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Special Topics

by: Krystal Ledner

Special Topics IDS 6938

Krystal Ledner
University of Central Florida
GPA 3.93

Michael Bass

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Michael Bass
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Date Created: 10/22/15
The State of Physics at the Start of the 3ml Millenium Michael Bass Professor of Optics and Physics School of OpticsCREOL University of Central Florida Orlando FL 32816 27 00 We live in a Newtonian world in an Einsteinian universe where quantum effects are critically important and yet gravity the weakest of all known forces governs the ultimate fate of all that there is We also live in a world in which science and technology are integral parts of our everyday lives You turn on a light use a cell phone put on glasses or corrective lenses use an automobile listen to radio watch TV travel on an airplane or bene t from some advance in medicine and don t think of the events in science which made these modern marvels possible We are concerned with how we came to understand the science that underlies our technological society who were the people who contributed to our knowledge how were they affected by the cultures in which they lived and how in turn they affected the culture in which we now live This review of the state of physics at the start of the millenium is a broadbrush approach to the general underlying principles in physics how they came about who developed them and how they impacted our society It should enable one to understand what has gone on in the past in the context of where we are today so that we may understand where we are headed Physics is the science by which we understand the workings of the universe It is the science that underlies all other sciences and the thought processes developed in Physics are those used in the other sciences For these reasons we consider its development to understand science in general To understand the universe 7 from sub nuclear quarks or even smaller super strings to the entire universe 7 physicists have identified just four forces Recent observations of the motions of galaxies and the recession speeds of galaxies at great distances suggest the existence of a possible 51h force that repels masses from one another sort of antigravity or that over very large distances Newton s law of gravity may be a little bit off These observations are so recent that they must be checked and rechecked to be certain One thing is clear though 7 the universe is even stranger than it seems The four forces themselves are not yet fully understood and yet they seem thus far to govern the interactions taking place between all particles In addition there are certain symmetries that result in the reality we perceive The first force we ever knew about 7 we all sense it 7 is gravity and yet it remains the most mysterious of all Perhaps because it is the weakest of all the forces gravity still defies complete explanation However since it is responsible for everything from the fall of an apple to the fate of the universe it has been a subject of continuing study While we all sort of know about gravity it was Isaac Newton perhaps the greatest physicist ever who in the mid l7Lh century synthesized the data of Tycho Brahe Nicolaus Copernicus Galileo Galilei and Johannes Kepler into his remarkable Universal Law of Gravity Coupled with his even more spectacular laws concerning the motion of bodies Michael Bass he showed the remarkable fact that the gravitational force that holds us to the earth is exactly the same as that which controls the movement of the planets stars galaxies and the universe Of course Newton didn t know about galaxies and the universe those are 20 century matters so he didn t do all ofthis but his law does Newton s Laws of Motion are simple statements about how the motion of bodies change or doesn t when acted on by external forces1 They are l A body in motion tends to remain in motion or to remain stopped if stopped except insofar as acted on by an outside force 2 The rate at which a body s momentum changes is equal to the net force acting on the body mathematically this law is dip dmv dt dt F where p is the momentum m is the mass of the body V is its velocity and F is the force acting on it Or if m is a constant we have the more familiar dV F mdt ma where a is the acceleration resulting from the action of the force 3 If object A exerts a force on object B then object B exerts an oppositely directed force of equal magnitude on object A As accurately as we can measure in every day life these laws work we nd no violations However as we will discuss later when the body s speed becomes too large the de nition of momentum in the second law must be modi ed To do that properly we will need Einstein Before we go too much further I must say a word about mathematics It is the language of science and just as you need Chinese to get along in China you need mathematics to get along in science Mathematics is used to represent in a sort of short hand notation the relationships between various quantities that constitute the body of knowledge called science As a result we must use a little math to talk about science To enable us to do this math had to be invented In fact that was one of the things that Newton did for science He established the basis of differential calculus so that he we could discuss his physics Of course DesCartes in France and Liebnitz in Germany were not doing nothing DesCartes invented graphing an essential Michael Bass 1 Sometimes in this review mathematical expressions are given This review can be read by the non scientist just by skipping the math In doing so the beauty that results from the elegance of the math will be lost but the main concepts can still be acquired contribution and Liebnitz in parallel to Newton invented the calculus We needed all of their work in math to be able to do the physics that we now consider Back to gravity Newton proposed that the magnitude of the gravitational force between two bodies of masses m1 and m and with centers separated by a distance r12 was 77717772 2 712 FG The proportionality constant called G was introduced to take account of the units if nothing else It is clear from correspondence between Newton and Robert Hooke that Hooke rst proposed the inverse square law and suggested that it might account for the motions of the planets Hooke however did not have the mathematical tools or skills that he would have needed to prove his point As a result he passed the suggestion to Newton and Newton a generally nasty man solved the problem but nowhere credits Hooke s suggestion Nasty or not Newton had the nerve to declare the gravitational constant and the law universally applicable Think of how bold this statement was 7 Newton able to measure things on the earth and read of others observations of the motion of planets was probing the entire universe and had the temerity to think he could describe it and to do so so simply In a moment