🚀 go-pugleaf

In article <1992Jul21.141253.17366@jlc.mv.com>, john@jlc.mv.com (John Leslie) writes...
>In article <mcirvin.711673227@husc8> mcirvin@husc8.harvard.edu (Mcirvin) writes:
>>dk@imager (Dave Knapp) writes:
>>
>>In fact, I think that a more important issue than the definition of
>>mass is the use of four-vectors in introductory classes teaching SR,
>>which I think should be encouraged, since it brings beauty and
>>simplicity to something which otherwise looks like an algebraic junkheap  
>>built on a shifting foundation of paradoxes. 
>>
>   Could someone have mercy on those of us whose college physics is
>twenty or more years in the past?  What is "four-vectors"?

A four-vector is a vector with 4 components.  Space-time is four-dimensional,
with each point being represented by a 4-vector in some arbitrary coordinate
system as (t,x,y,z).  All the equations of relativity (and any theory 
such as quantum field theory which you want to express in a relativistically
invariant way) are constructed in terms of 4-vectors and 4x4 matricies which
operate on the 4-vectors.  Other examples are the energy-momentum 4-vector
(E,px,py,pz) and the gradiant operator (dt,dx,dy,dz).  

Every four-vector transforms the same way under Lorentz boosts.  Therefore,
energy transforms like the time, while momentum transforms like a length.

When you get down to the nitty-gritty, things get a little more complicated, 
so that my last statement is not exactly true.  There are two classes of
4-vectors:  covariant and contravariant, which transform somewhat differently
under the Lorentz transformations. 

Reference:  Taylor and Wheeler's _Spacetime Physics_ is the classic. 

-Scott
--------------------
Scott I. Chase			"The question seems to be of such a character
SICHASE@CSA2.LBL.GOV		that if I should come to life after my death
				and some mathematician were to tell me that it
				had been definitely settled, I think I would
				immediately drop dead again."      - Vandiver