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Special Relativity | Lecture 10

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everything I have here In the wake of preliminaries before the room lectures tonight was also notes going to learn how summary Caroline swarms remarked on Susan hand she's going to up I will start talking about is known to be reproduced here book Byron Byron I have collected inconsistency if not inconsistency in mind the ropes it's an inconsistency between my notes of everybody else's Merops if you stick with the convention and you never change tonight pajamas right conventions on behalf of Watson point of different everybody knows this is a common thing for me ahead of time and reason I can't stand reading of people's origins it for me it's the the easiest thing to override the a text of a reader text work really was sold on and the repair of course I'm doing a step-by-step working out the equations working out the details an work if own locations Ridge Over the years you never know Best generally remain consistent with reveals whose there's always going across Russia have not always sometimes upon request which I have people conventions of different than other people's conventions in here is year of music correction although that that apparently my equations of different Maxwell's equations a couple of times no more than a couple of times but all signs actually are just conventions and operated precisely how relate overthrew were 2 sets of courage er if it has to do with definition of electric field light and Her he's a him and was index Europe's biggest from formats world Maxwell's definition of electric fear is it is a potential and secular the connection with the potential is there able to leave his electoral Americans base from Hungary's palatial rector Israel it a minus the derivatives all of England Rock of the vector potential madam provided by a team so as 1 internally which has time derivative on potential the vector potential army we component that the potential of largest sticks amenities are here I would say that this might be the X or Y Z component of electric field being related to someone on a on kind of and plus the gradient which is also operations we came from the potential up world Will from provide my definition that I have been using at black Israel radio for it is exactly the opposite across area at by at 4 Of my gradient of that the definition in anyway you want just makes European demand they the things it calculating compare experiment being compared Romania I purchase themselves of the shortly a she but but my definition measure Ross definition different minors I it but actually receives not there the convention also have Virginia Monday if Maxwell's equations the equations actual wrote formed Rossi Rice's Maxwell it is a quote from minus being being ID tedium now incidentally all agree on the definition of be alright game it is just a corporate Colonel I'll prepare that blacks were reminder renown when I said Maxwell around absorb meaning conventions conventions agrees I don't have to to Our indicate With the magnetic field whose conventions music service has equation which right around here would also right and not be at at but we were right across a yes but but Maxwell by Carson J. now all convention jail positive or negative Her comments on GATT what was established to remote world urgent course so if I lose definitions on GATT and Rome and charged in which the electron carries a negative charge report here Michael the also right go the emergence of electric is a charge density but with Frank Goings notation charge current Hawaii was being carried by electrons and now if you make the following changes of convention change I am elected that changes the relative value these tools and president and owner of crossed veterans elected know this possibly maintained the Beatles that doesn't change craft beers are a kind of reminds us where was no patient of electric field but but so my patient current it to but this
becomes a minus J talk about this 1 here this 1 doesn't change because of the size of the electric field and the size of the charge because of me I used to be patient doesn't change all over the main point is that Moon partly historical glitches and partly glitches and arm of the moon but I wonder women patient from electric field which was composed Maxwell and Aurora Roundup minus the importance of it is just to be consistent right the big consistent can greed and cost the end of the day a few looking up time series where they were expanded published and physical real and Physical Review quotes a number of electric field you better make sure Everton electric field was not on the same line as increments number of times in my wife I I have ever had who actually container where a number from physical Review was very small so I have to go through his message and women who have the wrong side we record they are but but are most likely to teaching undergraduates probably correct is the 1st burners on now next game next they preliminary I want discussed it is an emotional moment we have had only east me concept of at and the least told them more maybe so I want soon if I want to just go we can't striking a different here concept of 3 ways of thinking about saying things that we would think about 3 different things worse things which in general have different value rose different numerical value the 1st concept of momentum mechanical moment that would usually called memorandum alright chemicals Her what ah but the chemical the basophilia like hand rules Kong Carol P. mechanical P is just a group of masked Milosevic house on masses also mineral Australia's or piece of him we and Parliament ex-wife detainees momentum is part of a master assistant come with time derivative upon in fact it really is derivative of agent of mass position and the single-particle was just a position article yeah it's