we will see how this law actually re ects a symmetry of the world in which we live Meanwhile let s look at the consequences of Newton s Law of Gravitation He said 77717772 2 712 F G and was always attractive 7 pointing along the line from one mass to the other and was the force ofbody l on body 2 and ofbody 2 on body 1 Then using his 2quotd law of motion he set 77717772 2 712 FmlaG and used it to calculate the position of m1 as a function of time For the future note that E 2 712 aG Michael Bass is independent of the mass of the object m1 whose motion we seek to determine This is the one case in physics of a force giving rise to an acceleration that is independent of the mass being accelerated It is easy to calculate though I won t do it for you from this statement that the orbit of a planet around the sun is an ellipse and that Kepler s Laws of orbital motion are correct 7 they come from Newton s law Newton s Universal Law of Gravitation and his Laws of Motion were more general and we could use them to serve other purposes The demonstration that the proposed system of mechanics and the law of gravitation could result in the observed motions of the planets Kepler s Laws was Newton s crowning achievement He did what Hooke was unable to do and did so in a manner that showed how his methods could be used to solve any mechanics problem One early consequence of the success of Newton s Laws of Motion and Gravity was that the universe could not be static It had to either expand or contract but since gravity was always attractive the universe could not stand still This produced a major con ict with then existing theological models If the universe had to satisfy the law of gravity how could it be that which God established That is how could such a universe be established according to God s ideas and totally at his whim when here was evidence that it wasn t Curiously the scienti c community waf ed over this issue until well into the 20Lh century when we now have clear evidence that the universe is currently expanding and we have some notion of the laws which govern the expansion We will examine this issue in the course when we discuss cosmology Another major consequence of Newton s Laws but of less religious signi cance was what happens at the earth s surface We see that if m Me the mass of the earth then ml Me r62 mlaG but G M6 and re the radius of the earth are constants and so we can clean this up a little into the much more familiar F mla mg where g GMere2 is the acceleration due to the force of gravity This is what Galileo Galilei in Pisa observed by dropping balls made of different material off the leaning tower Actually this is just a good fairy tale While Galileo did live in Pisa and he did observe that all objects accelerated at the same rate no matter how heavy they were he did so by rolling balls down planes Balls rolling down planes moved slowly enough for him to accurately measure their displacements velocities and accelerations Objects dropped off the tower fell too fast for him to measure By performing these experiments Galileo not only demonstrated a critical fact of Michael Bass nature he showed us how to do experiments He set up a system in which he was able to make 39 39J correct and then 39 J his data for regularities that might reveal the principles governing that which he studied Speaking of Galileo it is important to note that he was also the first to make a telescope con rm its performance on the ground and then turn it towards the skies He was sponsored in this by the merchants of Venice who wanted to use telescopes to detect when a ship was coming into port before their competitors In those days as perhaps is still true a few hours advanced warning could mean fortune or failure We might say that the commercial culture of Italy gave rise to one of science s most important discoveries In today s parlance we would say that Galileo had industry sponsors for his research When Galileo looked skywards what he saw produced a revolution in how we see ourselves in the universe Galileo observed that Jupiter had moons Prior to his work the European world believed that the sun moon planets and stars were held in spherical celestial orbs rotating about the earth at their center This was Aristotle s universe and had been working pretty well with certain modifications called epicycles for nearly 2000 years There was no place in the celestial orbs for moons around Jupiter Worse yet for Galileo the Catholic Church had some time before accepted the Aristotelian view It had become dogma Galileo was given the choice of death or recanting At the time he was forced to recant in 1642 in Italy a Catholic country the Royal Society for the Advancement of Science was being formed in England a Protestant country The center of science moved out of the Mediterranean and to the north It is sad to say that it has remained that way until very recently when scientific inquiry in some of the Mediterranean countries revived in the 20th century Today we live in a world where Newton s laws of motion apply 7 from colliding billiard balls and swinging pendulums to racecars and spacecraft His law of gravitation explains the motion of astronomical bodies with great precision and with Einstein s refinements is used to study the fate of the universe There is something very very critical in the form of the Universal Law of Gravity giving a force which falls off inversely as the square of the distance between the bodies r12 Let s examine this question from a geometrical perspective Consider a mass m as shown No matter pm 0 TH Michael Bass how weirdly the body is shaped when we are far enough from it it appears as a point mass It is obvious therefore that its gravitational attractive force on mass m1 at a distance r12 away can only be determined by the total quantity of mass inside the sphere drawn in the picture Therefore we can consider the total ux or ow of gravitational force per unit mass across this surface sort of like water being pulled in through the sphere Since the problem is spherically symmetric and the total gravitational ux can only depend on m we can write g FodAocm where mathematically we have defined gravitational ux Pg as the integral or sum of the dot product of the force of gravity per unit mass F with the outward pointing surface area vector The force of gravity per unit mass can be thought of as the gravitational ux per unit area When we integrate over the whole surface of our spherical shell and when we realize that since the problem is spherically symmetric F can only depend on r we find F 047272 oc m 01 F F mlm r m1 0 cc 4722 which with G as the proportionality constant is Newton s Universal Law of Gravity Notice that we found the lrz or the inverse square law property of Newton s Law of Gravitation from the fact that the area of a sphere is 47Er2 What we have just done is apply to gravity the same thinking that led Carl Freidrich Gauss to what we now call Gauss Law in electromagnetics We will see the inverse square law again and