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Cusan Transformation

  1. Jan 17, 2009 #1
    Hello all.

    The following is a quote from The Routledge History of Philosophy, Vol IX, Pages 219-220.

    By the end of the nineteenth century, however, it had become clear that there was a transformation under which the laws of electromagnetism were covariant. This was the Lorentz transformation. The situation had now become very interesting. The Maxwell laws of electromagnetism are covariant with respect to the transformation of Lorentz but not with respect to that of Galileo. The laws of mechanics are covariant with respect to the transformation of Galileo but not with respect to that of Lorentz. Both are covariant with respect to the Cusan trnsformation, but this was taken to be so obvious as not to be worth remarking.

    What is the Cusan transformation.

    Matheinste
     
  2. jcsd
  3. Jan 17, 2009 #2

    robphy

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    I never heard of the Cusan transformations...
    but a Google book search turned up...

     
  4. Jan 17, 2009 #3
    Thanks for your reply robphy.

    I found references to the cardinal but none to the transform. It is strange that, although the quote from the Routledge History of Philosophy seems to assume that the reader requires no explanation because he or she will have some knowledge of it, it turns out to be so elusive.

    Matheinste.
     
  5. Jan 22, 2009 #4
    Hello all.

    For anyone interested i think i can answer my own question. Re reading part of the quoted book i found that it implies, without exactly stating, that the Cusan transformation is merely a change of position in space, a shift.

    Matheinste.
     
  6. Jan 22, 2009 #5

    robphy

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    Can you specify a particular section in that reference?
     
  7. Jan 22, 2009 #6
    Hello robphy

    Here is the reference. I have copied out the relevant paragraph in full for anyone interested who does not have access to the book.

    The Routledge History of Philosophy, Vol IX, Chapter 6-The Philosophy of Physics. Page 218.

    :- If a law of physics has the same form before and after the transformation is applied to the coordinates, we say that it is 'covariant under the transformation'. However, the technical idea is a version of a more fundamental conception. It expresses the idea that the forms of the laws of nature are indifferent to (that is unaffected by ) changes in location, epoch or relative velocity of the frame with respect to which they are studied. We can detect the very beginnings of the covariance or indifference to location idea in the writings of Nicholas of Cusa. Contrary to the Aristotleans, who believed that space and time had intrinsic structures, the laws of nature differing with the location in which they are studied within the structure, Cusa introduced a general principle of indifference. His elegant epigram ran as follows:- 'the centre and circumference of the universe are the same', or in other words, physical laws are indifferent to their location in space and also, he believed, in time.

    Matheinste.
     
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