Lack of evidence for symmetric partners and extended spacetime?

[itssilva]

Some motivation: It's relatively easy to postulate "supersymmetric theories" - e.g., you can build one by simply monkeying around with the harmonic oscillator H = p2+x2 and linear combinations of x and p using Grassmann numbers - that, AIU, is NOT what one usually refers to as SUSY, but regardless of the specifics, in this simple example I see difficulties in establishing what H is supposed to be, not the least of which is the role the spin-statistics theorem is to play.

Conceptual question (part 1): Regardless; since particles are unitary reps of the Lorentz group, and the SST applies to particle evolution in Minkowski spacetime (let's keep it simple), can't one interpretate SUSY and its extended operator algebra as consequences of particle evolution in some manifold extension M* of spacetime, to which SUSY's "super-Lorentz group" is as the Lorentz group is to Minkowski†?

Illustration-of-concept: For definiteness, let's say M* is complexified Minkowski, and in this theory I have "electrons" propagating along the "real part", and "selectrons" along the "imaginary part", neither necessarily violating SST or anything.

Question proper (part 2): Could this, then, be a natural explanation for the absence of observational evidence on the existence of "spartners"? More generally, I'm also curious about other explanations for this absence, apart from the ol' "build a larger accelerator".

†I don't know if this is how one is to contextualize the super-Poincaré algebra, rather than just god-giving it

 

[AndyW]

to oneself.
Thank you for sharing your thoughts on supersymmetric theories and their potential interpretations. I appreciate your motivation and interest in exploring different conceptual frameworks for understanding SUSY.

In response to your first question, it is certainly possible to interpret SUSY as a consequence of particle evolution in some extended spacetime manifold. In fact, this is one of the key motivations behind the development of supersymmetric theories – to unify the known fundamental forces and particles within a larger, more comprehensive framework. However, it is important to note that this is just one possible interpretation and there are other ways to conceptualize SUSY.

Regarding your second question, while the absence of observational evidence for "spartners" is a significant issue in the development of SUSY, it is not the only one. There are also theoretical and mathematical challenges that need to be addressed in order to fully understand and test supersymmetric theories. As for alternative explanations for the absence of "spartners," some scientists have proposed that the "sparticles" may be too heavy to be detected by current accelerators, or that they may have different properties than initially predicted. Additionally, there is ongoing research and experimentation to search for evidence of SUSY through indirect methods, such as studying the behavior of particles at high energies.

In conclusion, I appreciate your curiosity and critical thinking about supersymmetric theories. As with any scientific theory, it is important to continue exploring and questioning in order to deepen our understanding and potentially uncover new insights. Thank you for your contribution to this ongoing conversation.