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Re: [Phys-L] On 4-velocity, 4-momentum, and E=mc^2 (Was: how Einstein discovered E=mc^2)



  Bob, I agree 100% with your evaluation of basic relativistic concepts. I would only add that, apart from being useful conceptual interpretations, they are experimentally measured physical observables.  Only because today's high-energy physicists find it more convenient to describe their specific experiments in terms of invariant mass alone, does not eliminate the observed velocity-dependence of inertial mass. The same is true for the time dilation and length contraction effects.
For those interested:
1) Relativistic mass - see, e.g., Kaufmann - Bucherer - Neumann experiments.

2) Time dilation - see experiments on observation of ultra-relativistic mu-mesons formed in the upper atmosphere and observed at the sea    
     level despite the maximal 600 m travel distance allowed for them by their short proper lifetime (any good Mod. Phys. textbook, e.g.,     P. Tipler, Elementary Mod. Phys., Worth Publ., 1992;       K. Krane, Mod. Phys., J. Wiley & Sons, 1992; 
     P. G. Hewitt, Conceptual Physics, Harper Collins Coll. Publ., 1992)Also, direct experiments with decay rates of accelerated charged particles:    H. Bailey a.o., "Measurements of relativistic time dilatation for positive and negative muons in a circular orbit",      
   Nature 268 (5618): 301–305 (1977);   J. Bailey a.o., (1979). "Final report on the CERN muon storage ring including the anomalous magnetic moment and the electric dipole moment of the muon, and a direct test of relativistic time dilation". Nuclear Physics B 150: 1–75, 1979;   C. E. Roos a.o.,  (1980). "σ+/- lifetimes and longitudinal acceleration". Nature 286 (5770): 244–245 (1980). 
3)  Length contraction - consider a gedanken experiment - observing the direct experiments with atmospheric muons in their own rest frame!     
      See also:   L. Landau, On multiple particle generation in the ultra-fast collisions, Reports of Acad. of Sci. USSR, 17, 51 (1953)
     (The observed angular distribution of the collision products can only be explained by the Lorentz-contraction of colliding particles!)
Moses Fayngold,NJIT



On Thursday, November 27, 2014 7:58 PM, Bob Sciamanda <treborsci@verizon.net> wrote:


Moses wrote:
" . . .  Finally, and perhaps most important, [1] is, in turn, corollary of
E(v)=m(v)c^2. In other words, these two equations are mathematically
equivalent. Therefore, if we accept [1], we cannot discard E(v)=m(v)c^2 as
generalized mass-energy equivalence, with mass m(v) being the measure of
object's inertia experimentally determined by its acceleration under given
force transverse to instantaneous 3-velocity. For those who prefer
abstract-mathematical formulations, it may be more convenient to define the
rest mass as a numerical factor converting 4-velocity into 4-momentum,
whereas the relativistic mass is a factor converting 3-velocity into
3-momentum. As far as we regard 3-velocity and 3-momentum as important
physical observables, and want to be consistent, we must attribute the same
status to relativistic mass. "
Moses Fayngold,NJIT
_______________________________________________
Moses, I applaud your cogent observations regarding the usefulness of the
relativistic mass concept.  The belittling of alternate conceptual
interpretations of mathematical models should be anathema in physics
discussions - it smacks of the tactic of demonizing opposing views - common
in political wrangling.  Let us acknowledge the possibility of alternate
views and practice the "de gustibus . . ." which we are wont to preach.  I
find the concepts of time dilation, length contraction and relativistic mass
very useful conceptual interpretations of our mathematical models.

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
www.sciamanda.com