Bestand wählen
Merken

# General Relativity | Lecture 5

Embed Code
DVD bestellen

#### Automatisierte Medienanalyse

Beta
Erkannte Entitäten
Sprachtranskript
so a lance Steiger University Fry let's
talk about friend like space like em might like that we just go back pressure wrote to be served by whatever means of special relativity meant that we discusses meant that many times we call a proper time Bacau squared because Cuevas where the proper time some little the and as your number he squared minus 3 x square mile y square easy squared everyone the speed of light sometimes up with the speed of light the reason I put the speed of light and sometimes is to keep track of what small what big under certain circumstances for example if you want to study if you want to go the nonrelativistic limit The limit where everything is moving slowly that's got to put back the speed of light because he keeps track in the case of the fact that the speed of light is much bigger than any of the velocity the problem so that put in for the moment I'll put the taken out there are under various circumstances because it like that for overseas squared and if D-Calif squared is greater than 0 50 pal squared 0 now of course the square of a real number was always greater 0 but because quit is not defined by being square real real number it's defined by this combination over here and it can be positive or negative depending on whether the X clip was dealers Clippers was Desi squared is bigger than D squared all small squared off I said DX wept as why script was busy square but I'm in the X squared overseas square your square overseas so full of banana case if 50 he where is greater than 0 mental element here is said to be time like the got more time has space this card as big as part and that can be described in terms of like all like all like Conan books like that but and the boundaries of the cone called
itself of places would be key squared let's go for a moment I don't want to scores that fire BP square he
also DX equipped BY squarely busy square that's called like like D squared is bigger and DX quarter plus to 1 script was busy square it means little vector lies in the interior of a common like that a could also be lying in the backward direction in either case a little interval or vector of speak about veteran general Beckham general time like it's time component is is bigger than the sum of squares of space components of plan Mike space alike is exactly the opposite is deeply squared because less than 0 and that case we usually defined another quantity fate s squared which is just the negative did Bacau square by definition is yet square posted 1 square foot busy square minus squared the same object except for the relative with different glimmering assigned space like vectors all ones for which a the S squared is bigger than 0 because we're lesser 0 in space flight vectors lie
outside White Kong finally like like vectors the space flight and finally there are like like that there's and like like sectors on the ones for which indeed he
squared equals the X grapples grip was those are the trajectories of light rays and they lie in the may lie in the surface of the itself 3 kinds of vectors you can have on just from moment consider what would mean if they they want to negatives sorry to positive signs into negative signs that 1 positive sign and 3 negatives somehow this would correspond full time direction the that doesn't mean any anything thing experiment the 2 times the always 1 time and free space now could you on imagine a world with took I can't frankly I can't I can't imagine will mean that 2 different forms directions will simply take the view that the facts not option there's always 1 time like direction in the metric here and 3 states like but that doesn't mean that there's a unique direction which is kind like them any time like directions point with the slight come here the invariant statement is a statement about the Met cancer the metric tensor weaker write this summer form be pal squared is equal G communal where a minus sign VX mu VX know me might signed is a convention always defined so they're Gino TX new VAX goes With these bases like vectors having a positive sign incidentally 1 other thing it does remind you on proper time all along the trajectory like is a measure of 1 o'clock along the trajectory kicks off proper time is a kind of its kind red off by moving Clark the proper distance proper distance along a space like surface is distance measured by meterstick so proper distance square of the square root beer square really is a distant and proper time