Re: A Derivation of Special Relativity without Invoking Group Theory

From: David Evens (devens_at_technologist.com)
Date: 01/25/05 

Date: Tue, 25 Jan 2005 04:42:07 -0500

On Tue, 25 Jan 2005 02:47:39 GMT, Jesse Mazer
<vze2ztqw@mail.verizon.net> wrote:
>Eugene Shubert wrote:
>
>>>Nobody ever said anything about spacetime, itself, having a group
>>>structure.
>>>
>>>
>>
>>Is spacetime a geometry?
>>Does geometry have a group structure?
>>Do groups have a group structure?
>>
>>Consider what the following nobodies have said:
>>
>>"The geometry of Minkowski space is defined by the Poincaré group."
>>http://en.wikipedia.org/wiki/Poincar%E9_group
>>
>>"Every geometry is defined by a group of transformations, and the goal
>>of every geometry is to study invariants of this group." Klein,
>>Erlanger Program.
>>
>>"Each type of geometry is the study of the invariants of a group of
>>transformations; that is, the symmetry transformation of some chosen
>>space." Stewart and Golubitsky 1993, p. 44.
>>
>>"A geometry is defined by a group of transformations, and investigates
>>everything that is invariant under the transformations of this given
>>group." Weyl 1952, p. 133.
>>http://www.everythingimportant.org/relativity/special.pdf
>
>As long as it is possible for different inertial observers to build
>networks of clocks and rulers which are at rest relative to themselves,
>then these clocks and rulers will define different coordinate systems
>for different observers, and there must be some equations to transform
>between the coordinates of an event in one system to the coordinates of
>the same event in another system. These coordinate transforms will have
>a group structure, as Tom Roberts said earlier. And since the coordinate
>systems are defined in terms of physical clocks and rulers, the
>transforms are determined by the laws of physics (or, equivalently, by
>the geometry of spacetime).

This actually suggests that Ken Seto understands physics much better
than he appears to, since this would neatly explain his long-running
pretense about there only being a single valid coordinate system.

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