Einstein’s Special Relativity in VCE Physics

  • Published on

  • View

  • Download


Einsteins Special Relativity in VCE Physics. PHYSCON February 2012 Keith Burrows AIP Education Committee. Some reasons for including the Relativity DS in Unit 3: - PowerPoint PPT Presentation


Slide 1Einsteins Special Relativityin VCE PhysicsPHYSCON February 2012Keith BurrowsAIP Education Committee12012: This ppt is revised from the Feb 2011 teachers conference version. It is based on the 2007 & 2010 versions given at PhysCon that year, but amended to take in the FAQs and the thought experiments in the light of the difficulties in that area. The International Year of Physics was when we started teaching Rel! **Find out who... has taught it last year?intends to teach it this year? ....might teach it this year? ....has a good understanding of relativity? Please feel free to add or question! Spend some time discussing why we should teach it... and how we can teach it. Resources and activitiesWe cant cover the whole lot in one hour! We will skip through the content without much explanation pausing on some of the key sections.Some reasons for including the Relativity DS in Unit 3:Students fascinated by the idea of Einstein and Relativity. Expands their thinking and opens their minds and not only in physics. Its what they want from Physics! We need to attract non-physics students who will end up as journalists, teachers, business people, and even politicians. (Especially politicians!)Relativity is an excellent example of the way science works: Apparent inconsistencies creative thinking experiments new theories Science as creative and imaginative.Fundamental physics: Newtons laws, frames of reference, mass and gravity, relative motion, waves and light, nature of space and time, electromagnetism.Education should be expanding minds not closing them! Non-scientists need to understand how science works especially politicians! (CC science!) Inconsistencies which attracted Einstein were in electromagnetism (not relative motion). Science is not mechanical but creative. This presentation is copyright Keith Burrows but physics teachers are free to use it in their classrooms. It is not to be used for commercial purposes. Some diagrams from Heinemann Physics 12 are used with permission. Suggestions for improvement are welcome! Email me at keithphysics at optusnet dot com dot au (with the appropriate ats and dots)2Some reasons for including the Relativity DS in Unit 3:Classic physics experiments: Michelson-Morley, speed of light, Eddingtons eclipse, travelling clocks, muon lifetimes, etc.Much modern technology can not be understood without relativity: magnetism, nuclear energy, GPS, the synchrotron.And it is (almost certainly) to be included in the Australian National Curriculum.3Why Relativity?What is physics really all about?4Aristotle the world can be understood by careful observation, thought and reason. Copernicus the Earth moves around the Sun. Galileo there is nothing special about zero velocity. Newton too many to list! What physics really is all about:5Oersted found link between electricity and magnetism.Faraday electromagnetic induction, motors, generators, field picture. Maxwell light is an electromagnetic wave. Marie Curie radioactivity 6Relativity brings all these fundamental aspects of physics together in a new way!Einstein was Times Person of the century for good reasonRepresents not just the ideal scientist, but also an ideal public person:He questioned assumptions, he looked carefully at what was known, he used his imagination creatively, but intelligently to put forward new and radical ideas. He had a real concern for the social implications of science, as well as being a warm and compassionate human.Newton realised that we assume that time and space are straight...and that time and space are unrelated.7We normally assume no relationship between space and time! But most of us dont even realise that it is an ASSUMPTION. Einsteins relativity is about looking at that assumption more critically and discovering the real relationship between space and time.Einstein said that we should not assume this:He said that travel through time and space were intimately related.Special Relativity is about that relationship.These illustrations from Hawking: Universe in a NutshellThese illustrations from Hawking: Universe in a Nutshell8Travel through space and travel through time are related. One is at the expense of the other (sort of!)Why study relativity?Relativity represents a giant step in the story of physics. Why leave out the climax of the story?It is an excellent illustration of the process and nature of physics. Through it we can get a feel for real physics.Imagination is more important than knowledgeAlbert Einstein9To stop at the end of the nineteenth century seems to leave out the climax of the story! Imagination is as great a part of good science as it is of art...Think of the imagination needed to see that the Earth circled the Sun...or the imagination to see that time and space were not absolute!Einsteins LegacyIn many ways Einstein represents a new way of thinking, not just about space and time, but about everything.Will this new way of thinking have an impact on the way we see our world as profound as that of the physicists of the Enlightenment?