The Symmetries of the universe

[Music] welcome back to science clique today the symmetries of the universe there are many complex laws that seemingly govern our universe conservation of energy of momentum general relativity the standard model of particles yet all this complexity emerges from a deeper purer concept of which all these laws are only consequences symmetry [Music] in mathematics asymmetry is a transformation which leaves an object unchanged a sphere for example has a rotational symmetry you can turn it around change its orientation and it remains the same an infinite rope is symmetric by translation we can move along the rope it remains the same [Music] it turns out that the universe can also have symmetries a symmetry of the universe is a transformation that does not affect the laws of physics to understand imagine an empty universe in which we carry out a simple experiment we throw a ball once released it continues to move in a straight line at a constant speed now imagine that we travel through the universe and carry out the same experiment but somewhere else here too we observe that the ball continues in a straight line at a constant speed it behaves in the same way the laws of physics have not changed from one place to the other this universe obeys a translational symmetry we can move through the universe perform our experiment in another place the result is always the same this empty universe also obeys a symmetry under rotations we could have turned changed orientation the result would have been the same finally this universe is also symmetric through time we could have waited and thrown the ball a little later the laws of physics do not change from one instant to the next the fact that the universe obeys symmetries that the laws of physics remain the same under certain transformations imposes restrictions on the behavior of objects to understand let's go back to our empty universe and throw the ball [Music] once thrown the ball acquires a forward motion and at the next instant it is slightly further ahead it has moved but if we assume that the universe is symmetric under translation that the laws of physics remain the same when we change position then the situation is equivalent to the previous instance the ball is moved but the laws of physics remain the same there and at every instant the ball therefore evolves in the same way if the laws of the universe are invariant by translation symmetry forces the ball to conserve its motion which explains why it traces a straight line at a constant speed similarly if an object rotates on itself assuming that the laws of physics are invariant under rotations at the next instant the situation is equivalent and the symmetry will therefore force the object to conserve its rotation [Music] thus to be respected each symmetry of the universe imposes the conservation of a quantity conservation of momentum for translations momentum for rotations and energy for symmetry through time this principle is called nother's theorem each symmetry of the universe imposes the conservation of a certain quantity over time no this theorem also applies to the content of the universe and in particular the quantum fields that make up matter itself a quantum field can also present symmetries the field of electrons for example is made up of complex numbers and the laws of physics that describe electrons do not change if we alter the phase of all these complex numbers to understand imagine that we measure the altitude of an airplane on earth to express the altitude of the airplane we must fix a reference level for example the sea level by fixing this reference we can describe the altitude by a number but this choice of reference is arbitrary we could have chosen another level we would have measured different values but the physical situation has not changed the same situation can be described differently depending on the reference level we choose [Music] in the same way for the electron field we can change the reference level which corresponds to altering the phase of all complex numbers without this affecting the physical situation which is described this change of reference constitutes a symmetry and according to nother's theorem this symmetry also imposes the conservation of a quantity the electric charge conservation laws such as the conservation of energy or electric charge are therefore not fundamental in general these quantities are not necessarily conserved it is only when the universe presents an underlying symmetry that in order to be respected the symmetry imposes the conservation of a quantity the principle of equal and opposite reaction for example which boils down to the conservation of momentum when two objects separate is only a consequence of symmetry under translation if one object goes one way the other must go the other way thanks to this symmetry rocket can take off upwards by ejecting material downwards [Music] however a problem arises unlike the simplified example of an empty universe our real universe does not appear to be fully symmetric at a time scale of billions of years for example the universe expands and it is therefore not perfectly symmetric over time as a result on a large scale the energy of the universe is not conserved light for example gradually loses energy its wavelength gets stretched as the universe expands the universe is not perfectly symmetric under translations either it contains stars and planets and is therefore not the same everywhere at this scale thus if we throw an object in general its momentum is not conserved on earth for example an apple falls downwards it accelerates its movement changes over time because the situation is not symmetric [Music] at first glance our universe does not seem to respect symmetries even worse the laws of physics appear to be different depending on the frame from which we observe if we drop a ball inside a centrifuge from the outside the ball seems to conserve its movement but from the inside the movement of the ball is not conserved it accelerates towards the surface how can we explain that the ball behaves differently the laws of physics are absolute if we want a good description of our universe we would like all objects whatever our point of view to always obey the same laws when changing point of view the laws of the universe should not change they must remain the same for everyone yet the behavior of the bull is not the same [Music] to solve this problem to restore the invariance of the laws of physics for the ball to be described by the same laws from both points of view it would be necessary to add a new element to our description to understand let's go back to the previous analogy we measure the altitude of an airplane the plane is moving straight ahead and if we take the sea level as a reference we measure a constant altitude it draws a straight line [Music] that said let's imagine that we took the surface of the earth as a reference this time because of the mountains we measure an altitude that varies over time as if the plane was moving in zigzags taking the surface as a reference the behavior of the airplane now seems different but the situation is not changed the plane is moving straight ahead how can we explain that while it faces straight ahead its altitude varies over time to solve this paradox it is necessary to introduce some kind of force field that would push the airplane up or down depending on the reference level that we've chosen thus explaining its behavior when going from one reference level to another from sea level to land level it is necessary to add this force field to properly account for the behavior of the aircraft [Music] going back to the example of the ball in the centrifuge the situation is exactly the same moving from one point of view to the other from outside to inside the centrifuge the bull seems to obey different laws and it is necessary to add some kind of force field to our description this is what we call inertial forces and in particular the centrifugal and coriolis forces by adding these inertial forces we reinstate the laws of physics as absolute the behavior of the ball can now be understood very well in any frame of reference as long as we add this force field which depends on which point of view we choose introducing this kind of force field is also what gives rise to the concept of space-time curvature and to the theory of general relativity general relativity is a very powerful theory precisely because it restores the absoluteness of the laws of physics by adding a new underlying structure the curvature of space-time general relativity makes it possible to describe the universe from any point of view using the same equations [Music] surprisingly enough this reasoning adding a field to restore the invariance of the laws of physics is also the basis for all fundamental interactions in particle physics we have seen that the quantum field of electrons has a symmetry the laws which describe it are invariant when we shift the phase of all complex numbers globally but if we alter the phase differently in different parts of the field locally which amounts to choosing a reference level in zigzags like the surface of the earth the laws which describe electrons seem to have changed in other words this change of reference is not a symmetry if we want to re-establish the laws of physics as absolute for this to be a symmetry whatever reference level we choose we need to change our description we must introduce another underlying structure a kind of force field with which the electron field interacts to account for this change in behavior [Music] this other structure is called the electromagnetic field it contains particles that interact with electrons photons [Music] in a way if two objects repel each other due to their electric charge if we do not fall through our chair when we sit and if light exists in the universe it is thanks to this local symmetry being able to choose any reference level for complex numbers which requires the existence of a new field and new particles the photons with which the electrons interact [Music] to conclude studying the symmetries of the universe allows us to understand in a deep way the origin of the laws which govern it it is because the universe has symmetries that the objects it contains in order to respect these symmetries obey physical laws be it conservation of energy or momentum objects obey these laws only to respect underlying symmetries intrinsic to the universe by considering that the laws of physics must be absolute that changing our point of view or level of reference must constitute a symmetry that does not affect the physical reality we call this a gauge symmetry we deduce the presence of new structures in the universe like the curvature of space-time or the electromagnetic field [Music] experimentally symmetries also allow us to unveil the hidden mysteries of matter by measuring certain properties of particles and by studying the geometric diagrams that we obtain symmetries have allowed scientists to understand for instance that protons neutrons and other baryons are formed of three smaller objects which obey a fundamental symmetry based on the number three quarks there are also discrete symmetries for example inverting the charge direction through space as well as direction through time of all particles constitutes a symmetry an anti-particle can in this way be interpreted as an ordinary particle that moves backwards through time finally some speculative modern theories postulate that the universe could have an even deeper symmetry a symmetry between particles of matter and particles of interaction as if both obeyed the same laws this is what we call supersymmetry [Music] [Music] you

