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. ®
Gravity is a result of the bending of the fabric of space. Unless the graviton particle are proven real ....
so if your on a free falling elevator and jump just before you hit, you will be OK?
I knew it was true!
Looked at from the other direction .... I recently read that Einstein puzzled over "catching up" to a photon. If an observer is traveling at the same speed and in the same direction as a photon, the photon (which is massless) would be standing still. And, if it is standing still and has no mass, there is nothing there. So, he figured, it must not be possible to observe a stationary photon.
What would be the forward speed of the light coming from the flashlight?
This is fun (if mind-bending) stuff, so let me play a little.
Your spaceship cannot be moving at the speed of light, just really close to it. So try this:
Your spaceship is moving at 0.999c and you shine a flashlight forward. Two questions: (1) What speed do you see the light traveling away from you? (2) What speed does someone you fly past see (a) you moving, (b) the light moving relative to that someone, and (c) the light from the flashlight moving away from you?
Answers: (1) You see the light moving away from you at the speed of light. (2a) The person sees you moving at near the speed of light. (2b) The person sees the light from the flashlight moving at the speed of light relative to themselves. (2c) The person sees the light form the flashlight moving away from you at the speed of light, too!
What, makes no sense? How can that be? Without getting into the messy math, time and space distort in ways that make ALL of that happen. Again, as posted up thread, these effects occur at lower speeds, too, and in fact had to be accounted for to make GPS work.
Weirdly enough, that actually makes sense to me.
It is for this reason alone that I do not believe the speed of light is an absolute limit.
Wow! I did not see that coming.
Depends on what you mean IMO. You can’t accelerate to the speed of light, but current cosmology predicts “inflation” after the Big Bang that moved things apart faster than the speed of light by creating space between them. That is the most likely route for getting arouns the apeed of light limit. If we don’t nuke ourselves or suffer some other collapse od civthey might crack this nut in a few more centuries or eons...
It can be demonstrated quite readily.
Look at the sun.
Well, get some good welder's goggles, then look at the sun in the sky.
We know how long that light you see takes to get to the earth. (approx 8 mins if I recall correctly).
If you calculate out the motions of the sun, and earth, the gravitational effects you feel from the sun (this effects where the earth is in its orbit amongst other things), the sun is not in the position it ought to be by virtue of the gravity we feel from it.
This is because the effects of gravity travel faster than light.
Depends on what you mean IMO. You can’t accelerate to the speed of light, but current cosmology predicts “inflation” after the Big Bang that moved things apart faster than the speed of light by creating space between them. I think that is the most likely route we have some clue about today for getting around the speed of light limit. If we don’t nuke ourselves or suffer some other collapse of civilzation, they might crack this nut in a few more centuries or eons...
Just saying...
Is Gravity Really a Law? Let's knock some politicians off their perches and test it.
lol, I hear that if you find yourself in a free falling elevator the thing to do is lie down. I guess so your spine etc is better positioned to withstand the impact.
No, I was trying to describe:
< < < A < < < - - - B - - - > > > C > > >
A and C are moving in opposite directions, each moving away from B at the speed of light. It has been a few decades since I had quantum mechanics.
Not being Sheldon Cooper, I can't really keep up with the physics or math required to really understand this stuff, though I've always found it to be interesting. I've always suspected that inflation was hand waving by physicists to make up for the fact that they can't really explain what happened that soon after the big bang.
“If you calculate out the motions of the sun, and earth, the gravitational effects you feel from the sun (this effects where the earth is in its orbit amongst other things), the sun is not in the position it ought to be by virtue of the gravity we feel from it.”
If I’m understanding you correctly, you mean that the apparent visual position of the sun (transmitted by the light) is different from its actual position, deduced from gravitational effects. That alone demonstrates nothing, since it does not mean that any actual “motion” of gravity has occcurred, and without even being able to demonstrate motion, you can’t hope to make any conclusions about the velocity.
In fact, if gravity worked the way you propose, it would have to have an infinite velocity, since its effects are instantaneously apparent at any distance (if you can detect them). Anything with an infinite velocity would also have to be ever present in every location in the universe equally, so we would all experience the exact same gravitational effects as everywhere else. Since that is not the case, then it is apparent that gravity can’t work that way.
I think our spine was designed to resist vertical compression, like the constant pull of gravity, so I don’t see how that would work.
Actually, infinite velocity is exactly what it implies IMO. I don't see how it would follow that we would all experience the exact same gravitational effects as everywhere else. Gravitational effects are still bound by distance. Not inverse square, thankfully, but the effect lessens with distance, though in theory every single particle, no matter how separated by distance does have some effect on each other gravitationally.
I can't remember exactly where I first read about the discrepancy between the sun's apparent position and it's gravitational effect, as it was some time ago. I think it was a freeper who pointed it out to me, but I get old and forgetful. I'll do some searches on this tonight, if I'm not distracted by shiny things.
I thought that was true where we see its influence long before we should have if it was limited to light speed.
The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, c.[1] Within the theory of special relativity, the constant c is not exclusively about light; instead it is the highest possible speed for any physical interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space.[2] This makes it the only speed which does not depend either on the motion of an observer or a source of light and/or gravity. Thus, the speed of "light" is also the speed of gravitational waves and any massless particle. Such particles include the gluon (carrier of the strong force), the photons that light waves consist of, and the theoretical gravitons which make up the associated field particles of gravity (a theory of the graviton requires a theory of quantum gravity, however).
The speed of physical changes in a gravitational or electromagnetic field should not be confused with "changes" in the behavior of static fields that are due to pure observer-effects. These changes in direction of a static field, because of relativistic considerations, are the same for an observer when a distant charge is moving, as when an observer (instead) decides to move with respect to a distant charge. Thus, constant motion of an observer with regard to a static charge and its extended static field (either a gravitational or electric field) does not change the field. For static fields, such as the electrostatic field connected with electric charge, or the gravitational field connected to a massive object, the field extends to infinity, and does not propagate. Motion of an observer does not cause the direction of such a field to change, and by symmetrical considerations, changing the observer frame so that the charge appears to be moving at a constant rate, also does not cause the direction of its field to change, but requires that it continue to "point" in the direction of the charge, at all distances from the charge.
The consequence of this, is that static fields (either electric or gravitational) always point directly to the actual position of the bodies that they are connected to, without any delay that is due to any "signal" traveling (or propagating) from the charge, over a distance to an observer. This remains true if the charged bodies and their observers are made to "move" (or not), by simply changing reference frames. This fact sometimes causes confusion about the "speed" of such static fields, which sometimes appear to change infinitely quickly when the changes in the field are mere artifacts of the motion of the observer, or of observation.
In such cases, nothing actually changes infinitely quickly, save the point of view of an observer of the field. For example, when an observer begins to move with respect to a static field that already extends over light years, it appears as though "immediately" the entire field, along with its source, has begun moving at the speed of the observer. This, of course, includes the extended parts of the field. However, this "change" in the apparent behavior of the field source, along with its distant field, does not represent any sort of propagation that is faster than light.
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