Is lightspeed really a limit?

We don’t (yet) have any way to test this, but University of Adelaide applied mathematicians are suggesting that an extended version of Einstein’s Theory of Special Relativity also holds true for velocities beyond lightspeed.

One of the main predictions of Special Relativity is that the speed of light is treated as an absolute cosmic speed limit, the line which can never be crossed; and even the notorious “faster-than-light neutrino” incident in 2011 has left the theory intact as one of the most robust in physics.

However, during the speculation that surrounded the neutrino discussion last year¹, the University of Adelaide’s Professor Jim Hill and Dr Barry Cox considered the question of how the mathematical contradictions posed by a faster-than-light particle could be aligned with Special Relativity.

Their solution, which Professor Hill discussed with The Register,² rested on ignoring the speed of light’s status as an absolute limit, and instead, using the information where the relative velocity of two observers is infinite.³.

The surprising outcome: with just two assumptions, an extended version of the mathematics for Einstein's special relativity works just as well above the speed of light as below.

“Relativity is about frames of reference,” Professor Hill explained to The Register. That is, observers with different velocities see the same event from different frames of reference.

“Einstein started working from information where the relative velocity is zero – what we knew about, such as rest mass, kinetic energy and so on – and then extrapolated what is known in the Newtonian world for velocities lower than c.

“Our thinking was: how do we make use of the essential essence of Einstein’s theory for velocities above c?”

Mathematically, what the mathematicians assumed is that for infinite relative velocity, there is a fixed relationship between the velocities of the two observers: where u is the first observer’s velocity, v is the second, the product of the two velocities is always c².

“What we have is an equivalent theory [to Special Relativity] that applies for velocities beyond the speed of light. That theory is different from Special Relativity, but it has many of the same characteristics.

And readers with an interest in either physics or maths will be delighted with the vital assumptions: there has to be one, and only one, speed of light; and in all cases, a mathematical singularity occurs at the speed of light.

“If you believe what we’ve done,” Professor Hill said, “there can only be one speed of light in a universe. If there was a second speed of light, our mathematics wouldn’t work. If there is a second singularity [the one that occurs at the speed of light in Special Relativity – The Register] it wouldn’t work.

“This theory and method of solution is dependent on assuming that there is only one speed of light in any universe.”

To get from the theory to any practical test is another matter entirely, and Professor Hill freely admits he doesn’t know how that might be achieved (although The Register notes that the world took half a century to get from the maths of emission of radiation to the laser). He hopes, however, that a test can be devised.

“If you really don’t believe that faster-than-light is possible, then humans will be limited forever,” he said.

Einstein’s special relativity beyond the speed of light has been published in the Proceedings of the Royal Society. ®

A few thoughts from a layman’s point of view: Lightspeed may be the limit in the physical world, but in the spiritual world, travel is apparently instantaneous, i.e., at the speed of THOUGHT.

According to The Gospel of John, Chapter 20, verse 13 and following, on Easter morning Mary Magdalene encounters the Risen Christ.

When Mary falls at his feet in worship, Christ tells her not to hang onto him as he had not yet ascended to Heaven (to present His shed blood before the Mercy Seat). Keep in mind that now Christ is in His glorified spiritual body.

Several hours later Christ appears in a room in Jerusalem where His disciples are huddled in fear of the Jewish authorities. So He has obviously made the round trip in several hours or less. We do not know how long He spent when He got to Heaven, but both legs of the trip were probably instantaneous.

Besides appearing to those disciples that evening, he also (Gospel of Luke) appeared to Mr. & Mrs. Cleopas as they trudged home from Jerusalem to their home town of Emmaus, and He explained the Scriptures and God’s Plan of Salvation to them.

Now I haven’t heared a figure lately, but back in the 80s I heard an astronomer state that with the equipment they at that time they were able to see 12 Billion light years out into space. Assuming that Heaven, if it is not merely in another dimension or in a parallel universe, is 12 billion light years or more away, even at the speed of light and after all these years, Christ would not yet to this day have completed His initial trip TO Heaven, let alone returning to Earth.