(Not yet apparently )10The new ways of thinking introduced by Galileo and Newton had profound implications in areas well beyond physics.It was a turning away from declared wisdom to a new way of discovering truth through experiment and reason.One consequence was the mechanical universe, a universe which operates according to set rules and without any need for divine intervention.Still endless arguments about whether this universe needs a creator, or whether there is any room in that universe for something beyond the physical.The (unimaginative) Lego block universe has become well entrenched in popular culture.Led to a very materialistic culture in which things seem to matter more than people. Look at the mechanical view of education that thinks you can improve it by publishing scores for tests on websites, or the lack of imagination in understanding the effect of what we do on our environment etc..etc..In fact, in many ways politics and public discourse dont seem to have caught up to the enlightenment!Relativity could change the way we think!When the ideas involved in relativity have become familiar, as they will do when they are taught in schools, certain changes in our habits of thought are likely to result, and to have great importance in the long run.Bertrand Russell ABC of Relativity11What are these changes in our habits of thought? Consider the changes that Einsteins theory brought from the approach of 1900: From the mechanical universe where everything had a simple mechanical connection including human interaction to a universe of much greater subtlety and openness. We even find it hard to imagine a world different from the one we inhabit one where we are not tied to endless consumption and false and unsustainable growth. Or one where there are consequences to our endless fouling of our environment apart from the obvious ones that we can see immediately.Albert Michelson (1898)While it is never safe to affirm that the future of Physical Science has no marvels in store even more astonishing than those of the past, it seems probable that most of the grand underlying principles have been firmly established 12 and that further advances are to be sought chiefly in the rigorous application of the principles to all the phenomena which come under our notice.Physics at the end of the nineteenth century had become quite convinced of its correctness. Physics in the twentieth century shows the truth of the first part of this statement! And yet most of our current course is tied to those old grand underlying principles. Even in the Synchrotron DS we refuse to talk about relativity!The view in the early 1900sIn 1900 the mechanical world view seemed capable of explaining just about everything.Did this lead to the materialism and economic rationalism of the twentieth century?13What is the link between our view of the physical world and our philosophical/religious/spiritual views? The mechanical universe was largely responsible for the death of God in the 20th century. In many ways this might have been appropriate, but did we miss something else important? Was the old GOD the only way of considering the great mystery of the universe? Is economic rationalism the social equivalent of the mechanical universe of physics? In other words relativity, particularly when combined with quantum physics can open up big philosophical questions as well as simply a new link between time and space.Relativity could change the way we think!Could relativity really change the way we think?Science is not about collecting facts, but finding new ways of thinking about them. (Bragg)Imagine what could happen if we applied new ways of thinking to, say, energy production and consumption!14Einsteins thinking is characterised by: questioning basic assumptions, no blind acceptance of dogma, creatively thinking of new answers, great use of imagination.Economics seems rather like physics in 1900 rather arrogant and convinced it has all the answers. if the goal of economics became to find new ways to organise the way we do things instead of simply the application of preconceived laws (whether from Adam Smith or Karl Marx or )Its great physics!Relativity is about questioning common assumptions and finding new ways of looking at a situation. Its great thinking!What the world needs now Our students future leaders!So why study relativity?15Physics is about new ideas, about solving problems, about questioning assumptions (not just number plugging).What the world needs .... is a reasoned, thoughtful, and questioning approach to the social, political and environmental challenges we face The biggest problems we face are from fundamentalists of all sorts (religious AND political AND economic) who dont use this approach.Using Newtons laws to solve motion problems is clearly important, but it is not the big thinking that characterises so much of real physics.Relativity for allThis is not (just) for the specialists, it is for future...JournalistsTeachersPoliticiansLawyersHairdressersMothers and FathersCitizens16The specialists will obviously be interested, but they will get it later, the others wont this is their last chance.We can only provide it for physics students all year 12s should be getting it!ok so how do we do it?Developing the story: Overview1. Two principles Einstein did NOT want to