orlater. In recent years there have been great advances in using E = mc2 in themedical field, particularly to treat cancer. Again though, this can be seen aseither a good thing (i.e. curing a disease) or a bad thing (i.e. overburdeningan already over-populated planet).

Although these issues are very important it is not for pages such as this to

hold an opinion either way, but to merely explain some of the science behindthem. It is far too late to "un-invent" E = mc2 and the best we can do is touse it in an informed way for the things that we believe are worthwhile.

References

http://www.btinternet.com/~j.doyle/SR/Emc2/Derive.htm

http://www.btinternet.com/~j.doyle/SR/Emc2/Basics.htm

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http://www.drphysics.com/syllabus/energy/energy.html


www.worsleyschool.net/science/files/ emc2/emc2.htm

http://www.relativitycollapse.com/e=mc2.html

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http://www.worsleyschool.net/science/files/emc2/emc2.htm











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