complex system which just general met position and most of the chemical Roper next the concept of canonical moment promises this a more abstract but but after Clark some Of but not going but what and that comes about when we start thinking about grungy and formulation on the mechanics would have a look around Dourados star over here or grant hello I'm going to use the full grungy use a square descriptor ruined our function after he said Of course it's cold Q. and kind of not this was a particular QRE was set on corn was Pioneer and the structure of the it may begin with Cuba on 1 hand and queued up square based on something else around you may have a more general more complex but the definition of moment acknowledges peace they LP's I cannot was associated with canonical coordinated legal Her derivative of all around here with respect to Kewaunee it is no longer if the court music you will happen recalled X that at Texas for granted happens to be well equals 1 half a massive particle for example Q. would square Our aim however have to be argues equation square class perhaps some potential energy for my potential energy Miramax is the rule of and with respect of offered me is just the mechanical woman so that case this all around you an article where chemical movement was sent off like class of around in which Connecticut Energy is just expressed as a on a man whose terms expire square by abusing not rule or it's not correct where are not the same if particle couple owners in the presence of magnetic he you could easily get this from things we do this quarter are you grow back notes on classical mechanics where we discussed particles and magnetic field additional we can represent thing we the particle motion magnetic field my when you have a structural here on new electric charge if you want to keep track of speeds of light component of the monetary union or minus charge times lost got into a their potential on just a X are not on bounce from the potential now From this week the will also are working out around you equations of motion but the only emphasizing the town is comment conjugal XI now peace Hawaii it is not just a tax on not but it also has iii a scenario we should come from 1st a canonical Edwards saves from local moment
is really where chemical firms also come from rare ritual 1 week but yup picture about when we'll that Hamilton's equations when we do cannot delivery may not being me mathematics on that classical mechanics of a Hamiltonian for from example on the bullies means the canonical that doesn't mean we don't want the Sondheim shift Everything until an equation so a left-hand side you have and text novel got acceleration you might want to write equations with this peers army equations but cannot resist a subject the last notion a lot where also in many cases in some cases please our With the chemical but all of them sometimes argue Kaiser is the quantity which is conserved by virtue of America's appearance if yes Maria physical set up Is translation invariant and variant with respect the translations of nothing changes were granted in the whole change when you shift Courtnage ex post facto was a crimes is a conserved quantity of cockatoos called also remain so it yet I'm not saying it may or may not be approved this year may not be equal prevents and quantity consumers but virtual army John however it is also unfortunate call piece of piece of you them more around and they using wrote Mr. replaced not I that but we do need that point tonight as warriors are just click queuing for quantity of came when call people if you'll have Madrid if you have the surgery so that when Mr. military operations performed Q. was transformed supposed each Q grows when you do transformation operation app prime transformed accused of body what accused but but a small has more collection which we can called delegates are accused of our now if we have a symmetry which means a transformation of this type on the which grungy and doesn't change this will about program doesn't change it is a concern of quantity capital Hey which is equal to assign all the contribution from each corner all if please line your own account for more than a quarter of a canonical times Dr. accused right but so for for example if Q. What happens to be XVX provision of particle I wrote of more and kill happens to be the exposition article the newly translated text when you translate accord it all happened acts division and the amount which is why he is independent of x so you could say in that case that the dope accused by Exs just can't just a number the amount of money In that case was accused of just the number can we find a quantity which is just proportional Paul system problem back typically the public can a rose system can go anywhere an honor Gorman West concept of momentum is conserved quantities where you constructed figuring out how all the Cold War to Mr. all the canonical coordinates resist change when you do the operations and then multiplying or small changes the card you momentum heading gives you because of quantity which is also Magical Queue here on but it consider it if the world was published other 3 concept of momentum and then there is not necessarily the same as and we when the organization has the usual simple former somewhat Connecticut energies pose potential energies ordinary potential he's not kind just a summary usual kinds of kinetic energies and potential energy then they all tend to be playing various definition more generally not OK now wants to move on cool relationship between them we can and theory we used to use Auburn's uniformed forever after for fuel theory was about wolves and detail where my race at well the I'm really detail in 1 sense field theories it is just a version of classical Kerik's but the reason I'm going here because I want to get these questions and conserved quantities consider moment and also concerned energy but it before the end of the year at corner here the because of energy in classical mechanics because energy becomes Porter room grungy and is invariant under Prime transgression he goes keep us a constant an owner of municipal questioned doesn't depend on time you start expand I'm just like that before me was not was not given as a function of Cuomo's include shot but after but the book finally called sorry don't she was as part of a core Hamiltonian concerned it is the energy remind you it's given some or all of whom if where according to describe
