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A naive question from a hobbyist with over-average interest in particle physics: quantum theory is based on complex numbers. Has anyone considered that mass/gra

by zvrba 5y ago

A naive question from a hobbyist with over-average interest in particle physics: quantum theory is based on complex numbers. Has anyone considered that mass/gravity may also have an imaginary component that manifests itself as "dark matter"? (I.e., it's not "matter" at all, just an incomplete understanding of gravity.)

alecst 5y ago
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 https://en.wikipedia.org/wiki/Tachyonic_field > In physics, a tachyonic field, or simply tachyon, is a quantum field with an imaginary mass.
- henriquecm8 5y ago
  I hear the word Tachyon so much in science fiction that I was under the impression it was a sci-fi word.
  - Someone 5y ago
    It almost is. https://en.wikipedia.org/wiki/Tachyon#History 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 https://archive.org/details/galaxymagazine-1954-02)
wyager 5y ago
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.
- elcritch 5y ago
  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.
  - wyager 5y ago
    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.
SkyBelow 5y ago
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.

by zvrba 5y ago

alecst 5y ago

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 https://en.wikipedia.org/wiki/Tachyonic_field > In physics, a tachyonic field, or simply tachyon, is a quantum field with an imaginary mass.

henriquecm8 5y ago
I hear the word Tachyon so much in science fiction that I was under the impression it was a sci-fi word.
- Someone 5y ago
  It almost is. https://en.wikipedia.org/wiki/Tachyon#History 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 https://archive.org/details/galaxymagazine-1954-02)

wyager 5y ago

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.

elcritch 5y ago
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.
- wyager 5y ago
  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.

SkyBelow 5y ago

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.