Special Relativity | Lecture 10

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Special Relativity | Lecture 10
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(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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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
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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
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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 emerged product no as a historical fact Newton's equation looming around liquid Pa Maxwell's equations room before a reaction formulation are rare but Mr. Duerson West sauropod on let's talk about armed there were no through their actions by Rick Fox aluminum flocks which I did not want to 1st all we can talk about promotion of energy and momentum in electrodynamics the energy density and moment in or Ameritech's indicator of electromagnetic waves and I think probably important poor thing to do right now the energy momentum irked book this is quite keen on today In a few north Austria carriage I think all the energy momentum sir urging to the other components of it are associated with the flow of energy momentum will get a chance to talk about her Russia these objects here on and densities of a Hulu Schroedinger and general and do whatever they do play a huge role being the sources of gravitational field sorry we have we have to come back memory but have to do that cannot be necessary let's talk about applying good electromagnetic field you now we're apply some of these ideas particularly the idea of energy moment In the fuel fuel around we want apply those ideas of electromagnetic field all of whom have also might be a good electromagnetic field we could do it now using Lagrangian but and the formulation gave earlier Her past marchers be
feels were fuels the fields are components of a potential Ken Hill so far components a Becker potential pine component and priest a school Ahrens and granted he was written in terms of electromagnetic field cancers written in terms of derivatives space derivatives and derivatives and square of all things that gives us they around Jan now include where out having has 1 field we would have for your most of the things that principles but there is a bit of our short and that's much a shortcut simplification from remained firms and it really does go straight the some things about the idea of changing variants which are quite important to our that depict a potential was not unique there changes you could make a mail potential found trained workers are you can't Mueller's that freedom has was you could use as you can use the freedom that your our which is also a lack of freedom in your choice of rock warned all kinds of freedom was armed resurrects associated with conventions resource to coordinate frames associated with peaches are you could use your through will Armed Forces acquire by saying I'm not going to work with a full general Charles From freedom to do something a little bit of forward and pig the on 1st remind you were a gage transformation as a gage transformation U. N Carey McGrady across their but at us Oh there is below function as I can you likely uses freedom prepared panic and in a way that Greece will find my choice a more example it was a particularly simple provocation you could make angle Jews s in such a way that kind component of backup center with your kind that is not possible is a possible could shows start given anyway time for and a normal human nor Is it possible prepare 1st now new ways apparent from component SROs means invite me to me if we start with original work time compartment we change the time component by getting free Is it possible to choose ST some bad news is always Eagleton 0 answer yes you cannot given it any function at a point in space of this is a derivative with respect crying fixed positions priced forgot that positions based here a Hammer edge Pinder revenue it is my some preexisting operas specified can I chose s bird this is Yigal Amir interests me a north I need to adjust my nor they where yes you can always financed back its derivatives His particular option Vatican convince yourself you don't buy some integral of ignored by given any function on the right-hand side you could always find a function left inside whose par and the remains of of a lot of us are sequestered or ER rep but How can you find the answer is yes you always can do that sort iTunes ES so that time derivative as minors we all original vector potential coupons particle of manner the new vector potential scorer kid climbed Merrill for Harare raw time compulsive always do that call fixing gate agent called Aurora call fixing freedom around Gage freedom meaning Casavant you could change the vector potential are changing in the physics and you make a choice I chose to work so that kind of Congo and your other choices the rather just you but fire right changes number physics Jones we fix a north of bat completely eliminates prime component of that draw Norway have left space components are rare eventual 8 a Bob backs I'm supposed to what then on electric and magnetic fields while be electric now the question is sure I use my convention Maxwell's I will use my fault I do mind as Michael entrance noise plays rail or should remember America I are