Particle physics has originally been based on the rigid mass operator. Unkluckily only a few physicists understand master level rotating mass mechanics as this is a field used/covered by mechanical engineering.

Why physics did use the fringe Virial approach (square integrable functions..) is an enigma. May be most were mathematicians bare of any physics understanding.

The solutions of the rigid mass operator problems are torus surfaces! It is thus no surprise that all particles can be modeled by  higher order tori! Of course we do not need any fantasy numbers or point masses...


J.W.


On 27.06.2020 23:59, H LV wrote:
I am not sure if this is related but I always had a problem with the concept of a point mass or a point charge, since mathematically that would imply infinite mass density or charge density or alternatively zero mass and zero charge. However these conundrums are resolved mathematically by moving from the real number system to the hyperreal number system first formulated by Abraham Robinson in the early 1960s. The hyperreal number system extends the real number system by including  infinitely small numbers and infinitely large numbers and gives a logical foundation for the calculus of infinitesimals known as "non-standard analysis". Today  most physicists and students still learn calculus using "standard analysis" which is based on the notion of limits and was developed by mathematicians in the 19th century.

An interesting property of infinitesimals is that they come in different sizes. For example if ε   is an infinitesimal then ε < 2 ε < 3ε ...etc. The reciprocal of an infinitesimal number is an infinite number, so there are also different size infinities. For example 1/ε > 1/2ε > 1/3ε ...etc.

Harry

On Fri, Jun 26, 2020 at 5:35 PM Jürg Wyttenbach <ju...@datamart.ch <mailto:ju...@datamart.ch>> wrote:

    The fantasy of the old SM guard always seemed to be limitless...

    SO(4) physics exactly explains how the claimed force "gravity" is
    generated and mediated between hadronic masses.

    Since about 1 year there is game over for SM. No more cheating
    with point particles that do not behave as points because these
    points have a magnetic moment. No more cheating with massless
    charge as such an assumption simply is a form of infantile
    dementia if no proof is given why a massless charge does move
    without inertia and no force is need for a circular orbit. Most
    idiotic is the assumption charge is wave as the magnetic moment
    then would oscillate. We can go on with this as you only need
    college level understanding to find out that the foundation of SM
    is children logic.


    J.W.

    On 26.06.2020 20:20, bobcook39...@hotmail.com
    <mailto:bobcook39...@hotmail.com> wrote:

    
https://www.quantamagazine.org/the-cartoon-picture-of-magnets-that-has-transformed-science-20200624/

    some INTERESTING OBSERVATIONS….

    Loss of the directional control of angular momentum in nuclei  is
    probably is associated with the creation of unstable nuclear
     conditions and isotopic transitions.  It  may also  change gravity

    Of a group of nuclear magnetic dipoles, if the TOTAO magnetic
    dipole attraction is modified—either increases or reduced?  *This
    question   stems from the CONJECTURE that gravity results from an
    *_random_* collection of nuclear magnetic dipoles  and the
    respective 0  (zero) net angular momentum.

    The calculation of an attractive magnetic field at large
    distances between randomly oriented groups of magnetic dipoles
     supports the CONJECTURE  noted above IMHO.

    _http://downloads.hindawi.com/archive/1998/079537.pdf_

    __

    A better reference would be nice.

    .

    Bob Cook

-- Jürg Wyttenbach
    Bifangstr. 22
    8910 Affoltern am Albis

    +41 44 760 14 18
    +41 79 246 36 06

--
Jürg Wyttenbach
Bifangstr. 22
8910 Affoltern am Albis

+41 44 760 14 18
+41 79 246 36 06

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