Outside the box: Einstein's Special Relativity works inside the smallest square.
The University of Adelaide researchers have extended the mathematics
to a world beyond Einstein's limit. Image provided by Professor Jim Hill
Posted on 10/10/2012 10:41:01 AM PDT by ShadowAce
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.
Outside the box: Einstein's Special Relativity works inside the smallest square.
The University of Adelaide researchers have extended the mathematics
to a world beyond Einstein's limit. Image provided by Professor Jim Hill
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. ®
Yes!
Well, the way I’m conceiving of it, it would be something like the tidal effect. If you had two moons, we might have more than two tides per day, but we’d still have the same number of tides all over the planet, because the tides would be due to the net effect of both moons together.
“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”
Indeed, if there are more than 4 dimensions, then traveling in the direction of a higher dimensional axis could lead to instantaneous motion across distances in the lower dimensions, looking like infinite velocity. Yet, we wouldn’t have to accelerate; just make a turn in a direction that to an observer, would be “imaginary”.
Light can not escape the black hole because time has slowed down from the observer's point of view.
ME: "Does your question also include you? "
YOU: Yes!
If I interpret your comments in their proper context, what YOU are saying is that not even YOU really know what, who or how the universe was created......
Forgive me, I'm just being contentious. I'm still struggling with the belief in a God that supposedly created the universe with a big bang.
When it comes to religion, I am admittedly ignorant so I don't know how to put it into words but for everything there has to be a beginning and ultimately an end. And if the Big Bang was created by a God, wouldn't that God also have a beginning?
In other words, what created God and why shouldn't we question where HE came from?
If you were in a spaceship traveling at (just below) the speed of light and turned on the headlights the illuminated scene would look perfectly normal to you. To an outside viewer, however, the headlight’s photons would barely be making it out of the filament (or equivalent spaceship light emitter).
I am here at Hanford but with no special access to LIGO. Where are you getting the above information? LIGO has not yet detected a gravity wave much less measured its speed.
You ask an excellent and deep question! Rather than give
an answer I might believe, I am going to ask my Pastor today before responding to You. Thank you, I need to ponder this further before responding.
This is my belief, and I do not have any readily handy information to back this up:
God is Eternal. He is the Beginning and the End. Nothing made God as He has always existed. This concept is difficult for us to understand as we exist within Creation.
(Think about the relationship of this discussion to our discussions on "God's 'Universal Now'")...
["Catch-up" FReepmail in the works...]
Looks like a photon torpedo.
True only if "this" is all there is.
If c is the maximum detectable speed given our tech, then could it be going c+, but we just cannot measure it?
Great insight, Boogieman! Indeed, I suspect there are more than four dimensions.
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).
Here's another example to think about, namely knot theory and the unreasonable effectiveness of mathematics in the natural sciences.
I for a long time have tended to believe, at least ask/question, the possibility that the accepted speed of light is not a universal descriptor for any and all phenomena/happenings in the totality of the universe. I am a strong admirer of Einstein and his perceptions. However, when I think of the vast expanse of the universe which has yet to be fully known and to accept a human derived, local expression/factor for this vast unknown/undefined existence seems it might be a bit to much. Obviously, the use of a constant speed of light in our frame of reference has proven very useful to exploring ‘nature’. It might be that the simple mathematical relationship is usable in the sense the value of units used are what changes in outer universe. For example, What we use as a ‘meter’ or a ‘second’ are only relative to our restricted space and knowledge.
The above quoted from your link! I just loved the idea of mathematics as the "torch" that scientists use to light their way forward, the "active effectiveness" aspect.
An example of "passive effectiveness" might be Reimannian geometry — a species of non-Euclidean geometry developed by Hermann Reimann in the nineteenth century without any particular practical application in view. But then later on, Einstein picked it up "off the shelf," as it were, and employed it in the development of his theories of relativity.
Also at your link is a link to another interesting article on the Fibonnaci series — a numerical series that appears to be firmly embedded in the natural world; e.g., the branching points on stems, the "packing" plan of seeds on a sunflower seed head, et al.
Truly the "unreasonable effectiveness of mathematics" is amazing!
Thank you so very much dearest sister in Christ for the link, for your deep interest in this subject, and for your kind words of support!
I'm a Christian and viewing what we can see of the universe fills me with awe and wonder. We live in a fantastic universe the Lord has made.
One of the reasons I doubt the speed of light is an ultimate limiting speed is because I just find it hard to believe that all of that wonderful stuff that is a part of our creation is effectively out of our reach as a species. I take it as an article of faith. I may be right or wrong about this, and as the Bible is silent about it, I don't think it hurts us any at all to dream of what might be.
In other words, what created God and why shouldn't we question where HE came from?
You're asking a question that doesn't make sense when you think about it. Before there was a universe, there was no such thing as time. Without time, there is no concept of beginning or end. God exists outside of time, which is one of the reasons he is omniscient. He can see the whole of time at once, in the same way that you can see a book that has a beginning, middle, and end at the same time. We live inside the book so we can't see it in the same way.
On a side note, without time, causality is broken as well, because you need time or duration to have a cause and effect. In other words, since God exists outside of time, he could have created himself, because that wouldn't violate a causality that doesn't exist.
String theorists postulate at least 11 dimensions.
Then again, I'm one of those who thinks string theory isn't even wrong.
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