on a couple momentum and conjugated corporate now probably by the time derivative a corn that my list of oranges but all that work out was case just to remind you Our is Q. What happens to be it was just a quarter a numerology is 1 ham and pack stock a next potential energy Roger acts which has worked out with a hammer operators I was always a canonical momentum commander who moment as the river runs in with respect to a velocity P in this case as just quarter and spot just exactly what you'd expect if we multiplied but you not in this case is only one-quarter of the problem next there Richard P. stop which would just be minute ex parte square 1 ext . crimes killed on the other 1 comments from repeating plant a we might Ranjan stop my Mrs. Turner Murray warned him next up square before and mind part of it war now numerous times in Europe last time OK we have not square might have stopped square just to pass a mixed perhaps next quarter so what you get you get a arm of kinetic energy potential energy where are that but the definition definition of Pancho energy and kinetic energy In the case would be applied equally separate programs you nicely and our quadratic things important kind derivatives and all the pieces which depend on Congress to Medicaid where things which are quadratic in time derivatives and other things which bomb contained kind derivatives that a well-defined separation kinetic energy potential energy kinetic energy it is just require erratic expression and remove obsolete use the potential energy it is the peace program which doesn't depend on on I'm derivatives Hamiltonian the energy or comedic energy past potential energy and ground units kinetic energy miners potentially you did it will is not just a matter of Our velocities passes Woodstock organizers which don't depend on our surveys you could easily very quickly without doing any work what has come in from me on from around here it is changes which doesn't contain possibilities a Idaho prescription and we can use that term but we should remember really comes from what was the point of this time the point of this Hamiltonian is go back to the classical mechanics now using Lagrangian equations the problem this is conserve change your car the equations emotions Ranjan equations of motion applied everything on the side he would tell you Robert communis counselor and it is of course we energy it is of course the energy expressed sorrow over OK but through a field theory don't read In a special case ordinary classical mechanics slightly and viewers when we try to write it in relativistic fashion With are if we want to see the close connection between field period classical repair it is best to give up this call enterprise of trying to keep you all equations explicitly invariant under Lorentz transformations and that just I a somebody's your time all my time but a time variable picked frame of reference and stick with that bring reference and don't for the moment worry about going back and forth between different Ranger reference on take a frame of reference pick up time not try to keep the equations invariant under Lorentz transformation end it is easier and form seem a connection with classical repair OK so meanwhile appeared normally Walter I'm classical mechanics and you have a collection of being accused Cusimano of and you have a actually principle the action principle is Of was
function killing 2 all through you got but we're actually an action was a principal we stack after prime access was that of course would depend on the climax of an expression reaction which is an integral part part principal variation of reactions on reactions a stationary point on an article from here entered
the of period again we have time axis and the core 1 of the system Our functions of time away coordinator assistant about a quarter of the system I know I'm not labeled by an index of discrete index army according to the system of labeled by position the values of the field at each position in space if we wanted to we could imagine please was screen a at the but and her next goal horizontally the only physical only relevant points would be some discreet collection points and the the at each position with the final quarter but if you don't he the furor here few here over himself this would be his tactical 5 0 my once practical tones and the kilos cannot removes would be part instead of riding high on In the case which from except the fact that was an x-axis contracts at Sony Poindexter's as separate and independent field or a separate independent call not call me Action News quoted him as saying that use Q degree of freedom perhaps degree of freedom of award what Yahoo Quebec Pyrex is a degree of freedom and Texas will label and things I'm away Chris originally confused between somewhere else it is also of course Honda arms Of but although I think got no also depend not only on a fly in each point and also hand on derivatives with respect space let's think about former because they depend on things like we find a binding acts not he'd be fined typical grungy and destiny the Longyan feels but what is remove fire with respect Texas 1 it is really not always right but the distance between these points called Epsilon where more it's really fighting flying going to X plus Our minor point next provided by put residue it is really just a function of the prime is it doesn't most important thing is that I wasn't involved why yeah so in places with all of our energy might depend on spatial derivatives that's really part of its dependent on fire in this case it might depend on defies the same time that but I think they granting came and 2 kilos of a good Q 1 minus Q tool or something like that it's depending on Friday at 1 . 