The periodic table is a classification of the chemical elements based on their atomic number, electron configuration and chemical properties. It is a result of the empirical observation of the elements and their regular patterns. The periodic table does not depend on any particular theory of physics, but it can be explained by quantum mechanics and the structure of atoms.[1]
Grand unification is a hypothetical scenario in which the electromagnetic, weak and strong forces are unified into a single force at very high energies. This would imply that the elementary particles of the Standard Model are composed of more fundamental particles, such as quarks and leptons, that interact through a single gauge group. Grand unification is motivated by the observation that the strengths of the three forces converge at high energies, suggesting a common origin. Grand unification also predicts the existence of new particles, such as magnetic monopoles and proton decay.[2]
Supersymmetry is a theoretical framework that proposes a symmetry between fermions and bosons, two classes of particles with different spin properties. It implies that for every known particle, there exists a superpartner with the same mass and quantum numbers, but with a different spin. Supersymmetry is not based on any empirical evidence, but on mathematical aesthetics and theoretical convenience. Supersymmetry can solve some problems in the Standard Model, such as the hierarchy problem and the dark matter problem, but it also introduces many new parameters and complications. Supersymmetry has not been observed in nature, despite extensive searches at the Large Hadron Collider and other experiments.[3]
The main difference between supersymmetry and the periodic table or grand unification is that supersymmetry is not a natural consequence of any observed phenomenon, but an ad hoc assumption that has no experimental support. The periodic table and grand unification are based on empirical data and physical principles, while supersymmetry is based on mathematical beauty and speculation. Therefore, supersymmetry does not make any expected predictions, unlike the periodic table or grand unification, because it is not constrained by any reality check. Supersymmetry can be adjusted to fit any observation or avoid any contradiction, making it unfalsifiable and arbitrary.[4]
[1]Supersymmetry - Wikipedia. https://en.wikipedia.org/wiki/Supersymmetry.
[2] Supersymmetry and what it means for particle https://www.space.com/supersymmetry-particle-physics-string-....
[3] The status of supersymmetry | symmetry magazine. https://www.symmetrymagazine.org/article/the-status-of-super...
[4] Supersymmetry: what? why? when? - Ohio University
https://inpp.ohio.edu/~inpp/nuclear_lunch/archive/2005/kane_....