really is a kind of and keep them nite OK out of 4 this is our definition of the metric and for the case the we've written the metric To be written in France a matrix North Sea the matrix is minus 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 2 0 1 called a them you know like chronic Delta except that has a mind OK this thing has obviously 3 positive eigenvalue The Matrix 3 positive eigenvalue more negative argued that you and that's the invariant story wraps the story not that there's only 1 kind direction but that here 1 negative I give value yeah and they met trick which would have to negative Eigen values what really negative I mean values would have more than 1 time we just don't even think about that that there was something of a physics the Nazi toward me use 2 negative OK so bad so space flight time like like so but bird more generally it could be applied but certainly in curved space per space time the metric tensor GE the metric tensor cannot be chosen to be equal to the 8 a symbol here it's a general function genial or acts Virginia law G. Mueller Mexican not just be old man and every point that every acts as a matrix of every acts as a matrix of reporting and every X B there must be 1 negative Oregon value and 3 parts of and you are standing there you should experience a world with one-time direction we space or more exactly 1 negative eigenvalue to pass OK sure what that means what that means is is that every point in space has a light cone associated with that not enjoying it sort of had been killed bid that reflects the fact that the Cold that's themselves might be we need what so as you move around because the coordinates and also the metric tensor might be varying from place to place these like cone might have an apparent tendency to uh Oh different in different places but that is just because because as you move around the base of that kind of Cheney from place to place and accord change from place great fracture every point all I call there's shame like space of time like me crime like inside I Kong space like backers outside the light cone and like like promotion of white raise longer enjoyed the call itself the Collins surface when you have ice cream cones uh ice cream and inside is not part of the Hong Kong resurfaced self shelf so I have to make sure that we will only right that does have the property of the right number
of positive and negative barriers call that the property of having a certain number of eigenvalues past a certain number negative is called the signature of the wants as the signature of the method was a signature of the metric of would ordinary flat space the blackboard based Our blackboard has 2 dimensions and the signature of the blackboard plus plus the X squared plus wars the signature or Minkowski space special relativity is but Miners plus plus minus plus minds plus plus plus Excuse me my fault OK so we have to make sure that somebody a somebody gives a symmetric wherever we got from move we might get it present a mail right there we might go calculated from equations of motion some field equations always we should make sure that that Have signature miners plus plus plus and doesn't mean we did some wrong not only to have signature every poor and that at some point it should have every point not all the but there is a single I get eigenvectors so soon may I right now on the no no numbers there now there is no of is not a single was promising or anything anything in the interior of the light columns equivalent everything else by Larine's transformation Yukon Lawrence transforms vector of the not this now you see that supposing I gave you the metric plus plus plus plus resent look like it has only 1 positive start as I look like 3 positive eigenvectors and everything else is not remind you that there not any vector is the unit matrix any vector is that vector were plus 1 here it's true that you work this out any time like vector is an eigenvectors of this matrix whereby value minus 1 a space like back there is an eigenvectors this rhetoric with my plus 1 in any light like the terms of the deal Madrid from the Czech barrels of oil a day at the Shea Asia as well as jail Is the job now that while well large let's let's take this web stakes but let's take this Connolly here this like call with X Y Z T coordinates defined in this way 0 is a 45 degree call with video with the generators of the conga lines of across a 45 degree if I worked on multiplied let's say key squared by some number but Roberts work so provide this here now assistance base it's exactly the same space it just corresponds to changing