Channel: ScienceClic English

Views: 321,936

Rating: 4.9314766 out of 5

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Id: hF_uHfSoOGA

Length: 15min 34sec (934 seconds)

Published: Sat Feb 06 2021

Reddit Comments

[u/AlessandroRoussel]

I have recently published this pop science video on the symmetries of the universe, I hope you'll enjoy it. We discuss how symmetries (of both spacetime and quantum fields) are at the core of modern physics and our understanding of physical laws that describe the universe.

[u/MaxThrustage]

This is an excellent video. Clear and simple without being misleading -- which, with this topic, is tricky.

(The pronunciation of "Noether" is pretty far off, though.)

[u/Peter_avac]

What’s the last one?

[u/tagaragawa]

You got plenty of praise, so let me be the one nitpicking.

• Around 5min, you give a perfect example of a gauge transformation: the freedom to choose the reference level for altitude. The equivalent freedom ("gauge symmetry") of choosing a reference level for the phase does not lead to the conservation of charge. Instead, the same global symmetry as in the uncharged case (actually you write the Dirac equation for the uncharged case), leads to the conservation of mass particle number. The conservation law still has a freedom of choosing a reference frame, and that is the "global gauge symmetry", which is separate from the global physical symmetry. The difference can be seen if you have two isolated systems: each of them has conservation of mass particle number separately, and obey a 'global' symmetry transformation separately. Conversely, the global gauge transformation just sets the reference frame for everything everywhere: it's just setting the tick marks on your measuring device.
• Around 7m30s, you say that the structure in the universe causes loss of translational symmetry and therefore loss of conservation of momentum. Your example is that an apple accelerates towards the earth. But the latter is due to gravity, not due to broken symmetry. In a universe without gravity, the momentum would be perfectly conserved even in the presence of inhomogeneous structure. The symmetry is broken spontaneously by the state of the universe, but the laws are still symmetric, and conservation laws upheld.
• Personally I don't like the reasoning that particles interact because there is a local, gauge symmetry. This is backwards reasoning in my opinion. We want to model long-range interactions, and to do this using literal force fields (what we call gauge fields), the only consistent way is to have it be gauge invariant. The introduction of redundant degrees of freedom is not some deep beauty of nature or the like.

[u/kcsfx]

Been learning about symmetries in my particle physics class this week and this was super helpful, thanks!

[u/FanatiX31]

Super job comme d'habitude ! Tu as du courage de doubler tes vidéos en Français et en Anglais ;)

[u/GeneralDuh]

Your channel is awesome, thank you very much for the GR series.

[u/[deleted]]

Nice video my dude! I subscribed and have already watched a few others, QFT one was great as well and I'm gonna start the GR series once I have some more free time. Keep up the good work!

[u/kbl1tz]

Hey, I really like your channel. Do you have plans to make a series about QFT just like the one about GR?