In Theoretical Mathematics, Breaking The Speed Of Light Is Easy
    By News Staff | October 14th 2012 05:00 AM | 14 comments | Print | E-mail | Track Comments
    In a pinch and need to go back in time or flee to Alpha Centauri in a hurry?  Find a mathematician, quick!

    If only Einstein's theory of special relativity were extended to work beyond the speed of light, things would be easy.   But of course Einstein's theory holds that nothing could move faster than the speed of light. Special Relativity was published in 1905 and explained how motion and speed is always relative to the observer's frame of reference. The theory connects measurements of the same physical incident viewed from these different points in a way that depends on the relative velocity of the two observers.

    Professor Jim Hill and Dr Barry Cox at the University of Adelaide say they  have developed new formulas that allow for travel beyond this limit. "Since the introduction of special relativity there has been much speculation as to whether or not it might be possible to travel faster than the speed of light, noting that there is no substantial evidence to suggest that this is presently feasible with any existing transportation mechanisms," said Hill. "About this time last year, experiments at CERN, the European centre for particle physics in Switzerland, suggested that perhaps neutrinos could be accelerated just a very small amount faster than the speed of light; at this point we started to think about how to deal with the issues from both a mathematical and physical perspective."

    Really, that is all a mathematician needs.  Everything else, like the actual universe, is a pesky detail left to physicists.

    "Questions have since been raised over the experimental results but we were already well on our way to successfully formulating a theory of special relativity, applicable to relative velocities in excess of the speed of light," says Hill. "Our approach is a natural and logical extension of the Einstein Theory of Special Relativity, and produces anticipated formulae without the need for imaginary numbers or complicated physics."

    Their formulas extend special relativity to a situation where the relative velocity can be infinite, and can be used to describe motion at speeds faster than light.

    "We are mathematicians, not physicists, so we've approached this problem from a theoretical mathematical perspective," said Cox. "Should it, however, be proven that motion faster than light is possible, then that would be game changing. Our paper doesn't try and explain how this could be achieved, just how equations of motion might operate in such regimes."

    So don't plan on re-enacting that "Loopers" movie just yet.

    Published in Proceedings of the Royal Society A


    Wherher the hyothesis of the existence of faster than light is compatible with special relativity was first investigated in the most-cited paper in the American Journal of Physics was investigated by E.C.G. Sudarshan and his colleagues O.M.P. Bilanuik and V.K. Deshpande a full 50 years ago, in the October 162 issue of the journal. Under the assumotuions that energy is always positive-definite and that the laws of physics are the same for all inertial frames as the credo of special relativity maintains, they were able to show by an insightful physical analysis that such a hypothesis can indeed be maintained without running afoul of special relativity.. An essential ingredient of their theory was the 'reinterpretation principle'. Hill and Cox make out that their paper was the first to have sought consistency with relativity theory and that as applied mathematicians, they did not really bother tioo much about physics. That is decidedly weird as the theory of faster than light pariticles is an inalienable part of physics and before venturing into territory that is professedly unfamiliar to them, the least they could have done is to acquaint themselves with the landmark papers in the field. Had they done so, they would not be in the invidious position of doling out hallf-baked formulae in the forlorn hope that the darts they hurl in the darkness might somehow hit th bull's eye, Such desperate measures were not called for, unless they have a calculated disregard for theoretical physics for reasons best known to themmselves.

    Some typos escaped my notice. In the first line,
    first word should read 'Whether'
    after 'faster than light' insert. particles', delete 'was investigated'
    after 'American Journal of Physics'
    after 'October' change the year to 1962

    Incidentally, this paper was published in 'E.C.G. Sudarshan - Selected Scientific Papers' ed. Ranjit Nair, Scientia CPFS, New Delhi 2006 (pp 157-162).

    Tony Fleming
    "Really, that is all a mathematician needs. Everything else, like the actual universe, is a pesky detail left to physicists." 

    Then we discovered inflation at the start of the Big Bang with its .superluminal expansion and so..........

     "Really, up to inflation, that is all a ohysicist needs. Everything else, like the actual universe, is a pesky detail left to mathematical physicists."
    I seem to recall Einstein and Heisenberg had a conversation about theory and observation similar to this.
    Tony Fleming Biophotonics Research Institute
    The reason theoretical physics gets so little respect these days is because those guys are invoked to legitimize any and every crackpot idea. All it takes is mathematical sleight of hand. There is nothing even remotely close to a hypothesis in what they say; it is basically 'okay, we have what we do now, and then an infinite black box, and we can go faster than light.'

    "Our paper doesn't try and explain how this could be achieved, just how equations of motion might operate in such regimes" translates to 'there is no point in reading this paper'.
    Tony Fleming
    In the contect of the article by the two Aussies, that's all very well; but what about cosmological inflation? Do you trust Guth's work and all the subsequent work on inflation theory that basically says superluminal expansion was an early part of the Big Bang?
    Tony Fleming Biophotonics Research Institute
    I wonder though, if this is testable. We can't make objects go faster than light, but we can make a spot of light move faster than light, depending how we move the source.

    All these equations do is express the relative motion of super-luminal things. Would it be possible to exploit things like light spots? Maybe... longshot.