the x coordinate from X X divided by see a but if I don't show the light cone in the corps wouldn't extant teed it would look like this a C was launched will be squashed is reflecting the fact that like most of the speed of light and is large light goes a long way in those coordinates seems base and that changes based just change the quarter but by changing the court 2nd squashed like all I can even Filpo iconic into all sorts of things close call those like called it does not reflect a real change in the geometry right now since we have just arbitrary coordinates we're dealing with here we could for example have this s feel like depend on position dependent on positions that would change would have it position and metric would have some funny position the and that requires removed from 1 place to another would go from looking this way for looking that ways of pure coordinator issue whether looks 1 way or the other but we invariant statement is that there are space like that this time like that was like like vectors and the boundary between the space like white like vectors call us there is only 1 I 4 fine and in the state want them that not bad it transformed Lorentz transformation transformer Lieurance transformation from the sea now I didn't want to get into it with you you're right you're right but let's look so what's come back with correctly so I get I wanna get through the a metric of a black hole and I in wanna spend time with back of 1 eigenvectors 3 1 9 positive ID value when they tried to rip this metric transforms on the Lorentz transformations in the woods self transformed from the Lorentz transformation into itself for a dual Lorentz transformation we come back exactly the same rhetoric yeah that's the important issue I
told you what the rule for G Odessa growth West time time before it's the cold area derivative tangent vector 0 as you move along most parallel show itself and to give you a different definition for my which in many ways is more useful but money 1st right down the original definition these 2nd ex new bike Powell squares that's the theory of a change in vector DX new L is a derivative of the back Alonso Close ends should be plus some writers think plus Newell said no role the said found VX role that's the definition of overdue best but there's another definition which is many times more useful it's the analog of the definition of a dude desiccant Fortner respects based the shortest distance between 2 points of better yet stationary stationary distance between 2 points stationery distance between 2 points define defines our budget deficit so another way of writing Mr. a week extreme mobilize all we make minimum let's take a case of ordinary space ordinary blackboard for current version of the blackboard we calculated distance between 2 points were interested in the geodesic connecting those 2 points RVG Odessa connecting those 2 points calculated curve figured curve and calculated that was it and dissidents ordinary space would be for each will element of it we have the escalator equals GE and a B X MDX and now talking about space enough space time will come back her space-time moment square or DES is just square that words are factors steal OK that's see that's been dissidents along Lucas geodesic here we just a had not to sit curve and we a them off and they have them all up we just do an integral added that will sign just means a them all out a them all up let the distances Coke Zero yeah them all out and that's equal to the total distance between 2 points the rollover Mr. make that as small as possible to make it extreme all we learned only studied classical mechanics how do we learned only studied classical mechanics this is a problem in the calculus of variations that's a problem and allergist minimizing action for a particle the another words we could think of this as action for some kind of particle moving between hearing here and in extreme realize this will make it a maker of stationery is the rule for calculating that's what kind of equations do we use this Jinyan function of X here of course was the equation called back a lot of those equation that tells you have minimized and like that's called on Lula branch equations will grinders equations for a Lagrangian which is derived from this action think of this as an action particle from here minimizing it is like minimizing the police action when you go from the principle of action to be boiler grunge equations the principle of least action turns In the differential equation typically it turns in the air sequels and type of equation going from here 50 s is exactly that operation is actions or think minimize used a solution it in the form of a differential equation in fact that sort of looks like acceleration is equal to something that something is kind of like OK let's come for the real problem where we're not interested in distance but in proper time improper time if I want to calculate the proper time between 2 points based on points it'll exactly the same thing exactly the same thing except as a minus sign here the Mets people for the proper time between . 