{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-572d6a42.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-f4d0de30.css\" media=\"all\" /\u003e\n\u003cdiv data-title='The Mathematical Basis of All Matter Comes From This Useless Equation' data-url='/boclips/videos/68961e1b1e1ee9ae17f8fc16' data-video-url='/boclips/videos/68961e1b1e1ee9ae17f8fc16' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nThe Mathematical Basis of All Matter Comes From This Useless Equation\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30356011\" href=\"/search?publisher_ids%5B%5D=30356011\"\u003eCurated Video\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eThe Dirac equation holds the secrets to everything that we can see in the universe. In this video, I show how with this equation, we can start with a completely empty universe, make just one assumption, ask just one simple question, and...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eThe Dirac equation holds the secrets to everything that we can see in the universe. In this video, I show how with this equation, we can start with a completely empty universe, make just one assumption, ask just one simple question, and from that derive the entire theory of matter. We build a universe starting with a completely empty spacetime.  \u003cbr/\u003eI introduce the gauge principle, which is a physics principle that is the basis for all fundamental interactions in quantum field theory. This is the theory that describes all matter and all forces in the universe, except gravity. \u003cbr/\u003eSo now imagine an empty universe with nothing in it. Let’s now add a field that permeates the entire universe. A quantum field is not made of anything. It is a mathematical concept. You can think of it simply as properties in spacetime. We can model such a field with the Dirac Lagrangian, which is an equation describing all fermion fields, including our electron field. The Lagrangian simply describes the difference between a system’s kinetic and potential energy. It captures how particles move in spacetime. \u003cbr/\u003eYou'll notice an imaginary term. It is there because we are describing wave functions which have complex components. The “i” is necessary to describe them mathematically. It is a mathematical convenience. The “i” doesn’t represent anything physical. \u003cbr/\u003eWhat is fascinating about this equation is how useless it is, yet it’s fundamental. It’s useless because it doesn’t describe anything measurable. It just describes a field with no interactions. Without interactions we can’t measure anything. But it’s fundamental because this is the best thing we have that correctly describes how matter works. \u003cbr/\u003e#symmetry \u003cbr/\u003e#quantummechanics \u003cbr/\u003eThe equation describes the electron field with two excitations, that of an electron and that of the antielectron. An excitation is simply like a bundle of energy in the field corresponding to the energy of the particle. And this field spans all of spacetime. So very simply put, this is describing an electron with a mass m which can move in spacetime. \u003cbr/\u003eTo make this equation come to life we have to introduce the gauge principle. To do that we have to make a demand to this equation. The demand we’re going to make is that this equation must have a symmetry like that of a circle with a radius of one. Basically, what we are saying is that if we rotate the entire field in any direction, it should act the same. Nothing should change. \u003cbr/\u003eAfter doing the math, we find that the equation obeys the symmetry of our circle globally. In other words, if we rotate the whole field spanning the entire universe by any degree, it won’t change. This is called U1 symmetry, which this Lagrangian obeys. \u003cbr/\u003eBut what if we demand that this symmetry be valid locally at some arbitrary spacetime coordinate x. In other words, we are asking whether the equation changes if we rotate the field at some confined location, rather than globally. It turns out that the solution to regain symmetry is to introduce a new field, a force field - the photon field! If we go through the steps of the math, we can demonstrate that we can have local symmetry of the electron field if we introduce a new force field mediated by photons. \u003cbr/\u003eAnd we now have an interacting theory where the extra term we were forced to add is the QED interaction. This is  the basis Quantum ElectroDynamics, which is the theory of the electromagnetic force. It shows us how electromagnetism interacts with anything that has an electric charge. \u003cbr/\u003eThis is THE interaction of electromagnetism responsible for everything you see. because you need photons to see with your eyes. You feel electromagnetic interactions when something touches your skin. Electromagnetism is the way you experience the world, and it is how we measure basically anything. 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