became yacht OK my best this year that I might just be a bargaining chip class Marieann's a North Lebanon Simplified R S set in nautical 0 pain or doesn't exist anymore a talk electric field Maxwell's electric Bureau it is just minus the pine derivative of this Race component our real preference based on receipt of repressed basins and and director field is not being bought the derivative former Mayor potential what about the magnetic field opined that feel only depended on the space components of vector potential oppressed plays with just a corporate promo magnetic that change magnetic field has not changed our the space components of a about B is crossed an electric field with narrow mind this by and that simplifies all eyes a little bit we don't have to worry about current coupon Rebecca potential and the fields and degrees of freedom degrees of freedom are just the space component of find our prepare where some requires OK well below ground nor magic tomorrow isn't kind of electric and magnetic fields gap the afternoon near minus a quarter but I haven't been able to ease quarter or approval miners be Cuero the square of electric field minus the U.S. square magnetic field Our privacy moved however we make space time Pomerantz they have squared each component the next face time components source of electric fuel squares Andrew space space component was good too the magnetic field square it must be your best program dunes and now I can write the Lagrangian right How these quantities here and Overbeck the actual event the Pancho Ava Rio fuels but we know that we use in grant you sort her back a square Miners a square have a square mile swath square 1 half your square of budget your there's just me aII by D. she's where I like best why have the kind guru appeals court members not everyone journey of a reprieve times you His NEX square is trying remember excluded the kinder RAY square higher derivative of a easy square off it is a fine terms of exactly this type 1 in each component of a perpetual so the 1st thing we studied that a kinetic energy as a kinetic energy which is just
sums of squares Over is of Kinder absorber basic feels for about a 2nd tournament the 2nd has won have be square feet square worries were Han goes crossed a school look different from donors this can involves a history of not kind of rivers in here at all always based their cannot only space repertoire of coral only involves based around Our aII only has space components not a hair looks quite similar where are up here square derivatives minors the squatters were our various kinds of space to reporters who were gunned him looks nice and healthy remember making peculiar and I can exactly the rules we but we that we arrived ah before we go from your particular West Bank about me energy mammal I have to go all before we know that just tell you will go through the whole luau operation wicked short-circuited but you might guess what is canonical moment conjugated total particularly component of vector potential storage by definition of derivative of ground year with respect for Pinder Riviera Beach Cheney of a what clearly just the square ghost Cohen used remember most of OR queer of our proper there are 3 components X RAY these 3 components commune at 3 fields each 1 has a degree of freedom of its are each 1 of them has a canonical moment covers that means the canonical momentum also has an index x y and z car hi but Wash as with mineral a X with respect to be part why would be Europe a wireless whose secretary and likewise pricing recalled me a zany body this of course here stands firm Hi and the removal of a X squared must I'm doing a white squares the virus Hi quantity the canonical momentum also has an index and the index Mr. associated with the index are our but it also offer all the time to remove is just miners electric so far only interesting we cannot happen to be just might electric components of electric field but what if who wants worth a physical meaning In this case the physical meaning Chronicle comment from conjugate From prepares draw it is just a 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 nor Garcia was not prosecutors necessarily and particular notice on magnetic field would not electric field around the neck of the Energy Energy is possible square b square sources tell you for electromagnetic wave moving down Baxter's various ahead toward electromagnetic wave look like perhaps even components in 1 direction and then perpendicular direction trio brief a magnitude was famously field in phase with but Paul arrives in the perpendicular direction and this tells us that because of the electric and magnetic field energies are saying fuel managing electric field this your energy the magnetic field electromagnetic wave moving down the access times electric and magnetic energy may happened been same on have a square of be square mistrust the them membership twice is a pocket field energy or questions about Hill the next question is the momentum going to be no next the moment ring How much momentum is there and electromagnetic waves OK so back which grow by America the lawyer 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 size of our and component of the electric field is a particular from our home from a man packets multiplied by being a Emma the myriad by area of Kerberos slopes Garrard but new M. of a Saab Emma by acts Mr.
