The Symmetries of the universe

welcome back to today's scientific group the

symmetries

of the

universe

there are many complex laws that apparently govern our

universe

conservation of momentum energy general relativity the standard model of particles however all this complexity emerges from a purer and deeper concept of which all these laws are only consequences symmetry in mathematics asymmetry is a transformation that leaves an object unchanged a sphere, for example, has rotational symmetry, you can rotate it, change its orientation and it remains the same an infinite string is symmetrical by translation we can move along length of the string, it remains the same, 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 perform a simple experiment we throw a ball once released it continues we move in a straight line at a constant speed now let's imagine that we travel through the universe and perform the same experiment but in another place here we also observe that the ball continues in a straight line at a constant speed it behaves in the same way the laws of physics they have not changed from one place to another 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 rotated changed orientation the The result would have been the same.

In the end, this universe is also symmetrical over 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 remains the same under certain transformations imposes restrictions on the behavior of objects to understand let's return to our empty universe and throw the ball once thrown the ball acquires a forward motion and in the next instant it is a little further forward has moved, but if we assume that the universe is symmetrical 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 moves but the laws of physics remain the same there and at each instant the ball therefore evolves in the same way if the laws of the universe are invariant due to translational symmetry it forces the ball to conserve its movement which explains why it draws a straight line at constant speed in a similar way if An object rotates on itself assuming that the laws of physics are invariant under rotations.

In the next instant the situation is equivalent and symmetry will force the object to conserve its rotation, so each symmetry of the universe must be respected. It requires 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 in time no this theorem also applies to the content of the universe and in particular to 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 of them.

To understand these complex numbers, let's imagine that we measure the altitude of an airplane on Earth to express the altitude of the airplane we must set a reference level, for example, sea level. By setting this reference, we can describe the altitude using 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 changed it does not change the same situation can be described differently depending on the reference level we choose in the same way for the electron field we can change the reference level we corresponds to altering the phase of all complex numbers without affecting the physical situation described here.

The change of reference constitutes a symmetry and according to Nother's theorem, this symmetry also imposes the conservation of a quantity. The laws of conservation of electric charge such as the conservation of energy or electric charge, therefore, these quantities are not fundamental in general. are not necessarily conserved, it is only when the universe presents an underlying symmetry that, to be respected, the symmetry imposes the conservation of a quantity, the principle of equal and opposite reaction, for example, which reduces to the conservation of momentum when two objects They separate, it is only a consequence of the symmetry under translation if one object goes in one direction the other must go in another direction thanks to this symmetry the rocket can take off upwards expelling material downwards however a problem arises unlike the simplified example of an empty universe, our real universe does not appear to be completely symmetrical at once.

On the scale of billions of years, for example, the universe expands and is therefore not perfectly symmetrical over time. As a result, on a large scale, the energy of the universe is not conserved. Light, for example, loses energy gradually. Its wavelength stretches as the universe expands. is not perfectly symmetrical in translations, or contains stars and planets and therefore is not the same everywhere at this scale, therefore if we launch an object in general, its momentum is not conserved on Earth, for For example, an apple falls downwards, accelerates its motion, and changes over time. Because the situation is not symmetrical at first glance, our universe does not seem to respect symmetries, worse still, the laws of physics seem to be different depending on the frame from which we observe, if we drop a ball into a centrifuge from the outside , the ball seems to conserve its motion but from within the motion 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 all like it objects, regardless of our point of view, always obey the same laws when changing point of view the laws of the universe should not change they should remain the same for everyone however the behavior of the bull is not the same to solve this problem to restore 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 moves straight ahead and if we take the sea level as a reference we measure a constant altitude a straight line is drawn that says let's imagine that we take the earth's surface as a reference this time through the mountains we measure an altitude that varies over time as if the plane were moving in zigzags taking as a reference the surface the behavior of the plane now seems different but the situation does not change the plane moves forward as explained that while it looks forward its altitude varies with time To solve this paradox it is necessary to introduce a kind of force field that would push the plane up or down depending on the reference level that we have chosen, thus explaining its behavior when moving from one reference level to another from sea level to ground level.

It is necessary to add this force field to properly take into account the behavior of the plane returning to the example of the ball in the centrifuge the situation is exactly the same moving from one point of view to another from outside to inside the centrifuge The torus seems to obey different laws and it is necessary to add some type of force field to our description. These are what we call inertial forces and in particular the centrifugal and Coriolis forces. By adding these inertial forces, we restore the laws of physics as absolute. The shape 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 the point of view we choose.

The introduction of this type 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 absolute nature 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. From view using the same equations surprisingly this reasoning adding a field to restore the invariance of the laws of physics is also the basis of all fundamental interactions in particle physics. We have seen that the quantum electron field has a symmetry.

The laws that describe it are invariant when we change the phase of all complex numbers globally, but if we alter the phase differently in different parts of the field locally, which is equivalent to choosing a reference level in zigzags like the surface of the earth , the laws that describe electrons seem to have changed in In other words, this change of reference is not a symmetry, if we want to restore the laws of physics as absolute, so that this is a symmetry, whatever the reference level. Whatever we choose, we must change our description, we must introduce another underlying structure, a type of force. field with which the electron field interacts to explain this change in behavior this other structure is called electromagnetic field contains particles that interact with electrons photons in a way if two objects repel each other due to their electric charge if we do not fall our chair when we We sit down and if there is light in the universe it is thanks to this local symmetry, being able to choose any reference level for the complex numbers, which requires the existence of a new field and new particles, the photons with which the electrons interact to conclude the study, the symmetries. of the universe allows us to deeply understand the origin of the laws that govern it, it is because the universe has symmetries that the objects it contains to respect these symmetries obey physical laws, whether conservation of energy or objects of momentum.

We obey these laws only to respect the underlying symmetries intrinsic to the universe by considering that the laws of physics must be absolute, that changing our point of view or reference level must constitute a symmetry that does not affect physical reality. We call this gauge symmetry. Experimentally deduce the presence of new structures in the universe such as the curvature of space-time or the electromagnetic field. Symmetries also allow us to reveal the hidden mysteries of matter by measuring certain properties of the particles and studying the geometric diagrams we obtain. Symmetries have allowed us scientists to understand, for example, that protons, neutrons and other baryons are made up of three smaller objects that obey a fundamental symmetry based on the number three of quarks.

There are also discrete symmetries, for example, reversing the direction of charge in space and the direction in time of all particles. constitutes a symmetry an antiparticle can in this way be interpreted as an ordinary particle that goes back in time finally some modern speculative 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