Therefore, I surmise that there must be a much greater speed of travel in the spirit world in a spiritual body.

“I don’t see how it would follow that we would all experience the exact same gravitational effects as everywhere else.”

Well, you’re right that the field would lessen with distance, but if every particle in the universe was emitting a gravitational field that had infinite speed, you would see an effect of interference patterns forming as the gravitional fields would be colliding with every other field. The out waves from all the other fields in the universe would be surrounding every other particle as in waves, creating standing wave patterns. Those standing wave patterns would then harmonically resonate with the other standing waves surrounding all the other particles, and eventually, if the universe was old enough for the effect to be fully realized, the gravity would be the same in every location in the universe.

... a scientist thinking that since an equation comes out right, it must faithfully describe the real world.

Well, if mathematics is "God's copyright notice" on the world, then an equation that "comes out right" might very well be pointing to something real going on the the world, but real in a way that cannot be directly observed.

Professor Hill's reconciliation of the problem of a particle (e.g., a neutrino) with a faster-than-light velocity in terms of Special Relativity theory "rested on ignoring the speed of light’s status as an absolute limit, and instead, us[ed] the information where the relative velocity of two observers is infinite."

Once cannot imagine, from the standpoint of ordinary experience, what an "infinite velocity" is. Indeed, "infinite" is a mathematical term that is not ordinarily constructible in physics.

But then, the square root of the number –1 is also not constructible in physical terms. And yet this value, an imaginary number — i — is an extraordinarily useful number in the understanding and mathematical modeling of the real world.

All square roots of negative numbers are "imaginary." As Leonard Euler put it, "...of such numbers we may truly assert that they are neither nothing, nor greater than nothing, nor less than nothing, which necessarily constitutes them imaginary or impossible." [But there they are.]

According to George Gamow,

The family of imaginary numbers represents, so to speak, a fictitious mirror image of the ordinary or real numbers, and, exactly in the same way as one can produce all real numbers starting with the basic number 1, one can also build up all imaginary numbers from the basic imaginary unit [the square root of –1]....

...each ordinary real number has its imaginary double. One can also combine real and imaginary numbers to make single expressions.... Such hybrid forms are usually known as complex numbers.
For well after two centuries after imaginary numbers broke into the domain of mathematics they remained enveloped by a veil of mystery and incredibility until finally they were given a simple geometrical interpretation by two amateur mathematicians: a Norwegian surveyor by the name of Wessel and a Parisian bookkeeper, Robert Argand.
According to their interpretation a complex number, as for example 3+4i, may be represented [as showing that] 3 corresponds to the horizontal distance, and 4 to the vertical, or ordinate.
Indeed, all ordinary real numbers (positive or negative) may be represented as corresponding to the points on the horizontal axis [of a Cartesian plane], whereas all purely imaginary ones are represented by the points on the vertical axis. When we multiply a real number, say 3, representing a point on the horizontal axis, by the imaginary unit i we obtain the purely imaginary number 3i, which must be plotted on the vertical axis. Hence, the multiplication by i is geometrically equivalent to a counterclockwise rotation by a right angle.

My point in getting into this description of imaginary numbers is that it seems possible to me that, like i, "infinite velocity" is also a purely "imaginary" term — and one that might prove highly useful in extending Einstein's special relativity theory, just as imaginary numbers extended and supplemented number theory.

It has become customary to regard the speed of light as the absolute "speed limit" of the universe. But how do we really know this is a fact? We're speeding right along with it, in our own relativistic frames of observation.

In a situation like that, it seems to me mathematics is your friend — for it points beyond what can be ordinarily perceived and directly experienced.

I'm looking forward to seeing how Professor Jim Hill and Dr. Barry Cox manage to integrate a faster-than-light particle into Einstein's theory (assuming they're able to do that, of course).

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.