{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='How Everything Acts Like a Spring: A Physics Perspective' data-url='/boclips/videos/689565b27cbf35e76a835633' data-video-url='/boclips/videos/689565b27cbf35e76a835633' 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\nHow Everything Acts Like a Spring: A Physics Perspective\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'\u003eSUMMARY:Why Everything in the universe is a spring (kind of). Why everything is a spring. Classical springs like you might have in your mattress have a harmonic oscillation. And this behavior has a quantum mechanical analog in what’s...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eSUMMARY:\u003cbr/\u003eWhy Everything in the universe is a spring (kind of). Why everything is a spring. Classical springs like you might have in your mattress have a harmonic oscillation. And this behavior has a quantum mechanical analog in what’s called a quantum harmonic oscillator. And this model of the motion in quantum mechanics can model the motion of all fundamental particles in the universe, as well as the forces mediating the interactions between them. In fact, the prevailing fundamental theory of all matter and forces, called Quantum Field Theory, is built upon this type of motion. \u003cbr/\u003e\u003cbr/\u003eBut what happens if we now go to the quantum realm? The equation of energy for a quantum particle looks almost identical to the classical case. Except, now it is expressed as, H, the Hamiltonian, instead of E, energy. The difference is that the Hamiltonian is an operator. It has to operate on something to determine how its energy is evolving. In the case of quantum particles, the Hamiltonian operates on the wavefunction, since the wavefunction shows how a particle evolves over time. \u003cbr/\u003e\u003cbr/\u003eSo how do we show that the same spring-like behavior applies to quantum fields? The astonishing part is if you write a quantum field theory for a simple field, then you get a Hamiltonian this is almost exactly what we have in the quantum harmonic oscillator or quantum spring. But now it’s for a particle field. What’s different is that in the case of quantum fields, since they extend everywhere in the universe, it has to be integrated over the three dimensions of the universe. \u003cbr/\u003e\u003cbr/\u003eBut unlike quantum mechanics, where the number of particles are fixed, in quantum field theory, the number of particles in the system can change. We can add particles by adding energy to the field, or annihilate a particle by removing energy from the field. \u003cbr/\u003eThis aspect of quantum field theory is incorporated in the “a” and “a dagger” part of the equation. They are also known as the creation and annihilation operators. “a” is the creation operator and “a dagger” is the annihilation operator. \u003cbr/\u003e\u003cbr/\u003eWhat the Hamiltonian equation shows is that quantum field theory is essentially an infinite collection of harmonic oscillators or springs, extending out to all of spacetime in all 3 dimensions. Because it’s quantum it will never be still, so there is always some small oscillation or vibration in the ground state, which is the lowest state. This minimal oscillation represents quantum fluctuations, also known \u003cbr/\u003eas virtual particles. \u003cbr/\u003e\u003cbr/\u003eIf we give the spring a punch on the order of Planck’s constant, it will excite the spring to the next state, the one particle state. The spring now has a higher amplitude to indicate the extra energy we have added. \u003cbr/\u003e\u003cbr/\u003eWe can punch it an infinite number of times to increase the state to equal to 2, 3, 4 and so on particles. The amplitude can only be integer multiples of the Planck’s constant. This is the quantum world; everything is in steps ensuring, we have a discrete number of particles. \u003cbr/\u003e\u003cbr/\u003eWe can now imagine that this mattress is of infinite size. We can have waves representing particle motion and some of the waves can collide illustrating particle interactions.\u003cbr/\u003e\u003cbr/\u003eAnd if you can imagine 12 mattresses of infinite size, these would represent all the matter particles of the standard model. \u003cbr/\u003eFurthermore, we would have more mattresses that would act as intermediaries to exchange energy from one mattress to another. These represent the bosons of the standard model. 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