give up2. Einstein's crazy idea3. Time is not as it seems: Time Dilation4. If time is strange, what about space?5. Faster than light? Momentum, Energy and E = mcThis sequence includes all of the points in the SD, but orders them in a more historically logical way.18How to introduce relativity?The historical approach enables students to follow the argument their physics can grow just as did physics itself.The whole basis of relativity was the apparent contradiction between the fundamental principles of mechanics and those of electromagnetism.This is the sequence I have developed in Heinemann Ph12.Summary of 1: Two principles Einstein did NOT want to give up1. The principle of relativity (no absolute zero of velocity) seems universal.2. Maxwells (very elegant) equations suggested:light is an electromagnetic waveand has a fixed speed whatever frame of reference!this speed was assumed to be the speed through the aether (to make it consistent with the principle of relativity)But Michelson and Morley could not detect the aether and Maxwells equations didnt want it.The principle of relativity seemed inconsistent with the predictions of Maxwells equations!19We cant develop the whole of the theory in 1 hour! We will go quickly through the content slides just to get a feel for whats there. These black slides give a summary of each main section. Einstein regarded Maxwells equations as very elegant because they seemed to sum up all the best physics that was known to that time in four equations (actually many more in the original version) which seemed eminently sensible! [see them in 4 slides)1. Two principles Einstein did NOT want to give up (1)Galilean/Newtonian principle of relativity:Nothing special about a velocity of zeroVelocity can only be measured relative to some other frame of referenceNo absolute velocityForce changes velocityThe laws of physics are thesame in any inertial frame. Very fundamental physics that seemed to make very good sense!201. Two principles Einstein did NOT want to give up (1) The principle of relativity21Different frames measure different speedsBut the difference in velocity is the same in both cases: 20 m/s forward.1. Two principles Einstein did NOT want to give up (2) Maxwell and the speed of light In the 1830s Michael Faraday suggested that light may be some sort of electromagnetic wave phenomenon.In the 1860s James Clerk Maxwell developed Faradays idea into his famous electromagnetic equations.PS: Ideal examples of the excellent experimentalist and the excellent theoretician22Faraday actually discovered that the polarisation of light was affected by a strong magnetic field.1. Two principles Einstein did NOT want to give up (2) Maxwell and the speed of light The equations suggested the possibility of electromagnetic waves travelling through space from an accelerated charge.23Clearly we can not develop the equations to show this here, but a certain amount of hand-waving about electric fields and magnetic fields and the link between them suggested in equations 3 & 4 can help kids see how physics progresses. They will know that electric charges have an electric field (just a region where one charge affects another) and that moving charges (a current) produce a magnetic effect. The question then is, how fast will these effects spread into space? (Answer c). The equations basically tell us: 1) around a charge there will be an electric field (ie. there is a force between electric charges) 2) magnetic fields are continuous (unlike electric fields which originate on charges). 3) A changing magnetic flux (just field spread over area) will generate an electric field perhaps the surprising bit! 4) A magnetic field will be created from an electric current (as we know) or (again perhaps surprisingly) from a changing electric field. This all leads to the idea that a changing electric field can create a changing magnetic field which can create a changing electric field which can create. ie. fields which self propagate through space --- at what speed? Just need to do a bit of maths and we find .1. Two principles Einstein did NOT want to give up (2) Maxwell and the speed of light Maxwells equations predicted that electromagnetic waves would travel at a speed given by a simple expression involving electric and magnetic constants.The speed of light appears to depend only on the two electric and magnetic constants of nature (how much field you get from how much charge or current). Nothing in the equation (or more particularly its derivation) showed that the speed should depend on any relative motion.241. Two principles Einstein did NOT want to give up (2) Maxwell and the speed of light But this expression suggested that electromagnetic waves would travel at this fixed speed in any frame of reference.Most physicists, including Maxwell, thought this must be wrong and that perhaps this speed was relative to the aether... the aether being a hypothetical medium which filled all space.25It is the derivation of the expression rather than the expression itself that suggests it is an absolute speed. The main property of the aether was that it carried EM waves!1. Two principles Einstein did NOT want to give up Michelson and Morley look for the aether Was the speed of electromagnetic waves really relative to the aether an absolute frame of