Tachyon - assymetry between space and time

[Dmitry67]

Say, we have empty flat spacetime; there is a lab frame and 2 particles - bradyon and tachyon. While movement of bradyon is stable, tachyon is believed to lose energy because of Cherenkov radiation:

http://en.wikipedia.org/wiki/Tachyon#Cherenkov_radiation

if it is charged and even if it is not (gravitational cherenkov radiation). So there is an intristic assymetry between timelike trajectories of bradyons, which are stable, and spacelike trajectories of tachyons, which are not.

However, the metrics itself, if we take 2-D space is symmetric between space and time:

s^2 = r^2 - t^2

Question:
Is the symmetry I described above an indirect result of having more spatial dimensions than time dimensions (3 vs 1), or you need some extra assumptions (like arrow of time) to explain it?

 

[Bill_K]

Tachyons were once an interesting idea, but they quickly ran into logical inconsistencies. Not the least of which: if a particle can travel faster than light, then in another rest frame it has energy E < 0. This makes the vacuum unstable. It can and will create an infinite number of tachyons, leading to catastrophe.

 

[Dmitry67]

I know. But the question is - what part of GR (or EM) equations makes spacelike trajectories unstable, while timelike are stable.

 

[Bill_K]

Hm, well I guess from a mathematical point of view, the thing that makes bradyons physically possible in Minkowski space is that the interior of the light cone has two disjoint parts, and you can't go continuously from the future part to the past part without stepping outside. Or equivalently in momentum space you can't go from positive energy to negative energy. The problem with tachyons is that you can do this.

So the condition is that you must have time one-dimensional, or else you could rotate continuously from +t to -t and that would make even bradyons unstable.

 

[Dmitry67]

Bill_K, thank you,
you had even answered by another question here: https://www.physicsforums.com/showthread.php?t=489566

 

[HallsofIvy]

"Bradyon"? Do you mean "Baryon"?


(Obviously, a "Bradyon" is the elementary particle from which the "Brady Bunch" was created!)

 

[Dmitry67]

Bradyon - particle moving at v<c
Opposite to tachyon.

 

[JesseM]

To derive Cherenkov radiation we need either classical electromagnetism or quantum electrodynamics, but you restricted your question to a universe with 1 spatial dimension and 1 time dimension (since obviously there is an asymmetry in how light cones look if you have more than one space dimension), wouldn't we need to know what the analogues of these theories would look like in a 1+1 universe to answer the question? If we had a set of equations we could see whether they are asymmetrical if you exchange time and space, but electrodynamics might look quite different in a 1+1 universe, I wonder if the concept of electromagnetic waves would even make sense here (and if not then Cherenkov radiation wouldn't exist either)