A possible uncrossable boarder between bradyons and hypothetical tachyons

[Willowz]

A possible "uncrossable" boarder between bradyons and hypothetical tachyons...

I would like to ask about a correlation between baryonic matter and hypothetical tachyons.

(For ordinary bradyonic matter, E increases with increasing velocity, becoming arbitrarily large as v approaches c, the speed of light.) Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, since to reach the barrier from either above or below requires infinite energy.

From this I assume that there is a barrier between the highest speed a bradyon can achieve(infinetly close to c) and the lowest speed a tachyon could achieve(?)...

the speed of a tachyon increases as its energy decreases") and ("the speed of a bradyon increases as its energy increases")

So from the above I could assume that for the bradyon: v~e, and for the tachyon v~1/e. I'm not great at maths or physics, but could someone help me equate the two. Or maybe it would be better to equate e=mc^2(bradyon) and e^(-1)=mc^2 ?(tachyon)...but now I think we would need complex numbers. :( Thanks for any help
Maybe it's just c that can't be achieved by anything other than light?

 

[Willowz]

Maybe the sub-forum is wrong. Could a mod move this topic into "Particle Physics"?

 

[JesseM]

I think this is the right forum, since tachyons aren't part of any mainstream particle physics model, they are a hypothetical idea from relativity. It's assumed that for both bradyons and tachyons, the total energy is given by the formula $$E = \gamma mc^2$$ (which is another way of writing the relativistic equation $$E^2 = m^2 c^4 + p^2 c^2$$, where p is the relativistic momentum $$p = \gamma mv$$...the formula E = mc^2 is only intended to apply in a particle's own rest frame, for particles which aren't at rest you need an expanded equation which includes the kinetic energy due to motion). However, since the relativistic gamma factor $$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$ becomes imaginary when v > c, it is assumed that in order for tachyons to have real-valued energy and momentum, their rest mass m must be imaginary (see this page). You can see that with this assumption, E in the equation $$E = \gamma mc^2 = \frac{mc^2}{\sqrt{1 - v^2/c^2}}$$ can be a real number (since imaginary * imaginary = real), and its value approaches infinity as v approaches c from above.

 

[Willowz]

Thanks for the reply. I wanted to ask. If bradyons can't achieve c, and tachyons can't achieve c. And only light can move at c, then is it possible for one of the two to ever "jump" over this barrier of c? What is stopping them from doing so? Thanks for any replies.