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Can Relativity Explain Faster Than Light Particles?
gbrumfiel writes "Two weeks ago, researchers claimed particles called neutrinos were travelling faster-than-light and violating the laws of special relativity. But now it looks as though general relativity might be behind the experiment's unusual result. An independent analysis claims that the original experiment, known as OPERA, failed to take into account differences in earth's gravitational field between the neutrino source and the OPERA detector. As Nature News reports, gravity can distort time according to Einstein's theory, and the effect could explain why neutrinos appear to arrive 60 nanoseconds ahead of schedule. The OPERA team is now reviewing the new analysis."
Now we know why they had to raise the speed of light.
"I use a Mac because I'm just better than you are."
Except with all the math half-way worked out.
I called out warped space time as the cause. /win
whois gawk date unzip strip find touch finger mount join nice man top fsck grep eject more yes exit umount sleep dump
It's not just a good idea, it's the law.
he'll bitchslap you into oblivion
Nice try.
Sincerely,
Einstein
Faster than light is still possible, but now it's due to gravitational effects instead of innate property of neutrinos. It makes finding the Higgs boson more important than ever.
They are reviewing their own paper to make their methods clear. FTFA:
"Dario Autiero of the Institute of Nuclear Physics in Lyons (IPNL), France, and physics coordinator for OPERA, counters that Contaldi's challenge is a result of a misunderstanding of how the clocks were synchronized. He says the group will be revising its paper to try to make its method clearer."
Meaning: Contaldi didn't understand how OPERA did it, and thought they had commited a somewhat stupid mistake. OPERA says they didn't make that error, and that they'll rewrite that part of the paper to make this clear. In other words, this is not news at all.
NO ONE considered the time distortion of gravity? I mean, sure, it's the first time that the time distortion due to gravity has ever been significant in any practical application, but it's still a fundamen... wait, it's not the first time? You're saying that there's an 18-year-old system that relies on this principle to work properly? How many people use this obscure system? Every single person in the civilized world? You'd think that at least one of these researchers would have heard about it, then.
Mod parent up +5 informative - and thread over.
"The agriculture ministry is not in charge of Gundam" - Japanese ministry official.
This news is disappointing, but expected. I don't mean that I expected someone to give this particular explanation, just that I expected someone to provide an explanation that did not require the neutrinos to travel faster than the speed of light.
The truth is that all men having power ought to be mistrusted. James Madison
The researchers made no such claim! In fact they explicitly said they disbelieved they saw faster than light particles, and that they thought their data was faulty somewhere. But what they DID do is ask for other scientists to check their data and find their data, and if possible recreate the experiment to help track down where the error was.
THIS IS CORRECT SCIENTIFIC PROCEDURE!
My time travel method works!
They actually answered the clock questions on the first video conference feed the day after the press release.
"Beware, you who seek first and final principles, for you are trampling the garden of an angry God and he awaits you just beyond the last theorem."
-Sister Miriam Godwinson
Sorry, everything reminds me of a SMAX quote after i've been playing. :)
Explanation to this phenomena is simple. Neutrinos travelled through tiny wormhole and that caused them to arrive faster. I won Nobel Prize!
I'm certainly not disputing the legitimacy of science, but in this current age of misinformation, people need to realize that science is a discipline in constant flux. Nature and the Universe tend to stay constant, following their own laws--it's Man's perceptions and understanding that are continually changing. As we learn more and more, we tune our theories, hypotheses, and laws to better understand nature's hidden mysteries.
That the observation of a sub-atomic particle appears to confound or violate established scientific law really only means that it science has yet another mystery of nature that it does not yet fully understand. Maybe the methodology is flawed. Maybe the law is flawed. But that it happens at all should certainly not surprise any scientist--it should motivate to gain a better understanding.
My mom always said, "Jim, you're 1 in a million." Given the current population, there are 7000 of me. God help us all!
Are they using some other measurement of "speed" that isn't distance / time? It seems that slowing time down and going the same "speed" has the same net effect as going faster than the speed of light.
I'm impressed that you worked it out half-way ..
