That's exactly the kind of question a curious physics student would ask. This might be what you're looking for: https://en.wikipedia.org/wiki/Tachyonic_field

> In physics, a tachyonic field, or simply tachyon, is a quantum field with an imaginary mass.

I hear the word Tachyon so much in science fiction that I was under the impression it was a sci-fi word.

It almost is. https://en.wikipedia.org/wiki/Tachyon#History:

The term tachyon was coined by Gerald Feinberg in a 1967 paper titled "Possibility of faster-than-light particles". He had been inspired by the science-fiction story "Beep" by James Blish.“

I don’t think “Beep” introduced the word, though (https://archive.org/details/galaxymagazine-1954-02)

Good question. Imaginary mass -> negative 4-momentum -> momentum exceeds energy -> object is moving faster than light (backwards in time in some reference frames).

There are some reasons to suspect/hope such things might not exist, such as protecting causality.

In general, asking "what if <simple field type> was <more complex field type>" can actually produce super fruitful lines of inquiry. You can use "complex numbers", "quaternions", "finite fields", whatever you like. There's plenty of unexplored ground here.

Given the quantum eraser experiment and general lack of time directionality in particle physics it seems causality as an "axiomatic" physical truth is already broken. At least at a quantum level. My suspicion is that event-based causality falls into the 'its only resolved for >= hbar/2' realm. Then even if you had a bunch "tachyons" it'd be impossible to send a signal back in time more than a few planck constants of time much like its hard to entangle more than a few qbits.

Superluminality isn't required by all interpretations of QM. MW doesn't need it, for example.

I'm not aware of a mechanism by which causality would arise from known QM, so I wouldn't expect a priori planck scale to play into it. There would also need to be an energy term for h to make sense as the relevant constant.

The most compelling source of temporal direction I'm familiar with is that it's a regional cosmological entropy gradient rather than a fundamental aspect of physics, although it strikes me as suspicious that the time direction lies inside the 4-cone generated by the odd-dimension-out in our spacetime metric. That certainly lends some credence to theories which would predict the direction of time as fundamental to physics.

As someone who is similarly and over-interested hobbyist, I wonder what happens when you throw in even more, for lack of the proper term, deviant math systems. The cousins of imaginary numbers using either epsilon (where epsilon^2 = 0, epsilon not a member of R) or j (where j^2 = 1, j not a member of R). Or quaternions. Or the family of quaternions similar to the family of complex numbers. And so on.

My guess is that it falls back to Occam's Razor and there has yet to be any physics to use it thus it isn't a serious contender for current problems until much more work has been done on all the threads already being followed.