    It would help if I could look at the paper, or if it were not behind a firewall.

    Einstein's theory holds that nothing could move faster than the speed of light. Special Relativity was published in 1905 and explained how motion and speed is always relative to the observer's frame of reference.
    Nonsense! You do not counter nonsense with more nonsense. Relative velocity has been relative long before Einstein. Einstein's theory holds that one cannot continuously accelerate and thus reach lightvelocity in any Einstein-ether, which is called Einstein-ether, because Einstein thought about those first, not crackpots. The question of whether the ether is all there is, thus making it a fundamental, abstract space-time, is entirely beyond the reach of that theory! Whether cosmological reference frames (CMB) are "absolute" or particles can travel outside of the ether (and thus faster than the light inside the ether) is not part of Einstein's theory, because it is a theory that holds for low energy phenomena accessed from inside an Einstein-ether. What about Science2.0 wisens up to this after somebody here has written plenty of articles explaining these trivialities?
    If you have something reasonable to say against that Proceedings of the Royal Society A article, say it, otherwise, this article is mere anti-scientific kneejerk defense of long proven idiotic doctrines. Relativity is not a religion.
    The fact that it is possible to even formulate a mathematically consistent theory of FLT travel that meshes well with special relativity, even if the speed of light speed limit happens to be an absolute rule of nature and this is merely an intellectual exercise, is interesting in and of itself. It illustrates aspects of the deep mathematical structure of GR that may be important as one tries to sieve through different proposals for quantum gravity theories.

    One of the really impressive aspects of a lot of quantum physics is how many of its pieces have no mathematically consistent alternatives, or only a finite and very small number of mathematically consistent alternatives. Theory space only looks infinite from a distance.

    For example, given the existence of quark confinement and the fact that all physically observed particles have integer electric charges, there are very few sets of quantum numbers for fundamental particles and very few numbers of color charges that are theoretically possible.

    Johannes Koelman
    <nitpick> I am puzzled by the term "theoretical mathematics" in the title. Seems a tautology. You mean "theoretical" as opposed to "experimental"? Is there such a thing as "experimental mathematics" (drawing circles and measuring pi, anyone)? 
    The more common terms are "pure" versus "applied mathematics". Although probably unrelated to any physical reality (paper is behind paywall, so haven't read it, and can't judge), the stuff discussed here would fall under "applied mathematics". </end nitpick>
    Tony Fleming
    "While special relativity constrains objects in the universe from moving faster with respect to one another than the speed of light, there is no such constraint in general relativity." 
    This clarification is needed within the confines of this discussion. The distinction between SR and GR is important when it comes to understanding superluminal cosmology as below. 

    Figure 1. First instant and early stages of Big Bang.

    Tony Fleming Biophotonics Research Institute
    Faster than light is possible if we could understand special relativity according to quantum theory

    Right, which is basically the same thing as saying 'if physics did not exist'.  This same statement could have been made 100 years ago and we would be no closer to understanding how to do it or anything about how to do it.
    Taking just a cursory glance at the article, it looks like their transformations are the same ones considered also by Vieira in If so, then their work isn't relevant to the physical universe in any way, because they work only in 1+1, or generally n+n, dimensions; essentially, the possibility to swap space and timelike dimensions is exchanged for the need to introduce imaginary masses for superluminal particles in ordinary SR.

    Tony Fleming

    As a  bioeffects researcher for several decades now, let me discuss what is happening within the human body which is pertinent to the present discussion. I think we can all agree that the human body is 'within the universe'.

    The body is assumed to be an electromagnetic object. To calculate the electric and magnetic fields within a numerical model of the body we take the measured values of the constitutive parameters, the dielectric permittivity (a complex parameter), and the magnetic permeability, for each organ or tissue. We then use Maxwell's equations to determine the field levels within the body for a given situation, for instance, a mobile phone held near a model of the head.

    Bioeffects workers need to know the speeds within various media to calculate where minima and maxima are within the body. Now since the constitutive parameters within all tissues and organs are not those of free space but are numerically higher, we find that the speed of the electromagnetic fields (light) within the body can be different to the speed of light in free-space. 

    When Maxwell put the constitutive parameters of free-space into his equations in the 1860's he discovered that the speed of the wave was very close to the then known speed of light in free-space. This was what enabled him to unify electromagnetism and light.

    When Einstein was researching relativity some time later in1905 he was interested in free-space domains, or the 'vacuum of deep space' sohe could investigate the relativity between speeds on Earth or in the deep space between planets, and later as we know he went on to think about gravity and cosmology. 

    SR is thus a special case where 

    It must be stressed that this was a mathematical approximation to get around the enormous numerical problems of having a heterogeneous mathematical domain.

     The intent of this article seems to have been to pour scorn on mathematicians who dared to think about FTL. But it was Einstein who was the initiator of the approximation that remains SR. In fact it is well known that Einstein was NOT apriori a mathematician.  It is astonishing to realise that he invented both SR and GR with the assistance of others who helped with the mathematical details along the way, an amazing achievement for someone who was originally not a mathematician. 

    Tony Fleming Biophotonics Research Institute