Mathematicians at University of Adelaide say they’ve generalized the Theory of Special Relativity to include faster than light speeds up to infinite relative velocity. My question is how does this differ from the old theory of tachyons? What exactly does the new theory predict if FTL was possible?
Bumped because I’d like to know as well and I’m subbing to the thread.
It doesn’t seem to differ at all from what I can tell. It’s always (well, since Einstein) been known that the math works for speeds faster than light. The problem is that crossing that barrier requires infinite energy.
This article doesn’t seem to say anything different other than Hill’s claim that he doesn’t accept c as being an insurmountable barrier. That’s simply a claim with nothing in the article to back it up.
Actually, the way I read the Huff-piece, Hill does seem to accept c as an all but insurmountable barrier. The way it is depicted, FTL is possible, in a realm where the basic rules of special relativity are effectively inverted, but objects with mass at c are still out of bounds. It takes infinite energy to accelerate to c, but if you pass into FTL, it then takes infinite energy to slow down to c. IOW, nothing particularly useful here, just a theoretical mirror image.
http://rspa.royalsocietypublishing.org/content/early/2012/09/25/rspa.2012.0340.short?rss=1
So the big deal, such as it is, is that the transformation avoids imaginary mass. Don’t have a subscription so can’t see any more to it.
My recollection is that tachyons only had imaginary rest mass, but of course they were never at rest. Their “relativistic” (for want of a better word) mass was always positive. Criticizing imaginary rest mass for tachyons is a bit like criticizing the use of imaginary numbers in Schrodinger’s equation. Nothing real was ever imaginary (Pun intended). But then I could be wrong. It’s been very long since I was a Physics major.
It may be that the infinite velocity mass always had to be zero in the tachyon model as that abstract seems to imply.
OK I was able to open the pdf paper and here is a brief description:
The Einstein mass energy velocity relations are:
m = m[sub]0[/sub][1 - (v/c)[sup2[/sup]][sup]-1/2[/sup] and E = mc[sup]2[/sup].
The original tachyon formulation is (I think)
m = p[sub]inf[/sub]/c[1 - (v/c)[sup2[/sup]][sup]-1/2[/sup] and E = mc[sup]2[/sup]
where p[sub]inf[/sub] is the finite momentum at infinite velocity requiring that the mass at infinite velocity is 0.
Their new proposal includes the possibility
m = m[sub]inf[/sub]v/c[1 - (v/c)[sup]2[/sup]][sup]-1/2[/sup] and E = m(c[sup]2[/sup]+v[sup]2[/sup])/2 - m[sub]inf[/sub]c[sup]2[/sup]cosh[sup]-1/sup + E[sub]0[/sub]
where m[sub]inf[/sub] is the non-zero mass at infinite velocity and E[sub]0[/sub] “is an arbitrary constant.” They note that there is no limiting Galilean relation to pin down m[sub]inf[/sub] and E[sub]0[/sub] as there is in the sub-c realm where we want the rest mass to match observations and get the kinetic energy limit m[sub]0[/sub]v[sup]2[/sup]/2.
The basic idea is to use a local transformation, i.e., a derivative and then apply boundary conditions to the differential equation. For v < c, the boundary conditions are obvious, the world must be Galilean in the limit. But there is no obvious bounday condition for the v > c realm.
I thought the deal was that in the Tau equation, the denominator is cc -vv which goes to zero at v=>c, meaning it is mathematically impossible. 
I dropped third semester Physics over the Schrodinger equation, but dreamed in trig transforms in dif e. And had Schrodinger come up again in grad school.
This is neither new nor interesting, unfortunately. Vieira has discussed the same transformations, and also given the reason why they only apply in a 2-dimensional universe (with one time and one space dimension), and can’t be generalized to the realistic 3+1 dimensions of our universe (only to cases in which there are as many time as there are space dimensions). Basically, the trick is that one exchanges the spatial and timelike dimensions – which is of course only possible if there are equally many of each.