reference?Michelson and Morley decided to look for evidence of the Earths motion through the aether.26A velocity relative to the aether appeared to be contrary to the principle of relativity which said there was no absolute frame of reference but this was an open question at this point.1. Two principles Einstein did NOT want to give up. Michelson and Morley look for the aetherThe principle of their experiment an analogy:27Note that the frequency will increase as well (Doppler shift), but here we are concerned with the actual change in velocity as found from frequency and wavelength. (v = f)1. Two principles Einstein did NOT want to give up Michelson and Morley look for the aetherThe principle of their experiment an analogy:28Note that the frequency will increase as well (Doppler shift), but here we are concerned with the actual change in velocity as found from frequency and wavelength. (v = f)The principle of their experiment:1. Two principles Einstein did NOT want to give up. Michelson and Morley look for the aetherThey couldnt measure the actual speed accurately enough, but they could compare speeds in two perpendicular directions very accurately.They knew that these speeds should be a little different if the Earth was speeding through the aether at 30 km/sec.1. Two principles Einstein did NOT want to give up. Michelson and Morley look for the aether3030 km/sec compared to 300,000 km/sec. Only 0.01%, but measurable.1. Two principles Einstein did NOT want to give up Michelson and Morley look for the aetherA water analogy: The boat travels at 5 m/s in a river flowing at 3 m/s1. Two principles Einstein did NOT want to give up Michelson and Morley look for the aetherIt travels at 4 m/s across the river and so takes 2000/4 = 500 sec to complete a two way trip1. Two principles Einstein did NOT want to give up Michelson and Morley look for the aetherBut it travels at 2 m/s upstream (5 3) and 8 m/s downstream (5 + 3) and so takes:1. Two principles Einstein did NOT want to give up Michelson and Morley look for the aether1000/2 + 1000/8 = 500 + 125 = 625 sec for the two way trip parallel to the water. 34The point being that the average speed in each direction is different.1. Two principles Einstein did NOT want to give up Michelson and Morley look for the aetherSo the average speed seems faster going across than going up/down the stream500 sec 625 sec1. Two principles Einstein did NOT want to give up Michelson and Morley look for the aetherThey arranged to compare the speed of light in perpendicular directions to the Earths motion through the aether.36They couldnt measure the speed directly, but they could set up two beams at right angles and compare any change in speed when the two beams were rotated through 90 deg. The change would be detected as a change in the interference pattern produced as the two beams met at the end of their paths.1. Two principles Einstein did NOT want to give up Michelson and Morley look for the aetherWhen they rotated their apparatus they found NO DIFFERENCE in the speed of light in the two perpendicular directions!37There may have been other explanations for the result aether drag for example, but these all appeared to be inconsistent with other good principles of physics.1. Two principles Einstein did NOT want to give upEinstein apparently knew about the Michelson-Morley experiment, but he does not seem to have been particularly interested in ithis main interest was in Maxwells equations and their predictions about the speed of light and its relativity.1. Two principles Einstein did NOT want to give upEinstein thought the principle of relativity was so fundamental it should apply in all areas of physics including electromagnetism.He also thought Maxwells equations were so elegant they, and their prediction about the speed of electromagnetic waves, had to be true.But how could these two great ideas be reconciled? Surely the speed of light (like every other speed) should depend on ones frame of reference!39The aether comes in here also if light has a fixed speed relative to that, then it becomes an absolute frame of reference, which is right against the principle of relativity.Summary of 2: Einsteins crazy ideaEinstein thought about light and decided that it should be impossible to catch up to it. He also thought the aether did not make sense and scrapped the whole idea.This led to his two famous postulates:INo law of physics can identify a state of absolute rest.IIThe speed of light is the same for all observers.The implication of taking these postulates at face value is that time seems to be relative!40Time being relative means that simultaneity must be scrapped.Events which are simultaneous in one frame may not be in another.2. Einstein's crazy idea (1)Einstein had spent a lot of time wondering about the nature of light2. Einstein's crazy idea (2)... and concluded that you could not catch up to light or the electromagnetic waves would be frozen in space. This was something that had never been seen and seemed impossible.42Like having a charge which has a field which extends out to a certain distance and then stops.2. Einstein's crazy idea (2)Einstein did all his experiments in his head Gedanken experiments. (Much neater than messy apparatus!)This might sound odd but many of the greatest discoveries in physics were