WEBVTT Kind: captions Language: en 00:00:00.480 --> 00:00:05.120 Thank you to novium for supporting  PBS. What does an electron really   00:00:05.120 --> 00:00:11.440 look like? I mean if we zoom in all the  way is it a sizeless speck of charge? Or   00:00:11.440 --> 00:00:15.680 is it a multi-dimensional vortex  of quantum strangeness? Is it the   00:00:15.680 --> 00:00:21.643 boundary of a tiny universe with universe  electrons of its own? Let's find out. 00:00:27.880 --> 00:00:33.520 There isn't much that's simpler than the it's  one of the elementary particles something not   00:00:33.520 --> 00:00:39.000 made of smaller things at least according to the  current theory. It conjures to mind a single point   00:00:39.000 --> 00:00:44.280 or perhaps a tiny ball made of some electric  charge and mass and not much else - like in   00:00:44.280 --> 00:00:50.040 the cartoon description of the atom with electrons  as orbiting balls. But if you've paid attention to   00:00:50.040 --> 00:00:56.440 good pop-sci media you probably know that these  pictures aren't accurate. Perhaps you know that   00:00:56.440 --> 00:01:02.640 in quantum mechanics particles exist not as tiny  nuggets of matter but rather as wave functions   00:01:02.640 --> 00:01:09.920 fuzzy distributions that define the probability of  where or what the particle might be when measured.   00:01:09.920 --> 00:01:17.600 For example electrons in atoms are more accurately  depicted as blurred shells than as orbiting balls   00:01:17.600 --> 00:01:24.040 and a free electron might look like an undulating  wave packet capable of interfering with itself and   00:01:24.040 --> 00:01:30.720 doing other wave-like things. But are these  wave functions really what an electron looks   00:01:30.720 --> 00:01:36.960 like? These wavy structures seem more intuitive  for something like the photon which is literally   00:01:36.960 --> 00:01:42.320 a wave in the electromagnetic field and whose most  important properties like frequency and wavelength   00:01:42.320 --> 00:01:48.960 can be captured in wavy terms. But an electron  has mass, it has electric charge, it has spin.   00:01:48.960 --> 00:01:56.120 Where do these properties live in a fuzzy wave  function? There are valiant efforts to represent   00:01:56.120 --> 00:02:01.120 the non-spatial components of the electron wave  function in particular the spin or wave function   00:02:01.120 --> 00:02:06.880 which we talk about here but these are attempts  to visualize a pretty abstract concept not really   00:02:06.880 --> 00:02:15.240 what the electron looks like. So let's take a  look. Let's really zoom in. We can never actually   00:02:15.240 --> 00:02:21.880 see a fuzzy wave packet because the electron takes  on precise properties when we measure it. Looking   00:02:21.880 --> 00:02:27.920 at the electron means resolving its location and  spatial structure as we measure more precisely the   00:02:27.920 --> 00:02:35.400 wave function shrinks to something particle like.  But how far can we zoom? Do we eventually see a   00:02:35.400 --> 00:02:42.920 tiny ball or an infintesmal speck of charge and  mass? And where does that charge and mass live?   00:02:42.920 --> 00:02:50.080 What does an electron really look like up close?  There's an agenda behind this thought experiment.   00:02:50.080 --> 00:02:56.280 The very act of zooming in to see what an electron  looks like will reveal some vexing contradictions   00:02:56.280 --> 00:03:01.880 for example about why the electron has the  properties that it has. These contradictions   00:03:01.880 --> 00:03:07.400 foreshadow one of the biggest problems in  physics today but that's for future episodes.   