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A major point brought out by the answers to "Why are there only four fundamental interactions of nature?" is that there are signals that more forces might exist. What are some phenomena/theories we have currently which could need a new force to describe?

An example which an answer to this question can potentially discuss is the way in which supersymmetry indicates the likelihood of other forces. This is a point mentioned in the linked question which I didn't understand. However, I'm making the question broader to invite a discussion of ALL possible evidence, rather than just SUSY.

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It depends on the definition of fundamental. I have covered this ground in an answer here. It depends on the accepted standard model of particle physics which posits three forces, which obey symmetry groups, and allow to calculate all interactions among particles using a specific coupling for each force, . Gravity is a hopeful addition to the other three quantum mechanical forces with the hope that it will be definitively quantized.

The assumptions tied up with the data and thus really fundamental, are the coupling constants. The gauge symmetries corresponding to these coupling constants can be manipulated so that at high energies one coupling constant appears, so the adjective "fundamental" is transferred to the gauge bosons of the gauge symmetries.

So as I say in my answer linked above

The theory of particle physics is mathematically organized as a gauge theory with the group structure of SU(3)xSU(2)xU(1). These have exchange bosons, which before weak symmetry breaking have a zero mass, and after symmetry breaking have been associated with the three fundamental forces , electromagnetism, weak, strong. This association comes from the mathematical continuity that is necessary going from the microscopic frame of quantum mechanics to the macroscopic of classical electrodynamics, extended to the strong and weak forces.

Thus in the way particle theories are mathematically organized, a new fundamental force will have to be an extension of the symmetries of the standard model, introducing new symmetries which will have gauge bosons as carriers of the symmetries . An example is GUTS :

A Grand Unified Theory (GUT) is a model in particle physics in which, at high energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, or forces, are merged into one single force. This unified interaction is characterized by one larger gauge symmetry and thus several force carriers, but one unified coupling constant.

italics mine.

Supersymmetries by doubling the symmetry groups also introduce new gauge particles.

Because both the half-integer spin fermions and the integer spin bosons can become gauge particles. Moreover the vector fields and the spinor fields both reside in the same representation of the internal symmetry group.

The gauge particle exchange is the lowest order Feynman diagram for a given particle interaction.

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Gravity may or may not be a fundamental force. Recent work on gravity as an emergent phenomenon provides and alternative picture. See for example Erik Verlind's work on Entropic Gravity. I think the best answer is: we don't know. Every few years there is a new fifth force candidate. Supersymmetry is a beautiful idea, but is there any evidence to support it?

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  • $\begingroup$ This doesn't address the question. $\endgroup$ – Ben Crowell May 23 '18 at 16:39
  • $\begingroup$ I beg to differ. Why hypothesize forces ex nihilo when we don't fully understand even the "four fundamental forces?" The approach to gravity as an emergent phenomenon is directly addressed at the OP's "I'm making the question broader to invite a discussion of ALL possible evidence,..." $\endgroup$ – JohnS May 23 '18 at 17:14

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