1 and . 2 in space 1 . 2 with spacetime marriages that quantity Is it think New maximize it'd be Minamata voting no you minimize the amount that the of loss sorry humor will the sigh right next OK now let's opposes really corresponds to a motion of a particle with started the space time pouring in ends at the space the action depends on want more corn depends on the natural action but the actual action is a quote from might miss the kind the proper current between is definition is a definition of the putting Masson they will find out is important after thinking about energy and so forth but the minus sign it Cleo strictly definition the city where it comes in minus the mayor's here and in fact action I think is typically that minimize minimize the between them Our for particle moving her trajectories really deliver things a completely unrecognisable objects about it probably status of this will not only doing that counted captain
led can deal with that ability and with Darren really there means wasn't me Babruysk with rude of something BX BX what kind of things we usually understand his integrals have a D something 1 would be something of function right some functions the date could be could be time but they're normally we don't see funny things like this with square roots of XTX 5 so this is easy to and wet at the cap what let's break up the interval total times say little time segments Delta team and what's the vise here each 1 of the or but the fight each 1 of these DX is by pretty some of these DXM was might at B B C U S T is or CD 1 of the 4 quarters what happens if we have a deep PDT which Scott 1 1 of those of we haven't BXT recalled the velocity accord yawner lasting I did something here I can't get away with just biting things by decay but divided by he squared so I take outside for dt GAC did not do it In this can be Greek in spacetime another space time we Greek indices Evelyn but because you only have each 1 of these components it is equal to 1 man there is a or it sequel toward velocity along the trajectory of awards a thing like XTT along the trajectory is a component of the velocity of the particle all are just 1 so each 1 of these things has a definite value along the trajectory a certain function of the velocity of function of the velocity and the position where a square of things function of velocity and position kinds DT this now has the meaning of the conventional integral along with trajectory here early in the grand who and the trend is below ground here it is a thing which plays the role of a grand jury and action by definition is equal in the role of the law granting which is a function of velocity and position pretzel you treat we returned to a problem that we saw all quarter was last quarter to quarter who quarters ago the problem of classical mechanics how to calculate the equation motion from 9 from action that I'm not going to do it here Lebanon tell you that if you work out oil Lagrange equations me remind you what they are transient a definition now minus and the square root of minors Genia know of X X new by town PX nobody coincidental uses is the thing inside the square root is the thing inside the square root positive so the didn't think a square root covering signed here as positive and positive this it is the proper time and it's always positive for a time like trajectory particles always move on Mike Gehrke real particles do not move fast speed of light and circling case unless you missed a space like trajectory is 1 which is going faster than the speed of light so this is always positive inside here for a time like trajectory is grungy and I want to do it now then I received a Bird said just because we had now but but for a definition the modern definition of our June asked the minimize the action is equivalent to applying or the Lagrange equations granted what's right and that remind you what they are the derivative of the Lagrangian with respect through our court X new dock at the time the next new all incidentally on again be keyed is just 1 right so deeply by me just ignore that this is a function of the space component of the velocity and X itself right do we take brandy and we differentiate with respect to a of velocity and we think it's time derivative and said that people could be L by DXM this is 1 Lagrange equations motion that we learned all about in classical mechanics at the point is if you know the that correct you can work out an equation of motion for a particle was motion will be a G the definition of a geodesic in minimizes it minimizes the you have the proper time between 2 . 