*Is it possible that “Matter” is simply “Incompressible Energy”?…*

Coarse Harmonic Motion (CHM) would be the type of motion undertaken by a Coarse Harmonic Oscillator, an oscillator similar to a Simple Harmonic Oscillator but instead of pure continuous motion – this oscillator’s motion back and forth occurs in *Coarse Incremental Steps…*

Coarse Harmonic Motion (CHM) would be the type of motion undertaken by a Coarse Harmonic Oscillator, an oscillator similar to a Simple Harmonic Oscillator but uses discrete step-sizes instead of pure continuous motion – *a Coarse Step-Size of Oscillation.*

We will here examine what happens to the behaviour of a harmonic oscillator as we increase the *“coarseness”* of the increment step-size of oscillation.

__ω____1 is One Degree__

For ease of discussion, let’s say the fundamental unit of time is 1 second and the fundamental angular step-size (ω) is one degree per unit time – thus 1 degree per second translates to a fundamental angular frequency of 0.01745 radians per unit time.

**ħ = ^{1}/_{57} Ħ =57 d^{i} = (1 + i ^{1}/_{57})**

**and d ^{i(1Ħ)} = (1 + i ^{1}/_{57})^{1Ħ} = 1 Radian**

**and d ^{i(}**

^{2}

^{π}

^{Ħ)}**= (1 + i**

^{1}/_{57})

^{2}

^{π}

^{Ħ}**= 6.28 Radians**

Since 1 degree is approximately 1/57 of one Radian _{(the unit of angular frequency)} and exactly 1/360 of one Cycle/Oscillation _{(the unit of frequency)}; then this means that the fundamental frequency is 0.00278 oscillations per unit time, and the fundamental wavelength _{(in time)} is 360 steps of 1 degree (or 360 steps of 0.01745 radians which is equal to 2π Radians)!

^{[Note: }^{f =}^{ ω}^{/}^{2}^{π = }^{ 0.01745/2}^{π = 0.00278 oscillations per unit time] }^{[Note: 360 steps of step-size 0.01745 radians is equal to a total of 2}^{π Radians}^{]}

Here is the graph of that evolution as the system evolves at a step-size of one degree per unit time.

Now we double the step size (step-size = 2 Degrees)

Now let’s make it 10 times the fundamental step size (step-size = 10 Degrees)

Now let’s make it 33 times the fundamental step size (step-size = 33 Degrees)

Now let’s make it 73 times the fundamental step size (step-size = 73 Degrees)

Now let’s make it 134 times the fundamental step size (step-size = 134 Degrees)

Now let’s make it 154 times the fundamental step size (step-size = 154 Degrees)

Now let’s make it 166 times the fundamental step size (step-size = 166 Degrees)

Now let’s make it 172 times the fundamental step size (step-size = 172 Degrees)

Finally let’s make it 179 times the fundamental step size (step-size = 179 Degrees)

__Analysis of Waveforms__

As we can see, for small step-size, everything appears as expected, smooth harmonic motion. However as we increased the step-size, the synchronicity of oscillation (i.e. the ability of the oscillation to synchronize the starting point of a new cycle with the starting point of the previous cycle) began to be disrupted and as a result imbalances begin to emerge. Further increases in phase-size/step-size cause some curious patterns to emerge, and finally at high degree of coarseness, very well defined *“beats”* eventually emerge.

So why is this interesting? It is interesting because it shows that high energy ** “coarse oscillations”** exhibit

**. Coarse Harmonic Motion seems to suggest that symmetry-breaking, and its resultant complexity in structure, can emerge from**

*“matter-like properties”**coarse synchronization in time*.