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We've reached week five, now also, let'sdo a preview of the, the major topics ofthe week.We're, we've labeled it spacetimeswitches.There are actually a number of differenttopics we're covering.But the idea of space time switches comesfrom the Lorentz transformation, whichwe'll be talking about, enables us toswitch between different frames ofreference very easily.But before that, we'll have thequotations of the week will do that in aminute.We'll talk just briefly about convenientunits for the speed of light.The concept of a light year and the factthat if we measure distances in lightyears, a light year is a distance, thedistance light travels in a year as someof you may, may know.if we measure velocities in light yearsper year, then C, the speed of light is

simple one by definition.It's one light year per year, it's thedistance it travels in one year.And so, that and a couple other tipsthere will make things a little easierfor us calculationally when we do things.And then we're going to spend a littletime looking at a case of time dilationand length contraction to build on theideas we were working with last week.We introduced and derived last week toget some more familiarity within thestruggle a little bit.

Try to get a deeper understanding of it.And recalling this Star Tours part 1, theidea is we're going to send in this case,Bob will go on a trip to a nearby star, 5light years away the, the nearest star toearth actually is about 4.2 light yearsaway.We mentioned that in one of the one ofthe early problem sets.But I think we mention, mentioned interms of the distance not in light years,but just in how long light would take to,to get there is about 4.2, 4.1 and 4.2

years.Anyway so, we're just going to imagineBob taking a trip there.And we're going to analyze it fromAlice's perspective as she watches Bobtake the trip to the nearby star andshe's on earth, so will analyze it fromher perspective and Bob's perspective.We'll try to make sense of both theirperspectives, and then we'll sort of hit

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a wall, hit a puzzle in that there willbe something that really doesn't makesense.We'll get to, and so we'll have to holdthat aside for a minute.And because we won't be able to answer ityet, and that's really what the next parthere is.In order to answer it, we're going toderive the Lorentz transformation.Lorentz transformation, just like theGalilean transformation allowed us toswitch between different frame ofreference.in a non-relativistic manner, the LorentzTransformation, also derived by Einstein.But typically called the LorentzTransformation now, allows us to switchbetween different frames of referencewhen relativistic speeds are involved.And it actuallly is equivalent to theGalilean transformation for slow speeds,so, it subsumes the GalileanTrnasforation.

So, this will probably be the mostalgebra we do in the entire course.It will take us a while to get throughit, several, video lectures but we'llwork our way through it and,uh and, getthese transformation equations.And then we'll spend a little timeexploring those transformation equations,trying understanding them, seeing whatthey are telling us, seeing if they makesense from what we know so far.And then we're going to use thosetransformation equations, they, they're

very general, useful in all kinds ofways.But we're going to use them to revisitthis whole idea of leading clocks lag.because this will turn out to be the keyto understanding our Star Toursconundrum, that we end up with there.so we're going to revisit leading clockslag and do it quantitatively.Find out exactly how much do leadingclocks lag when you have, remember youhave a series of clocks moving by you,you're in one frame of reference, you

see, two or more clocks moving in anotherframe of reference past you.Then the leading clock, as it's movingpast you in that series of clocks, or twoclocks, lags behind the rear clock.And we, did that qualitatively before,now we'd like to figure out exactly howmuch does it lag behind that clock.And that's going to be the key, as wediscover, to, to figure out that problem

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we run into, that's Star Tours, part twohere.And then we'll say a few words about theultimate speed limit speed of light beingan ultimate speed limit, and why thatmight be so.What would happen if we could travel atthe, the speed of light.And then finally, talk about combiningvelocities.We did a little bit of this with theGalilean transformation idea where if youknow if you have a car and you have abasketball shooting machine that wetalked about.And then a tennis ball out of thebasketball, that type of thing.In our everyday experience, those typesof things just add.You add the velocities or if thevelocities are opposite to each other,you subtract the velocities.Well, a similar idea in terms of thespecial theory of relativity but it's a

little more complicated.Because if the speed of light is anultimate speed limit, what if you havesomething traveling at 0.9 C, say Bob onhis space shift travel at 0.9 C.And then he shoots out maybe an escapepod, or something, traveling at 0.5 Caway from him.So he's traveling at 0.9 C, 9 10th of thespeed of light.He shoots out an escape pod, at 0.5 C,that's 0.5 C with respect to himtravelling away.