Hey don't blame me, IANAB
If it turns out that time dilation due to gravity is the reason, then the error must be in the ETRF2000 or it was applied incorrectly in this case (Neutrinos moving from A to B). Considering that hundreds of people work on this project it seems unlikely to me that such an error slipped through. They even took into account the very small distance change induced by the L'Aquila earthquake.
xkcd reference
Even if it is just a matter of clarifying the paper, it's still peer review in action. When OPERA responds, Contaldi will have the opportunity to review their clarifications. Maybe he'll respond again and point out that OPERA is still in the wrong. Or maybe he'll be satisfied and move on. This is how science is done. How is that not news?
I can run faster then Forrest Gump on Bawls. It allows me to travel back in time.
Don't believe me? Fine, I'll go ahead and show you guys this one time....
Oh, it's news all right. Just not end-of-the-world-as-we-know-it news. As pointed out in TFA, it's awfully hard to critique the experiment unless you're there seeing exactly what has been done. While I don't find it surprising that a few printed (or electronic) pages cannot describe hundreds of tons of equipment and countless hours of work it does speak to the complexity of modern science.
You wonder how much that is published isn't repeatable or understandable. Dropping rocks off off buildings and counting seconds with a stopwatch just doesn't cut it anymore. I read somewhere (can't quickly find it) that one of the drug companies (Bayer, IIRC) felt that over half of the experiments from the literature that they tried to repeat to consider the possibility of pharmaceutical development from the discovery, failed outright or gave much different results than published.
It's frustrating I suppose. We all know most research is wrong / useless - the hard part is teasing out which is or isn't.
Faster! Faster! Faster would be better!
Contrary to what many news-sites keep repeating, it is well known that traveling faster than speed of light does not contradict special relativity. It is well known that tachyons are consistent with SR. SR only entails that a particle is either always slower than the speed of light, or is always faster than the speed of light, but can't cross that boundary from either side. The real issue is that these particles are neutrinos which are supposed to be able to travel with less than speed of light as well.
Attitudes make the difference between Space and Time: we want to MAX our temporal, and MIN our spatial extension.
I wonder if light is being affected by space-time some way and neutrinos aren't. Then they measure the true maximum allowed speed better than light does. Taking that into account, how the theories will look like using c @ neutrino's speed ?
sign(c14n(envelop(this)), x509)
extra-Special Relativity. breaking it's own rules for yet another reason.
It's everyday science in the works. He presented an alternative explanation that's just plain wrong (he's applying a correction that had already been applied). Will we report on every single paper published on arXiv? Most of them are more relevant than Contaldi's, now that OPERA reassured the effect had been already taken into account. And that happened before the sumbission.
Bummed SMAC/X no longer runs on my Mac after Lion update. Am dusting off an old Mac Mini to set up as game machine now. Wish someone would write a new SMAC/X style game. Other than time killers on phone, don't do any computer gaming anymore.
I drank what? -- Socrates
It's not news for one of two reasons, because one of two things is true:
Contaldi has poor reading skills. 'Peer review' is of low value from people who can't understand straightforward explanations that were understood by others.
or:
Science is proceeding as normal, and the outcome is still unknown .
Wake me when science reaches a conclusion, every minor typography fix on this paper is not newsworthy.
"Who is the Journal of Quantum Physics going to believe?" --Stephen Hawking
I'm a mathematician, not a physicist. In special relativity the Lorentz transformation has a singularity at the speed of light. Its perfectly defined below and faster than the speed of light. Richard Feynman suggested that unless the math prohibits it, it will be found in nature. Of course, if we see a particle hitting another before it was emitted, we'd likely interpret it as the target "pulled" the particle from the emitter. This explains the alternate view of physics -- all matter emits dark, and light bulbs and stars suck the dark in. Mathematically it makes just as much sense as emitting massless photons. Who's going to buy the idea of a massless particle that goes the speed of light? Its crazy talk.
This is just a reminder that like economics, scientific method is really a confidence game. Its all a matter of whether you believe the rules stated so far are consistent.
They could never duplicate this experiment in West Virginia because relativity is hard to define there.
"That's the way to do it" - Punch
It's not misunderstanding if there was no explaination in the original paper. Everyone I spoke to pinned the result as clock synchronisation error; this if they'd read the paper or not (well apart from one twat who started talking about "parallel universes, quantum physics and shit!").
CERN themselves believe there's an error contributing to these results and GPS is so complex when used at this precision that a time synchronisation error remains the most likely explaination.
I personally chalk it up to the measurement between the emitter and the detector.
Yes I know they say they are very confident within a margin of error and that amount they are observing is within that margin of error so it must be right??
