Conservation Law of Three Gunas

The 3 gunas constitute the foundation of the Brahmachakra theory which was modernized and reformulated by Shrii Shrii Anandamurti [1] [2] .

The 3 gunas explain not only the multiplicity and variation seen in the physical universe but the aspects of creation prior to the physical manifestation as well. In this article we focus our attention to one important aspect of 3 gunas in the physical universe, namely the conservation law of 3 gunas.

Rajoguna

The principle of transformation and change.
The principle of action.
The principle of evolution.
Basis of pulsations, vibrations, oscillations, and fluctuations in nature.
Basis of time.
Basis of energy.
Symmetry breaking tendency.

Tamoguna

Qualification principle.
Limiting, localizing, encircling, internalizing action.
Basis of dualities.
Basis of all forms (mental and physical)
The principle of stability and staticity.
Structure forming tendency.
The origin of coupling/interaction in general.
The source of all physical forces: gravitation, electromagnetic force, strong nuclear force, weak nuclear force.
Nonlinearity (outcome of coupling/interaction)
Curvature (outcome of nonlinearity)
Scale (emerges from curvature and nonlinearity)
Space (a manifestation of scale)
Gravity

Sattvaguna

The soul principle
The principle of sentience.
Principle of unity and unification.
Principle of symmetry
Freedom, salvation, liberation.
Resistance to binding action.
Resistance to curvatures in general.
Resistance to both positive and negative space-time curvatures
Resistance to citta forms (samskaras or memory seeds)
De-coupling and un-tangling principle.
Anti-objectivation tendency
Anti-coupling tendency
Anti-nonlinearity tendency
Anti-scale tendency
Anti-space tendency
Anti-time tendency
Anti-formation tendency
Basis of quantum mechanical (freedom seeking) behavior
Facilitates the reflection of Consciousness in the unit structure (whether the unit is the most basic unit of matter or whether it is the most advanced organism).

Logical Requirements

As the Rajoguna (mutative guna) increases, if the Tamoguna (static guna) is increasing the Sattvaguna (sentient guna) must decrease
As the Rajoguna (mutative guna) decreases, if the Tamoguna (static guna) is decreasing the Sattvaguna (sentient guna) must increase
The totality of the 3-gunas must be strictly conserved

The 3 gunas may have negative values in the mathematical sense. The interpretation of the negative guna value depends on the physical process we are describing. In the context of spacetime the interpretation of the negative value for a guna is to be found in the geometry of the spacetime. The negative value implies negative curvature (hyperbolic geometry) and a positive value implies a positive curvature in spacetime.

Elementary Particles

There are exactly 3 generations of elementary particles (fermions). This is the most profound experimental finding established by the high energy physics in the 20’th century. The current models in physics are totally inadequate when it comes to explaining the existence of the 3 fermion generations.

There are exactly 3 color charges (exhibited by the quarks inside protons and neutrons). The 3 color charges must be related to the 3 generations as well. Both the 3 generations and the 3 color charges must be the manifestations of 3 gunas. We are waiting for clear thinking physicists to explain these deep connections. You can read my attempt in this direction in a mathematical paper titled “Golden Biquaternions, 3 Generations, and Spin”

The conservation laws observed in physics emerge from fundamental symmetries or invariances of the physical processes. The laws of physics are the same no matter what time it is or what year it is. This invariance results in the conservation of energy. Similarly, the laws of physics are the same everywhere in space. This results in the conservation of linear momentum. When we rotate an object in space, the physics of the object does not change. This gives us the conservation of angular momentum. The conservation of electric charge is a result of the so-called gauge symmetry in particle physics.

There is a fundamental conservation law at the root of all physical processes. This is the fundamental invariance. Like the higher level conservation laws the fundamental one also emerges from a mathematical symmetry. Let’s examine this mathematical symmetry.

Mathematical Expression

There is a mathematical structure known as the Steiner’s Roman surface which exhibits an extraordinary 3-fold symmetry. To see the symmetry of this surface please rotate the 3-D image given in Wolfram MathWorld or watch the animation shown in this link.

The Steiner’s Roman surface is the image of a sphere of radius r centered at origin under the projection

$\mathbf{f(x,y,z)}$ -> $\mathbf{(yz,xz,xy)}$ (1)

The intrinsic equation of the Steiner’s Roman surface is given by the formula:

$\mathbf{x^2 y^2 + y^2 z^2 + z^2 x^2 - r^2 x y z=0}$ (2)

If we take r=1 and set xyz=1 the equation becomes a candidate for the mathematical expression of the conservation law of 3 gunas. Let’s identify x with the sentient guna (Sattvaguna), y with the mutative guna (Rajoguna) and z with the static guna (Tamoguna).