it will emphasize how the symmetry of our three space dimensioned world affects our every day lives We have seen what Newton did Through his laws of mechanics and his demonstration of the validity of the inverse square law for gravitational attraction he gave us a means to evaluate the motion and changes in the motion of everything He taught us how to deal with the motions of stars and galaxies as well as atoms and molecules of air when considering them to be just smaller than normal billiard balls The mechanics that results from Newton s contributions is one basis of our society s technology The others are rm A and 39 quot With these three aspects of physics most of today s technological world is comprehensible It is intriguing to consider that the fundamentals of all three were well understood before the 20Lh century started When we examine 20Lh century science we will see what it added to the body of physics and how some of that has permeated everyday life Then we consider what the future of modern science might be Michael Bass First though we examine thermodynamics Thermodynamics is actually the sum of several conservation laws that are powerful tools for understanding things Science invented conservation laws because they provide valuable guidance to the inner workings of the universe Newton s 2quot law 11 2 dltmvgt 2 F dt dt gives us our first conservation law For a system in which no net force is exerted on a body or bodies it says 11 2 dltmvgt 2 0 dt dt This reads that the quantity p mv the momentum for the system does not change with time A quantity which doesn t change with time remains constant we say it is conserved Another way of thinking about conservation laws is to consider them as prohibitions They prohibit any process in which the conserved quantity changes This allows one to rule out such things as perpetual motion machines or propelling oneself through space without propelling something else in the opposite direction Two billiard balls of masses m1 and m which initially have velocities V1 and V2 collide and bounce off each other There is ignoring friction no external force on the system and so we know that since momentum is conserved the final momentum of the system must equal its initial momentum Mathematically this means that mlvl mzvz befmz mlvl m2V2a 2r If you weren t a pool shark you could compete by calculating the momentum of the system before and after the collision when planning your shots No violation of the conservation of momentum law has yet to be found It applies equally well to billiard balls bumper cars and colliding subnuclear particles in multibillion dollar accelerators From the prohibition point of view we say that no event is allowed in which the total momentum changes when no external forces act on the system With the advent of mechanical machines water wheels for example we knew we were converting one kind of something into another By falling from some height the water made the wheel turn In the process we converted a property that the water had when it was up high and didn t have when it was down low into a motion of the wheel its rotational motion Later when steam engines were invented and science was forced to develop thermodynamics the conversion process got even more complicated Now we converted something which seemed to be stored in wood or coal their property of burning and making things hot into something in the Michael Bass steam its property of being hot and then into something in the motion of a wheel To explain all these somethings science was forced to invent the energy concept the something was energy and while we could transform one kind into another it soon developed that in a closed system the quantity called Total Energy didn t change it was conserved Temperature was introduced as a property of a system which enables us to believe that two objects are in thermal equilibrium that is two bodies are in thermal equilibrium when both have the same temperature and so no thermal energy ows between them This concept of temperature as de ning thermal equilibrium gave us the zeroth Law of Thermodynamics The law of conservation of energy is the First Law of Thermodynamics It states that in a closed system you can only convert energy from one sort to another you can t create or destroy energy This means that our machines can only do some limited sorts of things and we must put in energy fuel if we want to get something out motion of our autos for example The prohibition was that no machine could produce useful output energy without providing it with an appropriate input energy James Watt s steam engine could not turn a single spinner in a single textile mill unless the energy stored in the coal were released by burning to heat the water to make the steam Once we had these concepts and not wishing to let go of a good thing we tried to gure out how efficient one of our machines could be It seemed reasonable to ask IfI put in some energy stored in the fuel how much energy can I expect to get out in the form of useful work from my machine Sadi Carnot a French engineer analyzed this question for a certain kind of engine in the early 1800s and decided an instinctive and gloriously correct conclusion that it now called a Carnot Engine would be the most ef cient engine possible He wasn t vain he was right As a result all engines must be less ef cient and this comprehensive statement drew much study since many physicists wanted to have the most ef cient engine The result however was the development of a mathematical understanding of why Camot s was most ef cient and others not The mathematical statement of Camot s Ef ciency Law is that there is a quantity called entropy that for a closed system must increase or in ideal circumstances at least remain the same whenever a thermodynamic process takes place Entropy it turns out is a measure of disorder in a system Since in the real world entropy must increase it means that disorder must increase That means that events always happen from ordered past to disordered future states In other words Time flows forward The statement that entropy must always increase or remain constant is the 2quotd Law of Thermodynamics It is the only place in science where a law is asymmetric in time Other laws are the same if you reverse time For example when two billiard balls collide you don t know in what direction the clock was running You can only tell that momentum was conserved However you can tell that when a broken cup rises up off the oor and reassembles itself on the table top that time is running in the wrong direction This is because the broken cup is much Michael Bass more disordered than the assembled cup and the second law says that events progress towards more and more disorder The prohibition is that the cup never spontaneously rises off the oor Of all the laws of physics only the Second Law of Thermodynamics gives one a sense to the ow of time It is curious that a basic fundamental property of the universe results from asking about the efficiency