Personally I aint gonna start changing C based upon their confidence that their variation is within the margin of error that they say is within the margin of error of the distance between the gun and the target since everything else in GR & SR has been demonstrated correct thus far.
Hey KID! Yeah you, get the fuck off my lawn!
failed to take into account differences in earth's gravitational field
Even if they didn't account for it, so what?
The Schwarzschild solution for Time dilation has a C squared in the divisor.
Unless I'm doing the math wrong, It wouldn't even amount to 1 nanosecond, much less 60.
Physics allows for a clown to be in my basement, but that doesn't mean there IS a clown in my basement. Because some interpretations of general relativity allow for the possibility of faster-than-light particles does not, any any sense, mean that they exist. Right now, that is purely speculation with no evidence.
(Well, no evidence until OPERA.)
"let us assume that the TTD was stationary at the LNGS site for 4 days while the appara-tus for clock comparison was set up. Using the value of V/c2 quoted above this would result in a total shift of t 30 ns."
Let us assume a scenario which fits our desired outcome has actually occured without any supporting evidence since our own figures fall far short of a cogent explanation for the discrepancy.
Let us further overlook the fact PTB was mearly used to independantly *VERIFY* the nanosecond level clock synchronization calibrated by METAS of the time links between the two stations.
From the OPERA paper:
"The difference between the time base of the CERN and OPERA PolaRx2e receivers was
measured to be (2.3 ± 0.9) ns"
Ooops...
"More importantly, we have only considered the path taken by the TTD along a surface trajectory. The path taken by the neutrinos is some 3 kms below the surface at its midpoint along the trajectory connecting CERN and LNGS. At this level of accuracy the surface time mea-sured by all clocks involved will differ from the proper time along the true trajectory and this further compli-cates the interpretation of the OPERA results."
The difference between totally switching off the earths effect on spacetime as the neutrino beam moves 730km results in being able to cover .5mm more distance over the same time. The effect is not worth thinking about yet they deem it necessary to include it anyway. Their own figures come up short.
The problem here is that tachyons, if they exist, move faster with lower energy, and approach the speed of light at high energies.
IIRC the neutrinos from the experiment were at much higher energies than those observed from a supernova explosion
in the 80's i think, where the photons and neutrinos arrived about simultaneous.
The vacuum in the universe isn't actually a perfect vacuum, and thus it has a small refractive index,
meaning the the speed of light in the universe is a bit slower than in perfect vacuum, so those
neutrinos can travlel faster than light and could be used to tell us in advance when a supernova explosion occured,
so we can point our telescopes in that direction.
Actually, the theory of special relativity has no problem with particles going faster than light. The problem lies with accelerating particles from slower than light in vacuum to faster than light in vacuum. Or, for that matter, with slowing down from faster to slower than c.
Would it be possible to have neutrino generators and detectors at both sites and test the speed in both directions? That would probably mean testing the speed between CERN and Fermilab. That way, if there was an error in clock synchronisation, it would show up because the neutrinos would take longer in one direction than the other.
Wake me when science reaches a conclusion, every minor typography fix on this paper is not newsworthy.
It is to nerds. This isn't USA Today.
This was the first thing I actually considered when these results came out and I quickly dismissed the idea because I thought surely they would take into account a nonlinear path length. All I can say is that if they neglected relativistic effects when doing this experiment, why are we trusting these people with handling our physics. How embarassing.
I think you're being too harsh. Clarity is important. Misunderstandings get people on the wrong way. I think it's much better to add a clarification than to complain about people misreading the work.
"Dario Autiero of the Institute of Nuclear Physics in Lyons (IPNL), France, and physics coordinator for OPERA, counters that Contaldi's challenge is a result of a misunderstanding of how the clocks were synchronized. He says the group will be revising its paper to try to make its method clearer."
The heck with that! What I want to know is: How can a company that gives away a free browser possessing only a minuscule market share afford to employ a physics coordinator?
#DeleteChrome
Distort time by 60 nanoseconds over such a (relatively) short distance? That's a huge distortion. Something else is likely involved in the explanation than gravity.
I swear they give me mod points to shut me up.
"And when we find Him, Sister Godwinson, you'll be right and we'll be satisfied." -Me
Please consider this account deleted, I just can't be bothered with the spam anymore.
