Modern physics has a kind of fixation with symmetry which is striking to anyone who even remotely approaches the subject. It doesn’t matter if you’re talking about subatomic particles, galaxies, or a simple glass of wine: physicists return time and again to symmetries as if they were a compass for understanding the universe. And, honestly, they are. It’s often said, half-jokingly, half-seriously, that if we truly understood Where does symmetry come from? We could decipher the deepest secrets of reality. Behind that phrase lies something very serious: a good part of the laws that govern the cosmos, from the conservation of energy to hypotheses about dark matter, are written in the language of symmetries and, a step further, of supersymmetry.
What do we mean by symmetry in physics?
In everyday language, when we talk about symmetry we think of something visual and balanced, like the human bodyIf we disregard moles, scars, and minor imperfections, our left and right sides look remarkably similar. If you place a camera in front of a mirror and frame it correctly, the photo of your reflection and the direct shot of you would be virtually indistinguishable. The mirror is performing a very specific operation: it swaps left and right, and yet the result looks the same. Another everyday example is a well-made wine glass. If you place it on a table and rotate it on its vertical axis, Its appearance remains unchanged for any angle of rotation. If someone enters the room, turns it over, and you return later, you couldn’t tell whether the glass has rotated or not just by looking at it. The system is, to the observer, the same before and after the rotation. In physics, these examples are formalized by saying that a symmetry is an operation that, when applied to a system, It does not change its fundamental propertiesIn the first case, we speak of parity symmetry (left-right exchange), in the second of cylindrical or rotational symmetry. The trick is to identify which transformations are “harmless,” that is, which ones leave the equations describing the system intact. This concept goes far beyond the visual. Symmetry in a mathematical expression is also discussed when, after performing a certain transformation (for example, changing a variable to its negative or rotating a coordinate system), the resulting formula matches the original oneIn modern mathematics, symmetries are described by highly refined structures (groups, representations, Lie algebras, etc.) that have become indispensable tools for physicists. Detecting symmetries is not an aesthetic whim. It is the way to know what kind of operations we can perform on a system without altering its observable results. In practice, this greatly reduces the complexity of problems, because It immediately rules out a lot of possibilities. which would be incompatible with that symmetry.
Why symmetry rules in modern physics
Imagine you want to construct a physical theory for a world that is a perfect sphere. Intuitively, you know that any rotation of that sphere leaves everything the same: There is no privileged pointIf the laws of physics depended on the specific position on the sphere, you could distinguish one point from another through experiments, and the symmetry would break down. Therefore, the equations you write cannot make distinctions between points; they must respect this symmetry. This type of reasoning permeates all of modern physics. The Standard Model, which describes elementary particles and their interactions (except for classical gravity), is literally constructed on this principle. on sets of abstract symmetries that relate particles to one another and restrict how they can interact. These symmetries aren’t added at the end to embellish the theory; they are the very skeleton of the model. Something similar happens in general relativity, but with different symmetries. Einstein’s theory rests on the idea that physical laws must be valid in any reasonably moving frame of reference, which translates into a invariance under certain transformations of spacetimeAgain, symmetry is not just a curiosity, but a requirement for consistency. In the day-to-day work of a physicist, this translates into a kind of motto: “not everything goes.” Symmetries act as a brutally effective guide for discarding possible theories and for designing new ones. Many of the proposals in physics beyond the Standard Model, from grand unified theories to models of quantum gravity, arise precisely from demanding more symmetries, or from breaking them in very controlled ways.