of engines Using an analogy with gambling the laws of thermodynamics are sometimes stated as 0 You are allowed to play 1 You can do no better than break even 2 If you play long enough you must lose So science had already before 1900 not only created new and wonderful things it had upset some long held views the static universe was not possible and time owed from past to future time was not cyclic It had also begun to permeate how people thought and what they did Think of such phrases as they have the momentum and where does she get her energy to get a sense of how science had impacted every day life However science s most critical contribution to our lives was the electromagnetic revolution In the late 1700 s people were examining things that had been known for long time but with a new view to trying to understand what was going on Luigi Galvani was looking at frogs legs and saw them twitch when connected to a body charged by rubbing say cat s fur on glass Ben Franklin was risking his life to show that lighting was electricity just the same kinds of charges as produced by rubbing one thing on another Then in the early 1800 s August Coulomb a civil engineer with the French Army put forth a law that the force between two charged bodies of charges q1 and q and separated by a distance r12 was F2 2km 2 r12 where k was a constant introduced to get the units straight that is since you had a force on the left and charge squared divided by distance square on the right you needed a constant with the right units to make the equation consistent Later on in the study of electromagnetics physicists realized that k was not some arbitrary constant but a fundamental property of the universe related to the speed of light Notice in Coulomb s Law that once again a force law has the inverse square law form A German Carl Freidrich Gauss understood the implications of Coulomb s law and turned it into the mathematically elegant form now called Gauss s Law for Electricity which shows how electric fields are related to the symmetry of our three spatial dimensioned un1verse Meanwhile others were studying magnets and magnetic forces Biot and Savart again in France showed that moving charges currents gave rise to magnetic forces However no one Michael Bass then or since could nd a single north or south magnetic charge magnetic charges always came in pairs No matter how nely you divided a magnet you still got a northsouth magnet You never got just a north or just a south It seemed that while electric and magnetic forces might be related they were different Then Michael Faraday in England showed that when a magnetic field a spatial distribution of magnetic force changed with time you could induce an electromotive force a voltage in a circuit This brilliant former bookbinder s assistant had invented the concept of fields of force to explain his observations since he had no formal training in mathematics His conclusion Faraday s Law of Induction leads directly to all our electric generators and motors It is therefore the foundation on which our electronic world is built It is what allows us to generate electricity Think of our world without it It is interesting to note that Faraday was supported by the Royal Society for the Advancement of Science an organization that was funded by the British government The Prime Minister of Great Britain William Gladstone was not out of line when he asked Faraday what was so important about his idea Faraday s answer was that while he was uncertain of the details he was certain that Gladstone would tax it By mid century the stage was set for someone to see the implications of all of this It fell to James Clerk Maxwell in Scotland to see the symmetry He realized that electric and magnetic forces were different aspects of the same phenomenon now called electromagnetism Maxwell assembled 4 laws Gauss Law for Electricity Gauss law for Magnetism Faraday s Law of Induction and Ampere s Law for the magnetic fields due to currents modified them a little and showed that electric and magnetic fields were related They were not only related but were interchangeable With these four famous equations and some one or two others which describe the way different materials react to electromagnetic fields we can solve any problem in electromagnetism from the force between two charged pit balls to the design of a modern computer Maxwell went further He showed that his equations predicted electromagnetic waves that propagated in space with the speed of light In fact he showed that light itself was an electromagnetic wave phenomenon contradicting Newton s view that light was corpuscular and set the stage for the interpretation of light as a wave phenomenon As a result the phenomena of diffraction interference and ray propagation of light could be understood and it seemed clear to everyone that light was best interpreted as a wave of electromagnetic energy We shall see how this view was to be challenged in just about 50 years by the data that led to quantum mechanics Maxwell s was the first unification of two forces electric and magnetic into one it was the first use of mathematical symmetry arguments in establishing scientific principals and it worked It explained many things predicted many things and made possible our electronic world A physicist s tee shirt is sometimes seen with the words Michael Bass And God said v13 1 0 VB0 Vsz QB 3t 3E VXB 0J 0 07 and there was light The equations are Maxwell s Equations The quote is a physics joke In these equations E is the electric eld B is the magnetic eld q is the total amount of free charge in the region J is the density of currents owing in the region 80 and MO and are constants which were originally introduced to compensate for the units in less general equations What is remarkable and what Maxwell showed is that 80 and Mo are fundamental constants of the universe related to the speed of light through the relationship c 1 l 0 0 Further notice that Maxwell s Equations are symmetric in E and B For example a time varying electric eld gives rise to a magnetic eld in the fourth equation and a time varying magnetic eld gives rise to an electric eld in the third These equations help to explain how electric generators work or how energy in an electronic circuit gets through a capacitor Maxwell s Equations enable the solution of all problems in electromagnetics With them only you can analyze an optics problem design a starter motor for your car plan a computer or build a cable TV system While God may not have used Maxwell s Equations as mathematically expressed above they must have been what heshe had in mind when our universe got started because they are satis ed exactly in every experimental test yet conceived In other words they are how the world works No one knew this for sure in 1873 when Maxwell s results were made known In fact demonstrating that members of the British parliament were no more aware than any member of our congress might be when told of Maxwell s achievements one MP scoffed and said