Mathematicians Extend Einstein's Special Relativity Beyond Speed of Light

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.'"

Comments

The challenge of getting past c

[Martin Blank]

As I understand it from reading a few other articles, there still exists the challenge of getting past the barrier of infinite energy required to even match the speed of light. Perhaps there will be found a way to tunnel past it, but I expect that while all the math may work neatly, actually breaking through is going to be nearly impossible. Then there's the problem of slowing down which means tunneling back through the other way.

Much as I've been warned off by the articles that claim the paper to be fairly impenetrable to non-mathematicians, I'm tempted to pay the $30 to get the article anyway.

Re:The challenge of getting past c

[Charliemopps]

But the mathematics do not work out neatly. They just skipped a whole bunch of math where E = infinity and broke their equations and went strait to "Now we're losing mas as we accelerate! Neat! Forget that whole "We just consumed all the energy in the universe and collapsed into a blackhole business back there!"

Re:The challenge of getting past c

[lister king of smeg]

so the speed of light barrier is where the universe throws a divide by zero error, and things like tachyons are where the universe says fuck it lets do it anyway. maybe this math is for explaining how tachyons can get a way with saying fuck you to the math.

Re:The challenge of getting past c

[Anonymous Coward]

Tachyons probably don't exist. No one even has a way to find them yet if they do. People seem to hear about them and assume they do exist, but they are just a prediction dependent upon string theory being correct. It isn't even testable in theory (yet) . Since it isn't provable yet, it isn't really science, just a neat thought experiment.

Re:The challenge of getting past c

[ceoyoyo]

You'd think they were quantum theorists!

Seriously, theoretical physics has a LOT of "well, what if we didn't have that little problem...." Quantum mechanics has lots of awkward infinities that end up getting explained away (and lots more we hope will get explained away someday).

Re:The challenge of getting past c

[starless]

This is sort of like the idea that there are temperatures less than absolute zero. These would be negative kelvin temperatures.

The idea being that 0k means 0 energy, you would then have anti-energy, possibly anti-matter, and anti-physics.

Of course it's all just hokum, but hey, it's fun to theorize.

Negative absolute temperatures are fine. You just get a population inversion, such as in the case of lasers.
http://en.wikipedia.org/wiki/Negative_temperature

Re:The challenge of getting past c

[ldobehardcore]

String theory has a few testable predictions, but they would require particle accelerators the size of the solar system eating a whole Jupiter's worth of mass-energy every second they're running. And even then it would be testing only the string theories that have been found out mathematically to be wrong for our universe.

Re:The challenge of getting past c

[Grishnakh]

We're not talking about cars here, where you have to smoothly accelerate from a slow speed to a fast speed. Maybe there's a way to "jump" into this "hyperspace" realm and instantly be traveling FTL. Notice the way they did it in the recent Battlestar Galactica series; there was no "warp speed" there, only jumps of a limited distance. No one's walking around the ship during that time, they just disappear one place and reappear another, possibly by traveling at an absurdly-high FTL speed through a realm where physics are quite different.

Now obviously, figuring out how to shift into hyperspace is going to be a major challenge, but maybe before long we'll learn enough about exotic matter to be able to do such a thing.

Re:The challenge of getting past c

[Sentrion]

Presumably, any attempt to surpass the speed of light would required taking actions that will likely kill you. But if you succeeded you would be in a completely separate alternate universe. Since religion has taught us for millenia that you pass on to an alternate universe when you die, maybe the ancients were on to something. Since spirit beings would have zero mass they could theoretically, if they existed, shift into hyperspace. Test pilots just better hope there's a physical being on the other side to serve as a host body. I'm still waiting for the Heaven's Gate explorers to send back their message to let us know if they succeeded or not.

Re:The challenge of getting past c

[GerryHattrick]

I thought the speed of light was 'instant', for an observer sitting on the photon. The photon has no mass, which is why it's at c. And being at c, time dilation means there is no 'time' between departure and arrival (for that observer only). How do you go faster than that? (Or, what's wrong with my oversimplification?0

Re:What about the speed of information?

[Charliemopps]

Yes they have. It's the speed of light.
The speed of information and the speed of gravitational force were both predicted by Einstein.
The speed of information was proven rather quickly there-after in experiment. You'll have to wikipedia it for details because they escape me.
The speed of gravitational force was proven recently. Maybe in the 90s? I believe by measuring some gravitational lensing effect the sun had on stars just past its horizon or some-such. I don't remember the specifics. But if the sun vanished right now, it would take 8 minutes for the earth to stop orbiting and shoot off into space.

The speed of universal laws? I'd think that would fall under information... irrelevant however, as everything obeys the speed of light.

Re:What about the speed of information?

[tibit]

Because you made up a problem where there's none, that's why. Speed of gravitation is simply how fast change propagates. You wiggle something here, it makes wiggles on something somewhere else, but later. This doesn't preclude steady state. A gravitational potential well doesn't need a round trip to begin to affect something. If an object comes into being in a potential well, it is immediately under the action of gravitation of the central mass in said potential well. It will, alas, take light time for the effect of the object's being to affect the central mass, and whatever effects that had to propagate back. Same goes for a potential well in electric field, etc. Yes, there will be photons or gravitons that carry out the interaction, but if my outsider understanding is any good here, don't forget that those carriers are created on a whim, and their creation or destruction is all that you need for an interaction to occur.

There is only one speed: c

[qbitslayer]

'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.

Actually, the exact opposite is the truth: nothing can move faster or slower than c. It is an illusion that objects move slower than c. Motion is discrete and consists of discrete jumps at c interspersed with huge numbers of discrete wait periods. This is true regardless of how smooth you think motion is. Why is c the only possible speed? For two reasons:

Firstly, a time dimension is illogical. Why? Because a time dimension makes motion impossible? Why? Because it is self-referential. This is the reason that Karl Popper compared Einstein to Parmenides and called spacetime, "Einstein's block universe in which nothing happens. Surprise! So in order for an object to move at different speeds, nature would have to calculate temporal intervals, which is impossible.

Second, the universe is necessarily discrete. Why? Because a continuous universe would lead to an infinite regress.

Read Physics: The Problem with Motion for more if you're interested. Believe me, you don't understand motion especially if you think you do. The truth is weirder than fiction.

Re:What about the speed of information?

[Jack9]

> Yes they have. It's the speed of light.

> But if the sun vanished right now, it would take 8 minutes for the earth to stop orbiting and shoot off into space.

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html

There's a number of competing models which fit existing data.

http://scienceblogs.com/startswithabang/2010/08/25/what-is-the-speed-of-gravity/

See the closing paragraph referencing LISA ~ 2030 A.D.

The real way to measure the speed of gravity is to detect and study gravitational waves. By comparing the arrival of a gravitational-wave signal with that of an electromagnetic signal from an astrophysical source, one could compare the speed of gravity to that of light to parts in 10^(17).

As I understand it, we're still waiting to find out if gravitational waves/radiation propagates at the speed of light.

Zitterbewegung

[Roger W Moore]

Interestingly enough, while the OP is clearly not playing with a full deck, there is a phenomenon know as Zitterbewegung which is very similar to what the OP was suggesting. However this behaviour is suggested by free-particle solutions to the Dirac equation which is firmly grounded in both special relativity and quantum mechanics.

Essentially the solutions suggest that e.g. an electron may propagate by jittering back and forth at the speed of light such that the velocity averages out to the expected value. The frequency of this jittering is of the order of 10^21 Hz and so it has never been experimentally observed but it is, nevertheless, an interesting possibility. Sometimes reality is stranger than even crazy people think!