9 5 years or so young him Cos you go find was number of possible known as it is isn't Be careful what is not depending on because expert and X is just a weevil X is just going we could instead of calling this the x we call it the numerical access on and this would be a Friday or on right the fight general function of X me Our in this instance Q. warned depends on Friday and it depends on later just because of depends on which 1 you talking about what you wanted me to hear I'm talking about trying at 1 point ahead enough time for is on hold change as an independent canonical degree of freedom of others cup we have a very good question answering questions Ernie if you write the right kind of Nanjing or I kind of here then suddenly abrupt changes in the party From 1 . 1 0 will be very costly and energy at some of dynamics work Peru that but the book or comparable is a very good point What it that what is it that requires a flight very smoothly between 2 points now and the answers energy normalcy will usher her work OK so I'll his I don't think about what we would mean there be Over the years action actually but and classical X is always a kind of a long time sort of and the need to remain at all managers man in itself there's going to be any time all are based on capable of a space we find that this can be done this kind simply repeating we did earlier the program actually is an integral over space and time we separated of the kind of grow a R and right has an end a little bit of square that right this wasn't in the be Texan was DX me it can be incidentally I did not mean comply spaces one-dimensional we might have to of based but you get the idea but this could be a XTX who won means all runs as I am thing that we call script Allen field hearing which depends what depend on it depends on the field that Poindexter depends on the time derivative and may also generally does depend on 5 IDX at but Oh on I'm going back to early in locations where we wrote around and density here look and derivatives of fiery but I'm keeping separate the idea of kind derivatives based rivers and don't mix of Carpenter was single common notation I'm the of space that this receiver they all are just differences of prime so really just think of this as a function of all of the parties and why not if this is really just an hour emotional authority will also be barking up it missed form separate off a R In and the squalor around you this Lagrangian here set the removal of this is it or Grant is In the rural arm of business was not aimed at this city on did you hear me say integrator over find out what all around you you will think of it as a sum of terms each time and long a field the kind of feel perhaps neighboring areas of the field Booker such she that's reasonable agree now worth thing about what school for the Hamiltonian after August is a special case of mechanics the baby but From our and at yeah he we are right right now feel series like Maxwell's theory certainly have a notion of energy resource a repair light waves and emotion new association associated lightwave that shines on
Earth docket water it's about because transfer of energy do I'm not yours president of Warner New fields and I'm not have since been not something entirely new and energy is part of the universal conserve energy that is associated with time transgression we should be able to you lose formulas that we have if we applied correctly this kind of special case someone both our new person has struck me energy we the Hamiltonian the 1st thing we want we pleased accused of being secured arson we need Rogers OK is he is now do not mean more than a sense of community and nothing whatever to do with no good derivatives all-around years around here with respect what the loss was the last year it means of fighting up it doesn't mean velocity in space means velocity in feel how fast the yield is changing a particular point not changing the point point changing because the field at any given point changes are not enough here paying can't did open until we not patient is not patient quarters because we've already called for money things that call to say things arrange there is a standard not patient what are we talking about we're talking about a room derivative grungy and With respect fighting after what we find out war it actually a matter of if the look around you most of the programs each time programs you point X only a week only involves a point about that point next summer when you do differentiate public around you only picks we know particularly now I'm so we're interested and the regional manager respect the fine and that is the canonical momentum conjugate I don't call P because we people something else 1st so standard patient was piled sometimes it's not a canonical momenta conjugate purported client it both sides are functions of positions but functional position and his canonical momentum is also a function of position Ed back not many fields around there may be many fields of a problem not just fired by 1 5 2 3 and maybe a few pages and maybe a few other kinds of deals there will be 1 of change on his feature each kind of field found all of this will be a guest at party associated with the field at Poindexter and and replaced him with he E already probe OK so talented position to compute Lagrangian about how that's completely from all here 10 I Our 1st of all it assignment all I want is a foreigners proper I I I indexes finger labels of label the degrees of freedom the song authority is really going to be an integral and grooming X some of opposition but that's not what happened