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You are not logged in. #1 20090824 23:50:11
Faster than light speed possible?Let us define the “crossover point” of a pair of scissors as the point at which the blades cross (namely point C in the diagram). When the scissors are wide open, the crossover point is close to the pivot; as you close the blades, the crossover point moves towards to the tips of the blades until, when the blades are fully closed, it coincides with the blade tips. Now, here is stunning thought: it is possible for the crossover point to move arbitrarily fast! Here are my calculations. Let us assume our scissors have paralleledged blades pivoted at a point midway between the parallel edges of each blade. Suppose each blade has length (measuring from the pivot to the tip) and width , and that the angle between the blades is . Let be the distance of the crossover point to the pivot. Then a bit of geometry shows that . Differentiating with respect to time gives , where . Note that as . is twice the magnitude of the angular velocity of each blade and may safely be regarded as constant. It then follows that as , . Note that if the blades are of finite length, will never be zero. However the minimum value of is when the blades are fully closed, when more simple geometry shows that . Thus, if we allow to be arbitrarily large, then can be arbitrarily close to 0, and so has no upper bound. Now, does this go against Einstein’s theory of special relativity, which sets the speed of light in a vacuum as the absolute upper limit? The answer is: not at all. Special relativity only applies to physical objects. The crossover point on our scissors is not a physical object and thus is not bound by the laws of special relativity. http://math.ucr.edu/home/baez/physics/R … ssors.html #2 20090825 07:42:46
Re: Faster than light speed possible?There are many occurences of things travelling faster than the speed of light; for example the path of a beam of light emitted from a distant fast rotating pulsar. The Beginning Of All Things To End. The End Of All Things To Come. #3 20090825 11:48:39
Re: Faster than light speed possible?Hi Jane; Last edited by bobbym (20090825 12:36:32) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #4 20090825 20:32:14
Re: Faster than light speed possible?I think this argument may be abstracted too much. Why did the vector cross the road? It wanted to be normal. #5 20090825 22:41:48
Re: Faster than light speed possible?Hi Jane; Last edited by bobbym (20090826 01:35:15) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20090826 02:05:06
Re: Faster than light speed possible?bobbym, what you are referring to in your action at a distance is quantum entanglement, which is a perfectly real phenomena, but again, no information can be transferred. The Beginning Of All Things To End. The End Of All Things To Come. #7 20090826 02:16:38
Re: Faster than light speed possible?Hi lucadeltodesco; Last edited by bobbym (20090826 02:40:27) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #8 20090826 04:21:03
Re: Faster than light speed possible?spin and charge are inherit properties of basic particles, which cannot be changed, only observed. quantum entanglement describes what you are talking about though, if two particles for example are entangled, and you observe one to have a positive spin, then the other particle MUST have a negative spin. The Beginning Of All Things To End. The End Of All Things To Come. #9 20090826 19:54:30
Re: Faster than light speed possible?
#10 20090826 21:12:08
Re: Faster than light speed possible?Hi Jane; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11 20090827 01:01:38
Re: Faster than light speed possible?
You're saying it's not information because you can't change it? "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #12 20090827 03:35:41
Re: Faster than light speed possible?I think he's saying that you can't pass information using this method. For example, let's say you take 2 particles that are entangled and transport them 1 lightyear away from each other. If a scientist measures the first particle's spin then he immediately knows what the spin of the other particle is, even though it's 1 LY away. Wrap it in bacon #13 20090827 04:26:14
Re: Faster than light speed possible?
This is one of the hardest things to understand (or perhaps, simply become accustomed to) in quantum physics. The thing is that it didn't exist when the particles were created. There are several states (spins) a particle can have, and we can express the probability that a certain particle is in a certain state, called the wavefunction. When the state is actually measured, we know with certainty which state the particle is in, and the wavefunction is said to "collapse". "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 