## Mathematicians Extend Einstein's Special Relativity Beyond Speed of Light 381

Hugh Pickens writes

*"The Christian Science Monitor reports that despite an apparent prohibition on faster-than-light travel by Einstein's theory of special relativity, applied mathematician James Hill and his colleague Barry Cox say the theory actually lends itself easily to a description of velocities that exceed the speed of light. 'The actual business of going through the speed of light is not defined,' says Hill whose research has been published in the prestigious Proceedings of the Royal Society A. 'The theory we've come up with is simply for velocities greater than the speed of light.' In effect, the singularity at the speed of light divides the universe into two: a world where everything moves slower than the speed of light, and a world where everything moves faster. The laws of physics in these two realms could turn out to be quite different. In some ways, the hidden world beyond the speed of light looks to be a strange one. Hill and Cox's equations suggest, for example, that as a spaceship traveling at super-light speeds accelerated faster and faster, it would lose more and more mass, until at infinite velocity, its mass became zero. 'We are mathematicians, not physicists, so we've approached this problem from a theoretical mathematical perspective,' says Dr 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.'"*
## Did you take any science courses at all? (Score:5, Informative)

Anybody that took any science classes knows that the equations work fine as long as v != c. Just like I can get negative frequencies out of a fourier transform. The math works, but that doesn't mean I have actual, physical negative frequencies.

## Re:imaginary mass (Score:5, Informative)

If you just read the abstract to TFA you can see that the claim here is less novelty than the press release makes it sound like (the press overplays things - SHOCKER! ;-). They are really only presenting an alternate derivation without using mass of long-known results related to tachyonic physics and virtual particles and so forth.

Now, I am personally a bit dubious this is the first time the alternate derivation has been done, but I havne't read their particular approach. One would hope any reviewers assigned to the paper would have done reasonable due diligence/homework about the particulars (though sometimes that hope is in vain).

## Re:What about the speed of information? (Score:4, Informative)

Speed of information = speed of light (this is well known).

Speed of gravitation = speed of light (this is also well known).

"Speed of universal laws" is not a question that makes sense. "This isn't right. This isn't even wrong." -- Pauli (And the quote is well known).

## Re:imaginary mass (Score:3, Informative)

## Tachyons (Score:5, Informative)

I don't think there is much new here, several tachyon papers have trodden down this road before (e.g., http://arxiv.org/pdf/1112.4187v2.pdf [arxiv.org]).

If they somehow have figure out how to extend the lorentz transform for v > c in 4 dimensional space (vs 6 dimensional space as asserted in the above reference paper to void imaginary distances), that would be something.

Unfortunatly, I haven't found a way around their paywall (yet) to see what they are up to...

## Re:Tachyons (Score:5, Informative)

## Re:Infinite velocity (Score:5, Informative)

Some parts make sense: At infinite velocity, a particle would necessarily pass through every point in the universe.

Actually that happens at the speed of light: to a photon moving at the speed of light, time has stopped completely and the universe is forsehortened from a 3D volume to a 2D plane - so effectively the photon is at every point along it's path "at once", at least from it's point of view.

## Re:What about the speed of information? (Score:4, Informative)

A black hole doesn't "pull in light". Rather it bends space time to such an extreme that light travelling in a straight line does not exit the event horizon, because space time has "bent back on itself".

## Re:The challenge of getting past c (Score:3, Informative)

False. They were always testable, the ability to perform the test might be lacking, but that is two different things. As far s I know, string theory isn't even testable in theory.

## Re:Did you take any science courses at all? (Score:5, Informative)

When you use a fourier transform to put a signal into frequency domain you end up with positive/negative components. If you then bandshift, the negative component becomes positive and will actually exist when broadcast. But only the positive part is actually a physical thing. It's... weird.

This is one interpretation, and taught by some professors who think students can handle weirdness better than complex arithmetic, but it's much more elegant to deal in complex signals, where the negative- and positive-frequency elements are conjugates and sum to exactly the real signal.

Once you understand this, Fourier transforms will stop being magic crap and start making sense.

## Re:The challenge of getting past c (Score:5, Informative)

Special Relativity was immediately testable. In fact, one of the tests for its predictions turns out to be the Michelson–Morley experiment, which was first performed in 1887 before Special Relativity was even a gleam in Einstein's eye. The M-M experiment was refined repeatedly during the period that Special Relativity was first discussed (1905-06) to focus on testing one of SR's basic predictions, so a test of at least one of special relativity's predictions existed by publication date.

General relativity was immediately testable by measuring the Perhelion precession of Mercury. It was also possible to test it by observing solar bending of starlight any time there was a total solar eclipse. Yeah, you couldn't do that on the day of first publication because there wasn't a solar eclipse that day, but the researchers knew there would be total solar eclipses in the future and could set up to test the theory as soon as one happened. But, suppose they had had to wait until the next eclipse after that, or something? Do you really want to advance the claim that a theory isn't scientifically testable if a human event such as a war keeps the observers from getting to the location where it could be tested? Or if cloudy weather blocked observing? That nearly happened.

Normally, the rule that it isn't science if it doesn't make testable predictions doesn't mean that something becomes unscientific if there are budget cuts or other such events that aren't themselves part of the scientific method.

## Re:There is only one speed: c (Score:5, Informative)

Longer answer is, Quantum Mechanics and Relativity don't really fit together. One way to get around this is to impose a minimum amount of various quantities in relativity. If you set the minimum quantum of velocity all the way up to c, that's an admittedly extreme example of such reconciliation. The point is, to get a unified theory, either you take just about all the quantization out of quantum mechanics, or you add quite a bit of quantization to relativity.

Minkowski was the guy who showed Einstein that special relativity implied that the geometry of the universe was 4 dimensional. At first, Einstein though that Minkowski was just doing an interesting math trick, but he soon decided that the real shape of space was a 4 dimensional

inseperablespace-time. Einstein credited Minkowski's work with showing him the first steps to bridge the gap from Special to General Relativity. Unfortunately, Minkowski died in 1909, just three years after he started corresponding with Einstein on Spec. R. . The Minkowski model really is 'static' and 'blocklike' and nothing can really said to be happening, and that's the first place Popper got the idea from. Einstein himself later (1940's-50's) spent lots of time talking to Godel about just that, and if Popper was just a 'philosopher with superficial knowledge of physics', Godel was just the mathematician who Einstein went to when the math got really tough, and who had ready access to the then greatest living physicist in turn. Some of what Godel developed from General Relativity gives abstract geometric models of the whole universe which aren't "Static Block-like", but they also allow for the existence of time travel via 'closed time-like curves'. Godel's interpretation came just shortly before he published mathematical proofs of the existence of God and the Afterlife, and he later died basically from refusing to eat for fear he was being poisoned. Personally, I agree more with Godel's interpretation of the geometry of the whole universe than with Minkowski's, but given all the facts, I'm not going to dismiss Popper (and certainly not Minkowski) as easily as some people here are.## Re:There is only one speed: c (Score:4, Informative)

Actually, photos do have an effective mass (=relativistic mass). You could say that they have no rest-mass, though.

Photos are affected by gravity - light bends around heavy stars, for example: the gravity lens effect.

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html [ucr.edu]