The hierarchy problem and gravity
Another issue, however, lies in the practicality of achieving these higher energy collisions in particle accelerators. Consideration of the physical constraints that are faced when designing larger and higher energy accelerators contributes to the further complication of experimental confirmation of these particles. In theory, achieving collisions at Planck energy would require a particle accelerator of a size ten times greater than the Sun, rendering such experiments unfeasible. 28 As a result, this theory may not ever be directly validated in scientific research, hence failing to convince as a reasonable explanation for this hierarchy problem. It can be argued that the theory of the Higgs as a composite particle may be within our closest range of experimental validation, thereby allowing justification for its greatest potential as a theory to explain the multitude of problems faced by the Standard Model. Moreover, this application of supersymmetry establishes the strength of the weak force as natural, and gravity is weak in relative comparison due to this reasoning. However, other theories attempt to tackle this problem, with a common solution involving the addition of extra dimensions at extremely small distances. 29 According to general relativity, gravity is an intrinsic effect through all dimensions due to the curvature of spacetime. Therefore, in the consideration of additional dimensions, gravitational fields would permeate across a larger spacetime than previously thought and would consequently be weaker than the other three fundamental forces, which are restricted to the three classical dimensions. 30 It is important to note that this idea is purely theoretical, with no existing framework or experimental data; it provides a neat yet currently unjustified solution to this extension of the hierarchy problem. However, gravity might indeed be stronger than expected at smaller distances, at which the force has not yet been finely measured, so it is not entirely unreasonable to sideline this potential argument. While the Standard Model provides a thoroughly accurate description of three of the four fundamental forces, the hierarchy problem it faces when discussing the relative weakness of gravity, and the unnatural fine-tuning of the Higgs field and its effects in electroweak symmetry breaking, proves to be an underlying problem. Although potential ideas such as supersymmetry and additional dimensions offer theoretical solutions, they are yet to be proven experimentally, and so it can be concluded that our lack of evidence and capability for the required experimental research to justify such claims renders the hierarchy problem as arguably unsolvable. However, it is only through advancements in experimental capabilities at higher energies that we can hope to reconstruct our understanding of particle physics and the Standard Model. There remains potential for revealing the composite nature of the Higgs boson, yet there is little evidence aside from the conclusion that the Standard Model does indeed break down over several TeV instead of the Planck scale.
References
Atlas Collaboration. (2023a) ATLAS measures Higgs boson mass with unprecedented precision. https://atlas.cern/Updates/Briefing/Run2-Higgs-Mass. Consulted: 11/07/24 Atlas collaboration. (2023b) ATLAS measures the Higgs boson at 13.6 TeV. https://atlas.cern/Updates/Briefing/Run3-Higgs. Consulted 11/07/24
28 Loeb, Planck energy. 29 Strassler 2011. 30 Ibid.
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