Bell’s inequality in Fractal Mechanics: How does it look like in Geometric musical language

Bell’s inequality is very easy to understand. To understand it, we need three polarizers. What is a polarizer? Light has electric vector in all directions, a polarizer allows transmitting the part of light whose electric vectors are oriented in only one direction. Now, if three polarizers, A, B and C are kept in a line. Light enters through A, then passes through B and finally passes through C. If polarizers are rotated relative to each other, a part of the light is blocked. This is funny. Because just above, we have said that a polarizer allows only one vector to pass through. Then, any two polarizers with a relative angle should block all parts of light. But that does not happen in reality. If A and C polarizers are oriented 90 degree relative to each other, then, light is fully blocked. If angle between them is 45 degree then only 50% light passes through.

Coming back to a linear arrangement of three polarizers. If there is no B in the middle, the light enters through A and 50% of the incident light passes through C if relative angle between them is 45 degree. If we insert polarizer B, at 22.5 degree, then, light enters through A and 15% is blocked by B. 85% passes through B. Then C is also 22.5 degree relative to B, so 85% the incident light at B passes through C. This is interesting. A, B and C are kept in a linear arrangement. B blocks 15% of light coming through A. And then C blocks 15% of light coming through B. So, if 100% light coming through A, after transmitting from C we get 85% of the 85% light, it means 72.5% of light. It means 27.5% light is blocked by B and C. So, we reach an interesting fact. If only A and C are kept in a line, we get 50% blocked, but if we insert B in between A and C, then we get 27.5% blocked. So, we get more light.

In a classical scenario, when A, B and C are there, light blocked by B and C should be equal or greater than the light blocked when A and C are there. Addition of another polarizer in between must not increase transparency in classical. But in quantum more polarizers you add you would see more transparency. Now, Bell wrote classical possibility in terms of an inequality.

Light blocked by C alone (only A and C) <= light blocked by B plus light blocked by C (A, B, C are there)

The above statement is the Bell inequality. Now, explanation is that when the relative angle of polarizers is low, then it helps to correlate the light, so that more quantity of light passing through as a group. Different polarized lights if the angles between them are nearly similar get connected by the polarizers, and that is similar to GML where we bind clocks or periodic motions using a higher level clock. The binding of clocks into higher level is property of certain materials which we call quantum materials in terms of GML. When hierarchical levels are more than one, binding of clocks continues, then, it is fractal mechanics. The material is called fractal mechanical material. For details about Fractal mechanics read our book,

Nanobrain: the making of an artificial brain made of a time crystal

Now the question is that how do we test fractal mechanics in reality. Or Bell’s inequality to be precise? We have to show that a fractal mechanical material is binding the clocks and building hierarchical clocks. For us, we use organic jelly, namely brain jelly, which is primarily made of helical nanowires. These nanowires generate optical and magnetic vortices and those vortices self-assemble into hierarchical structures, or assembly of rings. We find them as holographic projection to the screen. Once we find that polarizer A and C kept at an angle 45 degree supposed to generate 50% emission, actually generates more if a helical nanowire solution is kept in between. This shows classical condition inequality set by Bell is violated and we get quantum mechanical feature generated by the fractal material. To prove hierarchical layers as required by Fractal mechanics, we pump electromagnetic signal and by tuning frequency we tune the transmission more than 50% to 90%. The tuning suggests that we can regulate the quantum mechanical property, i.e. we get fractal mechanical properties.

Thus far we have demonstrated fractal mechanical properties by showing CEES spectroscopic features in our PCMS nanobrain, an organic nano-machine, resonance peak inside a peak in the absorption-fluorescence spectrum. Then, we have shown, fractal resonance behavior in the 2D electromagnetic resonance measurements of the helical nanowire. Finally, we want to show hierarchical tunable violations of Bell inequality to prove that fractal mechanics is a reality.


  1. Thanks Dr. Bandyopadhyay! 1) What happens if circular polarizers are used? 2) Does color of the laser have different coupling to the CNT? I noticed that the red laser showed more rotation than the green or the blue.3) Yesterday I received the Red Point Laser with a power supply. This way I can expose the magnetic film to the red light for 3 hours like you had mentioned.

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    1. After I posted my colleague Dr. Pathik Sahoo asked the same question, he came up with an idea to add angular momentum to light beam. Red laser shows better rotation and coupling. We have seen the same. Why I don’t know.


  2. Ah this is a very simple way to start learning about how to use the helical CNTs as a simple real world application proof of magnetic vortex and these effects. I’ll have to give a go at this one as I have some linear and circular polarizers. Thinking of buying some helical MWCNTs from and the Hexane to test this out next on top of another project in parallel.

    Watching this vector visual I suppose the vector addition with 3 polarizers shows that imaginary worlds of information are required more than classical mechanics to explain 3 polarizer scenario.


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