9 others every late this definition over here well if you work out exactly this equation would be given that trickier you will discover exactly exactly these equations here so they will exercise work out the or the Lagrange equations and show that they are the same as Our areas requiring be trajectory to satisfy this equation here is is generally true that this is a much easier thing to work with the wouldn't do it tonight workout equations of motion for particles in a particular matter that will work it out and see how it
works method will be everybody's favorite we watch watch market rats were now from the problem of studying the motion of a particle or studying electric emotional particle in a real gravitational field the gravitational field son of a black hole In other words a massive object massive spherically symmetric object no outside the mass of the objects were far away from the rest of the objects were interested in the metric method of space OK so prefers I'm write a formula and they will check and see that this formula really metric really does make sense In this sense that would give rise using these equations of motion it would give rise to something that looks very very familiar namely Newton's equation for a particle moving in a gravitational field at least 20 of far away from the gravitating object Libya where the gravitational fairly weak Procter he is going to be the magical right down the let's say what's 1st start with flat space-time as just have geeky squared minus 1 overseas squared the X squared and now the expletive stands for the expo opposed to war Square D's you square so I won't write them all back now that would be flat space and we expect that as we go very very far From the gravitating object that spacetime looks flat we go forward but now we know that we could gravitating object does something space time so this should be exactly right let's put in here 1 that will be there when Yuri far away and now works put in something else and will call plus plus pass from my Mike Ms. when the word plus yacht went bust twice you will of position you was a function of position divided by sea square times DP squared everything else along the moment won't change anything else 1 post to you out they will you was right now the gravitational potential due to this object let's check that as long as our particles are moving slowly that the geodesic equation here Grosjean equation motion just becomes Newton's equation for a particle moving in a gravitational potential you will that lets let's see what we get for Haviland Jim now we can write relatives the miners and current square root OK but go back this form over here my guests 1 post to you will oversee Square D squared that I think plus 1 overseas Square D X squared plus Y squared busy for the but let's just Quebec squared the X squared not sorry beyond the action the action now the action is this thing right square Virginia PX mood by but will be for said they wrote down what's here Jimmy new DX no that's warned us to you oversee squared he squared Barbara square swarm squared the BX Quebec he squared if you don't understand where coming out square by decays Quebecers want so that's trivial the MDX but deeply squared with just call X stock squared their 3 of them early and we have it expects quick was 1 the a Dutch court in there that's our action that now NextStep let's work out now before we work it out what's approximated that's approximate we could work this out as India's lawyer I'm interested in it is very slow motion I'm interested in very slow motion because I'm interested in slow motion images in slow motion because someone so that this really does give rise and equation in the nonrelativistic limit the matter relativistic limit is 1 in which seat is taken to be very large now I could just erase anything with a 1 oversee square a would kill leader would tell everything right artillery at the a something are here Martinez M C squared from really putting sees in the action has an MC Square and embassies greatest as dimensions multiply as it is our action now that expanded for small quantities what is it Ressam John getting confused about the bad news is really mind this year How on note plus this might this but critics OK how do you what you do with a thing like if you are
