  # Mark Northrup

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1. My apologies for not poking around enough before posting the first time, this would have been a better place to ask my question. Dr. Rocket, I was able to acquire the Rindler text, thanks for the suggestion. I also understood what you said about Einstein's axioms and I am aware of the history and reasoning behind Einstein's leap in taking the results of Maxwell's equations at face value. Maxwell's results did not specify a reference for the velocity of light (electromagnetic waves) in a vacuum because the observed velocity of light is the same in all reference frames and for all observers (this is the second axiom-the first being the well accepted Galilean/Newtonian principle of relativity). Before Einstein, there was even something of a cottage industry among experimental physicists (though the distinction between experimental physicists and theoretical physicists was not what it is today) devoted to finding a medium or reference frame in which the speed of light (c) could be said to be in relative motion to. I also understand that if c is constant for all observers, in all frames, and given the fact that c is a speed or velocity, and is necessarily given in units of a distance divided by time, then the only way to get what is essentially a constant ratio equaling c, it is the measures of distance and time that must change. It is ironic that the Lorentz transformations were (as I understand their history) derived, in part, in attempts to account for the null results of experiments to detect the "æther flow." As I noted in my original question, I am looking at the equation for relativistic kinetic energy: (m*(c^2))/sqrt(1-((v^2)/(c^2))) (this was the "maths behind SR" I was referring to). The annoyance spurring my essay is that in popular expositions involving SR, it is invariably noted that it would take an infinite amount of energy to accelerate a mass to the speed of light because as any body with mass (from spacecraft to neutrinos) approaches the speed of light, its mass increases to infinity (a species of the old "irresistible force meets immovable object" philosophical chestnut). The reasoning or maths behind such statements are never elaborated upon and it is not that difficult. In Einstein's Relativity: The Special and the General Theory. (Three Rivers Press: 1961), p. 45, there is the following text: "In accordance with the theory of relativity the kinetic energy of a material point of mass m is no longer given by the well-known expression: (m*v^2)/2 but by the expression: (m*(c^2))/sqr(1-((v^2)/(c^2))) This expression approaches infinity as the velocity v approaches the velocity of light c. The velocity must therefore always remain less than c, however great may be the energies used to produce the acceleration." The reason the above "expression approaches infinity as the velocity v approaches the velocity of light c" is because the denominator is approaching zero and all kinds of crazy stuff can happen when one tries to divide by zero. Given the fact that some types of mathematical "singularities" can be the result of what is essentially an attempt to divide by zero, I am not convinced it is a coincidence that when the maths used to describe physical systems do things like produce infinities physicists call them "singularities." Or is it me that is crazy?
2. My first foray here. I am working on a blog post regarding a personal annoyance whenever Special Relativity (SR) is discussed. The kerfuffle around the FTL neutrino puzzle announced by the INFN's OPERA team finally pushed me over the edge. To put it bluntly, it seems like anytime SR comes up, science popularizers (including scientists that ought to know better) never actually show the straightforward math behind SR that shows why it is the "cosmic speed limit." As I understand the maths behind SR (I'm American, but "maths" is easier to type than "mathematics")-I have Einstein's 1961 popular exposition "Relativity"-it is basically a divide by zero problem; in Einstein's eq. for kinetic energy, when v^2=c^2 in the denominator, and if the c^2 in the numerator is moved to the left-hand side of the eq., the right-hand side becomes a quantity of mass, divided by a "pure number" (therefore retaining the mass units unsullied) which as the denominator approaches zero, the mass becomes infinite. Graphically, this would be sooooo easy to show in a TV documentary and anyone that has ever encountered a "Div/0" error in a spreadsheet program could grasp the salient point. I just want to make sure my math and general reasoning are sound. Thanks in Advance and Merry Christmas/Happy Holidays/Happy Hanukkah/Sumptuous Solstice or whatever! Mark Northrup