That's not the problem with this, though. The problem here is the supernova explosion in Andromeda, where neutrinos and photons arrived here at about the same time. (I forget the exact difference.) If their speeds were any different, then over that distance they shouldn't have arrived at anywhere near the same time. This makes almost all explanations of the time difference detected that don't involve experimental error to be very dubious.
I mean, if neutrinos can cycle into a fourth variety (the "sterile neutrino") that goes faster than light for some reason ("taking a shortcut through the bulk?"), then why did the neutrinos from the supernova arrive at about the same time as the photons? This question can be adapted for any other explanation that I've thought of for neutrinos actually moving faster than light.
OTOH, I don't believe that changing the "fastest particle" to the neutrino instead of the photon would noticably affect relativity. It would just make the tests more difficult. c would then be tied to the speed of the neutrino rather than to that of the photon, and all the other arguments would remain sound. And the speed of the neutrino being so close to that of the photon would probably mean that all the confirming experiments still fell within experimental error. (Of course, there's also the factor that if you accelerate something using electromagnetic forces, you CAN'T get it to move faster than light. And neutrinos would be very poor candidates for something to accelerate something else with.)
I think we've pushed this "anyone can grow up to be president" thing too far.
This is a great article describing how difficult it is to control systematic errors with clocks in this kind of Time Of Flight experiment. An undergraduate level of understanding of relativity is all that's required and it makes you think. Also contains some snarkiness.
This is why I've always been skeptical about a lot of what we think we know: Almost all of our data is derrived here on a node of mass, which is really a very special place in the universe. Until we do particle accelerators in space, we're not going to see the bigger picture (ie: never)
About Physics.
I don't know about most, but you obviously didn't, judging on your comment. Disclosure: I not only did do basic physics, but am actually a physicist.
Yes.
Then you have to relearn your math. Anything divided by zero is undefined. Something going to zero in the denominator makes the term go to infinity if the numerator doesn't also go to zero (or does, but slower). But that's irrelevant anyway. The energy-momentum relation of a particle in special relativity is E^2 = (mc^2)^2 + (pc)^2. For a particle at rest (p=0), this gives the well-known E=mc^2. For photons, we have m=0, and E=pc (as it must be, or the laws of classical electrodynamics would be wrong). No division by zero in sight.
They indeed haven't measures particles with no mass, but not because of the "problems" you claimed, but because, as we know today, the neutrinos do have mass. This is known due to the neutrino oscillations which have been found, and which were the solution to the solar neutrino problem. There are no theoretical problems with massless neutrinos (at least from the theories we know today; maybe some future unified field theory will not allow massless neutrinos). Indeed, for most of the time neutrinos have been thought to be massless.
The Tao of math: The numbers you can count are not the real numbers.
challenges to research are actively encouraged in some aspects of science whereas they are unfortunately denounced in others. I am glad to see this team inviting others to find the faults if any, now to see this applied to more politically sensitive subjects would be nice
* Winners compare their achievements to their goals, losers compare theirs to that of others.
Them pesky neutrinos mezzed decay rats of the sneezium in them their atomic clocks to fool uall.
Could they do the experiment in the reverse direction to test this hypothesis?
Two weeks ago, researchers claimed particles called neutrinos
Seriously, whomever wrote this summary must have been writing it under the assumption that the entire world is retarded.
SR is based upon three assumptions or principles:
1. Causality (cause before effect)
2. Relativity (the laws of physics are the same for all reference frames, i.e. there is no 'privileged' reference)
3. Constancy of the speed of light (as was implied by Maxwell's equations)
Maintaining all three principles at once is how we end up at the rules of time dilation. Because of time dilation, if one could communicate between two inertial reference frames faster than light, then some observer would say that the message was received before it arrived -- which violates Causality for that observer, which would violate Relativity. With a few messages between ships traveling at relativistic speeds, it is possible to craft a scenario where the ship that sends the first message receives a response prior to having sent it -- Causality is then broken according to all observers.
Any method of information transfer that occurs FTL -- regardless of method -- breaks causality, and thus Special Relativity.
However if no information is sent, then this isn't a problem. This is why Quantum Entanglement experiments do not violate SR, because no information transfer, and thus causality violation, is possible.
Tachyons that can be used to send information contradict SR.
There are other formulations of tachyons which do not allow information transfer, and they are the ones that are consistent with SR.
This experiment, however, definitely involved information transfer. If its results hold up, then SR and one of its basic assumptions is in trouble. It could be Causality. How effin' weird would that be?
