There is was a recent interesting article in Quanta Magazine about 'paraparticles' (https://www.quantamagazine.org/paraparticles-would-be-a-third-kingdom-of-quantum-particle-20250411) as a new type of particle. The article describes how these particles (strictly theoretic at this point) are different from current particles and derive from not squaring values in current measurements. When a measurement is squared, there are two possible solutions (one positive and one negative). Not squaring provides a means of identifying aspects that 'disappear' when squared.
I have given a couple presentations (and papers) suggesting we need new mathematical tools to expand science (and mathematics). In particular is the need for a new, more powerful numeric system that could provide single values for complex numbers.
Paraparticles research might find such a system very helpful, since it could distinguish between any complex values without needing to square results (to get a non-complex or 'Real' result) and therefore distinguish between measurements of paraparticles.
I note that complex numbers do not apply to 'real' measurements, since we do not know what to do with the 'imaginary' part (hence we square it to get rid of this part or simply drop it, as for some electronic measurements).
This is the first direct potential application I have seen for the need for such a complex numeric system.
I would be interested in other's comments.
Dear Donald,
Your question brilliantly highlights something we often sweep under the mathematical rug: how much of our physical interpretation is shaped—if not outright dictated—by the numeric scaffolding we choose to use.
The observation about squaring to eliminate imaginary components is more than a technical convenience—it’s a philosophical choice. It assumes reality must conform to scalar closure and that magnitude outweighs phase in physical relevance. But paraparticles, if real, might not respect such classical expectations.
What if the “discarded” imaginary parts of complex numbers are not just artifacts of computation but traces of actual, measurable phenomena that we’ve trained ourselves to ignore? Your suggestion of developing a new numeric system—one that avoids this forced duality—makes conceptual sense. Not necessarily in rejection of complex numbers, but in rethinking what it means to “measure” at the quantum frontier.
Paraparticles, by not conforming to the squaring paradigm, might call for a kind of algebra that permits directional state multiplicity without collapsing into mere norm. A number system that keeps track of phase not as a tool for calculation, but as a carrier of ontological data. Perhaps a hybrid of geometric algebra and non-commutative algebra could allow such a structure.
In any case, your call isn’t just for mathematics, but for a more generous physics—one where elimination of a component isn’t mistaken for understanding.
Warm regards,
Adam Nasser
Thank you for your generous comment, Adam Nasser
In my presentations, I have suggested there are physical measurements we currently cannot make due to our mathematical tools and that inventing new tools could expand our knowledge of the world. The ability to use complex values for measurements would need single-valued complex numbers (not our current x + iy dual valued ones). A complex number 'z' would be a single value that could be, say, a distance measurement, just as decimals (and variations) provide single valued measurements today.
I hypothesize such a system would include integration and differentiation in the definition of the numeric system - simplifying integration and differentiation arithmetic, thus providing significant power above our current numeric system.
In the presentations, I provide some historical evidence that our mathematical numeric systems are key to our science - since we could not have developed quantum physics using Roman numerals or just fractions.
The implication is that there is much we do not yet know about mathematics (what if there are more powerful systems than this suggestion?) and that such a system would expand both mathematics and science.
No paraparticles is already old idea.
Axions. Neither fermion nor bosons.
Maybe fractional stuff in 2D
- Badges
- Science method