Of what possible use can that be He was put down with the remark Sir the same can be asked of a newborn babe You may not think of Maxwell every time you turn on a radio or TV or use a phone or a computer or play a CD or get checked out with a laser scanner but his contribution to science enables them all Thus before 1900 science had produced the three underpinnings of our modern technological society mechanics thermodynamics and electromagnetics In fact it may be said and I say so here that if no new science only engineering had been carried out since 1900 our world would be quite similar to what it currently is today not identical not as comfortable but similar Michael Bass In the 20th century our view of the universe clari ed and became more complete However first it became more complex and less comprehensible Science would have to turn over some of its own apple cart to get a better understanding of how things worked At the turn of the century scientists were in a proverbial pickle According to Newton whose insights had been remarkably right in most things there could be an absolute reference frame in the universe and all motion could be measured relative to it Now in daily life we don t much care about such things After all the earth or your room is a good enough reference frame against which to measure motion What was bothering scientists was that if there were such a reference frame then we should be able to measure motion relative to it So for example when it was January the earth would be moving one way and when it was July the earth would be moving the other way IfNewton were right the speed of light measured on the earth would depend on the earth s motion relative to the so called rest frame or ether That means that we should be able to sense our motion with respect to the absolute reference frame We could do this by measuring the speed of light in the direction of the earth s motion and finding that it was different from that measured in a direction perpendicular to the earth s motion Now this sounds as though it would be a simple experiment However the speed oflight is very large 3 x 108 msec and the earth s motion in its orbit around the sun is very much slower 100 s of msec The result is that any differences in the measured speed of light due to the earth s motion would be very small and consequently the measurement would be very difficult In Cleveland Ohio an American physicist Albert Michelson invented an interferometer that would be capable of the measurement Together with an assistant E W Morley he put his interferometer on a concrete slab and oated it in a pool of mercury it is fortunate that they didn t both go mad because breathing mercury vapor causes madness When they looked at the interference patterns they found to their astonishment that the speed of light was the same no matter how the earth moved By rotating the interferometer so that different arms pointed in the direction of motion or perpendicular to it and observing that no change in the pattern of interference took place they were forced to this conclusion For his work on the speed of light Michelson became the first American to be awarded the Nobel Prize in Physics The year was 1907 The result of the MichelsonMorley experiment was that there could be no ether no absolute reference frame or else something very strange was happening to their instruments In fact a Dutch scientist Hendrik Lorentz who won the 1902 Nobel Prize in Physics for unrelated work on magnetism and independently William Fitzgerald in Dublin suggested that the arm of the Michelson interferometer oriented parallel to the direction of motion contracted a little Lorentz was saying the arm in the direction of the motion got shorter Therefore light traveled a shorter distance in that arm compensating for the movement in that direction and thus giving the same value for the speed of light as obtained for light traveling perpendicular to the earth s motion Since in the LorentzFitzgerald picture a ruler laid in the direction of the earth s motion would also shrink by the same amount as the length of the arm you couldn t measure the contraction directly As often happens a scientist had got it right but not complete That was left Michael Bass to a German born into a Jewish family and working as a clerk in the Swiss Patent Office in Bern In this job he had the time and freedom to think about the problem Of course we are talking about Albert Einstein While Einstein claims not to have known of the MichelsonMorley experiment in detail he certainly read the journals and knew of the difficulties engendered by its results Einstein in proposing his Theory of Special Relativity was about to overthrow the central construct of the Newtonian universe In it Einstein said that there was no absolute reference frame but instead he proposed that all motion is relative That is any motion must be described with respect to some reference frame which may be moving with respect to some other reference frame which itself might be moving In other words Einstein was claiming that there was no absolute reference frame The consequences of this idea revolutionized physics Since any non accelerating or inertial reference frame was likely to be moving with respect to any another Einstein reasoned it was essential that the laws of physics be the same in all inertial reference frames He was saying that all observers moving relative to each other without acceleration must decide on the same laws of physics This meant that we might measure different time intervals or lengths but we would always no matter how we were moving get c 2997924589 x 108 ms for the speed of light The implications of this were staggering Ifa body moved near the speed of light its length in the direction of motion would contract clocks on the body would run slower since velocity is lengthtime this had to be so in order to get c for the speed of light in all cases the mass of the body would increase becoming infinite when the speed equaled c and so the body could never reach a speed of c No material body could ever move at the speed of light since it would take an infinite acceleration to ever move that fast Einstein s philosophic point of view that physics had to be the same in all reference frames also led to his famous relationship between mass and energy E mc2 This relationship would make possible the nuclear science that led to nuclear weapons nuclear medicine and nuclear power systems What was amazing about Einstein s initial relativity work now called Special Relativity was that it was not only explanatory it was predictive and it worked It has never failed any experimental test Strange as it seems from a common sense point of view the twin who travels in a space ship at a speed near the speed of light ages more slowly than her sister who stayed on the earth You may ask how can we be so sure The answer is that we did the experiment Ultra high precision atomic clocks not twins were compared as follows One remained at the starting point