But most likely we live in a causal universe, and they did not send information FTL.
The enemies of Democracy are
How's that for a thought?
He isn't complaining about people misreading the work. He's complaining about people reporting on people misreading the work. If the challenge is answered and the response still leaves substantial controversy that might be newsworthy. If the challenge debunks the finding, newsworthy. If the findings are confirmed, newsworthy. Any of the steps leading to those... doesn't really need to be reported outside of the circles actually performing peer review.
Your knowledge is outdated. Today we know that neutrinos do have mass.
The Tao of math: The numbers you can count are not the real numbers.
I was about to mod you funny but then I tought it better: while he's not on peasant wages, the fact remains that even "just" senior engineers from Opera will probably earn more than that guy.
How the hell am I going to mod something funny when it makes me feel so depressed?
In the 1990s it seemed that extremely precise measurements of the gravitation force was failing Newton's r-squared law over relatively short distances (meters). This is fore gravimeters near the earth surface than can measure gravity force changes to better than a part in a billion. The experimental error faded as the modeling took more and more factors into account.
What if they oscillate into some form that is slightly faster than light? They'd be traveling slightly slower than light part of the time, faster than light part of the time, and their average speed might be exactly the speed of light. The amount of time spent on the other side of the lightspeed barrier would never be enough to be exploited to violate causality. But, the oscillations would cause some curious results that might sometimes show some neutrinos exceeding the speed of light.
The universe would give us hints of tachyons while at the same time not vanishing in a puff of logic, and would also demonstrate a means by which something that has mass could travel at light speed.
Not that I'm saying this is what's going on. I don't have the background; I follow what I can of these things as a hobby. It's just fun to think about.
Fun with Anagarams! LADS HOST, SHALT DOS. HAS DOLTS. AD SLOTHS, HATS SOLD. ASS HO, LTD.
It seems to make sense, the neutrino particle is just smaller than the light 'particle', therefore it has less mass, and can go faster. That's why all our current calculations for light etc. still work and are valid, the formula e=mc^2 is just bound to the resolution of light 'particles'. Maybe the 'constant' c needs to be re-evaluated so it takes particle size into account? It should be more of an asymptotic relationship: Q: Whats faster than light? A: The closest thing to 'nothing' (i.e. the mathematical limit in calculus)
Meaning: Contaldi didn't understand how OPERA did it, and thought they had commited a somewhat stupid mistake. OPERA says they didn't make that error.
OPERA says that they didn't make that error. But, they also learned about the mistake only through Contaldi's challenge.
Causality has been a bit off recently.
Free unix account: freeshell.org
The neutrinos are quite magnetically neutral, and thus not affected by the Earth's magnetic field.
To put it in a car analogy, as is the custom here: They are not passengers in this car.
The Earth moved in space while the neutrino was thrusting forwards. Even if the absolute momentum stayed within the constraint given by the 'speed of light'-- the Earth still moved its target closer to it's absolute origin, thus the neutrino traveled less than 720km. This way your calculations match and speed of light remains unbroken.
Have a nice day,
-j
Physics allows for a clown to be in my basement, but that doesn't mean there IS a clown in my basement.
Conversely, there is nothing preventing a clown from being in your basement, so you should engage in scientific testing of that idea and go check for one.
I am fascinated by your 'clown in the basement' metaphor. I think I need to work on integrating this into everyday conversation.
HA! I just wasted some of your bandwidth with a frivolous sig!
"Gravity 'can' distort time..."? Gravity always distorts time.
After I saw this quote I figured they'd have to find some error in their observations. (Emphasis added.)
"...If the observation is confirmed, it may be the most important discovery in science in the last 100 years.
"However, a big fly in the ointment is the supernova in the Large Magellanic Cloud, which sits just outside our galaxy 168,000 light-years from Earth. It was first seen by the naked eye on February 24, 1987. Three hours before the visible light reached Earth, a handful of neutrinos were detected in three independent underground detectors. If the CERN result is correct, they should have arrived in 1982. So, if I were a wagering man, I would bet the effect will go away because of some systematic error no one has yet been able to think of."
(Quote stolen from Quark Soup)
complete that C will still be a constant representing the maximum speed of the Universe, regardless of the frame of reference. It is, after all, the reciprocal of the square root of the product of two other physical constants.
Running with Linux for over 20 years!
