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[Music] welcome back to science clique today quantum field theory unlike a marble which has a definite position at the microscopic scale a particle does not really have a position its presence is distributed throughout space with more or less probability this description of particles as waves of probability is called quantum mechanics quantum mechanics allows us to describe the evolution of a particle over time however this description as effective as it is fails to take into account two considerations firstly quantum mechanics cannot describe situations where the number of particles varies over time however in nature we often observe that particles can appear or disappear like when a photon gets absorbed by an electron in an atom secondly quantum mechanics treats each particle independently however within a family of particles such as electrons all exhibit the same properties and behaviors how is it that an electron coming from the far reaches of the cosmos has exactly the same mass or charge as an electron in an apple to answer this question we will have to build a new mathematical framework a more general description that reconciles quantum mechanics with special relativity we will construct the most successful framework available for describing the microscopic world in this video we build together quantum field theory to begin with let's start with an empty universe relativity teaches us that the fabric of the universe is space-time to simplify we will represent only two dimensions of space as well as the dimension of time we now want to fill our universe with content mata we saw previously that all particles of the same type for example all electrons appear perfectly identical as if they were only local manifestations of a single underlying object which would fill the whole universe a field to add content to our universe we will therefore start by adding a field [Music] in mathematics a field is like a fluid which fills all space time each point of which is populated by a mathematical object it can be a field of numbers vectors or other more exotic objects that said special relativity imposes some restrictions it forces us to respect certain symmetries which correspond to the geometry of space-time symmetries of translation rotation or changing frame of reference [Music] these symmetries are only respected by certain mathematical objects and we can classify them with a parameter spin the simplest objects that we can use are numbers we give them spin zero because when we rotate space around a number it does not vary vectors on the other hand indicate a direction in space their appearance depends on the orientation in which they are observed we assign them spin one because when we rotate space by a full turn a vector also describes a full turn finally relativity also allows other more exotic objects and in particular spinners which have spin one half you have to make two turns around a spinner for it to come back to its initial state [Music] all these mathematical objects seem very abstract and some are difficult to understand but technically they all obey the symmetries of relativity and are therefore potential candidates with which we could fill our universe [Music] in addition to imposing the types of objects that are allowed space-time symmetries also set restrictions on the way objects behave inside the field each symmetry forces the field to respect the conservation of certain quantity over time to obey relativity our field must respect the conservation of energy momentum angular momentum and velocity of the centre of mass moreover the mathematical objects themselves can contain symmetries of their own if we decide to form a field with complex numbers for example they exhibit an internal symmetry which implies the conservation of another quantity over time related to the very nature of complex numbers the electric charge [Music] at this stage we have a space time which we have filled with a field which satisfies all the restrictions imposed by special relativity but our goal is to describe the microscopic world so it's time to turn our field into a quantum field [Music] in quantum mechanics to transform a classical object into a quantum object we allowed it to adopt several positions at the same time with more or less probability [Music] similarly to transform a classical field into a quantum field we allow it to adopt several configurations multiple ways it can evolve with more or less importance [Music] over time our field evolves as a superposition of all possible scenarios transitioning from a classical field to a quantum field results in a very interesting property just like an electron in atom has well-defined energy levels [Music] a quantum field also has energy levels it can only contain an integer number of disturbances quanta of energy that can appear or disappear these are particles much like a wave on the surface of water a particle is simply a disturbance which propagates within the field [Music] a quantum field is also agitated by fluctuations which keep popping in and out of existence these are called virtual particles these virtual particles exist only very briefly so that it is strictly impossible to observe them [Music] step by step our model universe is getting closer to reality we now describe a space-time filled with a quantum field inside which move disturbances particles in a soup of fluctuations virtual particles in our universe several fields coexist and constitute different families of particles some are vector fields spin 1 and the particles they contain are photons z and w bosons and gluons others are fields of spinners spin one half they are the fermions that make up matter quarks electrons muons tau particles and neutrinos finally there is a field of spin zero the higgs field among all these fields most have internal symmetries which provide them with quantities that are conserved over time charges which distinguish their particles between several versions we saw previously that fields formed with complex numbers have asymmetry which gives them their electric charge this symmetry allows us to distinguish two versions of the particles one with positive charge the other with negative charge this is anti-matter in a way the anti-particle is the complex conjugate of the ordinary particle other fields also have more exotic symmetries the quark fields for example exhibit a symmetry which assigns them another charge the colour charge which must also be conserved over time and that allows us to separate quarks into three versions red green and blue the set of all these fields that make up the content of our universe is the standard model of particle physics to this day this is the most successful description of our universe on the microscopic scale [Music] our model universe now contains the same particles as our real universe however it still isn't realistic indeed the symmetries of space time force all particles to move in straight lines forever independently one from the other to finally complete our model all we have to do is add one more fundamental ingredient we need to allow these fields to interact with each other [Music] to understand let's focus on one of the simplest interactions between the photon field and the electron field we will allow an electron to emit or absorb a virtual photon and vice versa allowing only this simple interaction will have drastic consequences for instance in the following situation we start with two electrons motionless over time the two electrons progress towards the future at first one might think that the two electrons remain motionless indefinitely but that would be forgetting that our electrons are constantly moving through the photon field with which we allowed them to interact [Music] we saw that a quantum field realizes all possible evolutions at the same time in a way each evolution describes a scenario and in some of these scenarios the electrons will interact with the photon field [Music] in this scenario for example the electron emits a virtual photon at a certain instant which carries away part of its momentum and the virtual photon is absorbed a little later by the other electron [Music] in this other scenario the electrons exchange this time two photons [Music] or again in this third more complex scenario the electron emits a virtual photon which is converted into a pair of virtual electron and positron that inhalate together into a virtual photon which finally ends up absorbed by the second electron by exchanging part of their momentum carried by virtual particles the two electrons will in some scenarios get closer and in others get further apart now consider the following analogy on a guitar a string can vibrate with different frequencies each of which corresponds to a pure sound but when we pluck the string it starts to vibrate in a superposition of all these frequencies with more or less amplitude and the synthesis of all these pure sounds together with different amplitudes is what makes the total sound produced by the string similarly a quantum field evolves according to every possible scenario with more or less amplitude and it is the synthesis of all these scenarios together that describe the real evolution of the physical system in particular in our example when we add up all these possibilities we observe that overall our two electrons are more and more deflected they feel a force repelling them because of the exchanges of virtual photons this is the electromagnetic force and if instead we had started with an electron and a positron of opposite charge the amplitudes of the different scenarios would have been different resulting this time in an overall attraction force [Music] by allowing particles to interact and exchange momentum quantum field theory explains how forces arise from simple symmetries the symmetries of the fields which make up our universe to conclude quantum field theory is a mathematical recipe for building a model universe we start with an empty space-time which we fill with quantum fields that satisfy the symmetries of special relativity quantum field theory thus makes it possible to construct a quantum description of our universe which satisfies the constraints imposed by relativity by allowing fields to interact with each other this theory makes it possible to predict with astounding precision the phenomena that govern our universe according to quantum field theory the evolution of our universe is described as the synthesis of all possible scenarios at the microscopic scale that being said this description remains incomplete as even though it satisfies special relativity quantum field theory cannot be unified with general relativity which describes gravitation by the curvature of space-time some results of the theory can already be calculated in curved space times such as the prediction that black holes evaporate over time however scientists are still looking for a unified theory that would explain microscopically why space-time gets curved and would reconcile the infinitely large with the infinitely small gravity with quantum a theory of everything [Music] you