what's going please part the are they Barbara sex crime of fighting next president all X yeah Harrah's are are you Our were subject only whatever it is examples of Austria has worked Soon reminders repaying yeah but the ground units also this is not correct was correct publicity world which I'm not us remember that nor are Her birth now I have to subtract offered poking around here but don't just missing here which is also in the world woke under the integral signed under these will be Cuba Texas Bq pacts where are subtract my store around mom who will work as an example soon enough Warriner we have energy which is expressed as an integral office space when you call thing in the bracket call the urgent answering energy density and that's exactly what this subject is the energy density going inside square OK so now Sinaloa Corcoran Macon agreed only pictures of proposed picture appeared world this project being prepared start Her right were a child back war but and let's do it example work the example I use all over with just pick one-dimensional space we really do we believe didn't chooses as you like but just a new group Richard III were me has a kinetic energy and 1 half why not squares a member Iran's in contains plant in find if bird did we put in minus 1 part of fighting with respect at that square uh and finally here but a just a general some sort of titled but rumors of the house that will cause all this is close to find a score of buying as find that square has gradient of climb squared and as we if we went back to thinking about relativity will recognize this quantity here as a scalar and this quarter arrests scalar and we will be doing the same kind of construction will begin with a rapidity will start Bonnie's 2 things call 1 have been find being new time so beautiful derided but we don't want to mix for her ranking separate time derivatives and space however all day we have smashed or not it is part of the a party at prices of buying using derivatives of Lagrangian with respect to find out there's just like that off praising the apple party orders party Mr. planes captain is read now offers a hand on him Bush for half a year earlier energy that at but French In but are pies and my times might not life is despite about quantity box his mind I was hoping he would just look around here my it is lower than a year but for so it is written off find out who administer have lined up squatters gives you just have square look by that great Mendoza have not all track on this thing over
wrong right on track this thing which already has a minus sign In the past our service becomes past the virus Hirschbeck X square possibly next book her I know we have no I didn't we have a kinetic energy related time derivatives which doesn't have time to derivatives and obviously this whole thing is playing the the role of potential energy piece of energy which doesn't have time read sometimes people call this field potential energy but it's really Hall combination everything which doesn't contain any kind derivatives which choose kind of potential ordered you want tampering and again we have comedic energy Minister my has potential energy we have passed prepared enamel prom but this is the energy of a few yeah kind derivatives are positive this or she was based there was a positive and V is a positive functions this would also be possible this wall what fine strategy of bribery of prime source of expert your right on depending on fire on a mostly from eastern earned them both passed over can as positive and negative it's not In general bribe Cheney only has positive terms Of course the house was the only way that this thing can be 0 0 is ii is constant so removes all 0 we are 1 example being fired is equal to 0 a fire is equal to 0 this and but it can be so energy is typically something which operated out of it and With leaves or chorizo yeah it can be made viewed who but you can get trouble unbounded from there is that if the law will be leave used at constant would make it possible change so you can arbitrarily assume with this part of it is not from both not stable images grossed wearing a normal part of such a theory I soon you could assume the positive also 3rd and the energy warns not Tony configurations in which a sequel to 0 what it sworn in no time is constant now and probably also have a minimum of this potential here but she sought to conference be spent the Carol if but the rock at well I just kasparov our guest this study the field scale of and relativity hearing on we use the copper principles the 1st being low-calorie prime calorie needs and derivatives we use the principle that should be learned Marion Lorenzen French means should be made of scalar and this is just most gala obtained from being merely trying a new trial at but workers fight up square miners proprietor quarters the mightiest miners and funny minus which commuter rail with your car I'll think so 1st thing at 1st might appear report being refined might use notion I feel the energy and especially field energy density and In the 1st place Our fuel energy concern that energy density and Maine Webster already in wrong we're close Iran's survey I'm really give us a mail room where she met the at op How world but well Gerber the had no idea where it comes from remote doing what from Ali get drop so I guess I can erase the are being now who during but don't why now on voters the June users and internal office space we're every point every quarry after each plan to devote space sergeant was and each point of space it involves a fine and find out Corning replying to fire the those differentiate popular around what reduces was researchers granting legal test you got to differentiate people around here With respect of might not fight about some specific point systems but point here where different shape ground with respect for year well we find her only occurs in 1 think of this as a sign of this summer