00:03:07.400 --> 00:03:14.760 Today we're just looking at the electron. Let's  try constructing an electron first using classical   00:03:14.760 --> 00:03:19.680 physics. We'll do that by gathering enough  electric charge from the surrounding universe   00:03:19.680 --> 00:03:27.360 and sticking it together. Like charge repels via  the Coulomb force and Coulomb's law tells us that the   00:03:27.360 --> 00:03:32.400 closer we want to drag two bits of charge the more  force it takes. That means it takes more energy   00:03:32.400 --> 00:03:37.760 to assemble a more compact ball of charge than it  does a more diffused one assuming the same amount   00:03:37.760 --> 00:03:45.040 of charge. A bit of calculus gives us the energy  needed to assemble a ball of any given radius and   00:03:45.040 --> 00:03:51.520 this is the potential energy that that ball holds  after assembled the smaller the ball the more   00:03:51.520 --> 00:04:00.480 energy from Einstein's relativity we know that  bound energy is equivalent to mass e =mc^2. So now   00:04:00.480 --> 00:04:08.040 we can ask the question if we drag in one electron  worth of electric charge until it's in a small   00:04:08.040 --> 00:04:13.840 enough ball that its potential energy is equal  to the known mass of the electron how big would   00:04:13.840 --> 00:04:24.480 that ball be well around 2.8 by 10 ^ -5 M. This  is the classical electron radius it's the size   00:04:24.480 --> 00:04:31.400 an electron would have to be if its mass was all  from the potential energy of it contain charge.   00:04:31.400 --> 00:04:37.880 But it's not the real size of the electron.  Our experiments tell us that the true size of   00:04:37.880 --> 00:04:45.920 the electron is smaller than 10 ^ -7 M at least  100 times smaller than the classical electron   00:04:45.920 --> 00:04:52.040 radius. But if we continue to crush our ball of  charge down to that size the mass equivalence of   00:04:52.040 --> 00:05:00.760 that potential energy is 10G electron volts which  is 20,000 times larger than the actual measured   00:05:00.760 --> 00:05:10.200 electron mass of 511 kilo electron volts and if  our electron really is point like, having no size   00:05:10.200 --> 00:05:16.040 then Coulumb's law gets a zero in the denominator  and the energy summed all the way to that central   00:05:16.040 --> 00:05:25.000 point is infinite. Now the electron isn't really a  ball of electric charge mutually repelling itself.   00:05:25.000 --> 00:05:29.960 Its charge does self- interact in complex  ways manifested in the activity of quantum   00:05:29.960 --> 00:05:37.440 field surrounding electron as we'll see but the  equations and numbers I came up with do still give   00:05:37.440 --> 00:05:43.480 the energy contained in the electromagnetic field  that emanates from a bundle of charge of the same   00:05:43.480 --> 00:05:50.880 size. And so this energy does still contribute  to the electron observed mass. This issue of the   00:05:50.880 --> 00:05:57.640 electron's electric field containing vastly more  mass than the electron itself is or at least was   00:05:57.640 --> 00:06:04.080 a real problem and one that persists even when  we switch from classical to quantum mechanics.   00:06:04.080 --> 00:06:10.240 But for now we get back to the electron what  does our zoom in look like when we switch to   00:06:10.240 --> 00:06:17.400 quantum mechanics or more precisely quantum field  theory? In qft we describe electromagnetism in   00:06:17.400 --> 00:06:23.040 terms of the activity of a quantum field and each  elementary particle is an excitation in its own   00:06:23.040 --> 00:06:29.200 quantum field. So the photon is an excitation of  the EM field and the electron and positron are   00:06:29.200 --> 00:06:35.160 excitations of the electron field. Quantum fields  are sometimes described as these roiling oceans of   00:06:35.160 --> 00:06:40.720 virtual particles appearing and vanishing. This  isn't very accurate. Instead think of a quantum   00:06:40.720 --> 00:06:45.680 field as having the potential for complex  and random fluctuations when it encounters a   00:06:45.680 --> 00:06:52.360 real particle whose fluctuations can be modeled  using virtual particles. As a mathematical tool   00:06:52.360 --> 00:06:58.600 we can model the coulomb force in terms of virtual  photons in the EM field imparting momentum between   00:06:58.600 --> 00:07:05.200 charged particles or we can model the spontaneous  transfer of energy between the em and electron   00:07:05.200 --> 00:07:12.800 fields in terms of a virtual photon turning into  virtual matter anti pairs pair production. In this   00:07:12.800 --> 00:07:19.800 case a virtual