What does an electron really look like I mean  if we zoom in all the way is it a sizeless speck   of charge or is it a multi-dimensional Vortex of  quantum strangeness is it the boundary of a tiny   universe with Universe electrons of its own let's  find [Music] out there isn't much that's simpler   than the electron it's one of the elementary  particles something not made of smaller things at   least according to the current theory it conjures  to mind a single point or perhaps a tiny ball made   of some electric charge and mass and not much else  like in the cartoon description of the atom with   electrons has orbiting balls but if you've paid  attention to good popside media you probably know   that these pictures aren't accurate perhaps  you know that in quantum mechanics particles   exist not as Tiny nuggets of matter but rather as  wave functions fuzzy distributions that Define the   probability of where or what the particle might  be when measured for example electrons in atoms   are more accurately depicted as blurred shells  than as orbiting balls and a free electron might   look like an undulating wave packet capable  of interfering with itself and doing other wav   likee things but are these wave functions really  what an electron looks like these wavy structures   seem more intuitive for something like the photon  which is literally a wave in the electromagnetic   field and whose most important properties like  frequency and wavelength can be captured in wavy   terms but an electron has mass it has electric  charge it has spin where do these properties   live in a fuzzy wave function there are Valiant  efforts to represent the nonsp special components   of the electron wave function in particular the  spinal wave function which we talk about here   but these are attempts to visualize a pretty  abstract concept not really what the electron   looks like so let's take a look let's really zoom  in we can never actually see a fuzzy wave packet   because the electron takes on precise properties  when we measure it looking at the electron means   resolving its location and spatial structure  as we measure more precisely the wave function   shrinks to something particle like but how far  can we Zoom do we eventually see a tiny ball   or an infinite tesm or Speck of charge and mass  and where does that charged Mass Live what does   an electron really look like up close there's an  agenda behind this thought experiment the very Act   of zooming in to see what an electron looks like  will reveal some vexing contradictions for example   about why the electron has the properties that  it has these contradictions for shadow one of the   biggest problems in physics today but that's for  future episodes today we're just looking at the   electron let's try constructing an electron first  using classical physics we'll do that by gathering   enough electric charge from the surrounding  universe and sticking it together like charge   repels via the kolum force and kum's law tells us  that the closer we want to drag two bits of charge   the more force it takes that means it takes more  energy to assemble a more compact ball of charge   than it does a more diffuse one assuming the same  amount of charge a bit of calculus gives us the   energy needed to assemble a ball of any given  radius and this is the potential energy that   that ball holds after assembled the smaller the  ball the more energy from Einstein's relativity   we know that bound energy is equivalent to mass  eal mc^2 so now we can ask the question if we drag   in one electron worth of electric charge until  it's in a small enough ball that its potential   energy is equal to the known mass of the electron  how big would that ball be well around 2.8 by 10^   of -5 M this is the classical electron radius  it's the size an electron would have to be if   its mass was all from the potential energy of its  contained charge but it's not not the real size   of the electron our experiments tell us that the  true size of the electron is smaller than 10 the   power- 17 M at least 100 times smaller than the  classical electron radius but if we continue to   crush our ball of charge down to that size the  mass equivalence of that potential energy is 10   gig electron volts which is 20,000 times larger  than the actual measured electron mass of 5 under   11 kilo electron volts and if our electron really  is pointlike having no size then kum's law gets a   zero in the denominator and the energy summed  all the way to that Central Point is infinite   now the electron isn't really a ball of electric  charge mutually repelling itself its charge does   self interacting complex ways manifested in the  activity of quantum field surrounding electron   as we'll see but the equations and numbers I came  up with do still give the energy contained in the   electromagnetic field that emanates from a bundle  of charge of the same size and so this energy   does still contribute to the electrons observed  Mass this issue of the electron electric field   containing vastly more mass than the electron  itself is or at least was a real problem and   one that persists even when we switch from classic  I to Quantum Mechanics but for now we get back to   the electron what does our zoom in look like  when we switch to Quantum Mechanics or more   precisely Quantum field theory in qft we describe  electromagnetism in terms of the activity of a   Quantum field and each elementary particle is an  excitation in its own Quantum field so the photon   is an excitation of the EM field and the electron  and positron are excitations of the electron field   quantum fields