In classical physics, we say you just addthe velocities 0.9 C plus 0.5 C.Alice watching it over here as Bob goesby and shoots off the escape pod, Alicewould say presumably 0.9 C plus 0.5C, 1.4C is the velocity of this escape pod asshe sees it.But in actual fact you'll never seeanything go past the speed of light.And so combining velocities here, show usthe new formula for doing that.Such that no matter you know how fast Bobshoots out that space pod or whatever,

Alice will never see it go faster thanthe speed of light.Actually it will never get up to thespeed of light, but it will never exceedthe speed of light.Okay, so that's sort of a rundown ofwhere we're heading this week.Let's do the quotations of the week.Two short ones this time, first one,Einstein.

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It's not that I'm so smart, it's justthat I stay with problems longer.It's not that I'm so smart, it's justthat I stay with problems longer.Now, I said Einstein, quotation ofEinstein.In actual fact, Einstein probably did notsay this It's one of those things thatsomebody invented at some point and itsounds good.It sounds like Einstein could have saidit, it's certainly inspirational.and therefore, you see it all over theplace.In actual fact, it's something he couldhave said, because he certainly did staywith problems longer.He certainly was very, very smart, youknow hard to measure those types ofthings at a certain level.But, great scientists also have thistenacity about them.And he was tenacious when he got onto aproblem, we saw that in the special

theory of relativity.It was about 10 years of thinking aboutthat, other things as well, but 10 yearsfrom About 1995, 1996, when he started inthe university to year 1905, 19, yeah, Ishould have said 1896, if I said 1996, to1905, ten years.And then actually the next ten yearsafter that he spent a large part of timeworking on his general theory ofrelativity.And took about ten years to work on thatas well as a number of other things as,

as well.So that, that tenacity, that idea thatI'm going to stay with this problem, nowit's not always a benefit.Because if you, you know, go off in thewrong direction you may be going off inthe wrong direction for a long time.In fact many physicists who werecontemporaries of Einstein during thesecond half of his life felt that he hadgone off in the wrong direction.in terms of the physics of the day, whichhad gone in a much more quantum

mechanical direction.And Einstein had some real problems with,with that.And, and so, really for the last half ofhis life, from about 1925 around or so,he was he was out of the mainstream ofphysics.He's certainly revered by many people andphysicists, but just did not reallycontirbute anything major at the time

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from about 1925 until he did in the1950s.So, again, it's a good quality to have,no matter how smart you are, or howeveryou want to, to measure that.But that just staying with the problemlonger, that struggle for understandingwe've talked about before.so even though Einstein probably didn'tsay it, it certainly captures one aspectof his scientific personality.and the second quotation, similar to thefirst and this one is something he said.One should not pursue goals that areeasily achieved.One must develop an instinct for what canjust, what one can just barely achievethrough one's greatest efforts.And so there, there's that, insight into.you know, you want to tackle problemsthat are challenging for you, but youalso have to have some insight sometimes,is it just too hard a problem.And scientists have to have that as well,

they have to understand you know, givenour current capabilities, our currentunderstanding, my current abilitiesmaybe, that's just something it, it's notgood for me to tackle.Leave it to somebody else or leave itfor, you know 20 years from now maybewe'll be able to come back and tacklethat problem again.On the other hand, sometimes the reallyhard problems like that, the only way youreally do crack those nuts as it were isfor somebody to take it on.

Or a group of people, really to take iton and just stay with that problem untilit gets, gets solved.Okay, so that's overview of the week,where we're heading, quotations of theweek.And again, we're going to be building onthe things we've been doing the lastcouple weeks now.With the, the key concepts of the specialtheory of relativity and seeing what someof those implications are for.our situation is not only with the value

of the stars maybe, but also combiningvelocities and ultimate speed limits andthe like.