electron and positron. So if the  EM field in quantum field theory is an ocean of   00:07:19.800 --> 00:07:26.480 virtual photons at least mathematically. What does  that look like? Well viewed from afar the activity   00:07:26.480 --> 00:07:32.440 of these virtual photons is averaged over in  into the smooth field described by classical   00:07:32.440 --> 00:07:38.680 electromagnetism but as our zoom in reaches  a certain point around 100 times larger than   00:07:38.680 --> 00:07:46.360 the classical electron radius we transition to a  regime where we can't ignore the quantum behavior   00:07:46.360 --> 00:07:52.600 of the field. For example as the field strengthens  and our view narrows we see that the interaction   00:07:52.600 --> 00:07:58.640 between the em and electron fields strengthens.  We can describe this as an increase in the rate   00:07:58.640 --> 00:08:04.440 of pair production an increasingly active  flickering of virtual photons and the virtual   00:08:04.440 --> 00:08:11.160 electron positron pairs that they spawn this cloud  of activity appears to grow stronger the closer we   00:08:11.160 --> 00:08:16.080 get to the electron. It's not just that we're  seeing the quantum properties of the stronger   00:08:16.080 --> 00:08:23.880 em field - the very act of probing the electron  this closely amplifies quantum fluctuations. The   00:08:23.880 --> 00:08:29.520 Heisenberg uncertainty principle tells us that  precision in spatial or temporal measurement   00:08:29.520 --> 00:08:37.560 leads to larger uncertainty in momentum and energy  respectively the more precise our snapshot of that   00:08:37.560 --> 00:08:45.160 electron the more energetic quantum fluctuations we'll observe. We talk about this effect in more   00:08:45.160 --> 00:08:51.040 detail in this video but the upshot is that  the universe looks very different depending   00:08:51.040 --> 00:08:59.720 on the scale that it's probed and so does the  electron although somehow all scales knit together   00:08:59.720 --> 00:09:04.960 into a unified whole. We are now at very small  scales quite a bit smaller than the classical   00:09:04.960 --> 00:09:11.960 radius here. It's clear that the bare electron  appears to be dressed in this cloud of virtual   00:09:11.960 --> 00:09:18.080 activity this dressing is the source of our self  energy and the extra mass from the electron's EM   00:09:18.080 --> 00:09:24.200 field. As we zoom ever closer to the electron  the energy in the field approaches the rest   00:09:24.200 --> 00:09:32.560 mass of the electron and a new interaction becomes  important. Now the virtual electron positron pairs   00:09:32.560 --> 00:09:39.440 have a decent likelihood of directly interacting  with the central real electron. Sometimes a   00:09:39.440 --> 00:09:45.720 virtual positron will actually annihilate with  the real electron which then promotes its once   00:09:45.720 --> 00:09:53.120 virtual partner electron to reality, it's as  though the original electron shifted position.   00:09:53.120 --> 00:09:59.840 There are two important implications to this.  Effect one is that this effect actually recueses   00:09:59.840 --> 00:10:05.120 the electron from having the colossal or even  infinite mass predicted by classical physics.   00:10:05.120 --> 00:10:12.400 More on that next time. Unfortunately the second  implication of this self annihilation interaction   00:10:12.400 --> 00:10:20.120 is that we're never actually going to get a clear  view of the electron no matter how far we zoom in.   00:10:20.120 --> 00:10:27.960 The closer we zoom the stronger the surrounding  cloud of virtual fluctuations but also the more   00:10:27.960 --> 00:10:35.120 frequent these interactions become. At some point  the electron become this flickering blur that we   00:10:35.120 --> 00:10:43.280 could never quite fix the location of the mass  ends up smeared out both by the self energy mass   00:10:43.280 --> 00:10:51.360 and by what is ultimately Heisenberg uncertainty.  