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==A Topical Example: Speed of Extremely Energetic Neutrinos==
==A Topical Example: Speed of Extremely Energetic Neutrinos==
Here is another example of the use of this formula in physics calculations. Recently there has been quite a controversy over whether neutrinos were observed traveling at a speed faster than light. Relativity doesn't allow that, and, since neutrinos have nonzero (but incredibly tiny) mass, they aren't even supposed to travel ''at'' the speed of light. This very issue came up on the [[Talk:Main_Page#Neutrinos]]. The speeds under discussion were calculated by the use of E=mc<sup>2</sup>.
Here is another example of the use of this formula in physics calculations. Recently there has been quite a controversy over whether neutrinos were observed traveling at a speed faster than light. Relativity doesn't allow that, and, since neutrinos have nonzero (but incredibly tiny) mass, they aren't even supposed to travel ''at'' the speed of light.
The mass of a neutrino is about 0.44x10<sup>-36</sup>kilograms. (Normally all of these things are measured in more convenient units such as Giga-electron-Volts, but that makes implicit use of E=mc<sup>2</sup>. If we don't accept that, we have to do the calculations under classical physics, using SI (meter/kilogram/second) units.) The neutrinos were accelerated to an energy of about 17GeV, or .27x10<sup>-8</sup>Joules. Using the classical formula <math>\mathrm{E} = \frac{1}{2}mv^2</math>, we get v=110x10<sup>12</sup>meters per second. This is about 370,000 times the speed of light.
The mass of a neutrino is about 0.44x10<sup>-36</sup>kilograms. (Normally all of these things are measured in more convenient units such as Giga-electron-Volts, but that makes implicit use of E=mc<sup>2</sup>. If we don't accept that, we have to do the calculations under classical physics, using SI (meter/kilogram/second) units.) The neutrinos were accelerated to an energy of about 17GeV, or .27x10<sup>-8</sup>Joules. Using the classical formula <math>\mathrm{E} = \frac{1}{2}mv^2</math>, we get v=110x10<sup>12</sup>meters per second. This is about 370,000 times the speed of light.