are sometimes described as these  roiling oceans of virtual particles appearing and   Vanishing this isn't very accurate instead think  of a Quantum field is having the potential for   complex and random fluctuations when it encounters  a real particle those fluctuations can be modeled   using virtual particles as a mathematical tool  we can model the coolum force in terms of virtual   photons in the EM field imparting momentum between  charged particles or we can model the spontaneous   trans transer of energy between the emn electron  fields in terms of a virtual Photon turning into   virtual matter anti pairs pair production in this  case a virtual electron and positron so if the EM   field in Quantum field theory is an ocean of  virtual photons at least mathematically what   does that look like well viewed from afar the  activity of these virtual photons is averaged   over into the smooth field described by classic  clal electromagnetism but as our zoom in reaches   a certain point around 100 times larger than  the classical electron radius we transition to a   regime where we can't ignore the quantum behavior  of the field for example as the field strengthens   and our view Narrows we see that the interaction  between the em and electron Fields strengthens we   can describe this as an increase in the rate of  peir production an increasingly active flickering   virtual photons and the virtual electron  positron pairs that they spawn this cloud   of activity appears to grow stronger the closer  we get to the electron it's not just that we're   seeing the quantum properties of the stronger  em field the very Act of probing the electron   this closely amplifies Quantum fluctuations  the Heisenberg uncertainty principle tells us   that Precision in spatial or temporal measurement  leads to larger uncertainty in momentum and energy   respectively the more precise our snapshot of that  electron the more energetic Quantum fluctuations   will'll observe we talk about this effect in more  detail in this video but the upshot is that the   Universe looks very different depending on the  scale that it's probed and so does the electron   although somehow all scales knit together into  a unified hole we are now at very small scales   quite a bit smaller than the classical radius  here it's clear that the bare electron appears   to be dressed in this cloud of virtual activity  this dressing is the source of our self energy   and the extra mass from the electrons em field  as we Zoom ever closer to the electron the energy   in the field approaches the rest mass of the  electron and a new interaction becomes important   now the virtual electron positron pairs have a  decent likelihood of directly interacting with   the central real electron sometimes a virtual  positron will actually annihilate with the real   electron which then promotes its once virtual  partner electron to reality it's as though the   original electron shifted position there are two  important implications to this Effect one is that   this effect actually rescues the electron from  having the colossal even infinite Mass predicted   by classical physics more on that next time  unfortunately the second implication of this   self Annihilation interaction is that we're never  actually going to get a clear view of the electron   no matter how far we zoom in the closer we Zoom  the stronger the surrounding cloud of virtual   fluctuations but also the more frequent these  interactions become at some point the electron   becomes this flickering blur that we could never  quite fix the location of the mass ends up smeared   out both by the self energy mass and by what is  ultimately Heisenberg uncertainty the electron's   charge is also smeared out by the latter and also  smeared by something that I haven't told you about   yet even before we got close to the central  electron virtual electron positron pairs were   smearing out that charge those pairs interact with  the ambient em field with the positrons tending   to shift closer to the center while virtual  electrons shift further away this so-called   vacuum polarization happens all around the  central electron and has the effect of screening   the external Universe from that Central charge in  fact The observed charge should appear to rise as   we get closer to the Center past this screening if  you calculate the effect of charge screening all   the way to infinite decimal distances that Central  charge has to be infinite that means the central   electron would need to have infinite charge itself  to overcome that infinite charge screening of   course we now know that we can never probe the  electron down to a perfectly localized point so   that Infinity is probably meaningless however it  is true that the strength of the electromagnet   IC Force increases at extremely small distances  when charge screening is overcome even though   we can't catch our electron in our infinite  Zoom The elusive particle is extremely well   understood at least mathematically we even know  how to rescue the electron from having its mass   and charge explode due to its interaction with the  surrounding Quantum Fields although to understand   that we need a tool called renormalization which  we'll explore soon and we'll also see how this   tricky issue with the electron foreshadowed  a much much bigger conundrum in physics the   hierarchy problem and will meet the particle  that has yet to be rescued from this issue   but that is also another story for now let's  admire the tiny electron outwardly simple but   inwardly Mercurial and it's a strangeness that  only compounds as we localize it in SpaceTime