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A tachyon (/ˈtækiɒn/) or tachyonic particle is a hypothetical particle that always travels faster than light. From en.wikipedia.org as of 2020-04-21.
I do not know and have no proof whether tachyon particle exists, if yes, which type of matter it can interact with, and whether tachyon can interact with which type of matter.
However if there are more than one tachyon particle, there then it can be hypothetical tachyon wave and field of such tachyons.
In relative relationship with MathML and LaTeX formula generators at wiris.com:
E=\;m\ast c^2\;=\;E\;=\;\frac{m\ast c^2}{\sqrt{1-v^2/c^2}}
And in one case the solution is v = 0 m/s.
The steps for solution are at: this link at symbolab.com.
In this proposal solution it is not clear whether hypothetical tachyon particle exists, if yes, which mass and type of mass it has and whether it interacts or not with which type of matter.
So if hypothetical tachyon particle speed is 0 m/s and in other words it does not move, and its definition is a tachyon is a hypothetical particle that always travels faster than light, then those two statements sounds like a contradiction. If to measure from the point of view of the photon in vacuum and to assume that the tachyon is hypothetically rather static and it has own coordinate system (also as well whether tachyon still moves in the opposite direction of the photon movement direction as of https://uk.wikipedia.org/wiki/Екзотична_матерія#Уявна_маса and https://en.wikipedia.org/wiki/Tachyon#Mass as of 2020-04-21), then such representations hypothetically suffice sometimes.
Another thought experiment which does not prove the previous statement.
A photon from the surface of the Sun takes about 8 minutes and 20 seconds for it to reach the Earth. In the mean time I recall the Sun and the Earth and the travel in between them in faster than 8 minutes and 20 seconds and I am not moving during this period relatively unless other biological processes do. So such recalling act is hypothetically faster in its speed than light. I do not know whether I have operated in hypothetical tachyon field while recalling those objects, moreover they are memories not up to date and they are knowledge, while the photon travels in its real time both encountering two objects.