Neutrinos do have mass, this is why they oscillate between 3 states. However the mass is very slight.
Also the neutrinos arrived ahead of the photons in SN1997 by a small amount (days, IIRC. it should be years at the speed discrepancy quoted by CERN). This different is explained by the fact that neutrinos hardly interact with matter and so could escape the core of the supernova before the photons could.
Actualll no, they explained that on the conference. The fact that they took this effect into account was clear from the way they treated the data, but looks like it was lost on Contaldi.
The arxiv blog recently had a roundup of papers discussing this: http://www.technologyreview.com/blog/arxiv/27212/ They fall into three groups: (1) Suggestions of how the experiment might have given a wrong result. (2) Theoretical arguments that constrain the interpretation and make the result seem implausible if taken at face value. (3) Theoretical papers saying what it could mean if it really was new physics. The Nature article seems to show that the Contaldi paper was based on a misunderstanding of how the experiment was done. However, the Nature article points to a new paper by Henri that wasn't included in the arxiv roundup: http://arxiv.org/abs/1110.0239
Find free books.
Yes, I know photons don't have mass...
I'm trying to teach myself to set people on fire with my mind... Is it hot in here?
That's not surprising. A significant percentage of published results are wrong, even in mathematics and physics. It's not a question of "feeling", it's a fact.
Nor, for that matter, does the fact that General Relativity forbids some effects mean that they can't occur. After all, it's clear that GR is wrong somehow since it is incompatible with quantum mechanics.
Relativity only works in the relativistic range. Outside of this we still use Newtonian Physics, nevermind that generations of the best and brightest scientists humanity has to offer have yet to merge Relativity and Quantum Mechanics or how Relativity cannot deal with the wave-particle duality of light, or even the concept of anything moving at the speed of light itself.
Of course there is a piece missing.
Stupid fucking Slashdot. The researchers made NO such claim. They KNEW they were missing something, but just couldn't find it on their own. That's why their work is being reviewed by other scientist. That's how science WORKS.
It's thought that the OPERA experiment didn't account for differences in the Earth's gravitational field between the neutrino's origin and that of the OPERA detector? If it's not accounted for, won't other things seem to go faster, too? Could it be that photons and all other energy have mass, so E=MC squared needs to be rethought to account for that, and to explain the faster speed of neutrinos?
why wouldn't you have an expert on time help you with the clocks?
example:
www.nist.gov/pml/div688/grp40/tmas.cfm
neutrinos can.
I like my spaghetti with source.
In what way do your clowns contradict what I wrote? I did not say that SR supports the existence of tachyons, I said it is compatible with it. The summary (and many articles) say, however, that traveling faster-than-light violates the laws of special relativity. That is false, and that is what I wrote.
Attitudes make the difference between Space and Time: we want to MAX our temporal, and MIN our spatial extension.
..the evidence is flawed. It's entirely possible that the neutrinos did in fact arrive in 1982 and that the observation three hours before the visible light reached Earth was merely a coincidence. After all, you can't tell whether the neutrinos and the light originated from the same source or low long they have been traveling to reach earth.
They've got it nearly right. The problem is that the earth's gravity is bending the light we use to measure distances on earth but for some reason it does not bend the neutrinos so the neutrinos take a short-cut across the chord.
This also explains why the neutrinos from the supernova were "normal" speed. They are coming into our gravity well, not traveling across it.
Just be happy it wasn't "BING," the results would be "Windows 7 faster than neutrinos."
Vote monkeys into Congress. They are cheaper and more trustworthy.
The question here's: Did the TTD stop
for lunch at a scenic spot in the Alps?
TFA convinced me.
What's even more worring is that the scientific method does not prevents that, they use statistics and stuff, but their results were obtained by following the same mistakes every time
I'm positive, don't belive me look at my karma
No need for string theory to wrap that package.
Santa Claus is imaginary, therefore has imaginary mass, but his energy is real (causes parents to do a lot of work)
E =gamma mc^2, which can only be true if gamma is imaginary.
gamma= 1/(1- (v/c)^2)^(1/2) = an imaginary number iff v > c,
therefore
if Santa Claus is imaginary, he must move faster than light.
"Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?" - Patrick Henry
http://public.web.cern.ch/PUBLIC/en/About/WebStory-en.html :-)
The bartender shouts, "Hey! We don't allow faster-than-light particles in here!"
A neutrino walks into a bar.