## Wave Equation in an Elastic Wave Medium

Deducing Matter Energy Interactions in Space. Einstein's
E=mc^{2}, Planck's E=hf, Newton's F=ma.

Hi Everyone,

I am working on this page over the next few weeks. The purpose is to show that all matter interactions are really wave interactions in an elastic / kinetic wave medium, space.

The fundamental equations of physical reality are the two simple wave equations for an elastic kinetic wave medium.

c=fy

and

c^{2} = F / m_{d}

Written as one equation

c^{2} = (fy)^{2} = F / m_{d}

Where;

c = velocity of light

f = frequency

y = wavelength

F = Force = constant (k_{a}) by amplitude (x) = k_{a}x

m_{d} = mass density = mass (m) / wavelength (y) =
m / y

Let us assume that amplitude is proportional to wavelength

F = k_{a}x = k_{w}y

Energy (E) = force (k_{w}y) by distance (y) thus;

E = k_{w}y^{2}

## Deduce the Famous Energy Equations E = mc^{2} =
hf

### Einstein's E=mc^{2}

c^{2} = F / m_{d}

We can re-write this substituting F = k_{w}y and m_{d}
= m / y

c^{2} = k_{w}y^{2} / m

Substitute E= k_{w}y^{2}

**Thus E = mc ^{2}**

To deduce mass

k_{w}y^{2} = mc^{2}

m = k_{w}y^{2} / c^{2}

m = k_{w}y^{2} / (yf)^{2}

**Thus m = k _{w} / f^{2}**

### Planck's constant h and E = hf

Substitute c = fy into E = mc^{2}

E = mc^{2} = mcfy = (mcy)f

If we substitute known values of m, c and y for electron we
get;

mcy = 9.1 × 10^{-31}× 3 × 10^{8} × 2.4 ×10^{-12}
= 6.5 ×10^{-34} = Planck's constant h

**Thus h = mcy**

E = (mcy)f

** Thus E = hf**

This tells us that for light interactions the quantity mcy
remains constant. If we rewrite this with m = k_{w} / f^{2}
we get k_{w} y^{2} / f remains constant.

For further thought - it is interesting that the only difference
between E = mc^{2} and E = hf is c=fy

Does this mean that c=fy only applies to light energy (what they currently
call em waves) where E = nhf (the frequency is quantised by n).

### Newton's Law of Inertia F=ma

E = Fy = mc^{2}

and

acceleration (a) = meters (y) / seconds^{2} where
time = 1/f thus a = yf^{2}

F = mc^{2} / y

F = my^{2}f^{2} / y

F = myf^{2}

Substitute a = yf^{2}

**Thus F = ma**

## All Energy is Wave Energy

What does this tell us? That the energy, mass and force equations in physics are just wave equations. This is consistent with the fact that waves propagate energy, a wave is an oscillation between the kinetic and elastic energy of space. This obviously explains why matter and energy are equivalent - because matter is made of waves.

This also tells us that all forces are just a change in the velocity of the waves which causes a change in velocity (re-positioning) of the wave center. We currently call this a force accelerating a mass particle - but it is really a spherical standing wave where the wave center is the 'particle'.

## All Forces are Changes in Wave Velocity

From the wave equation we can then see the source of charge and gravity forces.

**c ^{2} = F / m_{d}**

**Charge:** The charge force relates to the force
F required to displace (amplitude and wavelength) the elastic wave medium.
The larger the displacement, the higher the wave velocity where c is proportional
to the square root of F.

**Gravity:** The gravity force relates to the
mass density m_{d} of space. The higher the mass density the slower
the wave velocity where c is inversely proportional to the square root of
m_{d}.

How simple - here is the unification of light and gravity, mass and charge.

I will explain this further over the next month - I am working on some wave diagrams to help you visualise this.

Below I have added links to some important work from Michael Harney who has also deduced the Wave Structure of Matter (WSM) in an elastic wave medium (space).

Geoff Haselhurst

## Waves in an Elastic Wave Medium

By Michael Harney

The waves are transverse - the first obvious evidence of this is that EM waves are transverse and EM waves (photons) are the result of resonance between wave centers. If the waves making up wave centers resonate to produce transverse waves, then by nature of resonance (which is not a vector operation - strictly scalar), the waves making up wave centers are transverse.

Now for the mathematical argument.

The formula for the speed of waves is speed = sqrt (kx/mass density) where
mass density is Mass of Universe / Radius of Universe and x is the peak
amplitude of the wave. If we plug in x = Radius of Universe, k = 7.18 x
10^{17} N/m, we get speed = speed of light (3 x 10^{8} meters/sec).

But this is only true based on the linear mass density (mass/length) which
is only true because the waves are scalar and the mass density is independent
of any vector quantity. If the waves were longitudinal they would be heavily
dependent on the volume of space (sound waves depend on the cubic density
of air - mass/volume).

I have tried the mass/volume density in many formulas and it never works
- only mass/length works and this is definitely much like a 1 dimensional
string/wave formula which is also the same as a uniform spherical wave (only
depends on r, not theta or phi from spherical coordinates).

