Bestand wählen
Merken

# Special Relativity | Lecture 2

Embed Code
Video lizenzieren

#### Automatisierte Medienanalyse

Beta
Erkannte Entitäten
Sprachtranskript
Stecher University but we were
last time we worked out basically rents transformations relating to frames of reference on weather and I said it but missed it now will mainly dealing with problems in which all of motion and in particular the relative motion of different observers is a long 1 particular axis we didn't try the things go fully three-dimensional in the picture you go have head is we have a long railroad track one-dimensional sunset of observers is sitting still at the station because Yukos the station observers say 5 and other observers are in train and then moving relative to each other along the one-dimensional axis when worry much about the other taxis we we I 1 of 2 things about how we talked about how you relate it coordinates 1 observer relative to the other and particularly wrote down warrants transformations they on the basic hypothesis of Einstein's that all reference frames see the speed of light exactly the same factory said would be unit so we used all observers see the speed of light being 1 that course choice Of units Oregon years light years on a 2nd white 2nd whatever choice of units if we choose and correctly we can make speed of light 1 and that simplifies equation of course if we really want the plug even the real observational physics we might want to use the fact that the speed of light common units in the common units the experimental physicist would narrow use is not 1 its 3 times tend to be a and some units and so we would talk back the speed of light there's always a unique way to do that the unique way to do it is to make sure simply stated that you modify the equations by appropriate factors of the speed of light see so that the equations of dimension we consistent Our I will go back and forth mostly I will use the speed of light equal 1 but every now and then just to illustrate a point I was stick speeds of life and there you could go through the equations sells OK joy observers 1 moving down the axis with a velocity V relative to the stationary mowing down track of velocity v wrote the stationary observer stationery observer season observer of Warrington v units of space per unit time leaving velocity and of by symmetry just by the symmetry of a problem if we believe that all coordinates frames are equally valid after we say relationships the same kind of Lorentz transformations will relate the stationary observers coordinates Tony moving
court the two-way street stationary observer ascribe stationary coordinates moving observer ascribes link warned his coordinates and they can each be related to each other reciprocal I'm a reciprocal relations truly reciprocal exactly the same relations X set their whereas if I were moving to the right you're right a file of moving you alright you would say my velocity it is positive you would be moving to the left as far as I was concerned I would say your velocity was negative and soon relating the 2 frames of reference the only thing we have to remember is assigned change of velocity when you go back and forth OK so for example it X probably it is coordinates as scene In a train is a train or a yellow structuring trained cases of observer in the trained as an observer on the tracks or observer the station is observer in the station it observer on the train and observe the train is moving with velocity V 3 The Observer and the train as stocks and scandal on floor year performer great observe also has a pint beast Clark likewise be observer at rest arrest respectable rests with respect to the station the Observer arrest with to station also has played out and also has and make various comparisons in hours worked in the event which takes place an event which takes place in the event means a event happening at a point the space and a point of time and the words some point of space time I like to think of it as a flashbulb exploding someplace going off some someplace doesn't matter whether it's in the train or outside the train but in the train for committing flashed bomb off over here at a time that these stationary observer reckons the be punchy at position Exner opposition X means coordinate X in the stationary reference frame extra at at time t according to be kind piece of the stationary observer so the stationary observer describes to coordinates extant cheat and observer describes the same and coordinates X Prize enterprise work at the last time the relationship so necessary between XT an expansion team Friday such that everybody will always agreed the speed of light is we want learn down quickly X Prize is an old French transformations next time musical acts miners VT and no 1 would recognize that body when the recognized was a square root of 1 might be squared downstairs and if you want to Pope back the speed of light it goes right over here put in and take it out these squared overseas cornered and of course if the velocity is small by comparison with the speed of light is a terribly tiny correction was just 1 might be square and Prime is equal minus V. X. divided by the same score 1 might be squared if we want it and the other 2 0 directions and particularly the directions out of the board and vertical in other words a directions perpendicular tracks we could have been very simply perpendicular directions don't change under a change of velocity along the given access if the changeable at velocities Of the 2 frames wrote the velocities along the x-axis than the coordinates are unchanged by Prime very wide equals y and z chronicles but I won't write it better
if we needed will use it we can avert these relations misses simply a matter is nothing the sophisticated going on here this is simply a matter of solving for exit in terms of next time and keep trying but may remind you what the result would be a it would be x equals X Prize last VT Prime provided by that Assange square root and T equals prime plus V X prime divided by square of 1 mind squared the only difference only asymmetry is where you so of velocity over here the sign of the velocity just to account for the fact that the road velocities are opposite direction you could also really off if somebody view this form for of the relationship between the coordinates you could easily read off what the relative velocity between the 2 observers if you look at the X equation here and you say they only observers coordinate his ex time equals 0 right at the position of the origin of um coordinates inside the train at Prime equal to 0 ext time equals 0 corresponds to X equals Vt it just look at this and you say molding observer pride of their effect on moving the manager over Our is at rest lowly position next time arrest of equal to 0 excuse me X prime is equal to 0 the origin of the prime coordinates How response that X equals VT you not to know about the nominated area just look at x equals VTE that specifies that chronicles 0 that shows you X Eagles bt because of the relative velocity between the 2 of them is by now we want to do another exercise the donor exercise is to assume there's a 3rd observer of the fair observer is moving relative to the railroad car of the train is going Kitty car inside the train but his relatives thirdly passenger with score and the passenger is moving relative to the passenger with velocity you want a passengers it is a little kitty car will kid in the car peddling then are via a video I O of the train with velocity you would relative to himself a question What does the stationary observer ascribed to a car 1 velocity does the stationary observer unless all this is just to use that I know of no waited DSC answer the answer is some velocity widow given name we can call at velocity W I don't die you could use V-1 veto would be free but I hate subscripts and so I prefer to say the velocity of the train Is VU relative to the stationary observer the velocity of the Colorado the train is you end the velocity of the car relative to the stationary observer so-called W.
