Physics and Maths
“s a conclusion, Maxwell is not correct because, in science, the equations we write
should not be correct only dimensionally and quantitatively, but they must also
correspond to observed phenomena.
Substituting .... .... in Ampere’s law, although correct mathematically and dimensionally, is not correct phenomenologically, because the interpretation of the law thus modified leads to absurdities not observed in real world” – Ionel Dinu in http://vixra.org/pdf/1206.0083v1.pdf
Your use of the word “phenomenological” is important.
See the last paragraph in http://www.ivorcatt.org/x121.pdf starting with “Blindness”.
Nobel prize winner Professor Brian Josephson is the extreme example of what has gone wrong in physics. Note his remark; http://www.ivorcatt.co.uk/x23p.htm “This is the problem if you work with simplified physics rather than follow the maths.”
This was his response to The Second Catt Question. He evaded an obvious physical contradiction in classical theory by saying one should not look at the physics (the physical reality), but rather at the maths! Mathematicians have captured physics, with disastrous results.
Note my remark, also in http://www.ivorcatt.co.uk/x23p.htm
The simplest case, http://www.ivorcatt.co.uk/cattq.htm , has perfect conductors and perfect dielectric. Imperfections can be added later. Mathematical manipulations can be added later. However, the fundamentals are in the physics, not in the mathematics. Examples of features missing from the maths are causality (only the = sign) and superposition – can two physical situations be superposed?
Note that the number of Google hits for “mathematics is the language of science" is 50,000.
Another interesting event occurred in the mathematicisation of electromagnetic theory when it migrated from equations like δE/δx = -δD/δt , which mapped reasonably well onto a TEM Wave step travelling down guided by two parallel conductors, to today’s divs and dels
where it becomes impossible to see the relationship between the maths and the TEM step. Of course, this is allied with the tradition in academia of ignoring any waveform except the sine wave.
(Irrelevant to the above is the fact that Brian Josephson is marginalised because he tried to bring the paranormal into science.)
Recently I came up with the question; “Is the mathematical derivation of something which is physically real always also physically real?” I honestly don’t know how Josephson would answer. I suspect he would think that mathematical manipulation cannot drive one from the physically real to the non-real.
Note that there seems to be no discussion anywhere on this matter. This is why I jumped on your (Ionel Dinu’s) use of the word “phenomelogical” as a single sign in a desert of indifference.
An interesting example of a dilemma, showing that this may not demand a yes/no answer in a particular case, is distance, velocity, acceleration .... x, dx/dt, d2x/dt2, d3x/dt3 . It is not obvious at what stage in this progression we move from the physically real to the unreal.
In “Death of Electric Current” http://www.ivorcatt.com/2608.htm I write; “Although a cloud cannot exist without edges, the edges of a cloud do not exist They have no width, volume, or materiality. However, the edges of a cloud can be drawn. Their shapes can be manipulated graphically and mathematically. The same is true of the so-called ‘electric current’”. Electric current is a mathematical derivation from magnetic field. This is the first time in science that the first differential of something real (field) has been regarded as real.
Ivor Catt 15 September 2012