Noether’s theorem: the bridge between symmetry and conservation
At the beginning of the 20th century, the German mathematician Emmy Noether formulated a result that many consider one of the most profound gems of theoretical physicsHis theorem establishes a direct link between symmetries and conserved quantities. Put simply: whenever a theory has a continuous symmetry, a quantity that remains constant over time appears associated with it. For example, the conservation of energy is related to the symmetry with respect to displacement in timeIf the laws of physics don’t change from one day to the next (that is, they are the same today as tomorrow), then the total energy of an isolated system is conserved. The conservation of linear momentum is associated with translational symmetry in space: if moving the entire experiment a few meters doesn’t alter its results, the momentum remains constant. Something similar occurs with angular momentum, which is linked to the rotational symmetryIf rotating the entire system doesn’t change its physical properties, then the total angular momentum remains constant. And so on with other conserved quantities, such as electric charge, which correspond to more abstract internal symmetries. The incredible thing about Noether’s theorem is that it allows us to extract powerful information from a theory without having to solve all its equations. Simply identifying its symmetries is enough to know which quantities remain immutable. This trick applies from classical mechanics to quantum field physics, and every student who encounters it experiences a small shock. It seems that a very deep truth suddenly emerges about how the universe is organized.
Bosons and fermions: two very different families
When we move on to the quantum mechanics of systems with many particles, we encounter two main types: fermions and bosonsThis classification is not arbitrary; it is linked to an intrinsic property of particles called spin, related to quantum angular momentum. Fermions (such as electrons, protons, or neutrons) have half-integer spin (1/2, 3/2, etc.) and obey the Pauli exclusion principle. This means that They cannot share exactly the same quantum stateIn practice, this means that they “don’t like to cluster together” with all their identical properties. This simple rule explains everything from the structure of atoms to the stability of the matter we touch every day. Bosons, on the other hand, have integer spin (0, 1, 2…) and are much more sociable. They can occupy the same quantum state without problems. In some systems, in fact, all bosonic particles end up in the same stateas occurs in lasers or Bose-Einstein condensates. The photon, the Higgs boson, and pions are examples of bosons that we know well in the laboratory. This difference in collective behavior makes fermions and bosons seem like two separate worlds. One builds “matter” (electrons, quarks, leptons in general), while the other is usually responsible for mediate the fundamental interactions (photons for electromagnetism, gluons for the strong interaction, etc.). They don’t seem to have much in common… unless there’s a deeper symmetry linking them. And that’s where supersymmetry comes in, an idea that suggests that, perhaps, fermions and bosons are two sides of the same coin, connected by an even more subtle transformation.
From ordinary symmetries to supersymmetry
Starting in the 60s and 70s, theoretical physicists began to wonder if it was possible to imagine new symmetries that went beyond of those already known in the Standard Model. If the usual symmetries had proven so useful for building theories, why not explore whether there could be an expanded version of the concept that directly related fermions and bosons? Historically, there were some very interesting previous steps. The Japanese physicist Hironari Miyazawa proposed in 1966 a kind of hadronic supersymmetry between baryons (composite fermions, such as protons and neutrons) and mesons (bosonic hadrons). To describe these relationships, he introduced mathematical structures that today we would identify as SU(3|3) type superalgebras, even without yet using that modern terminology. Shortly afterward, in the early 70s, several groups worked on dual models and early string theories. Gervais and Sakita introduced what they called “supergauge” transformationsThese were direct precursors to current supersymmetric transformations. In parallel, Golfand and Likhtman extended Poincaré algebra (which describes the basic symmetries of relativistic spacetime) to a “graded” version, incorporating generators that mixed bosonic and fermionic degrees of freedom. Specific models also emerged, such as that of Volkov and Akulov, which predicted a spin 3/2 fermion associated with a nonlinear supersymmetry. But it was the model formulated by Wess and Zumino in 1973 that truly made the breakthrough. the one that finished consolidating supersymmetry as a serious and systematic extension of the framework of quantum field theories. From 1974 onwards, the idea took off and began to be naturally integrated into attempts to extend the newly consolidated Standard Model. There is even a more remote “prehistory”: in 1937, Wigner had classified the irreducible representations of the Poincaré group and found mathematical structures with infinite towers of integer and half-integer helicities. These representations, which at the time seemed like exotic objects with no physical application, turned out to be naturally related to supersymmetric ideasalthough no one saw it until decades later.