made through Gedanken experimentsIncluding Newtons three laws!I wonder what would happen if2. Einstein's crazy idea (2)Einstein realised that the principle of relativity was an extremely elegant principle. The real world would be very messy without it!2. Einstein's crazy idea (2)If there was a way to find an absolute velocity (a veelo) whose system is absolute? It seemed more likely that the universe was truly democratic!2. Einstein's crazy idea (2)All motion is relative there is no absolute frame of reference. (However changes of velocity are absolute acceleration is absolute.)Perhaps more particularly, a zero acceleration is absolute. If an object has an acceleration all observers will see that it has an acceleration, but their measurement of it may differ according to their relative motion. 462. Einstein's crazy idea (2)But then, what is the point of the aether?Einstein decided that it should not be possible to use an aether or light to determine an absolute velocity.47But if this that light moved in an absolute frame.2. Einstein's crazy idea (2)He therefore scrapped the idea of the aetherand concluded that any measurement of the speed of light must give the same result:2. Einstein's crazy idea (3)INo law of physics can identify a state of absolute rest.IIThe speed of light is the same for all observers.He decided to keep these two great principles and so put forward two postulates which embodied them:I is basically the same as the principle of relativity. II is what followed from Mazwell492. Einstein's crazy idea (4)At first sight these seem quite simple and straightforward except that in classical physics they are inconsistent!Einstein said the aether was unnecessary, but this still left the problem of the relative velocity of light in different frames.How can the speed of light be the same as we approach the source as when we recede from it?502. Einstein's crazy idea (5) There was another difficulty: Einstein realised that there was a problem with simultaneity if all observers saw light with the same speed...Ana and Ben see the light hit the ends at the same time...51The observers inside see the flash hit wall at same time same distances same speed so same time.2. Einstein's crazy idea (5) but Chloe sees the light travelling at c as well, and so it takes longer to reach the front of the train.So what Ana and Ben saw as simultaneous, Chloe saw as separate events!52The obs inside see the flash hit wall at same time. Outside obs sees back flash first. ie. non simultaneous. Note this is not due to any look-back time effect we have to take all that into account in figuring out when the light actually hits the walls.David Jamiesons sequence showing a light flash in a lecture theatre and from a spaceship could also be used here. See slides at end.From http://www.ph.unimelb.edu.au/~dnj/jl/jl.htm From D.Jamieson Melb Uni Physics http://www.ph.unimelb.edu.au/~dnj/jl/jl.htm53Also see collection of train slides etc at end of this ppt.2. Einstein's crazy idea (6)This can only mean that there is something strange about time! Time appears to be relative.Salvador Dali The Persistence of Memory63Remember this is NOT due to look-back effects it is that time measured in different frames is different.Summary of 3: Time is not as it seemsWe can put numbers into this flash-in-the-train situation and find out how different the times are.The light clock enables us to generalise.We find that time in a moving frame appears to run slow (to the stationary observers)The time dilation equation: t = to where 64Delete this if equation doesnt show properly. use next slide instead.Summary of 3: Time is not as it seemsWe can put numbers into this flash-in-the-train situation and find out how different the times are.The light clock enables us to generalise.We find that time in a moving frame appears to run slow (to the stationary observers)The time dilation equation: t = to where 65Delete this slide if previous ok3. Time is not as it seems (1)We can look at the train situation qualitatively:For Ana & Ben the time for the light to get from the centre and back again is 2l/c.66In this section we assume that A&B see the same length l as C sees.Later we find that is not true, but this is an interesting example of the way apparently reasonable assumptions may turn out not to be true.Doing this also helps us to come up with the length contraction equation very simply.The maths of Chloes view. Time taken for light to get to (either) end of carriage and back again:Tc = t1 + t2 = l/(c + v) + l/(c v) = l(c v + c + v)/(c v) = 2lc/(c v) = 2lc/[c(1 v/c)] = 2l/[c(1 v/c)]= 2l/c 1/(1 v/c)So: (Remembering that TA = 2l/c) Tc = TA where = 1/(1 v/c)(But note that we cancelled the ls in the two expressions to obtain this!)67Remember we cancelled the ls because we assumed they would be the same.This highlights the importance of being careful about assumptions we normally make in working with relativity.Gamma is squared for consistency with later work3. Time is not as it seems (2)For Chloe the time is 2l/c 1/(1 v2/c2). Remember that Chloe sees the light travelling at c, not c v.We can write this as Tc = TA where Delete this if equation doesnt show properly use next slide683. Time is not as it seems (2)For Chloe the time is 2l/c 1/(1 v2/c2). Remember that Chloe sees the light travelling