Reidy at overturned GM sorry it was disarmed only in 1 hour contains particular buying a fine not associated with this particular porn only occurs In 1 namely 100 associated with that point if that's the case program James we knew they usually are man differentiating with respect to a specific might not a specific point throws away all always terms 1 and acts of point her right now on I can't think of any actually not pathological released not around to their offhand topic of it also in a position to answer the question our let's power was jumps team what was it that requiring find very smoothly Harold the separation between these points while while jacket for example really independent degrees of freedom while only Jack facilities distances going 0 means bigger and bigger derivatives somewhat derivative the difference between no 1 has separation as a small separating its more and more given this given different McGrady and probably gets bigger and bigger and that would mean big energy density in here is getting bigger and bigger the where Mr. I'm interested in finite energies I'm interested in configurations with energy is not going to be something huge these derivatives refinery a new revenues of finite that's what controls mission young background Oh now serves it and he was gone I was on our to on I told reply he don't where it came from stands something new historical engine it does have me Irish or because I'm working on that Our express Wong In and this could be interested
really optimistic it is not just hearings energy Is time component on a format wrap factories usually call for a things of being copied usually liquid paint and kind of energy high-end component for emerging Norman OK want to 1 factor remember energy is some Oh America associated with kind component for that and then there's a lot of interesting where do you have a concern quantity In a relativistic period a sensible during conservation Israel that means that the quantity just doesn't disappear over here and reappear someplace our way there was no locality conservation law energy or charge or murders could disappear over here we a period after surgery an experiment taking place was laboratory for all practical purposes there would be no energy conservation is not the way things work as well as explained it is a real concern quantities only change if our if you could pack a flock of our current demand testing through the walls of of your laboratory olivetti varieties there aren't any destinies common test are or and this city and the current combined get her for but None of that but J. that that kind of Parliament urging you space component of GATT is what we a floor of a I'm With this idiot on them using language of charge density you now but more generally referee like kind component From what we have address all of energy is solved what kind of suffering the Pine who and this me it is the 4th component or something kind four-dimensional current star this study on energy it was good Pennsylvania the time component are that's why use euros appeal 1 of those plans for the fact that we're talking about energy and the other 1 this has to do with the fact that we're talking about identity but I think 2nd you have to do with the energy of the first one Harrington who would be packed to the city we can't leave her continuity equation which is important and that is a continuity equation energy the continuity equation for energy sectors if you CV Energy changing someplace energy density changes because a flower report public Service is normal energy you not love were density corridors that while you're at figures is that came back with an integral yes but a source from the case of 1st of for today remember where is equal in the growth of piety fight back my I at but at so this is nothing in the prior year I was listening manner energy around 300 right Berger but suggesting that our energy density was the flow of energy earlier time discussed are it is button because OK you what about the the not that I don't need command when among them which is consider it be costs on translation the general concept the time was asymmetry in the world as Christian because what a part I am going to call on P I apologize is just many things copy historically were related to which I'm now talking on work Of In this sense of nerve but having to do with translation right now to but the which is a special case of the thing call Q. What happened to the computer after all of on
the canonical moment but at where where now if the Chronicle rivers arrange and what's Friday voters what but a piece of work you know procurer remember this year we figure out Ecuador's figuring out how to military operations affects the quartet piece of Bahrain peace of mind occupied court martial right now and we can get from formerly answers are being based on Monday replaced by integral I Lee plays by at he was wounded in the text I fear what's pining but Of prior conjugate defying and then we have to to figure out what Delta Five years what is the fiery when you make a shift of course we're talking about translation of where we original course which displaced from 1 point to remain poor what happened what happened so far what was originally called next buff but we come Asia but what do we shift with shift by and from now Dr. we're not a small what happens if I X finally the 6 becomes my arm I'm using my Isabella but report which was originally called acts after the shift Courtnage becomes called point X miners belt as sequined those who X you Her after wish if they are returned becomes even at miners dump it doesn't matter miners doctoral course poachers OK so what is the change and Co them the change in at I thought it was volume X minors the body of text done at but but the change Friday when you shift course really relatives who have your ran over much has of changed it changes must be proportional change or through changes and that