and one was own around the earth on a series of jet planes The one that traveled came back having counted off less time than the one that stayed home Einstein is completely correct the twins age differently depending on their motion relative to one another Einstein published this and other critical papers in the wonder year of 1905 yet he Michael Bass remained a clerk in the Swiss Patent Office and then a junior professor in Prague until 1914 when he was appointed Professor of Physics at the University of Berlin During this time he worked on the principal of general relativity in which he examined the properties of physics in accelerating reference frames and in the presence of gravity He proposed another brilliant insight He suggested that being in an accelerating reference frame is indistinguishable from being in the presence of a gravitational field From this equivalence principle Einstein was able to show that gravitational fields caused the shape of spacetime he proposed that we live in a 4 dimensional 3 space and 1 time universe to be curved Light would follow the shortest path from one point to another in this curved spacetime and so light from a star would be bent by passing close to the sun The observed position of the star when viewed close to the sun would be displaced a little from the position viewed from another place as sketched below True position of distant star lo lApparent position of distant star Light is bent as it passes through the sun s gravitational field Observer on the earth An expedition to test Einstein s prediction that gravity bends light was planned to take place in the Crimea in Russia in 1914 where a complete solar eclipse was to occur To see a distant star in the light of the sun would be impossible However during a total eclipse when the moon blocked the sun s light it might just work Particularly if you were careful and lucky Luck was needed because the weather had to cooperate Unfortunately while the weather may have been all right in 1914 luck ran out and World War I started The test of Einstein s prediction didn t occur until 1919 when a British expedition to the island of Principe off the west coast of Africa under Sir Arthur Eddington confirmed the theory proposed by Albert Einstein a German Not only was Einstein instantly more famous than ever but the British German aspect of the scientific endeavor was viewed as an aspect of rapprochement between the two former enemies Many hoped it would signify the start of an era of cooperation between these countries and between others as well As you know that turned out to be wishful thinking If light were bent by a gravitational field then light leaving a star would follow a curved path If the star s density became large enough the local gravitation would curve the light paths Michael Bass back on themselves and the light would not escape the star s gravity Since no information would ever get out of such a concentration of mass it would in effect vanish from the universe Today this vanished concentration of mass is called a black hole and is the subject of much research It is the fate of large stars when they have burned their nuclear fuel and can no longer avoid the pull of gravity They collapse and form black holes Black holes also seem to be present at the centers of galaxies and may have been present in the early universe Such primordial black holes some speculate may be the cause of the nonuniformities we call galactic clusters and galaxies themselves If so they may be the reason be why we are here to wonder about black holes Meanwhile Einstein in evaluating his theory realized that it required that the universe had to either expand or contract or expand so that eventually it would exactly stop Einstein couldn t accept the expansion or contraction he believed the universe was static and invented a term to add to his equations called a cosmological constant which like antigravity just balanced the universe so that it would be static This was before an American using the Mount Wilson Observatory in California Edwin Hubble showed that the galaxies were rushing apart The universe was indeed expanding When he learned of these results Einstein admitted his error calling the cosmological constant his biggest scientific mistake Today it seems Einstein had it right after all as the cosmological constan may be the cause of the acceleration in the galactic expansion More on this later Einstein won the 1921 Nobel Prize for physics He did not win it for his work on relativity that restructured our view of the universe and opened up unimagined possibilities While relativity revolutionized our world the Nobel committees knowing Einstein deserved the prize but not understanding or thinking of relativity gave him the prize for his critically important contribution to the understanding of the photoelectric effect In this work Einstein made a major contribution to the development of quantum mechanics which along with relativity is one of the two major revolutions to affect physics in the 20th century While relativity explained the universe as a whole and the very large scale of things such as stars black holes galaxies universes and so on quantum mechanics proved necessary to understand the very small The workings of molecules atoms electrons nuclei protons neutrons quarks and so on are only understandable using quantum mechanics Classical mechanics fails completely when applied to things that are very very small Here small means having dimensions of a molecule or less than a micron or two As quantum mechanics developed it became clear that the very small was governed by a principle called after its originator the Heisenberg Uncertainty Principle In simple terms it states that if we measure one property of a body called A with some degree of precision AA then there is a conjugate property B whose precision can only be determined within the limit set by the relation AAABZh where h 663 x 103934 Js is Planck s Constant Michael Bass This means that if we know position with exact precision we can t know momentum at all Or if we know a particle s energy precisely we can t know when it was present The Uncertainty Principle in fact sets a boundary to the early universe when the whole universe was very very very small The Uncertainty Principle also set the stage for the Copenhagen interpretation of Quantum Mechanics Niels Bohr a Dane proposed that we could only know the time averaged probability that a body be in a place Einstein while understanding quantum mechanics couldn t accept this probabilistic view of the world and pontificated that it couldn t be so since God doesn t play dice with the universe In fact all our evidence says that on a certain scale God if there is one doesn t care that the universe can only be described statistically On that scale the world of the very small things are not deterministic Now let s consider why we had to have quantum mechanics in the first place In the second half of the 1800 s spectroscopists people who measured the spectra