In one of my previous articles, I was discussing particles and quantum fields, and more in particular how to introduce those concepts to laymen (and thus Steemians) in a correct and simplified manner. <div class="pull-left"> <center> !(https://s26.postimg.org/h7qolfqbd/collision_lhc.jpg) <sub> [image credits: [CERN](https://home.cern/about/updates/2015/05/first-images-collisions-13-tev)]</sub> </center> </div> I move on here and tackle the concept of **gauge symmetries**. I will in particular use timezones (something that everyone knows) to explain how this works. In particle physics, this is crucial **to describe how all fundamental interactions work at the level of the elementary particles** (except gravity). <br /> ___ ## GAUGE SYMMETRIES ## Let us start with the concept of a symmetry. **A symmetry is a transformation of the mathematical objects of the theory that does not alter the physics, or in other words, the predictions.** <div class="pull-right"> <center> !(https://s26.postimg.org/ouhffjrax/image.png) <sub> [image credits: [Wikipedia](https://en.wikipedia.org/wiki/Time_zone)]</sub> </center> </div> Now, let us move on with gauge symmetries and an explicit example. Let us imagine we carry a physics experiment somewhere on Earth. Obviously, **the timezone corresponding to the place where the experiment happens does not influence the results**. That is exactly a symmetry: **we are allowed to use different timezones in different places** and the physics is invariant of that. We now need something that tells us how to the timezone changes from point of space to point of space and to relate the different possible choices. Obviously, this must be some vectorial object (with a direction in tridimensional space). **Generalizing this to the quantum field theory level, the vectorial object becomes a field, and thus a new particle: the so-called force carrier**. Things are actually slightly more complicated, but I hope you got the main concepts here: **interactions are connected to force carriers**. ___ ## INTERACTIONS IN THE MICROSCOPIC WORLD ## We should first forget gravity. The reason is very simple. The gravitational interactions involve the masses of the particles that interact. However, the masses of the elementary particles are small, so that **the resulting gravitational strength is tiny and negligible**. This even holds for the heaviest of all known particles, the top quark. Of course, when one says negligible, it is always negligible relatively to something else. Here, the something else consists of the strengths of the other interactions. Consequently, **the Standard Model of particle physics is the theory that describes how the elementary particles propagate in space-time and interact**, and by ‘interactions’, we mean electromagnetic, weak and strong interactions only. ___ ## ELECTROMAGNETISM ## <div class="pull-left"> <center> !(https://s26.postimg.org/b9qngfbi1/magn.jpg) <sub> [image credits: [Pixabay](https://pixabay.com/en/money-magnet-success-wealth-profit-1015585/)]</sub> </center> </div> **Electromagnetic interactions involve electric charges**, and their strength is actually proportional to these charges. At the macroscopic level, **matter is generally neutral, and thus electromagnetically blind**. Matter is indeed generally comprised of an equal number of positively-charged and negatively-charged constituents. All electromagnetic effects that would be induced by the positive charges constituting matter are thus compensated by those of the negative charges. At the microscopic level, the situation is very different. **Elementary particles are mostly not neutral**, and electromagnetism consequently plays a role. It explains, for instance, how atomic nuclei and electrons form atoms. Equivalently, electromagnetism is crucial to explain the **structure of matter**. <br /> ___ ## THE WEAK AND STRONG FORCES ## <div class="pull-right"> <center> !(https://s26.postimg.org/aufdnepkp/radio.png) <sub> [image credits: [Pixabay](https://pixabay.com/en/earth-3d-magnetic-2653031/)]</sub> </center> </div> **The weak and strong forces have been discovered in the contest of radioactivity, and they are purely related to the microscopic world.** There is no macroscopic effect at all (those forces are actually short-ranged). The **strong interaction** is responsible **for the cohesion of the protons and neutrons**. Neutrons and protons are composite objects made of elementary quarks and gluons that are glued together by virtue of the strong interaction. At the atomic level, **neutrons and protons form atomic nuclei**, once again by virtue of the strong interaction. As a consequence, the strong interaction is one of the main building blocks to explain the structure of matter, as for electromagnetism. The **weak force**, much weaker, has in contrast not any effect on the structure of matter. It instead renders **decay processes possible**, and these processes are slow as a consequence of the weakness of the weak force. This slowness for instance allows our sun to burn its fuel at a moderate pace. ___ ## SYMMETRIES AND INTERACTIONS ## Starting from a symmetry concept, gauge theories explain how **the interactions of the elementary particles are modeled by the exchange of force carriers**, namely the photon (electromagnetism), the W and Z bosons (weak interaction) and the gluons (strong interaction). <div class="pull-right"> <center> !(https://steemit-production-imageproxy-thumbnail.s3.amazonaws.com/U5drqkAbYxvZWNnN7X6vLUaGcv9LoAv_1680x8400) <sub> [image credits: homemade]</sub> </center> </div> This exchange of a force carrier is illustrated on the picture on the right. The ball stands for a gauge boson (which is the fancy word used for a force carrier). The two little guys are two particles and the ball is passed from one to the other. As a result, the two boats will move away from each other. One says that they interact. A good question is **why we are so sure that this picture involving gauge symmetries is the correct way to describe the microscopic world?** We can never be sure, and a theory has to be tested. Data then tells us. The predictions of the Standard Model have been intensively confronted to data during the last 50 years. We are talking of **several thousands of different measurements**. There is (almost) not a single sign of any deviation up to now. **Relying on gauge symmetries seems thus suitable to explain all particle physics data available today**. More importantly, predictions are made for future experiments so that further tests will be carried on. ___ ## SUMMARY AND REFERENCES ## In this post, I have discussed the notion of gauge symmetries and how it is related to the fundamental interactions. I have first defined what is a gauge symmetry and show how this is related to the so-called force carriers. Then, I have focused on the fundamental interactions that are actually described by gauge symmetries. The topic discussed in this article has been inspired by my reading of [**this paper**](https://arxiv.org/abs/1709.02697) that addresses the teaching of particle physics. The last part of the post is made of well-known stuff that can be found everywhere (just wikipedia it for instance or check my old blog).