of course just proportional grew who delivered party with respect for change in the field up when I'm home I had a little bit correspond to Guam the rulers of mobile the change in light of ICE and a particular point Kumar rulers proportional through the Rural Fire with respect was notified just being kind called New require workers my symbol for mail she and if not River rise 1 of our right now here's yeah answering please consider a concerted multiply out there was no record when questioned by the answer is we just trying to find conserved quantities and at will official definition of the moment is defined in such a way that the quiet about at 80 meters of India where the dollar because it does not have the resources and an air force brat Taipei is the defined away near is could shift Antwerp previous missions around the world bird Burke frenetic pace quite concern but 1st cocaine I but if basic component From a former for example what but their 1st space component From this will be my mind he examines where shifting which had been wrongly and access each content on own and 1 . 3 what each can be represented in the rule of the dancer so quickly clear that the momentum
necessary the momentum density book but what should we use for it but the 1st thing was 2nd next all as for moment answering er it is a fact that has an opponent met with talking around Brazil from the fact that we're talking about me With talking about destiny is a bone density eventually would jury up Gerald Colorado your so we're talking about me that makes us a prime time cause this city With of and component of momentum an article 0 manner but 0 0 density I energy apart
from 0 and those space component we would arrive by bananas Madrid but we know table brush global price on Friday I would derivative of fire with respect acts sorry stood before a road hiding be fired if I'm ready acts after which X X Arab it would about what X component facts of white component as well verdict let's get out possible field theory is to be read by supplied who has written off your areas just equal man were Abdul I was part of his time prior to team crime if I would check excess personal and supports pressure option 1 of the women and their the union agree for example an electromagnetic wave upon wave I find it literally is the a momentum carried by here it's combined together Hey yet With the momentum carried all particles and if you think about ways to America the system was only translation invariant if when you translate feels you also translate articles if the particles charged particles so it's not located just translate the electromagnetic waves and not translate particles and I mean you translate everything so we will if we want to keep track of not only the field all articles and interact where they would be contributions to a momentum coming from those particles you literally be talking about a conservation of momentum of particles and field as well as black as white board here it is made up of articles we shining light I wish I lying on was to which I'm also like what's opposes blackboard were really hanging around freely in space we had a good pulse of light on light reflects off it the momentum of a white Ms. transferred maybe going be absorbed what absorbed the moment light is absorbed by the system here what happens is that we call girls now full of life from on the pulse of orders was so feeble where pretty darn hard Primerica Major can't be required on anything but maybe the lightest filament of some sort this Ford membranes neutralize like ordinary white whose Yukon around brokers extremely people in the but a really powerful laser beam at OK because of laser beams that they use in the afternoon across a bay you're Livermore I have so much more I'm that will make them is absorbed kind of material has been adjusted squashed yes White has momentum has energy Hey we're just done simple way up I'm not going to say I'm not sure I want to do this to remain your was the question that we haven't addressed yet and that may not addressed score but the other questions was the full these entities of these quarrel what about the fuel and energy them where'd you more and I'm that so what but with originally part saying the for space yah granted that you approved chose right wants that do you want Russia which also not so what what cost cast lost a his own permissible for your the equation of motion some sometimes some cars especially in modern how's ranks you don't stop requires which are known for use in use by measuring you start refused trip principles and gasses or fields are around here it was around you but we have our Newton's laws would the field equations a 2nd Friday square minus a 2nd square what 1 there was a quarter things being 95 so you wait equity so where Israel away from choice the authors of this issue not on beach you have to higher you is not really gets about isn't derived review equations or you go experiments and the paper which parents and a a prime of experiments arrived field equations and the right action all trio visitors Higgs field how banks he was a really measure earlier could be pursued could this time could stand from a position of extract between 2 . when you could derive From the fact of a rope is made up of a bunch of particles which bitter comedic and potential avenues of particles make but what more and more modern physics revolves around trying to guess I'd soon the principles from basic ongoing workers were physics trying to get around him further and and arriving offer you don't know know what a few equations are the Our so In a statement here attempts to build 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electric field that at but it should look at as a sort of wages this nor backed by now that around him has quarter Hamiltonian we could go through with the construction of our army and now I have no reason is we can look at this ground units it is a kinetic