The Steiner’s Roman surface is the best mathematical construct to express the conservation law of 3 gunas. Not only does it satisfy the logical requirements but it leads to deeper insights as well. The conservation law for the 3 gunas can be written as follows

$\mathbf{S R T = S^2 R^2 + R^2 T^2 + T^2 S^2 = 1}$ (3)

where we used S,R,T instead of x,y,z. The S is the Sattvaguna, R is the Rajoguna, T is the Tamoguna. Note that if S,R,T reside on a Steiner’s Roman surface the SRT is always positive; either S,R,T are all positive or else exactly two are negative. This will be clear when we examine the geometric shape of the Steiner’s Roman surface.

Hypothesis: A physical process can be represented by the guna vector (S,R,T) whose trajectories always remain on a Steiner’s Roman surface. The totality SRT is strictly conserved. The zero vector (0,0,0) is not possible.

This hypothesis applies to all physical processes whether it is taking place in microscopic or macroscopic levels. The S,R,T will have appropriate correspondences to the variables of physics at each level.

When none of S,R,T is zero, the conservation law of 3 gunas can also be written as follows

$\mathbf{S T / R + S R / T + R T / S = 1}$ (4)

Eq.(4) is a more restrictive version of the conservation law.

Steiner’s Roman Surface

The Steiner’s Roman surface has 4 bulbous lobes. In Figure 1 below, one of the lobes is seen frontally. The overall symmetry of the Steiner’s Roman surface is tetrahedral. Suppose we place this object inside a tetrahedron, then the 4 lobes of the Steiner’s Roman surface would be under the 4 vertices of the tetrahedron. Similarly, the 4 “faces” of the Steiner’s Roman surface would correspond to the 4 faces of the tetrahedron.

Figure 1

In Figure 2 below one of the 4 “faces” is shown

Figure 2

Between each pair of lobes there is a line of “double-points”. The terminology comes from projective geometry. Recall that the Steiner’s Roman surface is the image of a sphere under the projection described by the Eq.(1). The so-called “double-points” are the intersection lines under such transformation. The concept of “intersection” is expressed with the terminology “double-points”. Similarly, the center point (origin) of the Steiner’s Roman surface is known as the “triple-point”.

The line between two lobes end in “pinch” points. Again, if we go back to the imagined situation where the Steiner’s Roman surface is placed inside a tetrahedron. These pinch points are the points where the tetrahedron edges touch the Steiner’s Roman surface. Figure 3 below shows one of the “pinch” points.

Figure 3

Boundary Lines and Pinch Points

The boundary lines (double-points, intersection lines, or the lines connecting the center to the pinch points) correspond to the 3 axis of S,R,T. We declared before that S,R,T reside on a Steiner’s Roman surface excluding the center. Let’s clarify the situation of the boundary (axis) lines. On these axes we would have points like (S,0,0), (0,R,0), (0,0,T) where S,R,T can be between -1 and 1. These are the “phase transition” lines which are fundamentally unstable. The terminology of “double points” is helping with the guna interpretation. On these boundary lines there is degeneracy. The boundary points belong to 2 different “lobes” simultaneously. In the conservation law of the 3 gunas the boundary lines are allowed. The state of the physical structure can transition from one “lobe” to another. The state of the physical structure, however, cannot remain on the boundary. The pinch points of (1,0,0), (-1,0,0), (0,1,0), (0,-1,0), (0,0,1), (0,0,-1) are theoretically possible but extremely unlikely to manifest.

Note that there are no (0,R,T), (S,0,T), (S,R,0) points on the Steiner’s Roman surface. This is yet another reason to choose the Steiner’s Roman surface to represent the conservation law of 3 gunas. The logical requirements dictate that it is impossible for exactly one of 3 gunas to be zero and this condition is satisfied by the Steiner’s Roman surface.

Non-orientable Surface

The Steiner’s Roman surface is non-orientable which means it is a one-sided surface. According to conservation law of 3 gunas the center point (origin) is excluded. Any transition between the “lobes” has to be realized by a trajectory on the one-sided surface described by Eq.(3). The transition through the origin is not permitted.

Bulbous Lobes

The 4 bulbous lobes correspond to (|S|,|R|,|T|), (S,-|R|,-|T|), (-|S|,-|R|,|T|), (-|S|,|R|,-|T|). Here the | | notation is used to indicate the absolute value of the variables, the signs are made explicit. In other words |S|,|R|,|T| vary between 0+ and 1. Remember 0 is excluded in the conservation law of 3 gunas.

* Shrii Shrii Anandamurti uses the nominative case of “Brahman” throughout his writings.

References

[1] Avadhutika Ananda Mitra Ac., The Spiritual Philosophy of Shrii Shrii Anandamurti: A Commentary on Ananda Sutram, 2^nd Edition, Ananda Marga Publications, ISBN 81-7252-119-7
[2] Ananda Sutram

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