What does supersymmetry actually propose?
In its most basic form, supersymmetry (SUSY, for short) states the following: to every known particle there must correspond a supersymmetric partner with the same set of internal properties (charge, modified spin, etc.) but with an exchanged bosonic or fermionic nature. Thus, each fermion in the Standard Model is associated with a supersymmetric boson and vice versa. The electron, for example, would have a partner called the selectron, which would behave like a boson with very similar properties, except for that key change in spin type. Similarly, quarks would be paired with squarks, and Bosons like the gluon would be accompanied by a fermion called gluinoPhotons would be paired with photinos, gravitons with gravitinos, and so on for the entire catalog of relevant particles. If the symmetry were perfect, each pair would have the same mass, which would mean that in experiments we would always see the particle and its supersymmetric partner produced without difficulty. But this is not the case: to this day, None of these superparticles have been observed conclusively. To salvage the theory, physicists introduce the idea of supersymmetry breaking: symmetry exists in the fundamental equations, but in our universe it is “broken,” so that the masses of superparticles are much greater than those of their ordinary counterparts. This implies that detecting them requires extremely high energies, such as those achieved in LHC (Large Hadron Collider) accelerators. According to many models, the masses of these superparticles should be in the window between about 100 GeV and 1 TeV, an energy range that It has been explored in experiments such as ATLAS and CMSSo far, no convincing evidence has emerged, which is pushing us to refine models, broaden the search range, or question some assumptions.
Why supersymmetry excites so many physicists
Supersymmetry is not just a mathematically beautiful construct, although it certainly is. Its main appeal lies in the suggestive answers it offers to several open problems in current physicsOne of the most talked-about is the so-called hierarchy problem: why the weak interaction is so strong compared to gravity, or, put another way, why the mass of the Higgs boson is so “small” compared to the Planck scale. Without supersymmetry, quantum calculations of the Higgs mass tend to yield absurdly large results, requiring extremely fine adjustments to reconcile them with observations. With SUSY, the contributions of fermions and bosons to these corrections are partially canceled, which It alleviates the problem naturally. and allows us to keep the Higgs mass within the appropriate range without resorting to numerical manipulation. Another strength is dark matter. Cosmological observations indicate that approximately 85% of the matter in the universe is of a type that It neither emits nor absorbs lightbut it exerts a gravitational influence on galaxies and clusters. The Standard Model does not offer good candidates to explain this dark matter, beyond neutrinos with mass, which appear insufficient. In many supersymmetric models, however, the lightest supersymmetric particle (LSP) is stable and neutral, and fits quite well with the properties expected of a dark matter particle. Furthermore, supersymmetry facilitates the unification of the fundamental interactions. If we extrapolate how the coupling constants (those that measure the strength of the forces) evolve with energy, In a model without SUSY, they do not intersect cleanly. at a single point. With added supersymmetry, these curves tend to come together better at very high energies, fueling hopes for a grand unified theory where electromagnetism, the weak interaction, and the strong interaction are manifestations of a single force at extreme energies. Finally, supersymmetry plays a key role in string and superstring theories, which attempt to describe gravity using quantum rules, and in the quantum gravity theoryWithout supersymmetry, string theories suffer serious consistency problems (tachyon emergence, divergences, etc.). With it, The models become much better behaved and rich structures of dualities and mathematical correspondences appear that have revolutionized theoretical physics and entire branches of mathematics.
