Many of us have seen the experiment that demonstrates vibrational normal modes on a drum...:) For people who is not musically inclined, a drum is an acoustic cavity covered with a leather or elastic membrane...
The stretched material (leather) will vibrate and have normal modes defined by the boundary conditions. In this case, the boundary conditions is to have zero amplitude on the circular wooden frame that holds the leather sheet.
As you can see, the mode (1,1) has a node right in the middle. That is where the grains of sand will go.
Up to now this has been just High School Science...:) How come such a trivial problem can explain the whole Universe???
The answer is always in a change in paradigm or how do you look at what everyone have looked before and see something nobody has ever seen...:)
The solution is to think about our minute grain of sand as my four-dimensional dilator..>:) and the vibrations on the drum as the dilaton fields on the 3D Shock-Wave Hyperspherical Universe. Let's take it slowly... One don't want to have a mental cramp...:)
If one considers how the standard experiment is done, one will probe only the second harmonic, that is, one will excite the drum membrane using a sound wave with the second harmonic frequency while pouring sand over the membrane.
As the frequency of the sound wave comes close to the second resonance frequency mode (1,1), the sand motion changes from chaotic into a coherent displacement and all the grains of sand move into the nodes. I mentioned the second harmonic because the first has no nodes...
That is how everyone plus the kitchen cat sees the experiment... That will not bring you any wisdom...
To see what I see, you have to see the grain of sand as my four-dimensional dilator. Since the grain of sand doesn't vibrate, one should consider it a zero amplitude dilator with undefined phase. Under these conditions the grain of sand (zero amplitude dilator) will move into the node where the vibration (dilaton field) has zero amplitude.
Up to now, there is no new wisdom... Now consider that the drum is excited by a sound wave with frequency equal to the sum of the the first and the second resonance frequencies. This frequency is the sum of the w1 and w2, first and second resonance frequencies of the drum.
Now add to the grain of sand an unique vibrating amplitude, the difference beating (w2-w1) and a random phase. The difference beating frequency is choosen because I wanted to make the correspondence between the dilator and a coherence between two normal modes as in my model. The beating or difference frequency is the tunelling frequency between two eigenstates of the 4D tunelling rotating double well potential.
The usage of the sum frequency to nonlinearly excite the two modes of the drum was used just to simplify the experiment (not to introduce sub-harmonics).
Now that we have the two normal modes beating with a fixed phase shift between them, one can start pouring the vibrating sand on the drum...
The first thing you will notice is that the grains of sand will not all want to move into the nodes... All of them vibrate and they don't want to be in a region where nothing is happening...:)
They will relocate themselves into the regions where their vibration is in phase with the supporting vibrating drum and the local membrane vibrating frequency is equal to the difference beating.
This simple thought experiment - I don't have vibrating sand nor a drum - explains my Lagrangian Principle. Dilators will move into regions where they are in phase with the dilaton field. Using this simple argument I reproduced all forces of nature.
The quantum part of it comes about if you make the sand very thin along one coordinate and make them to rotate, thus impacting the vibrating membrane differently depending upon their rotational phase. When the grain of sand is flat on its back, it impacts the most the drum membrane...(not a perfect analogy...but...:) When it is on its side (90 degrees rotated), it is too skinny to interact appreciably with the drum membrane. I guess I would have to make the membrane porous, such that the skinny grain of sand would not interact at all with the membrane....:)
This kind of on and off interaction is the basis for the Pseudo Time-Quantization.
Applied to our drum it would mean that all the grains of sand would interact only at specific phases of their rotation and would all move towards the maximum amplitude or zero phase, thus creating a Cosmological Sand Coherence....:)
Rotational and dilator frequencies have to be related due to the fact that we only see one side of these rotating dilator at each de Broglie step.. An electron is always an electron - has always the electron mass - and a proton is always a proton -has always the proton mass..
This is the basis for Pseudo Time-Quantization...:)
This is a lot of Wisdom to be in such a small grain of sand...:)
It is also im my paper - the same one that Los Alamos is censuring..>:)
It is a National Shame...:)
PS_ I finally learned how to allow you to forward the blog to someone you might consider to benefit from it... The envelop icon below allows for you to email my blog to everyone...
Please do so and also visit the Philica link on the top of the page... It is important that everyone who can understand it, learn about this theory....
I still don't have a review at Philica... I understand why... The paper is difficult to read... complex concepts, some math... and people don't want to stick their neck out ... like the Los Alamos ArXives moderator... It is safer just to say nothing than to express an opinion...:)
I exhort you to do it differently... Take a position!!!... bring this blog to all your friends and colleagues... This might be difficult, but I am blogging it into simple bits... hoping everyone can understand...
The more people visits my Philica Paper the more likely it will be seem by the scientific community and some resolution will take place...:)
New theory proposed that the 3-D Universe is a shock wave traveling at the speed of light along a fourth-dimension.
This Thin Hypergeometrical Universe together with a de Broglie formulation of the forces yield the Holy Grail of Physics, the Theory of Everything.
The light speed moving Universe explains the origin of the E=mc^2 energy as kinetic in origin, thus precluding the existence of Strong and Weak Forces.
Time Quantization is proposed