🚀 go-pugleaf

"bcaton" <bcaton@sia.net.au> writes:
>
>It's quite true that any object of non zero mass accelerated will increase
>in mass, especially as it approaches the speed of light; so that the energy
>expended in acceleration doesn't result in a proportional increase in
>velocity... 

 To repeat: it is more precise to say that the work done on the 
 particle increases its energy and momentum.  The mass does not 
 change.  Further, the increase in energy is never proportional 
 to velocity, even non-relativistically, if you mean a linear 
 relation.  Again, it is more precise to say that the momentum 
 (by which I mean the 3-momentum) is given by p = m gamma v. 

 That way, you realize that all relativity has done is alter the 
 v-dependence of momentum from linear [v] to non-linear [gamma v 
 = v*(1-v^2/c^2)^{-1/2} = v*(1 + 0.5*v^2/c^2) to lowest order]. 
 You do not notice the effect of using m*(v + 0.5*v^3/c^2) in 
 non-relativistic [v << c] situations. 

>instead, you have the situation where more and more of the
>energy used in the attempt is transmute to the mass of the object, 

 This suggests an actual change in the mass, while the real 
 situation is that the energy is frame-dependent while the 
 mass is not (the mass is invariant).  There is nothing 
 mysterious about this, since energy is frame dependent in 
 classical physics.  The only difference is the dependence 
 has changed so that v --> c as E --> infinity instead of 
 having v --> infinity at sqrt of the rate of increase in E. 

 All this infinite mass stuff is an attempt to keep the formulas 
 of Newton, but gets you into trouble when use that frame-
 dependent "relativistic mass" for other things.  Specifically, 
 you cannot use it for gravity and you must use two quite 
 different "relativistic mass"es depending on the direction 
 of the force being applied.  Messy and unnecessary. 

-- 
 James A. Carr   <jac@scri.fsu.edu>     | "What are those, Daddy?"
    http://www.scri.fsu.edu/~jac/       |      Young girl at Smithsonian 
 Supercomputer Computations Res. Inst.  | exhibit of objects and letters 
 Florida State, Tallahassee FL 32306    | left at the Vietnam Memorial.