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E = mc^2
Please explain to me why the speed of light is squared.
Please explain to me why the speed of light is squared.
something happened to the textbook notation since i was in school. i was taught (ca. 1975) that the famous equationJames Jackson said:Firstly, in your counter-argument for the dimensional analysis, you're ignoring the fact that the 'full' equation really reads
[tex]E^2=m^2c^4+p^2c^2[/tex]
So in the case where the particle is at rest, this simplifies to [itex]E=mc^2[/itex]. Anywho, ignoring all that, the equation is pretty simply derived by applying the relativistic Lorentz transforms to energy and momentum. The transforms themselves are derived from the postulates of special relativity (Physical laws hold in all inertial reference frames and the speed of light is constant in all intertial reference frames).
That will sufficeJames Jackson said:In that 'derivation' you're assuming that [itex]E=mc^2[/itex] to begin with. Einstein derived it by looking at momentum carrying photons being emitted and adsorbed.
He actually starts with the relativistic mass = m.James Jackson said:In that 'derivation' you're assuming that [itex]E=mc^2[/itex] to begin with. Einstein derived it by looking at momentum carrying photons being emitted and adsorbed.
Anyway, I can't see how your final equation can possibly become [itex]E^2=m^2c^4+p^2c^2[/itex] (note this is Lorentz invarient - it holds in any frame).
no, James. the assumption that i started with was the relativistic expression of kinetic energy:James Jackson said:In that 'derivation' you're assuming that [itex]E=mc^2[/itex] to begin with.
perhaps ... i dunno. i am only reverberating what is in my "modern" physics textbook and it's a treatment that i understand. i dunno how they teach it now.Einstein derived it by looking at momentum carrying photons being emitted and adsorbed.
remember, my [itex]m[/itex] ain't the same as your [itex]m[/itex]. your [itex]m[/itex] is my [itex]m_0[/itex]. all's i was doing was showing thatAnyway, I can't see how your final equation can possibly become [itex]E^2=m^2c^4+p^2c^2[/itex] (note this is Lorentz invarient - it holds in any frame).
but it's not what you said. you said that i started with the assumption [itex]E = m c^2[/itex] and i said that i started with [itex]T = m c^2 - m_0 c^2[/itex].James Jackson said:"the assumption that i started with was the relativistic expression of kinetic energy"
You said it yourself.
no, i started with [itex]T = m c^2 - m_0 c^2[/itex] and i never attempted to prove it. i did not start with [itex]E = m c^2[/itex].This isn't a derivation of [itex]E=mc^2[/itex] as you started with that!