approximated wants to use large well you right thing inside the square root as 1 class something smaller something small has a white honesty squared and and then what is it gets to you Midas next stop square brings MC Square many of the binomial expansion you the binomial expansion the square root of 1 plus a small quantity is 1 plus a half a small wanted racers becomes minus MC Square crimes 1 now class 1 0 with to see square kind told you minus X . square finally we look at Paris has a constant minus MC Square at constant in all of our energy and makes no difference so the only thing you do with a Lagrangian differentiated so you differentiate this term makes the difference the rest of it here has termed my nest C square cancels get and took cancels Elliott minors and currency EU the other half of it has Lucy squared provided by Tutsi Tutsi squared plus am over to X . Rossello Granzien if you expand that out small quantities in the number of mystical Muslim that is constant which is irrelevant it has a car rental kinetic energy warm have them square and has a pencil and as a potential energy this is just a function of X as a potential energy which we get to chew we chose whether we like the potential energy there incidentally from gravitational problem the potential energy of a particles always proportional man reviews the potential energy proportional merits if you work out From this if you work out from the equations of motion of costs would you going to get his just no equations for a particle in a force of a gravitational field of gravitational field you what equations be there will be extra will not AMEX about is equal to minus M D you by DX that's for us but here's the acceleration of the mayor's canceled OK so that main point here was that this action which is equivalent to the geodesic here is easily work that would just by thinking of the or Lagrangian equations and it seems easier to work out if you're in the nonrelativistic limit we just say is very very large policy squares small just expands Frankfurt an ICC easy Pincus but the important point is that we we learned that there is some 1st approximation small quantities Jean or not minus gene or not is approximately perhaps exactly equal but 1 was twice the the gravitational potential the vibrancy square sure he is always learned we learned the the metric metric now cost and maybe additional playing in here which are even smaller than 1 oversee square this example oversee fall OTTAWA oversee sex or anything like that and you can see it would not be important in the nonrelativistic limit so we can say with complete confidence the G nor nor was 1 plus twice the potential energy particle abide by sea square but we can't say that must be be true tool the 1st order in small quantities small quantities means war overseas work but so attractive and now works right down the middle of the room in your ride again but after wanna do is you will put the mass of the sun summers of the sent there the mess of the sun provided by the distance of the sound in front describes whether might decide this the standard gravitational potential energy the massively gravitating object G divided by distance away your Rex and now I can write down offers guests at the Met trick of space time surrounding the gravitational met areas he cows squared leading order is equal to 1 Martinez true with Emma G aura C squared the from here at the the and of RC square house could squared minus DX glare mind as to why square minds busy square that's cow court and of course plus overseas quarters plus smaller thing further beginning the familiar 29 recognizes peace watch which were chilled medical metric of a black hole but not quite C squared horror here Mary next let's take DX square post BY square was busy square as the is that just ordinary metric of three-dimensional space and this formula over here only the time component of metric In fiddled with the space-based components of the metric and everything else not yet been filled with they will pay but not much IPX let us BY Squibb was busy square is just the usual method of about ordinary flat space let's take flats space polar coordinates coordinates three-dimensional Pola Court three-dimensional polar coordinates characterized by a distant namely a distance from the center of the case dissidents and a pair of angles the pair of angles Kabila polar angle an azimuthal angle so states works drove fear him point on the surface of the sphere the sphere Is that distance all Our is
