PBS Space Time

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