at c, not c v.We can write this as Tc = TA where Delete this if previous slide ok (equation is pic)693. Time is not as it seems (3)We need to note here that to obtain this result we cancelled the two ls in the expressions for the times in the two frames of reference.70This is important as we see later3. Time is not as it seems (4)As gamma, = 1/(1 v/c) must always be greater than one, we see that time as measured from the rest frame is greater than that within the moving frame.Chloe sees Ana and Bens clocks going slowly!3. Time is not as it seems (5)To be sure about this time dilation we need to be a little more careful about the way we measure time. A light clock overcomes the problems of possible changes in lengths because it uses light itself.We will call TA the time for a one way trip of the light pulse.72Note that the light bounces perpendicular to any motion.The previous development gives us a nice way to illustrate non-simultaneity and links in with the easy to imagine light flashes in the train idea. We need to use the light clock in order to develop the idea of relative time more fully.3. Time is not as it seems (6)As we watch a moving clock the light travels further between bounces but still at speed c!TC is the time for one zig in this frame.The rocket travels vTC in the time for one zig.73As the light bounces perpendicular to the motion we assume d is not affected.The maths of the light clock:For A: d = cTAFor C: Pythagoras tells us (cTc)2 = (vTc)2 + d2 Eliminate d gives: (cTc)2 = (vTc)2 + (cTA)2 A little reorganising gives: (Tc/TA)2 = c2/(c2 v2)Or Tc/TA = = 1/(1 v/c)74Dont need to dwell on the maths just show it is simple enough.3. Time is not as it seems (7)We find Tc/TA = = 1/(1 v/c)Or more generally t = to where t is the time as measured from a stationary frame and to is the time as measured in the moving frame.Einsteins time dilation equation:t = to75As gamma must be greater than 1, time in a moving frame (as measured from another frame not within the frame!) is always longer.3. Time is not as it seems (8)Earlier we wrote Tc = TA for the time ratio. Why the difference? To obtain this we cancelled the length of the train as seen in one frame with that seen in the other. This assumed they were the same!But if time behaves strangely so maybe does space...76This is important as we see laterSummary of 4: Space is strange too!We cancelled the ls as seen by A&B on the one hand and by C on the other.But the l Chloe saw had shrunk! by a factor of The length contraction equation: l = lo/Moving objects appear shorter because of their motion.This is because space itself contracts, not the object.The twins paradox illustrates the strange nature of spacetime.774. Space is strange too! (1)Einsteins time dilation equation is correct!So perhaps the extra gamma in the earlier equation is due to the fact that the ls were different by the same gamma factor.The time was too long so maybe the length was actually shorter by a factor ?This would account for the extra .4. Space is strange too! (1)So Einsteins train was contracted in the direction of its motion this is why the time appeared to have slowed by more than . In fact the light pulse didnt go as far as we thought.4. Space is strange too! (2)Einstein showed that in fact, as observed from one frame of reference, something moving will appear shorter by a factor .This is not because the object itself shrinks it is the space it is in that contracts.In fact we see everything in a moving frame (relative to us) contracted in the direction of its motion.4. Space is strange too! (2)A space ship moving at close to c will appear contracted in the direction of its motion.At 0.9c the ship will appear to be about half (1/2.3) its normal length814. Space is strange too! (3)Lengths are contracted by the gamma factorRemember that this is in the direction of motion only other dimensions are unchanged.Einsteins length contraction equation:l = lo/4. Space is strange too! (4)Remember that this contraction is all relativeFrom Mr Tompkins in Wonderland by George Gamow83We see someone moving relative to us has contracted.That person does not see us expanded they also see us contracted (next slide)4. Space is strange too! (4)Remember that this contraction is all relative84From the bicyclists point of view the passing scene has contracted!4. Space is strange too! (4)How can space be different when seen from a moving (relatively) frame?We need to be careful to remember that we only assume that large scale space is an extrapolation of small scale space! We have no experience of it.Einstein pointed out that space and time are inextricably connected in a 4 dimensional world.We can not imagine 4 dimensional space, but we can imagine a 2D to 3D analogy 85How can we imagine space contracting? Very difficult to visualise it, but if we use a 2D to 3D analogy we can get some idea of what it is about.4. Space is strange too! (4)A two to three dimensional analogy for a three to four dimensional situation: How far is it from Sydney to Perth?86How can we imagine space contracting? Very difficult to visualise it, but if we use a 2D to 3D analogy we can get some idea of what it is about.4. Space is strange too! (4)It is hard to picture space that is not straight but not so hard to picture curved 2D space.4. Space is strange