Criticisms, doubts, and the role of experiments
However, it’s not all unbridled enthusiasm. Within the theoretical physics community itself, there are critical voices pointing out that, despite decades of work, We haven’t seen any superparticles yet. in the most powerful experiments built to date. Every time we expand the range of energies explored without finding signals, certain simple models of SUSY become less plausible. There is also debate about how these topics are presented to the general public. In public lectures or videos, a lot of time is sometimes spent reviewing very basic physics before getting into supersymmetry, which can frustrate enthusiasts who already have some background knowledge. And vice versa: some people think that certain popularizers They sell supersymmetry as if it were an established truth.when in reality it remains a hypothetical framework awaiting clear experimental confirmation. A striking example of the disconnect between theory and experiment is found in the case of neutrinos. For decades it was assumed that they had no mass, partly for theoretical convenience in various models (including some inspired by string theory), but neutrino oscillation experiments demonstrated that Yes, they possess a small but not zero mass.This forced a revision and expansion of the models, and serves as a reminder that nature always has the final say, whether our elegant constructs like it or not. In the specific case of supersymmetry, LHC data have been placing increasingly stringent limits on the minimum mass that many superparticles could have. It’s not that supersymmetry has been “refuted” outright, but some of its simplest and most optimistic scenarios They are already pretty corneredPhysicists continue to explore more complex versions, models with different SUSY breaking, or more sophisticated extensions, but the landscape is less comfortable than it was twenty or thirty years ago.
Supersymmetry, dark matter and supermassive black holes
The question of dark matter intersects with supersymmetry in very suggestive ways. The only thing we know for sure about this matter is its gravitational footprint in the universeGalactic rotation curves, gravitational lensing, large-scale structure… But we haven’t directly detected any of its particles, neither in underground detectors nor in colliders. Some supersymmetric models offer very natural candidates for this dark matter, such as certain weakly interacting stable LSPs. However, so far, experiments searching for signals from these particles, whether in space or in laboratories, have not yielded conclusive results. The situation is similar to that of SUSY in general: The experimental windows are gradually closing.But there’s still room for some variant to work. On the other hand, astrophysics is revealing phenomena that are difficult to fit into the classical framework. The James Webb Space Telescope, for example, has identified extremely old supermassive black holes, almost as old as the universe itself. According to traditional ideas, these monsters should form from smaller black holes that swallow gas, stars, and other black holes over billions of years. However, some of those observed seem too big for their ageThis is where a compelling hypothesis comes in: that dark matter directly influences the formation of these primordial black holes. Researchers like Alexander Kusenko and his team have proposed that, in the early universe, the presence of dark matter would have hindered the cooling of hydrogen, preventing the normal formation of stars. Instead, a gigantic, hot cloud of gas could collapse suddenly into a supermassive black holeskipping the intermediate stellar phase. The problem is that the gas tends to cool rapidly, especially when hydrogen molecules form, acting as efficient “radiators.” Dark matter would have to exert a very delicate influence to maintain the necessary conditions. Theoretical models and simulations are being developed to study these scenarios, and the James Webb Space Telescope, along with future observatories, could provide crucial clues. If any of these hypotheses are confirmed, the connection between dark matter, supersymmetry, and black holes It could become even narrower. For now, however, the situation is honest: we know that dark matter exists because of its gravitational effect, we have reasonable ideas (including many supersymmetric ones) about what it might be, and we are accumulating interesting clues about its role in the formation of cosmic structures… but We still haven’t grasped the concrete particle by the neckTo put it bluntly. Overall, the history of symmetry and supersymmetry in physics shows the extent to which the universe appears to be organized according to deep patternsFrom the human body or a glass of wine to elementary particles and distant black holes, classical symmetries, formalized in results like Noether’s theorem, have allowed us to understand why certain quantities are conserved and how the laws of physics must be to respect basic invariances of space and time. Supersymmetry, with all its mathematical elegance and its potential to solve enigmas such as the hierarchy problem or the nature of dark matter, remains a major theoretical endeavor awaiting a definitive experimental verdict. Whether it is ultimately confirmed or forces us to invent even bolder frameworks, it has already left a profound mark on how we think about reality. [related url=”https://www.cultura10.com/teoria-de-la-gravedad-cuantica-mapas-pruebas-y-encrucijadas/”]