of light emitted or absorbed by various things reported curious lines in the spectra of the sun and of hydrogen and other gas discharges Since classical theories of these systems no matter what they might look like in detail could not give discrete sharp spectral lines physics was in a quandary Also if one heated a body to some temperature classical theories predicted that the body would emit far more ultraviolet light than was observed Again there was a problem In 1900 Max Planck in Germany proposed that light could only appear with nite energies given by Ehv where h was a constant now called Planck s constant and V the frequency of the associate light wave Only now it was a quantum of light or a light particle with energy determined by the frequency of the light wave Already there was a problem Planck introduced us to light quanta but could not do so without retaining some of the wave nature of light The problem was and remains to the present the issue of the particlewave duality of light It was and for many is still a very unsatisfying way to understand how things work After only about half a century the wave theory of light which had been so successful was challenged by the notion that actually light was in some sense particle like in nature It seemed that Newton s idea that light was made up of corpuscles was in some respects correct Planck s idea that light came in quanta enabled him to explain the spectra of black bodies and overcome the deficiencies of earlier classical models His idea was applied by Einstein in 1905 to explain the photo electric effect By about this time electrons and nuclei had been discovered and the planetary model of the atom had been proposed However the classical model where an electron circled the nucleus like a planet circling the sun had a problem The electrostatic attraction between the negatively charged electron and the positively charge nucleus would eventually cause the electron to collide with the nucleus producing no atoms at all But there are atoms and they are stable Niels Bohr and the quantum theorists proposed that while in the classical model electrons could occupy any orbit they wanted to in the proper quantum mechanical model the electrons were restricted to only a few special stable orbits The orbits Michael Bass were quantized and when an electron changed from one quantized orbit to another it changed its energy In so doing to conserve total energy the atom either absorbed or emitted a quantum of energy in the form of one of Planck s quanta But think for a moment since only certain transitions could occur only certain discrete quanta were possible and only certain speci c spectral lines wavelengths of light could be expected These would be characteristic of the atoms and would explain the spectroscopists results Bohr s model was given mathematical rigor by Erwin Schrodinger Werner Heisenberg Paul Dirac and others The accuracy and utility of quantum mechanics was proven by numerous experiments Both theory and experiment were eventually demonstrated with very high precision Quantum mechanics now forms the basis of our understanding of all sorts of things Today the combination of quantum mechanics with gravity a relativistic but classical theory is the goal of physicists seeking to understand such things as black holes star histories and the early universe They seek something called quantum gravity By mid century physics had Newton s mechanics which worked perfectly and quite precisely for speeds much less than the speed of light thermodynamics telling us how energy changes types and why time ows from past to future electromagnetics giving us electricity radio TV and electronics relativity explaining the structure of our universe and quantum mechanics explaining the structures of atoms and subatomic particles so that we have lasers and solid state electronics and nuclear magnetic resonance As all this developed researchers began to understand that only four forces were needed to explain the interactions between the particles which we could observe The weakest force is gravity It is always attractive and is the interaction between all bodies having non zero mass The range of gravity is unlimited The next strongest force is electromagnetism describing the interaction between charged bodies and which can be either attractive or repulsive It is many millions of time stronger than gravity and also has unlimited range Then comes the weak nuclear force that is responsible for holding nuclei composed of protons and neutrons together It is attractive has a range of the order of the radius of a nucleus 103913 m and is much stronger than the electromagnetic force Finally comes the strong nuclear force that holds individual protons and neutrons together It is always attractive very short range it acts inside a proton and very very very strong Modern physicists are trying to unify these forces Maxwell had shown that electric and magnetic forces were different manifestations of one force electromagnetism Today physicists are trying to nd out if all four forces are different manifestations of a single force Their thinking goes something like this if the energy of the particles were suf ciently high the interactions caused by all these forces should look the same The problem is when if ever could this have been so As far as anyone can tell only once in the history of the universe could such conditions have existed Only at the instant of its beginning could all forces in the universe have been indistinguishable At that instant when energies were extraordinarily large temperatures many trillions of times that of the sun s interior when the universe was pure energy too hot to contain particles there was only one force As the universe expanded and things cooled down it Michael Bass became possible for particles to exist and the symmetry of having only a single force was broken The forces separated and our universe of particles and massless quanta of light came into being So far we know of Maxwell s uni cation of electric and magnetic forces Then between 1961 and 1972 Sheldon Glashow Steven Weinberg and Abdus Salam showed how to unite the electromagnetic and weak nuclear forces Their electroweak unification has been demonstrated experimentally and led to their sharing the 1979 Nobel Prize They and others have pursued grand unified theories to try to unify the electroweak and the strong nuclear forces A number of models have been proposed but there are problems These models called GUTs predict that a proton will decay in 10 years Now the time since the big bang is only 1010 years and we only live N102 years so this isn t easy to measure However if we take 10 1 protons we can try to see if 1 proton per year decays The experiment is conceptually very simple Take a tank of very pure water put it underground where the cosmic ray background radiation is weak surround it with detectors to sense a decay and watch and wait and wait and wait So far we have no evidence for a proton decay and so its lifetime