too! (4)It is hard to picture space that is not straightBut do our X-Y-Z axes eventually bend around and join up again? ... just as a 2-d grid does on the Earths surface.4. Space is strange too! (5a)Einsteins Twins Paradox illustrates the strange relationship between space and time.Imagine one twin travels to Vega, 25 ly. away at 99.5% of c ( = 10)His trip will take 25.1 years as measured from Earth (although we wont get his signal for 50.2 years)89Drawing from Hawking: Universe in a Nutshell. Trip takes d/v = 25/.995c = 25.1 yr (c = 1 in those units)4. Space is strange too! (5b)But although, from Earth, the traveller takes 25.1 years to get to Vega ... the traveller will only experience 2.5 years because his time, as we see it, is going slowly.Note that we both agree on what his clock says, that is, 2.5 years.4. Space is strange too! (5c)Note that he does not feel that time has slowed down. It is from our point of view his time has slowed.But what he sees is that the space he is travelling through is contracted by 10 times and so it only takes him 1/10 of the time we calculate.4. Space is strange too! (5d)When he gets to Vega he doesnt like the Vegans and so turns around and comes straight back, taking another 2.5 years for the return trip.(He is a Gedanken traveller and doesnt get squashed by the acceleration involved!)4. Space is strange too! (5e)But what took him 5 years, we saw over 50 years! He returns 5 years older but his brother is 50 years older!This is not a paradox it is true! Clocks flown around the Earth, and in satellites have confirmed it.From Hawking: Universe in Nutshell4. Space is strange too! (6)This is true for train travel too its just hard to measure!Summary of 5: Momentum & Energy As the speed of an object gets greater, approaches infinity. Time slows to a stop and length contracts to nothing.Why cant we accelerate past c?Momentum also increases with , which makes it appear that mass does also. Hence more impulse increases momentum but the m, not the v.Total energy also increases in a similar way, but there is a rest mass component: E = mcEnergy has mass.955. Momentum & Energy (1)The Lorentz factor (gamma) approaches infinity as the velocity approaches the speed of lightv/c1%1.0000510%1.00590%2.2999%7.0999.9%22.499.999%22496Every increase of two 9s after the 99. increase the gamma by ~ x105. Momentum & Energy (2)So what happens to time and length?Time slows down to a standstill!Length contracts to nothing!97As gamma increases t gets longer (that is, things take longer, go slower) and l approaches zero.5. Momentum & Energy (3)But why cant we just keep accelerating beyond the speed of light?98From Beginners Guide5. Momentum & Energy (4)Einstein showed that momentum was also affected by the Lorentz factoror simply p = po5. Momentum & Energy (4)Einstein just used momentum, but we can go a little further and suggest that it seems as though the mass of a speeding object increases. p = poor mv = movSo m = mo5. Momentum & Energy (4)The increase of gamma, and hence mass, with speed.5. Momentum & Energy (4)This is why we cant reach the speed of light a = F/m So a = F/mo So the acceleration decreases to zero as the ship approaches c!5. Momentum & Energy (4)Remember that this slowing down of acceleration is what we see watching the rocket.The pilot will see the world (and us) going by at a speed which approaches, but again cannot reach c. He will also deduce that his relative acceleration has decreased.5. Momentum & Energy (4)But he will not feel heavier!This is where we must leave special relativity and wait for general relativity which deals with accelerated frames of reference and gravity.5. Momentum & Energy (5)Only massless photons can travel at the speed of light.For photons time has slowed to nothing... ...and length to zero.A photon crosses the universe in no time in its frame of reference. (Which is why it lasts forever!)105The universe is zero wide in the photon frame!5. Momentum & Energy (6)Einstein also showed that the kinetic energy of a mass is given by: Ek = ( 1)mocThis looks odd, but (with the help of the binomial theorem) does reduce to Ek = mv at normal speeds. (Remember the v is in the .)Reorganising the expression gives: moc = Ek + mocwhich he said was the total energy.106Total energy was kinetic energy plus mass-energy5. Momentum & Energy (7)The total energy: moc = Ek + moc So what is the moc ?Einstein said it is the energy associated with the mass of an object.In fact energy and mass are different manifestations of the same thing: mass-energySo E = mc (or moc) actually represents the total energy of an object (including kinetic).Usually, however, the kinetic energy is a miniscule part of the total.5. Momentum & Energy (8)But, in some nuclear reactions the energy released is so great that there is a significant decrease of mass:When uranium splits into fission fragments the mass of the fragments is about 1% less.5. Momentum & Energy (8)When hydrogen fuses to produce helium, the helium has less mass than the hydrogen.We find that the energy released is just equal to E = mc where m is the lost mass.5. Momentum & Energy (9)However it is important to realise that this mass has not been converted into energy!This is a common misconception created by popular accounts of the meaning of E = mcEnergy and mass