
Maths
and Physics 
A very large number of emails over a period of years which started by discussing "The Catt Question" but drifted off course has recently entered a very fruitful phase on another subject, the relationship between maths and physics. My own position has been extreme for many years, see for instance 1986, "A mathematical rake's progress" . There are also specific criticisms of the role of mathematics in physics in my books "Electromagnetic Theory" on Forrest Bishop's website Now for an analysis of Josephson's email below. It is useful to compare his view with three major scientific advances. First, my article "Displacement Current" . Maxwell invented "Displacement Current" because he failed to notice that electric charge/current entering a capacitor plate from the input wire has first to spread itself across the capacitor plate before questions like "Displacement Current" can be raised and discussed. How would or could mathematics be usefully introduced to the subject of such an oversight lasting more than a century; that nobody has noticed that the first thing that tlectric current/charge must do on entering a capacitor plate is to spread out across the plate? Second, the Contrapuntal, or Catt, model for a charged capacitor. Coming from his work on high speed digital electronics, Catt thought about how a capacitor is charged. He realised that the charging energy arrives at the capacitor's terminals at the speed of light. It enters the front ends of the capacitor's plates at the (lower) speed of light for the dielectric, and traverses to the far end, where it reflects without change of polarity towards the input end. This process is described in mathematics and graph at "Displacement Current" . However, the mathematics is subsidiary to the physical statement that the charge, or energy, in a capacitor continues to reciprocate from end to end at the speed of light because there is no mechanism for it to slow down. How could these last nine words be described in mathematics? The Contrapuntal, or Catt, model for a charged capacitor is a statement about the physics of a capacitor, and no mathematics is involved in this very important advance in our grasp of the component, the capacitor. Thirdly, we come to Maxwell's Equations, supposedly the crowning glory in the mathematicisation of physics. In my articles "Maxwell's Equations Revisited" and "The Hidden Message in Maxwell's Equations" I develop these same Maxwell Equations, supposedly about electromagnetism, for a piece of tapering wood moving forward at constant velocity. If they also describe a piece of tapering wood, then they cannot actually tell us anything significant about electromagnetism. These three examples show how illusory is the idea that mathematics is at the core of physics. These three examples are extremely important in the history of science, and they are devoid of mathematics. The coup de grace is "Theory C" . When a battery is conntected to a lamp via two conducting wires, no electric current is involved. The believed electric current and electric charge are merely the mathematical manipulation of real electric field and magnetic field. Mathematical manipulation of something which is real does not necessarily lead to something else that is real. In the case of electromagnetism, the manipuation of field remains merely the manipulation of field. Mathematics is a language, much less rich than English or French. To force physics through the hoop of mathematics is to strangle it. @@@@@@@@@@@@@@ On Friday, September 26, 2008 9:53 0400 "J. R. Graham"
"Professor Josephson,  I am intrigued by your commentary on logic and mathematics. You say that logic is transformative, but not creative, and that mathematics is creative. But certainly you are not saying that mathematics properly invents inferences which do not actually follow from original premises."  J R Graham Josephson'd reply; "It does not invent inferences, it is true, but the fact is that you can't even formulate the original premises until you have created the mathematical concept involved in that formulation. For example, the idea that the acceleration of an object is proportional to the force on it can't be formulated as a premise until you have first defined acceleration, and that definition itself involves the notion of the derivative, which only existed after Newton and Leibniz had dreamed it up. The mathematical ideas are created from the mind, and then one sees if they can be useful in a given physical context."  Brian Josephson (Nobel Prizewinner.). * * * * * * * Prof. Brian D. Josephson :::::::: bdj10@cam.ac.uk
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