[Physics] Why is a new beginning in physics necessary? *

[Arend Lammertink]

Dear Maurice,

On Thu, Dec 8, 2016 at 5:49 PM, Master Inventor
<mdaniel at masterinventor.com> wrote:
>
>
> The greatest omission of classical physics is  the failure to deal with rotations.  Because rotations are non-linear, physicist wrote simplified linear relationships to deal with them.  They failed to consider that rotations add 4 more dimensions to all the laws of physics (3 rotations in space and one rotation in time).  The physics we were taught compresses 8 dimensions into 4 dimensions, resulting in strange and unexplained behavior, such as quantum mechanics.
>
> If physics is to have a new beginning it must be expanded to a framework having 8-dimensions.
>

I agree wholeheartedly that the incorporation of rotation is the key
for formulating a new physics foundation.  However, that does not mean
one would have to add 3 spatial dimensions and/or an extra time
dimension. After all, the rotation of a fly wheel, a tornado, etc. all
take place within our normal interpretation of 3D space and 1D time.
And in practice, there's not only rotation which occurs in a vortex,
but also a pressure variation. In other words: rotation and pressure
c.q. density variations c.q. material tensions go hand in hand, so you
can't just decouple them completely in a 6 dimensional spatial
(coordinate) system and thus define the inter-relations between
rotational and translational movements away.

The model I made is in the form of differential equations within a
continuous fluid dynamics context. The latter means the equations do
not describe the exact movement of each "particle" within the fluid,
but rather describes the flows and the pressures within the fluid on a
more macroscopic level, where you don't "see" the individual
particles.

Using differential equations in this case means that one describes the
fluid movements and tensions/stresses over an infinitely small volume,
which means that one can consider all relationships to be linear
within such an infinitely small volume.  In computer simulations,
these infinitely small volumes are approximated with "small enough"
volumes with respect to the phenomenon one is studying. This is called
the "finite element method":

https://en.wikipedia.org/wiki/Finite_element_method

For example, if one is interested in simulating weather phenomena, one
can consider the air pressure and wind velocity to be constant across
a volume of, let's say, 10-100 meter in diameter. When one would be
interested in studying a vortex in a cup of water, one would use
volumes with a diameter in the order of 1 micrometer to 1 millimeter.

Another way of thinking of it is to consider that any non-linear
relationship/function can be approximated by a "piecewise" linear
function:

https://en.wikipedia.org/wiki/Piecewise_linear_function

The more "pieces" one uses, the better the approximation. So, when one
takes the length of each piece infinitely small mathematically, one
ends up with a 100% exact "approximation" using only linear
relationships.

In other words: differential equations allow you to use linear
equations, regardless of whether or not the "macroscopic" relations
are linear or not.


Now let's address the need for 8 dimensions. At this moment, I don't
see any reason to consider time to have a rotational component within
our physics model. Sure, it could very well be multi (3?) dimensional,
but if one wishes to describe that, one would need to define a
coordinate system for time and define some trajectory trough that
time-space which makes sense. In that case, it would be the
"observer", our consciousness, which "moves" trough "time-space".
While that is certainly an interesting subject of study, at this
moment I don't think such considerations should be incorporated in our
physics model. At some point in time (pun intended) we might be able
to go in that direction, but not now.

So, then we would end up with 7 dimensions, variables or degrees of
freedom. We would need 6 spatial parameters and 1 time parameter.
However, this does not mean we would need 6 spatial dimensions in our
coordinate system. If we find a method whereby we can model 6
parameters as 3 translational related parameters and 3 rotational
related parameters, we arrive at the situation where we can model the
aspects we need within a 3 dimensional spatial coordinate system.

Now enter the Helmholtz decomposition:

https://en.wikipedia.org/wiki/Helmholtz_decomposition
"n physics and mathematics, in the area of vector calculus,
Helmholtz's theorem, also known as the fundamental theorem of vector
calculus, states that any sufficiently smooth, rapidly decaying vector
field in three dimensions can be resolved into the sum of an
irrotational (curl-free) vector field and a solenoidal
(divergence-free) vector field; this is known as the Helmholtz
decomposition. It is named after Hermann von Helmholtz.

Because an irrotational vector field has a scalar potential and a
solenoidal vector field has a vector potential, the Helmholtz
decomposition states that a vector field (satisfying appropriate
smoothness and decay conditions) can be decomposed as the sum of the
form − grad ⁡ Φ + curl ⁡ A  where Φ is a scalar field, called scalar
potential, and A is a vector field called a vector potential."


What we have here, is a mathematical method to "split"  3 dimensional
laws of physics into two 3 dimensional components, which may be
evaluated separately and thus give you your 6 parameters, without
actually requiring the addition of 3 extra actual spatial dimensions.

In other words: when we use differential equations, which are by
definition linear because of the infinitely small "piecewise"
elements, we can achieve the goal of modelling rotational movements
separately from translational movements in a natural, consistent and
mathematically proven way within a model which completely describes
these within our normal, natural 3 dimensional understanding of
"space".


When I applied this reasoning to Maxwell's equations, I discovered
that in the textbook definition for the electric scalar potential
field Φ, which should be rotation-free within the Helmholtz
decomposition, there is a term which incorporates the rotational
vector potential [A] (i;e; the axis of rotation):

https://en.wikipedia.org/wiki/Magnetic_potential#Magnetic_vector_potential
"The magnetic vector potential A is a vector field defined along with
the electric potential ϕ (a scalar field) by the equations:

B = ∇ × A ,  E = − ∇ ϕ − ∂ A ∂ t , "


So, the magnetic vector potential field [A] is defined as:

 Any vector field [A], which curl equals the magnetic field [B]..

However, for the scalar potential Phi, we can write:

∇ ϕ  = −E  − ∂ A ∂ t

So, the scalar potential field Phi is defined as:

 Any scalar field, which gradient equals minus the electric field [E]
minus the time derivative of a vector field [A] which curl equals the
magnetic field [B].

So, the term dA/dt introduces a *rotationa*l term into an equation
which *should* be *rotation-free*, as per the Helmholtz decomposition.
In other words: in the textbook definition the "rotational dimensions"
are mixed with the "translational dimensions" in the definition for
the scalar potential field Phi, which is clearly wrong when considered
this way.

What's more, the Helmholtz decomposition is supposed to decompose a
"deeper" vector field into two components, in this case the rotation
free scalar potential and it's divergence (the electric field [E]) and
a divergence free (incompressible) vector potential and it's
rotation/curl (the magnetic field [B]).

Now this "deeper" field isn't even defined!  WTF??

Now what would you think would happen if we defined this "deeper"
field as being the flow velocity field [v] - as defined in textbook
fluid dynamics for an ideal, compressible, loss free fluid we call
"aether" - and split this field up in a curl-free and a divergence
free component using the rotation and divergence operators, as done in
the Laplacian operator, and deleted the term dA/dt?

Well, we get a proper Helmholtz decomposition, without mixing of
rotation free terms with rotational terms AND we no longer have the
"gauge freedom" which allows us to define all kinds of imaginary
fields AKA Quantum Field Theory:

https://en.wikipedia.org/wiki/Gauge_fixing


To cut a long story short: when we delete the term dA/dt in the
definition for the scalar potential field Phi and assume the "deeper"
field causing the electromagnetic fields to be the bulk flow velocity
field of a fluid-like medium called "aether", everything drops into
place and we get the 3 extra dimensions you seek in a natural and
mathematically consistent way., yet still within our normal
understanding of space to have 3 dimensions.


Best regards,

Arend.