song on an hour if there are several fields in a problem but take me difficult plan B and component of performance among men along the x acrimony and textures Rasmus Lindgren axis In North it is buying a fire there are several fields in a problem of we had more will last several fields of a problem and the social fields and the problem of 3 components of that potential stock quotes and not derivative is with respect X a unit and their authority and component of momentum we have assigned already aired story borrower arriving summation sign will use the summation convention the momentum and field elected freely a piece of em and component of our time others at for care took frosting eh Peace Dam and enormous that Baez a movement 1 but yeah lost assigned Hurricane by our our our had a hand rusher I R please farmer starring issues please send em me a sub and buying me acts as a mere Rex twit now this a funny this he is a member of Unix that's very him for war on terror poet minors being a 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 feel bound magnetic field and call will forever electric field up magnetic field which way Crosby but Bull 4 but but arrival both a prank so our momentum is going way here what about gender can't be have changed signed but Crosby Truman from foreign here and of course that's the directions on the way the Norway of moving down the Baxters carries a moment which is you Crosby not attack on news that means be a perpendicular to to each other they want perpendicular that's not social Maxwell equation of perpendicular you would think them some server momentum appointing back as a consequence of a perpendicular being it all traces back to and they know it was wonderful Iran's about the connection between concerned momentum and translation of various special translation but all countries behind him want peace classical mechanics electromagnetism gets all those things toss from principle we faction and I think that's probably a good place to start yacht it is not sure but I'm having track of voices that eschew if you can show that were where were What a Wizard with coach bomb hears oral or Robbie option go label from minors what's taking and component of a larger field minors the derivative of BN component of a vector potential respect time horse derivative of component the potential British back X an end to the rest of the year
I figures Mr. Maxwell yuck for some reason I don't have a stroke or electric applause elected him director viewers for commerical from unit at a hearing on that and I believe that at least 40 years that moved Sunday probably mentally I knew I knew it wasn't right notice that expressions are probably yarns the energy density stop for change Chang River because we now have a cap of Utah OK this is the expression of electric field the magnetic field was just me because crossway merit if you were a few tracked this trick or fixing a game of using the gage freedom cassette a nautical was or there is easier actor here was just the time derivative father danger fragile bro all actor Creole I'm derivative magnetic field related space yacht light but more and more but when I am permanent minor more but think some questions and answers yourself farmers if you formulate a theory we just Reg named magnetic also potential of Hollywood hearing from the beginning I think you would more fundamental and the other hand this obscure back for the record potential as are not unique airport from measurable we're where all measurements are unchanged by gage transformations Joel From a 1 hand it's more fundamental from the point of view of mathematical formulation of the theory of another poured you would not directly measurable sorry cap but Shepard 4 areas for he said Yulia past 2 0 rich that now or you have the more serious pastors install momentum must 0 yard at energy yes it hasn't your question about remembers six-year rule on entering the with yes that drip I'm are packed I'm you have a right to ripped Brett pointing reactor has proceedings are required now right Turkey that goes back to human cancer but 2 member personal Nowak new award areas at me this city on music component of men there are always mayoral Biggers kept is quite clear must have something lure Paratore armed as we move along a horizontal axis were changing this thing here reserves energy of scores P normal and a P X Y and P's any user things for quantities was that we were talking about but what'd our right down here time say Gujral and what about murder quarry where about vertically or from foreign equity we go back and we remember the suppressed person next year and I think takeover it of Ministry of something this is was something of some of the general are well they have also have injury in Austria which is not of Matt corn a song that sounds like maybe was a bigger quantity closed Keaton whom you when with special means a flock when a ways I'm like it means end and fear of being century here would be key North North not want in through it in I think the best way energy density of PEX PY immigrants presented really combat coral Pete 1 this will be read it down governor think of going a relief were not he featuring rock but army matters this is the best way of managing a flocks of energy the extra action of flocks of energy a direction a lot of energy in leader Ford right 0 0 of a 2nd back tears as energy fraudulent acts as locks locks the recon Mauritania came 1 warn me how Warner me for a while as best so OOX command man the flock Of the X X flocks of the ax moment a wife books of the X momentum and Izzy flocks of was a means each box of white folks remains the amount of X moment passing through a window or re-enter the wider action European drug as well the following want a cancer we that now obvious form of cancer but former From was more reforms met her early this is not something approved tonight and forms a symmetric answers which means that he's not 1 Was he warned us think about what that this I mean is any of X momentum and this is X flocks of energy x 4 also retreat near moles Desirae Bodda X manner what we worked out the density of momentum and was appointing rep why didn't tell you it is also the lot of energy the flock of would you call the power according to our eventually the power of Italy got the that's a flow Our energy so a flow of energy along Mexico's is the same as the density of the momentum along with and a moment of nickel flock emerging pointing the therefore has to me those pointing record it there's a point report PORT from our crossed from elected when things are storming English Turn it free-fall of energy and it been emerged from a but if you're our as a full of energy you could think of it as Power Hour of Power per unit area it through a year the region are actually missed this energy plays a really really big role general committee we look back will contact with Rivera Republic different way are where we got to rip this quarter ruler Friday rewarding yet and I want to get to work so you have a look the product Our general we and country the energy momentum tensor is variety can sign of arms your right now not an insignificant or pocket Ford auto for more please visit us
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