Link text: https://www.youtube.com/watch?v=yu6x9sJCGfo
This is
cool. Falling balls keep on going. Rolling and sliding constraints are fulfilled
at the same time. The acting forces are electromagnetic field and gravity
field. By idealising this toy to a model
we see that this mimic a problem of two things experiencing electromagnetism and
gravity at the same time (earth gravity field and electromagnetic field between
the parts). With earth this is a tree
body problem.
Lift the
toy to the space, then the constraint to roll on the table is realised and
earth gravity does not affect to movement. Then the toy mimic two things in electromagnetic
field. The toy becomes a model of atom. The great ball is nucleus and the
smaller cut ball is electron. Both have spin, they are spinning. Electron is
rolling on nucleus with its spin keeping constant value and nucleus is spinning
too.
Electron is
on an orbital around the nucleus. The orbital create one constraint, the
electron slides (without friction) around the nucleus. If we idealise again. We
see that here is spinning disk sliding on rolling ball. Both part have their
spinning axis and they keep their orientation constant. Both are spinning
independently and under one constraint to keep electron on the orbital.
A step to modelling
this toy by Quantum Mechanics is that the spins of the nucleus and the electron
are coupled by nuclear force (spin-spin interaction). Solving Schrödinger equation
for the hydrogen atom with spin interaction we observe result that ground state
of the electron is split (to two states): This means spins are on the same
direction or to opposite direction. This splitting is measured very accurately.
This toy
model is funny and as by diminishing it to atomic scale, we get out of it
atomic model for Hydrogen. Now make the toy bigger. Then gravity turns on
again. This is a model of two spinning stars or system like moon and the earth.
Orbiting around is not frictionless because of tidal forces use a part of
spinning energy of the moon. Moon is travelling of the earth. Earth and moons
spins are locked by gravity. Moon rolls around earth so that its surface keep
on same position and we do not see its rolling once a month. Earth is rolling once
a day (actually the day is the rolling of the earth). For moon and earth magnetic
effects are small and the dominating force is gravity. Now speed up system and
let the upper ball become a black hole with charge (electric field). The Black
hole is spinning disk.
With
charged Black Hole we have a gravity model for the system. Charge behave like a
different mas and there is two event horizons in this type of Black Hole (outer
and inner horizon). Now we have a problem. We have not managed to model the
situation that both balls here are electrically charged. We do not know how
electromagnetic field and gravity field should be put together. In small scale
the solution was to take nuclear field as spin-spin interaction to the model.
This is the same that we had to take the quantum mechanics account.
Rolling
disk sliding on a ball success now at this extreme limit of Black Holes, that
we should take account one additional "gravity spin field" to
account. This may be new force field we do not have a model yet. The Dark Force
at short distance and in strong gravity, may couple the spins of the stars new
way. We do not have a model for this yeat.
This toy is
funny and very inspiring theoretically. Model for atoms follow from it. Maybe
it also can lead us to unite gravity and electromagnetism and if we keep in
mind that nuclear forces can be taken account, we can think this toy is a model
for uniting all physical base theories to new theory, a Grand Unification Toy.