are different manifestations of the same thing.The energy associated with bonding (whether nuclear or chemical) has mass and it is this mass that is lost when energy is released by a reaction.5. Momentum & Energy (10)If we could contain an atom bomb in a (very strong!) box, would it get lighter after the explosion?The answer isNo the energy is still in the box, and so is its mass.But as the hot box radiated energy away it would lose mass.The relevance of relativity (1)Is it all just something of concern for space travellers? Of course not!It tells us something very fundamental about the nature of our universe. It takes us beyond the clockwork universe picture.It has many practical consequences.Mostly though, it shows us the power of human reason and gives us cause to wonder in awe at the mysteries of the universe in which we live.The relevance of relativity (2)Some of the practical consequences include:The GPS system.The Synchrotron which could be a few centimetres in diameter if it werent for the huge increase in mass of the electrons at 99.9999% of the speed of light.Nuclear energy The relevance of relativity (3)Curiously enough, magnetism can only be understood properly with relativity.In the late 1800s it was realised that there was a problem with the theory of magnetism.The relevance of relativity (3)A moving charged particle is deflected by a magnetic field. This is the origin of the force that drives all electric motors.Faradays original motorA modern AC Induction motorThe relevance of relativity (3)A moving charged particle is deflected by a magnetic field... whether in a wire, a TV tube, or in free space116Auroras are charged particles moving in the Earths magnetic fieldThe relevance of relativity (4)but what if we observe it from a frame of reference moving at the same speed?In this frame it is not moving (although still in a magnetic field) and so...should not experience a force! This cant be true if it experiences a force in one frame it must also in another.The relevance of relativity (5)In fact Einsteins paper was called On the Electrodynamics of Moving Bodies It starts with the question of how a force could be velocity dependent and not contravene the principle of relativity.The answer is that it cant! So what about F = qvB?That is, force depends on charge, velocity and magnetic field.The relevance of relativity (5)Relativity says that magnetism and electricity are aspects of the same force.119..called the electromagnetic force.The next slides illustrate this...The relevance of relativity (6)We often think of relativity in terms of high speeds. But actually it is needed to explain the magnetic force between parallel currents moving at millimeters per second!But the electrons in one wire are at rest with respect to those in the other wire!120The fact that we havent drawn the +s in the second wire doesnt matter. They may or may not be there.The relevance of relativity (6)If we look at the situation from the point of view of the electrons, the positives are moving but the electrons are at rest and should not experience a magnetic force (F = qvB)The moving positives create a magnetic field, but as v = 0 there should be no force on the electrons!121v=0 for the s The moving +s create a static magnetic field.The relevance of relativity (6)Actually there is a balance between the forces between the electrons and the positive atoms in the wires But separately, these two forces are HUGE! but slightly different because 122The magnitude of the coulomb forces is comparable to the gravitational force between the Earth and the Moon! Only very slight differences are needed to give a reasonable magnetic force.The relevance of relativity (6)the positive atoms are in motion relative to the electrons and are therefore Lorentz contracted that is, their density increases and the electrons see more positives than negativesAnd are therefore attracted to the other wire! 123So the apparent magnetic attraction has actually become an electric (Coulomb) attraction.The relevance of relativity (6)The magnetic attraction in one frame of reference is simply the electrostatic attraction in another frame of reference. Magnetism and electrostatics are the same after all!124Ask what this means about magnetism and electricity.The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.Albert EinsteinResources126Scheider as it saysWolfson very goodBrian not much physics but good background on EinsteinResources127Actual papersEinsteins popular account (VEA video)Gardner goodResources128E Mirror is nicely presentedE=mc2 is not much about relativityRussell philosophical approach good.Resources129Tompkins great intro to the ideas of space and time Heros is good background particularly on MaxwellCartoon books quite good, but ...Resources130The serious booksResourcesLibrary must have Very good biography131Serious booksResources132Walter Fendt appletDavid Jamieson websiteVEA DVDActivities133These spreadsheet activities are from the Heinemann TRAD:Gamma GraphsSimulation of non-simultaneityMichelson-Morley exptDownload these presentations from:And watch for further developments.orgwww.The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.Albert Einstein136This ppt is available on Vicphysics. (With some reductions and deletions due to copyright problems.)


View more >