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Re: Annotated version of SRT

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Am 10.04.2022 um 11:54 schrieb J. J. Lodder:

>> What does have the right transformation properties is a rank-2
>> tensor (skew-symmetric in fact, so a 2-form) which includes both
>> the  E  and  B  components in a single package.
>>
>> When Maxwell's equations are written using this 2-form (call it  F),
>> they assume a form that's even more succinct than Heaviside's:
>>
>>      dF = 0
>>      *d*F = j
>>
>> ...where  j  is the source 1-form combining charge and current,
>> "d" is the exterior derivative, and "*" is the Hodge star operator
>> with the Minkowski space signature.


Maxwell used actually quaternions.

> To avoid misunderstandings:
> there are vectors and vectors.
> The E field -is- a vector in 3-space.
> It is -not- part of a 4-vector.

You can add a time component and get a four-vector from a 3-vector, if 
you like to do that.

In case of the electric field strength vector this would in fact make sense.


> For others: In general a vector is defined to be something
> that transforms as a vector under a transformation group.
> So it isn't an absolute concept.
> What is a vector under one group of transformations
> need not be a vector under another group,
>
Well, actually the term 'vector' was coined by Hamillton for the 
imaginary part of a quaternion, which denotes a direction.

The other part was called 'scalar'.

I don't think, that group theory was already known in the mid 19th century.

TH

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Re: Annotated version of SRT Coke Hishikawa <uhva@blseummh.nm> - 2022-04-09 11:33 +0000
  Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-09 13:08 -0700
    Re: Annotated version of SRT nospam@de-ster.demon.nl (J. J. Lodder) - 2022-04-10 11:54 +0200
      Re: Annotated version of SRT Thomas Heger <ttt_heg@web.de> - 2022-04-10 21:10 +0200
      Re: Annotated version of SRT JanPB <filmart@gmail.com> - 2022-04-11 12:43 -0700

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