energy depends on square declined and he is a potential energy Turner has no prime of all voters kinetic energy potential energy only know what the answer the answer is going to be being a kinetic energy plaster potential energy are set so we can guess the Hamiltonian energy is going to be 1 hand he's however that 1st Turner they got square class born Africa be square but the correct expression we are electromagnetic field urging electric and magnetic field settings speed of light 1 Bureau article 1 1 hair a square pass Quebec analogous reading is entirely in our heroes on identical the program in being fined about square over to miners gradient of fire squares and Carnelian being fired about square profile square not again saying 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appeared her the yield over here too said that meant was equal and that score of fuel jiggle Megan there'll be echoes off hiding apparently fired IDX reminder where it came from pioneers a car or momentum and be fired by the attacks is the amount the fight changes when you of concern on any concern by virtue of there was a arms contains opined that contains 5 IBX if it was several fields and a problem we would it not yet women ended up and they answer a few of us in this problem but that's all it is the collection of relief meals each 1 those exactly the same thing here is that for Harry the electric field Arias mind surrogacy or P.O. be will have a PX that's all soros basically Assange Procter and leaders who was going to be replaced by me and on Pine riches related a mail electric field cairo Brett UM set there you are but you are a bar from your shirt a rebel group signed Nichols here offhand Iowa have figure it out big time figure it out on the so let's just not worry about the 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sub and mines and wireline isotopes tempting because it could you really want to put a magnetic field not just damn prepares short of pocket sort out what damage doesn't do O P and put if I did put 2nd time hasn't changes whoever goes hawkers arm was playing and and eased Emma these days and buying Saab the the anger of a ENDS IDX and I that thing in or or off NO now I suggest that maybe it's OK program maybe miss after In the groom I think you back when I hope everybody knows doing will but part partial aggression where do happened to like With derivative on 1 thing another yes equal worth I think you're making assumptions going with a view of goes 0 are wary of thermal boundary but you could take as derivative and shift the other factors at the cost of a minor sorry this is equal Pearl miners near the role of me being Obama by the a and reversed take the derivative from 1 factors put on the back from fully integrating but parts of them over and over and over this is just another example of that we have here Bernie the origins of the electric field they gone he and that's 1 of Maxwell's equations that nobody is equal to 0 song visited wrong Brazil Turner is the integral and the integral doesn't contribute anti bear that means that Apollo momentum can be written in terms of electric and magnetic fuels and this is actually crossed beam if you work out you'll find our where are we S Moore may from is creating crossed again the cyanide for that he Crosby is a momentum and the PX think you back Negroes who crossed Park between me is a Mormon of that it is a factor sorry direction of this vector tells you the direction of a moment on electrical France sample example reply create an electric field picking a capacity Boss crossed paths crossed my mind Martinez director your that way and that's make a magnetic field a roaring into the black for its output off and in here a electric field on 1 one-way magnetic field going the other way and crossed Park proposing which direction all right way Hamrich that way games a local here was a moment there's a moment and then or momentum that's moving arrive at are that's meaning of it this is called pointing that parents pointing out because a pointer Mubarak tumor point POY and ING point was made yacht of that I guess is not charge after assuming now free electromagnetic waves of discharge and you have to account for the momentum of particles making up the moment we're just doing pure electric and our printer electromagnetic field chart that's right the report by so much just as a just look look at this expression from electromagnetic waves perhaps electromagnetic wave rural electric field for example pointing up over here what's a magnetic field pointing out a Blackwater over yet you move down use the electric field was the film I know him carefully and magnetic field was income a blackboard which way is seen Crosby start here but and of course kid fossil rating what you feel up magnetic field I work you 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Metadaten

Formale Metadaten

Titel Special Relativity | Lecture 10
Serientitel Lecture Collection | Special Relativity
Teil 10
Anzahl der Teile 10
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/15001
Herausgeber Stanford University
Erscheinungsjahr 2012
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Physik
Abstract (June 18, 2012) Professor Susskind clarifies how some of his notation differs from the standard convention and then moves back into the concepts of momentum and conserved energy as it relates to special relativity. In 1905, while only twenty-six years old, Albert Einstein published "On the Electrodynamics of Moving Bodies" and effectively extended classical laws of relativity to all laws of physics, even electrodynamics. In this course, Professor Susskind takes a close look at the special theory of relativity and also at classical field theory. Concepts addressed here include space-time and four-dimensional space-time, electromagnetic fields and their application to Maxwell's equations.

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