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|Re: Mass Energy
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Posted by Zephram Cochrane/">Zephram Cochrane on November 19, 1999 00:49:30 UTC
: Local, shmocal.
GR is a local gauge theory. You must think locally in order to understand what I'm saying.
:"Center-of-momentum frame energy" is "proper frame energy".
Nope. Proper frame energy in this context applies to an individual particle, one at a time. Center of momentum frame energy in this context is the net energy according to a frame in which the net momentum of the system of particles is zero. In this case, the final center of momentum frame energy is the sum of the energy of the photons after the explosion, as observed from the center of momentum frame. I get the impression that you didn't read the entire thread and mistakenly think we're talking about an individual particle. Proper frame energy in this contextmeans you look at the energy of an individual particle from it's local coordinate frame. Each component in the sum of masses(proper frame energies as defined below) is zero for the photons and so it does not give you the same thing as the center of momentum frame energy(not zero) which is simply the net energy according to the center of momentum frame for the entire collection of particles. The point is that the term proper frame is not the same as center of momentum frame in this context.
: Indeed, "mass" and "energy" are two very different things.
I didn't say they were the same thing. In one paradigm they are the same thing and there is nothing wrong with using that paradigm. There is more than one paradigm or set of definitions in use to describe the same basic principle of relativity. Two people using different definitions for the same word does not make one right and one wrong. Its simply a matter of translation between the different definitions used by different physicists. In my paradigm as well as yours, we are agreed that they aren't the same thing. But in my paradigm mass is proper frame energy as defined below ,but is not center of momentum frame energy in this paradigm. Mass is not even a term that applies to the collection in this paradigm.
:The former is the magnitude of the energy-momentum 4-vector,
No, in this paradigm the latter(proper frame energy) is the magnitude of the momentum four vector for an individual particle. This is my definition of proper frame energy. Proper frame energy is the magnitude of the momentum four vector of an individual particle. This is why it is invariant. The full contraction of any tensor is invariant. Thus, using this as the definition of mass makes mass invariant. Proper frame energy is not center of momentum frame energy in this paradigm in the case of a collection of particles, as proper frame energy is intentionally only applied to an individual particle here.
:the latter is simply the timelike component, p0.
:No its not, in this paradigm. In this paradigm it is the timelike component for an individual particle in the case of no gravitation. In the case of gravitation and in this paradigm it is the mass of an individual particle proper frame energy = m =( gmnPmPn)1/2 As I've said you must think locally to really understand it. Locally this is understood because it is proper frame energy = m = (hmnP'mP'n)1/2 = P'0
:There is no "conversion" of one into the other.
I get the impression that you didn't read the entire thread.
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