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[BLANK_AUDIO].We've reached Week 5 now, so let's do a,a preview of the, the major topics of theweek, where we've labeled it SpacetimeSwitches.there are actually a number of differenttopics we're covering but the, the ideaof Spacetime Switches comes from theLorentz Transformation, which we'll betalking about, enables us to switchbetween different frames of referencevery easily.But before that we'll have, we'll havethe quotations of the week.We'll do that in a minute.we'll talk just briefly about convenientunits for the speed of light.The concept of a lightyear.And the fact that if we measure distancesin lightyears, a lightyear is a distance,the distance light travels in a year, assome of you may, may know.if we measure velocities in lightyearsper year, then c, the speed of light, is

simply one.By definition, it's one lightyear peryear.It's the distance it travels in, in oneyear.And so, that and a couple of other tipsthat will make it a little easier for uscalculationally 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, and derived

last week, you get some more familiaritywith them, just struggle with them alittle bit.Try to get a deeper understanding of itand we're calling this Star Tours part 1.That is we're going to send, in thiscase, Bob will go on a trip to a nearbystar, five light, lightyears away.The nearest star to earth is actuallyabout 4.2 light years away.We mentioned that in one of the one ofthe early problem sets.But I think we mentioned, mentioned in

terms of the distance not in lightyears,but just in how long light would take to,to get there, it's about 4.2, 4.1, 4.2years.Anyways, 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 store, andshe's on Earth.

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So analyze it from her perspective, andBob's perspective, we'll try to makesense of both their perspectives.And then we'll, we'll sort of hit a wall,hit a puzzle in that there will besomething that really doesn't make sense,we'll get to.And so, we'll have to hold that aside fora 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 frames ofreference.in a non-relativistic manner, the Lorentztransformation also derived by, byEinstein.But typically called the Lorentztransformation now.allows us to switch between different

frames of reference when relativisticspeeds are involved.And it actually is equivalent to theGalilean Transformation for slow speeds.So it, it subsumes the GalileanTranformation.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'll workour way through it and, and then getthese transformation equations.

Then we'll spend a little time exploringthose transformation equations.Trying to understand them, seeing whatthey are telling us, see if they makesense from what we know so far.And then we're going to use thosetransformation equations.The, they're very general.They're useful in all kinds of ways butwe're going to use them but we're goingto use them to revisit this whole idea ofleading clocks lag because this will turnout to be the key to understanding our

Star Tours conundrum that we end up with,with there.so we're going to revisit leading clockslag and do it quantitatively, find outexactly how much do leading clocks lagwhen you have, remember when you have aseries of clocks moving by you, you're inone frame of reference.You see two or more clocks moving inanother frame of reference past you, then

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the leading clock as it's moving past youin in that series of clocks, or twoclocks, lags behind the rear clock.And we did that qualitatively before, nowwe'd like to figure out exactly how muchdoes it lag behind that clock.And that's going to be the key as wediscover to to figure out this, thisproblem we run into, that Star Tours part2 here.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 youcould travel at the, the speed of light.And then finally talk about combiningvelocities, we did a little bit of thiswith sort of the Galilean Transformationidea where if you know, if you have a carand you have a basketball shootingmachine that, that we talked about, andthen a tennis ball out, out of thebasketball that type of thing.In our every day experience, those types

of things just add, you add thevelocities, or if the velocities areopposite each other you subtract thevelocities.Well, a similar idea in terms of thespecial theory of relativity, but it's alittle more complicated.Because if the speed of light is anultimate speed limit, what if you havesomething travelling at 0.9c, say Bob onhis spaceship travelling at 0.9c.And then he shoots out maybe an escapepod or something, travelling at 0.5c away

from him.So, he's travelling at 0.9c.9 10th the speed of light.He shoots out of the escape pod at 0.5c,so that's 0.5c with respect to himtravelling away.in classical physics we'd say oh, youjust add the velocities.It's 0.9c plus 0.5c, Alice watching itover here.As Bob goes by and shoots off the, theescape pod, Alice would say presumably0.9C plus 0.5C, 1.4C is the velocity of

the escape pod as she sees it.But actually in fact you will never seeanything go past the speed of light.And so, combining velocities here, andshow us the new form for doing that, suchthat no matter you know, how fast Bobshoots out that, that space pod orwhatever Alice will never see it gofaster than the speed of light.Actually, it will never get up to the

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speed of light, but will never exceed thespeed of light there.Okay.So that's sort of a rundown of wherewe're heading this week.Let's do the, the quotations of the week.Two short ones this time.First one, Einstein.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, I said Einstein quotation-wise, inactual fact, Einstein probably did notsay this.It's one of those things that somebodyinvented at some point and it soundsgood, it sounds like Einstein could havesaid it, it's certainly inspirationaland, therefore, you see it all over theplace.In actual fact, it's something he couldhave said because he certainly did staywith [UNKNOWN].

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 tenaciouswhen he got onto a problem.We saw that in the special theory ofrelativity.It was about ten years of thinking aboutthat, other things as well, but ten yearsfrom, about 1995, 1996, when he startedin the university to year 1905, or[INAUDIBLE] 1896, if I said 1996, to

1905, ten years.And then, actually, the next ten yearsafter that he spent a large part of timeworking on his general theory ofrelativity.It took about 10 years to work on that,as well as a number of other things as,as well.So that, that tenacity, that idea thatI'm going to stay with this problem.Now, it's not always a benefit because ifyou, you know, go off in the wrongdirection, you may be going off in the

wrong direction for a long time.In fact many physicists or contemporariesof Einstein during the second half of hislife felt that he had gone off in thewrong direction in terms of the physicsof the day, which had gone in, in muchmore quantum mechanical direction andEinstein had some real problems with,with that.And, and so really for the last half of

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his life, from about 1925 on or so, hewas out of the mainstream of, of physics.He's certainly revered by many people andphysicists but just did not reallycontribute anything major at the timefrom about 1925 to he died in 19, 1950.So again, it is a good quality to have.No matter how smart you are, or howeveryou want to measure that, but that juststaying with the problem longer, thatstruggle for understanding we talkedabout 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's, there's that insight into

you know, you want to tackle problemsthat are challenging for you, but youalso have to have some insights.Sometimes it is just to hard a problem.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 its, its not goodfor me to tackle.Leave it for somebody else or leave,leave it for, you know, 20 years from now

when maybe when we'll be able to comeback and tackle that, that problem again.On the other hand, sometimes the, thereally hard problems like that, the onlyway you really do crack those nuts as itwere is for someone to, to take it on agroup of people really to, to take it onand to stay with that problem until itgets, gets solved.Okay, so that's overview of the weekwhere we're heading, quotations of theweek and again, we're going to bebuilding on the things we've been doing

the last couple weeks now with the keyconcepts of the special theory ofrelativity and see what some of thoseimplications are for are situations notonly with traveling to stars maybe, butalso combining velocities and ultimatespeed limits and the like.