stationery observers car move with velocity W and the question is what is w in terms of you would think this is just the use of the logic that of logic is but the relationship because 1st of all we should give Fabio be also excuse there also coordinates in the car moving with the the car this could be a 7 sticks laid out on the floor of the car and also kind peace that the driver of the car has was really sets of coordinates in this case ex ante are the coordinates of the stationary observer uses prime anti-crime RV passengers coordinates bid for a 3rd set of coordinates which would give them the name X double prime anti double prime X double prime and he doubled and other coordinates that a kid in the candy car uses to describe things relative to the position relative to ozone no frame of reference right now just it's a little bit of logic say we know what the relationship is between the double prime coordinates and the single prime coordinates those are related by velocity you you is the velocity of the double primed growth the Frank would silica right down those relationships straightforwardly but we don't need this over here but them down here X double prime is equal saying that kind of relationship want that kind of except for put financier and set of v e we will use the relative velocity you serve as X Prize you keep price divided by square root of 1 mind this EU square services tolerance transformation between the double time frame and the single primed for a prize minus you X foreign over of warm Tigers you square writes about how we following the connection between the double prime coordinates in the car and they under unkind coordinates an arrest in the railroad station and that's simple always do is let's take this equation over here with focus on this 1 of kind equation also works out very nicely but must focus on the space equation he and we know what X primaries In terms of ex ante how we know what time in terms of ex ante so all we have to do is to plug a do some good Rice paid much O X Prize is X miners VT divided by the square root of 1 minus V squared that just X Prize here so far this research price might this you keep trying must couldn't prime prime it T minus V X and all thing again divided by the square root of 1 mind square now so far I've only written this in there so I have to put in the denominator to put on the Data I just put another factor of 1 mind you squared 1 minus you Square Square of 1 square so that is the relationship between X double Parnham X writers Will more simply let's focus on what the votes some big denominated dominated involves a product of the 2 square research fibers per square inch square makin a ride out what's inside the square root it's just a product reviews to square respond interested in the numerator really the normal writer has an X and it has a plus you will be X X here and plus UV acts was plus UVX as a minus sign you a minus sign X times 1 plus you 1 course you read x more about t t you will multiply my guess viii plus here all kinds minus V and minus you thirsty and this is the answer but Favre transparent what it means but all we need to do to figure out the relative velocity of the double time frame relative to the untried adjustable exactly what we did over here if we want to
find out what extra nickel 0 means just set X might equal to 0 and tells you that X is equal to VP tells you have a fellow at rest here who is an expert legal 0 how is moving Road prime frame we do it exactly the same thing here said X double Prime will be 0 X double time of course being 0 means the position of the kid inside kitty Garcia X double prime equals 0 is the same thing as the numerator here being 0 but leader who cares about the denominator it's not a but we can set the normal rate a quarter 0 here and that will tell us under what circumstances X double prior musical 0 so what does it say X double prime is equal to 0 when 1 plus you X is able to you'll plus she said this equal to this To make the numerator 0 war if I divide by 1 pursue me because me X is able to you'll plus v all over 1 class you really fit so what is the relative velocity so I guess what it is the velocity this tells us these excellent teacher Jack theory of the kid in the car here the trajectory of the shot over where it is in the kitty car is X is equal to you closely over 1 plus UV times that corresponds that X double prime equals 0 but another way to say it is just that the stationary observer the kiddie she's the cake are moving along with velocity you plus veal over 1 plus you so we now know what W is that's exactly what W is W worked out we can now we can write it in the form of the form X double is equal to T minus W X provided