must be gt1035 yrs There is a problem here to be solved More disturbing and vastly more complex is the problem of unifying the quantized forces electromagnetism weak and strong nuclear with that classical force gravity Trying to do this is the field of many researchers However time and space restrict this discussion to the work of Stephen Hawking He contributed significantly to our understanding of that ultimate gravitational event the black hole From this work he realized the thermodynamic properties of black holes and showed that they don t can t violate the second law of thermodynamics Stated differently Hawking showed that no black hole is naked They are all surrounded by an event horizon that remains forever in our universe but which prevents any information from the interior from leaking out and violating the 2quotd law Hawking then became interested in quantum gravity and now studies it He has done all this while suffering from amyotrophic lateral sclerosis ALS or Lou Gehrig s disease He can t speak understandably use his hands to write or draw or use a conventional computer He must carry out his research entirely in his own mind and use a special computer to communicate his results Given the fact that the universe is expanding and the body of knowledge we now have it is only reasonable that physicists are trying to construct a picture of how the universe came into existence and what is its future If we trace the expansion back to the beginning it seems as though the universe started with a very hot Big Bang about 135 billion years ago The evidence for this is overwhelming First there is Hubble s evidence for the motion of galaxies away from each other Then there is the universal N3 K black body radiation which is a remnant of the radiation present at the moment of the Big Bang and which is seen virtually uniformly throughout the sky Amo Penzias and Robert W Wilson of the former Bell Telephone Laboratories won the 1978 Nobel Prize for discovering the presence of this cosmic background radiation Further evidence for the Big Bang model of the universe comes from the fact that the measured ratio of helium to hydrogen in the universe is what the model predicts Michael Bass There are issues to be resolved concerning the model such as how did the nonuniformities we see form in so little time For example as we look out into the universe we see galaxies galactic clusters and super clusters as well as immense regions void of any visible matter The Big Bang model must allow for such structures and it is being studied and revised to do so Another intriguing feature of the Big Bang as alluded to earlier is that at the beginning energies were so high that the four forces were uni ed Thus the study of the very small is being united with the exploration of the entire universe in efforts to understand how unification occurs Cosmologists are also concerned with the future of the universe Humankind won t likely be there to see it but we would like to try to figure out what is the ultimate end of all things Consider the Big Bang to be analogous to firing a rocket off the earth If it has too little speed gravity will cause it to fall back to the surface If it has too much speed it will escape the earth s gravity and y off into space or it could have just exactly the right speed to slowly rise into a permanent orbit around the earth In the case of the universe the Big Bang is like firing the rocket The universe itself is like the rocket Depending on how much mass is present how much gravity there is the universe can expand for a while and then fall back in a Big Crunch go on expanding forever or expand but ever more slowly until after an in nite time it comes to a halt with all matter if any remains infinitely far from all other matter We don t know which of these scenarios will play out The problem is in determining how much matter there is in the universe The visible matter in the universe is barely a few percent of the critical mass needed to produce closure However there is evidence from the motions of the galaxies that there is a great deal of matter that we can t detect This so called dark matter interacts gravitationally with other matter and could provide enough additional mass to cause the universe to either recollapse the Big Crunch or slowly stop expanding One of the most interesting problems in modern physics is to try to identify the dark matter It may be in the form of huge numbers of Jupiterlike objects that do not emit enough radiation to be detected or it may be black holes Another possibility is that the fundamental particle called the neutrino thought to be massless may actually have a very small mass Since there are immense numbers of neutrinos in the universe a small mass could have major consequences In fact experiments have shown that some neutrinos do have a finite amount of mass These experiments showed that one type of neutrino changed into another type and that can only happen if they are traveling at less than the speed of light In that case they have mass No matter the source of the dark matter we have to have dark matter to explain the motion and distribution of galaxies in the universe and so our cosmology is incomplete In the next paragraph you will read how it is even more incomplete than we thought In the first years of the 21st century astronomers made a startling discovery Since Hubble s work it was know that the galaxies were ying apart from one another Further it seemed that the rate was constant and was a measure of the universe s age With better telescopes and light detectors evidence began to come in that showed that galaxies that were more than about a billion light years away were moving away faster than they should have been The recessional speed was accelerating The explanation of this is a difficult problem for scientists They have to determine either that there is some as yet unknown force driving the acceleration or that Newton s inverse square law breaks down at very large distances At the present time we don t know enough to explain the observations but surely scientists around the world are working on nding one that works and satis es our ideas on what is good science The foundations of our technological world were established before the start of the 201h Century Since then physics has continued to develop making it possible for the rst time to seek scienti cally valid answers to such questions as how did the universe come into existence and what is its fate We may have asked those questions in the past but then the only possible answers would have come from theologians Today science may provide them That is it may give answers based on a method allowing for testing and veri cation answers not requiring belief alone We are a long way from complete answers but parts of them are in hand and with the effort to nish the work comes a deeper more complete and more satisfying understanding of the universe and our place in it Michael Bass 20


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