Re: [Phys-l] Types of scalars

[Moses Fayngold <moshfarlan@yahoo.com>]

1) From Vikipedia:
    * Scalar (in Math) - a quantity used to multiply vectors...
    * Scalar (in Phys) - a quantity which is independent of specific classes of 
coordinate systems (= invariant, MF)
    * Scalar (in Computing) - an atomic (?-MF) quantity that can hold only one 
value at a time

2)  From André Angot, Compléments de Mathématiques à l'usage des ingénieurs de 
l'électrotechnique et des télécommunications, 
                                    6ème edition. Paris: Masson, 1972. 809 p. A 
French classic during 1950-80:
      "A quantity is called a scalar if it is (after the choice of unit of 
measurement) specified by one number. One has to distinguish between pure       
         scalars and pseudo-scalars. A pure scalar is completely defined by one 
number independent of choice of coordinate system (=invariant, MF)
       (Ch. 3, Sec. 3.1)

3)  From John David Jackson, Classical Electrodynamics, Third Edition, John 
Wiley and Sons, New York, 1999, p. 550:
       "A scalar (tensor of rank zero) is a single quantity whose value is not 
changed by the transformation (=invariant, MF)"            

   I believe, anyone who is interested can find more.

Moses Fayngold,
NJIT



________________________________
John Denker wrote on Tue, January 4, 2011 10:04:02 AM:

 Moses Fayngold wrote:
>    I think that in discussing this topic, we have to agree on some 
conventional
> definition of the notion of scalar. In one such definition a "scalar" is 
> synonym
> of an "invariant". 

But that's not the definition.  Never has been.  Never will be.
.............
The whole idea of scalar=invariant is Dead on Arrival.


_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l