please visit us at Stanford . EBU
Magnetisches Dipolmoment
Kraftfahrzeughandwerk
Kombinationskraftwerk
Lichtgeschwindigkeit
Begrenzerschaltung
Kardieren
Gleiskette
Übungsmunition
Sprengring
Satzspiegel
Druckfeld
Fahrgeschwindigkeit
Ersatzteil
GAL <Mikroelektronik>
Feinschneiden
Bahnelement
Greiffinger
Raumfahrtprogramm
Gleichstrom
Magnetisches Dipolmoment
Intervall
Elektronisches Bauelement
Fuß <Maßeinheit>
Übungsmunition
Array
Messung
Kaltumformen
Raumfahrtprogramm
Summer
Magnetisches Dipolmoment
Licht
Längenmessung
Closed Loop Identification
Erdefunkstelle
Schwächung
Rootsgebläse
Griff
Trajektorie <Meteorologie>
Übungsmunition
Angeregtes Atom
Weiß
Gleichstrom
Matrize <Drucktechnik>
Ersatzteil
Negativ <Photographie>
Walken <Textilveredelung>
Array
Unterwasserfahrzeug
Kaltumformen
Direkte Messung
Band <Textilien>
Licht
Bergmann
Lichtgeschwindigkeit
Tag
Proof <Graphische Technik>
Leitungstheorie
Angeregtes Atom
Videotechnik
Weiß
Schwarzes Loch
Holz
Großtransformator
Matrize <Drucktechnik>
Ringgeflecht
Negativ <Photographie>
Familie <Elementarteilchenphysik>
Array
Erder
Virtuelles Photon
Magnetisches Dipolmoment
Mechanik
Mondphase
Lichtgeschwindigkeit
Dreidimensionale Integration
Caudill, Rowlett, Scott
Satz <Drucktechnik>
Schraubverschluss
Teilchen
Juni
Kesselanlage
Gasturbine
Fahrgeschwindigkeit
Brechzahl
Bahnelement
Array
Kaltumformen
Entfernung
Schraubstock
Windrose
Elektronisches Bauelement
Längenmessung
Eisenbahnbetrieb
Rootsgebläse
Übungsmunition
Trajektorie <Meteorologie>
Atmosphäre
Absolute Datierung
Lineal
Analogsignal
Eigenbewegung <Astronomie>
Unterwasserfahrzeug
Drosselklappe
Schreibware
Schaft <Waffe>
Fahrzeugsitz
Summer
Schiffsartillerie
Masse <Physik>
Magnetisches Dipolmoment
Kraftfahrzeugexport
Sonnenstrahlung
Bergmann
Geokorona
Begrenzerschaltung
Armbanduhr
Jacht
Teilchen
Rungenwagen
Kopfstütze
Brewster-Winkel
Herbst
Speckle-Interferometrie
Tagesanbruch
Relativistische Mechanik
Kaltumformen
Elektronisches Bauelement
Längenmessung
Geldausgabeautomat
Rootsgebläse
Übungsmunition
Druckkraft
International Centre for the Study of the Preservation and the Restoration of Cultural Property
Schiffsklassifikation
Werkzeug
Schwarzes Loch
Jahr
Halo <Atmosphärische Optik>
Anstellwinkel
Drosselklappe
Schaft <Waffe>
Magic <Funkaufklärung>
Messung
A6M Zero-Sen
Geokorona
Hobel
Wasserbeckenreaktor
Computeranimation
Teilchen
Zentralkraftfeld
Negativ <Photographie>
Knoten <Astronomie>
Bahnelement
Rundstahlkette
Kaltumformen
Stutzuhr
Windrose
Türglocke
Druckkraft
Schiffsklassifikation
Schwarzes Loch
Gleichstrom
Sprechfunkgerät
Ersatzteil
Dipol <Nachrichtentechnik>
Anstellwinkel
Drehen
Magnetisches Dipolmoment
Erwärmung <Meteorologie>
Leitungstheorie
Juni
Kompressibilität
Monat
Fahrgeschwindigkeit
Vorlesung/Konferenz
Patrone <Munition>
Kaltumformen
Floß
Längenmessung
Rauschsignal
Rootsgebläse
Übungsmunition
Werkzeug
Tonbandgerät
Raketentriebwerk
Satzspiegel
Römischer Kalender
Jahr
Halo <Atmosphärische Optik>
Lineal
Absolute Datierung
Anstellwinkel
Direkte Messung
Bergmann
Begrenzerschaltung
Armbanduhr
Object Management Group
Zeitmesser
Reaktionsprinzip
Teilchen
Sternmotor
Spiel <Technik>
Dosieren
Herbst
Stunde
Relativistische Mechanik
Umlaufbahn
Kraft-Wärme-Kopplung
Stutzuhr
Windrose
Elektrogitarre
Schwarzes Loch
Nassdampfturbine
Gleichstrom
Böttcher
Sprechfunkgerät
Ersatzteil
Schaft <Waffe>
Intervall
Parallelschaltung
Lichtgeschwindigkeit
Erdefunkstelle
Armbanduhr
Satz <Drucktechnik>
Leistungssteuerung
Computeranimation
Woche
Grau
Sternmotor
Fahrgeschwindigkeit
Negativ <Photographie>
Starkregen
Kaltumformen
Licht
Längenmessung
Swatch
Elektrizität
Tag
Mohair
Standardzelle
Rootsgebläse
Nivellierlatte
Druckkraft
Werkzeug
Weiß
Eisendraht
Strahlung
Ziegelherstellung
Jahr
Scheinbare Helligkeit
Halo <Atmosphärische Optik>
Sprechfunkgerät
Erder
Gagat
Parallelschaltung
Sonnenstrahlung
Lichtgeschwindigkeit
Konfektionsgröße
Photon
Astronom
Fahrgeschwindigkeit
Endeavour <Raumtransporter>
GIRL <Weltraumteleskop>
Kaltumformen
Licht
Längenmessung
Elektronisches Bauelement
Standardzelle
Übungsmunition
Elektronische Medien
Angeregtes Atom
Römischer Kalender
Jahr
Feldquant
Planet
Masse <Physik>
Kontrolluhr
Kraftfahrzeugexport
Mechanik
Stringtheorie
Wetter
Erdefunkstelle
Mitsubishi Pajero
Armbanduhr
Korporale
Teilchen
Umlaufzeit
Phototechnik
Starkregen
Kontraktion
Schreibschrank
Tagesanbruch
Stunde
Schusswaffe
Front <Meteorologie>
Gauß-Bündel
Tag
Rauschzahl
Druckkraft
Schwarzes Loch
Nassdampfturbine
Gleichstrom
Scheinbare Helligkeit
Sprechfunkgerät
Material
Magnetspule
Segelschiff
Schalter
Computeranimation