The electron's charge is also smeared out by the   00:10:51.360 --> 00:10:57.560 latter and also smeared by something that I  haven't told you about yet. Even before we got   00:10:57.560 --> 00:11:04.000 close to the central electron virtual electron  positron pairs we're smearing out that charge   00:11:04.000 --> 00:11:11.400 those pairs interact with the ambient em field  with the positrons tending to shift closer to the   00:11:11.400 --> 00:11:19.320 center while virtual electrons shift further away.  This so-called vacuum polarization happens all   00:11:19.320 --> 00:11:25.400 around the central electron and has the effect of  screening the external universe from that central   00:11:25.400 --> 00:11:33.120 charge. In fact the observed charge should appear  to rise as we get closer to the center past this   00:11:33.120 --> 00:11:39.800 screening. If you calculate the effective charge  screening all the way to infinitesimal distances   00:11:39.800 --> 00:11:45.360 that central charge has to be infinite - that  means the central electron would need to have   00:11:45.360 --> 00:11:50.520 infinite charge itself to overcome that infinite  charge screening. Of course we now know that we   00:11:50.520 --> 00:11:57.360 can never probe the electron down to a perfectly  localized point so that infinity is probably   00:11:57.360 --> 00:12:04.240 meaningless. However if it is true that the  strength of the electromagnetic force increases at   00:12:04.240 --> 00:12:10.240 extremely small distances when charge screening is  overcome even though we can't catch our electron   00:12:10.240 --> 00:12:16.480 in our infinite zoom the elusive particle is  extremely well understood at least mathematically.   00:12:16.480 --> 00:12:22.200 We even know how to rescue the electron from  having its mass and charge explode due to its   00:12:22.200 --> 00:12:26.920 interaction with the surrounding quantum fields -  although to understand that we need a tool called   00:12:26.920 --> 00:12:33.040 renormalization which we'll explore soon. And  we'll also see how this tricky issue with the   00:12:33.040 --> 00:12:39.800 electron foreshadowed a much much bigger conundrum  in physics - the hierarchy problem. And will meet   00:12:39.800 --> 00:12:47.480 the particle that has yet to be rescued from this  issue. But that is also another story. For now   00:12:47.480 --> 00:12:55.680 let's admire the tiny electron outwardly simple  but inwardly mercurial and it's a strangeness that   00:12:55.680 --> 00:13:04.040 only compounds as we localize it in SpaceTime.  Thank you to Novium for supporting PBS. Inspired   00:13:04.040 --> 00:13:09.520 by space, the Novium Hoverpen: Interstellar is an  otherworldly gift idea for yourself or the amazing   00:13:09.520 --> 00:13:14.320 people in your life. The Hoverpen Interstellar  is available in Space Black, Starlight Silver,   00:13:14.320 --> 00:13:21.000 Mars Magma and Neptune Blue and is refillable. The  Meteorite Embedded Space Black edition contains a   00:13:21.000 --> 00:13:27.360 subtle reminder that we here on Earth are truly a  part of a greater galactic whole. Each Meteorite   00:13:27.360 --> 00:13:33.480 edition features a fragment of the Muonionalusta  meteorite confirmed by a stainless-steel   00:13:33.480 --> 00:13:39.480 certificate. 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There's international   00:14:21.320 --> 00:14:27.120 shipping for most countries and orders are still  available for delivery before the holidays. 00:14:27.120 --> 00:14:31.840 Hi Everyone. It’s that time of year again. We  want to hear your thoughts and opinions on the   00:14:31.840 --> 00:14:38.320 PBS Digital Studio Survey! Every year, the Space  Time fans have been the most active fan group on   00:14:38.320 --> 00:14:44.000 PBS Digital Studios audience survey, which  we and the rest of PBS Digital Studios use   00:14:44.000 --> 00:14:49.600 to help understand what you enjoy on YouTube  and what you would want to see us make more   00:14:49.600 --> 00:14:57.240 of. You also get to vote on new show ideas. There  is a link in the description - thanks in advance! 00:14:57.240 --> 00:15:02.320 Hey Everyone. Before we go, we just wanted to  let you know, there will be 15% off the whole   00:15:02.320 --> 00:15:07.760 Mercch store for all of December. 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