This also shows you that the wave speed is non-linear (quadratic formula of square root of the amplitude) in relation to the amplitude of the wave. It is not non-linear from the standpoint of differential equations though (some people say non-linear and mean unsolvable - other say non linear as not a linear slope, e.g. f = kx, we mean non-linear in that f = k*sqrt(x)).

A fundamental formula of physics that nobody should ever disagree with is this one: wavelength = speed / frequency. Even though the speed may vary based on physical factors, the wavelength, speed and frequency formula does not change and you can always find one of the quantities with the other two.

As far as the frequency (or wavelength) of the wave based on the mass, it's not mc^2 = hf as most people think. This formula ONLY applies to photons conversion to mass or vice versa. Unfortunately it is not that straight forward or mc^2 = hf would be used to predict the mass of the photon based on it's wavelength which we know is not true.

The article I wrote about Heisenberg's uncertainty principle shows how to calculate the mass of a particle based on wave number (how many nodes, or peaks, are in the wave) which also relates to frequency once the speed of the wave is known. This does use Schrodinger's equation but it can be boiled down to just the wave number aspects of fundamental waves.

The velocity of waves derived from the energy density of space is in the paper I submitted to GED "Derivation of the Schwarzchild Solution from a Scalar Model of Spherical Quantum Waves"

In fact, this is the same waves-in-an-elastic medium derivation:

M = the mass of the Universe, 1.44 x 10^{53} Kg

R = radius of the Universe, 1.9 x 10^{26} meters

Mass Density 1.44 x 10^{27} Kg/meter

v = velocity of waves

k = elastic constant

v = sqrt(kr / (M/R)) = R*sqrt (k/M) = speed of light (c), if k = 7.18
x 10^{17} N/m

This is the in-wave velocity. The out-wave velocity is determined the same
way except the formula is v = sqrt(kr / (M/R)), where r replaces R in the
numerator.

r is the compression length (the bend radius in space) that creates the
mass source. If we are looking at the outwaves from the sun, r is found
from the formula;

mc^{2} = kr^{2}, where m = mass of the object (sun, planet
whatever the outwave is coming from), r is the compression length found
by solving the above equation and k is 7.18 x 10^{17} N/m. Then
Einstein's familiar time-dilation formula is found by taking the Lorentz
transform of the outwave velocity with respect to speed of light:

Time-dilated on out-wave = Time with respect to in-wave / sqrt (1 - v^{2}/c^{2})
where v is the out-wave velocity determined with v = sqrt(kr / (M/R)) as
described above. This is all based on mass-density of space and the elastic
constant which is uniform.

Michael Harney

### My work in progress!

The following is just my rough notes as I write this page up. Geoff Haselhurst

### Calculating the constants k_{a} and k_{w}

For the electron

m = 9.1 × 10^{-31} Kg

c = 3 × 10^{8} m/s

y = 2.4 ×10^{-12} m

f = c/y = 1.2345 x 10^{20}

mass density space = 1.44 x 10^{27}

Planck's constant h = mcy = 6.5 ×10^{-34} Kg m^{2
}s

m = k_{w} / f^{2}

k_{w } = mf^{2}

k_{w} = 9.1 x 10^{-31} x (1.2345 x 10^{20})^{2}

k_{w} = 1.38 x 10^{10} Kg / s^{2}

F = k_{a}x = k_{w}y

c^{2} = (fy)^{2} = F / (m/y) = Fy/m

c^{2} = k_{a}x y / m

k_{a}x = c^{2} m/y = 9 x 10^{16} x
9.1 × 10^{-31} / 2.4 ×10^{-12} = 1.96 × 10^{-1}

E = k_{a}x = mc^{2}

k_{a} = mc^{2} / x

c^{2} = 9 x 10^{16} = 1.96 × 10^{-1}
/ 1.44 x 10^{27}

I am still working on this. ???

For further analysis.

1. How does the velocity and wavelength change with radius of spherical wave.

Amplitude ~ 1/r^{2} ~ y ~ c

Thus half the radius is 4 times the wave amplitude.

2. There are three different waves, two that are formed from the fundamental spherical matter waves.

i) The spherical in and out waves where v = c (local)

ii) The em wave of hills and hollows on the surface of the spherical waves (local)

iii) For relative velocity (v_{r}) the de Broglie phase wave with
velocity v = c^{2} / v_{r} (non-local)

-----------------------------

I need to think about this.

c=yf

thus c^{2} = y^{2} f^{2}

Thus c^{2} = E / m

thus E=mc^{2}

### Calculus and Infinitesimal Time and Motion

In calculus we use infinitesimal time, motion and distance

Because time is really frequency then it seems to me that you cannot use
an infinitely small time, the shortest time is 1.23 * 10^{-20} seconds,
the frequency of the electron.

e.g. c=dx/dt = dy df

I am not a mathematician - just logical!

Does any of this make sense to you?

Cheers,

Geoff

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