by square root of 1 minus W squared and he double price is right there right now X minus W C & C minus W that makes Over same square root from the square root and modifying W. lens W is just that's that's how fast Katie cars moving as seen from the stationary Frank Searle yes you have because we sets eagled 1 right but that the back admitted young will come back and get your era you're having a step ahead of me fokker 5 so X is accomplice of W speed W. physical to double EU plus VAT divided by 1 plus you need enough I want to restore the units would that this could answer question again if we set the speed of light equaled 1 Of course we're working units in which velocities of dimensionless but we want restore the dimensions we simply look at this equation we sailor W it was you pass me that's dimension with find its a getting 1 U V which Curia but we restore the images by putting in square 1 SUV oversee squared UV oversee squared is damaged so this is the year equation with see being restored was the Newtonian equation early corresponding 3 Einstein's equation wealth stationery person sees passenger moving with velocity you passenger is cake are moving sorry stationery observer sees passenger moving velocity v passengers cheesecake are moving velocity you the answer naively would just be you plus lead but let you positive view but divided by something which is a lot as you and significantly smaller than the speed of light you ve overseas squared will be very small world will put some numbers of Ameritrust protest about but as well as you and these are small compared with the speed of light that this will be negligible it's a product of told ordinary velocity 100 meters per 2nd or whatever it is you are putting divided by 3 times tend to be 8 meters per 2nd all squared this is a very very small number it's a very small correction on the other hand when you and we get up near the speed of light it can get very significant but to at 1st but still a case where you and we are small velocities compared to the speed
at stanford . EDU
Jukos
Personenzuglokomotive
Direkte Messung
Licht
Lichtgeschwindigkeit
Wetter
Besprechung/Interview
Gleiskette
Steckdose
Großtransformator
Jahreszeit
Bildfrequenz
Zylinderkopf
Jahr
Fahrgeschwindigkeit
Schreibware
Schaft <Waffe>
Verbunddampfmaschine
Bombe
Kraftfahrzeugexport
Bergmann
Lichtgeschwindigkeit
Besprechung/Interview
Leisten
Erdefunkstelle
Dreidimensionale Integration
Abformung
Feldeffekttransistor
Deutsche Sprengchemie GmbH
Bildfrequenz
Kopfstütze
Fahrgeschwindigkeit
Kristallgitter
Feile
Klangeffekt
Stunde
Kaltumformen
Zugangsnetz
Personenzuglokomotive
Eisenbahnwagen
Rootsgebläse
Band <Textilien>
Serientor-Sampling-Leitung
Gleiskette
Übungsmunition
Videotechnik
Gleichstrom
Großtransformator
Bestrahlungsstärke
Jahr
Sprechfunkgerät
Schreibware
Holzfaserplatte
Toleranzanalyse
Direkte Messung
Kraftfahrzeugexport
Bergmann
Erwärmung <Meteorologie>
Lichtgeschwindigkeit
Besprechung/Interview
Treiberschaltung
Erdefunkstelle
Satz <Drucktechnik>
Antiteilchen
Nanometerbereich
Digitalschaltung
Textilfaser
Bildfrequenz
Kopfstütze
Ozonschicht
Fahrgeschwindigkeit
Vorlesung/Konferenz
Speckle-Interferometrie
Steckverbinder
Kaltumformen
Brennpunkt <Optik>
Rootsgebläse
Übungsmunition
Trajektorie <Meteorologie>
Mikroskopobjektiv
Schiffsklassifikation
Geländelimousine
Großtransformator
Jahr
Schreibware
Greiffinger
Messung
Magnetisches Dipolmoment
Intervall
Erwärmung <Meteorologie>
Lichtgeschwindigkeit
Konfektionsgröße
Leisten
Fehlprägung
Geokorona
Schwächung
Grau
Rotationszustand
Regelstrecke
Bildfrequenz
Fahrgeschwindigkeit
Personenzuglokomotive
Längenmessung
Licht
Elektronisches Bauelement
Geschwindigkeitsmesser
Übungsmunition
Tauchanzug
Flüssiger Brennstoff
ETCS
Anstellwinkel
Schreibware
Gewicht
Direkte Messung
Höhentief
Kraftfahrzeugexport
Erdefunkstelle
Remanenz
Hobel
Jacht
Zeitmesser
Nanometerbereich
Taschenlampe
Kopfstütze
Spiel <Technik>
Herbst
Stunde
Zugangsnetz
Kraft-Wärme-Kopplung
Windrose
Kombinationskraftwerk
Glasherstellung
Trajektorie <Meteorologie>
Schiffsklassifikation
Gleichstrom
Großtransformator
Source <Elektronik>
Ersatzteil
Gewicht
Magnetisches Dipolmoment
Kraftfahrzeugexport
Intervall
Bergmann
Mondphase
Gesenkschmieden
Photonik
A6M Zero-Sen
Auslenkung
Begrenzerschaltung
Teilchen
Hochspannungsmast
Fahrgeschwindigkeit
Vorlesung/Konferenz
Brechzahl
Treibriemen
Bahnelement
Array
Stunde
Zugangsnetz
Röntgenstrahlung
Behälter
Windrose
Waffentechnik
Längenmessung
Elektronisches Bauelement
Licht
Proof <Graphische Technik>
Standardzelle
Rauschzahl
Rootsgebläse
Trajektorie <Meteorologie>
Übungsmunition
Regentropfen
Gleichstrom
Großtransformator
Bestrahlungsstärke
Matrize <Drucktechnik>
Luftstrom
Marsflug
Anstellwinkel
Drosselklappe