XPost: sci.physics.relativity
From: nospam@de-ster.demon.nl
Bill Sloman wrote:
> On 23/02/2026 8:38 am, J. J. Lodder wrote:
> > Bill Sloman wrote:
> >
> >> On 22/02/2026 9:25 pm, J. J. Lodder wrote:
> >>> Bill Sloman wrote:
> >>>
> >>>> On 21/02/2026 10:46 pm, J. J. Lodder wrote:
> >>>>> Bill Sloman wrote:
> >>>>>
> >>>>>> On 21/02/2026 5:52 am, Ross Finlayson wrote:
> >>>>>>> On 02/20/2026 10:31 AM, Bill Sloman wrote:
> >>>>>>>> On 21/02/2026 3:47 am, Ross Finlayson wrote:
> >>>>>>>>> On 02/19/2026 11:45 PM, Bill Sloman wrote:
> >>>>>>>>>> On 20/02/2026 10:48 am, Ross Finlayson wrote:
> >>>>>>>>>>> On 02/19/2026 11:19 AM, Bill Sloman wrote:
> >>>>>>>>>>>> On 20/02/2026 2:44 am, Ross Finlayson wrote:
> >>>>>>>>>>>>> On 02/19/2026 01:45 AM, Bill Sloman wrote:
> >>>>>>>>>>>>>> On 19/02/2026 6:13 am, Ross Finlayson wrote:
> >>>>>>>>>>>>>>> On 02/18/2026 11:06 AM, Ross Finlayson wrote:
> >>>>>>>>>>>>>>>> On 02/17/2026 08:35 PM, Bill Sloman wrote:
> >>>>>>>>>>>>>>>>> On 18/02/2026 5:37 am, Ross Finlayson wrote:
> >>>>>>>>>>>>>>>>>> On 02/17/2026 09:47 AM, Thomas 'PointedEars' Lahn wrote:
> >>>>>>>>>>>>>>>>>>> Ross Finlayson wrote:
> >>>>>>>>>>>>>>>>>>>> On 02/17/2026 03:49 AM, J. J. Lodder wrote:
> >>>>>>
> >>>>>>
> >>>>>>
> >>>>>>> I.e., mathematics _owes_ physics more and better mathematics
> >>>>>>> of continuity and infinity.
> >>>>>>
> >>>>>> Mathematics doesn't owe physics anything. Physics exploits tools
> >>>>>> developed by mathematicians, which makes physicists customers for the
> >>>>>> work of some mathematicians.
> >>>>>
> >>>>> That is quite arguable.
> >>>>> Much of mathematics wouldn't exist
> >>>>> without (what was once) new input from physics.
> >>>>> Many a luminary, Von Neumann for example,
> >>>>> has said that mathematics will go stale
> >>>>> without regular fresh input from the natural sciences,
> >>>>> bringing new needs.
> >>>>>
> >>>>>> A mathematical physicist like Paul Dirac is an interesting hybrid, but
> >>>>>> his biography is titled "The strangest man".
> >>>>>>
> >>>>>> https://en.wikipedia.org/wiki/Paul_Dirac
> >>>>>
> >>>>> Why discredit him by calling him 'a mathematical physicist'?
> >>>>> He was a theoretical physicist,
> >>>>
> >>>> He invented the Dirac function, and bra-ket notation. He was notably
> >>>> more deft with math than most of his contemporaries.
> >>>
> >>> Arguably. The real inventor was Oliver Heavidise.
> >>> (who loved to pester mathematicians with it)
> >>>
> >>> Dirac just gave it another, more elegant name. [1]
> >>> ( \delta(x) versus D H(x) or 1/2 D \signum(x) )
> >>>
> >>> And that 'most of' will depend on how wide you want to draw the circle.
> >>>
> >>>> https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation
> >>>
> >>> Nothing but notation. You can do without just as well.
> >>> Mathematicians object to it,
> >>> because the notation assumes without proof that adjoints exist.
> >>> (which often needs to be shown, by their standards)
> >>>
> >>>> He reconciled several ostensibly different quantum theories by pointing
> >>>> out that they were notational variations of the same basic idea.
> >>>
> >>> Yes. But imho his most important contribution
> >>> was getting quantum field theory started,
> >>
> >> "Quantum field theory" is just words to me.
> >
> > That is just too bad.
>
> I'm good at learning what I need to, and getting deep into quantum
> physics never turned out to be necessary.
>
> > All of physics is quantum field theory these days,
> > at least in principle.
> >
> >>> [1] Dirac was an electrotechnical engineer by training.
> >>> He must have known about Heaviside and his operational calculus.
> >>
> >> Perhaps. He did his first degree at Bristol in 1921, and went on to do a
> >> separate degree in math in 1923. Heaviside was a controversial figure,
> >> and might not have been much cited at Bristol back then.
> >
> > Being controversial leads to being well-know.
> > And Heaviside solved a number of fundamental problems
> > in electromagnetism, so any electrical engineer
> > must know about his work.
> >
> > Even Maxwell's equations are only known nowadays
> > in the form Heaviside gave them.
> > Some people even call them the Maxwell-Heaviside equations.
>
> Heaviside's version wasn't quite what Maxwell had originally produced.
Indeed, it was much better.
Maxwell was still stuck on potentials,
and his formulation was not properly gauge-invariant.
Heaviside's version, which focussed on the directly observable fields
made practicl applications much easier.
But Maxwell made the crucial step of identifying,
and adding the missing term.
> >> Looking at Heaviside's wikipedia page, I note that he was the first to
> >> use the impulse function (now known as the Dirac function). If Dirac had
> >> known much about Heaviside's work, he probably would have called it the
> >> Heaviside function when he first used it.
> >
> > 'Heaviside function' is already in use for the unit step function,
> > (don't know about when that name originated, guess well before Dirac)
>
> The Heaviside step function is just the integral of the Dirac function.
> If Dirac had known about it he'd probably have called the impulse
> function the derivative of the step function.
It is obvious that you have not seen Dirac's original work,
where he introduces the \delta-function.
He explicitly says there that introducing the \delta-function
as the derivative of the unit step function,
(which he calls the \epsilon-function)
is an alternative and equivalent way of introducing the \delta-function.
He doesn't mention Heaviside by name,
Jan
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