i.4 The Principle of Love and Stationary Action

The principle of stationary action is applied to the action of a mechanical system to obtain the equations of motion for that system. The principle can be used to derive Newtonian, Lagrangian and Hamiltonian equations of motion, and even General Relativity as well as some quantum calculations. It is also applied in thermodynamics, fluid mechanics, particle physics, and string theory. Planck considered the principle of least action as a significant step towards the aim of attaining knowledge about the real world, and he concluded that among the achievements of physical science the principle of least action comes closest to the final goal of theoretical research. Even Einstein came to the conclusion that the principle had to be an essential element in his general theory of relativity.

Historically this principle was called least action because its solution requires finding the path that has the least value, but the stationary action method helped in the development of Quantum Mechanics. The action is stationary at the configurations that satisfy the physical equations of motion, but it can be a maximum, minimum, or saddle point. It can be demonstrated that even for the simple harmonic oscillator, the action is often maximized rather than minimized along the equations of motion.

The action principle is preceded by earlier ideas in optics, where it had been noticed that the path of light, for example when reflecting from a mirror, is the shortest length and least time. Historians often credit various scientists for formulating the principle of least action, such as Maupertuis and Euler who wrote about it in 1744, but also some evidence shows that Leibniz preceded them by 39 years. Euler made an equivalent and apparently independent statement of the variational principle in the same year as Maupertuis. In his Reflexions, Euler called the quantity effort , which corresponds to what we would now call potential energy, so his statement of least action in statics is equivalent to the principle that a system of bodies at rest will adopt a configuration that minimizes total potential energy. However, much of the calculus of variations was stated by Lagrange in 1760 and he proceeded to apply this to problems in dynamics, deriving the general equations of motion of a mechanical body. In 1834, Hamilton applied the variational principle to the classical Lagrangian function  to obtain the Euler Lagrange equations in their present form.

In 1842, Carl Gustav Jacobi tackled the problem of whether the variational principle always found minima as opposed to other stationary points, such as maxima or stationary saddle points. Most of his work focused on geodesics on two-dimensional surfaces. The first clear general statements were given by Marston Morse in the 1920s and 1930s, leading to what is now known as Morse theory. For example, Morse showed that the number of conjugate points in a trajectory equaled the number of negative eigenvalues in the second variation of the Lagrangian. Other extremal principles of classical mechanics have been formulated, such as Gauss s principle of least constraint and its corollary, Hertz s principle of least curvature.

The action principle involves integrals over an interval of time and extended region of space in the case of fields. The mathematical formulation involve specifying the initial and final states of the system in order to find the physical trajectory that connects these two endpoints, by extremalizing the action integral. Due to this fact that it is not localized to a point, the principle of least action is thought to have a deeper philosophical significance because it seems to suggest that physical systems are governed by final causes. The principle of least action was therefore connected with teleology, which contends that natural phenomena have intrinsic purposes. The variational calculus itself, which helps to find the minimum of the action integral over a scalar Lagrangian energy quantity, has also been repeatedly discussed in a controversial way that involves teleology. However, some researchers argue that the teleological approach presupposes that the variational principles themselves have mathematical characteristics, while other critics maintain that this apparent teleology occurs because of the way in which the question was asked. By specifying some, but not all, aspects of both the initial and final conditions, we are making some inferences about the initial from the final conditions, and it is this backward inference that can be seen as a teleological explanation. Teleology can also be overcome if we consider the classical description as a limiting case of the quantum formalism of path integration, in which stationary paths are obtained as a result of interference of amplitudes along all possible paths.

Nevertheless, the fact that the action principle is so essential in all physics regimes led many researcher to ask about the intuitive reason behind this principle. The justification is more clear in quantum mechanics, where the least action principle is the same principle of least time in geometric optics, but here applied for matter waves, which then make the trajectories perpendicular to constant-phase lines. But historically, the Lagrangian formulation was recognized to be more fundamental a century before Hamilton conjectured that classical mechanics was a wave mechanics, and this was many decades before the development of Quantum Mechanics, which then explains the laws of dynamics in terms of stable quantum states.

In the Duality of Time Theory, the hidden symmetry between the two complementary arrows of time, or the physical and psychical worlds, can solve this fundamental observation that nobody is even questioning; namely: the perpetual motion of subatomic particles. It is true that these particles are quantum objects that exist in bound quantized states, so they do not loose any energy as far as they do not change their quantum states, but the fundamental question is still why ? In this regard, Quantum Mechanics or Quantum Field Theory, describe this quantum behavior, but without answering or even asking the main question as to why they prefer these apparently stable states in which they can move without losing energy. Answering this question in terms of Newton s laws is also not sufficient, because these laws are also descriptive. For example the first law says that the state of motion of an object does not change unless acted upon by an external force. This is of course a correct universal observation, but why is this the case? In other words: why energy is conserved even when the object is moving, in a frictionless medium of example!

This fundamental question is also equivalent to: why energy is quantized? Fundamental particles are quantum objects, whose states are changed through the fundamental interactions between quantum fields, by exchanging particle-like properties such as spin, charge, momentum and energy. So if we could explain why energy is conserved, we will be able to explain how these quantum fields and all the subsequent fundamental particles came to exist after they were nothing , but not from nothing , because their origin is vacuum that the absolute existence described the spherical  three-dimensional flat space, without time. When this hyper-symmetrical space is broken into the two arrows of time of the physical and psychical worlds, , , respectively, we get the two folds of super-symmetry. The current laws of physics are concerned only with the first half, of the physical world whose vacuum state is , and that s why we are faced with the various problems, such as the arrow-of-time, matter-antimatter asymmetry hierarchy and homogeneity, and that s why our laws are fundamental descriptive rather than answering the essential questions.

With the Principle of Love, which describes the momentary splitting and subsequent reunion of these two arrows of time, the stationary action becomes a consequence rather an unquestionable principle. With this grand step, causality itself becomes a consequence of the Universe being a closed system, but including all matter, energy and the background space, and not only the stuff that exist in space. Only when we include all these constituents of existence the Equivalence Principle will be derived mathematically, as we shall show in Chapter III. Therefore, explaining why energy is conserved means that causality itself is no longer a fundamental principle, but it can be explained by a more fundamental concept that is the Principle of Love. Accordingly, we could also explain how causality, and the conservation of energy, could be broken in special cases, such as entanglement and other non-local interactions.

In chapter 295 of the Meccan Revelation, that we quoted at the top of this Introduction, Ibn al-Arabi states the Principle of Love as the fundamental reason of all motions. After explaining how the abstract four elements , , , and  were originated and how they gave rise to the physical elements which subsequently condensed into the stars that occupied the orbs of constellations, he adds:

The planets (stars) appeared in these orbs, and all other heavens, from the movement of these four mentioned spheres (of elements) by which Nature was completed, thus they appeared in the physical world after they were only abstract reasonable concepts, because meanings are the origin of all things, which are in themselves abstract and reasonable, but then they become sensible in the Presence of Sense (that is the physical world) and imaginable in the Presence of Imagination (that is the psychical world), ... so the first thing to be created was Earth which is the bottom of void and the most extreme density and darkness, and which is still continuously receding for ever, because void is an imaginary infinite extension without composition (or body). The whole World is always descending in seeking the center on which it can settle, but since this is not possible, its motion is going on for ever. In this motion, the world is seeking the ultimate Real, that is its goal, due to the initial manifestation that caused this passion ; so the World is always passionately seeking the Real. All kinds of motions are caused by Love and Passion, it cannot be otherwise, and who does not love this unique manifestation that is described by Beauty, since beauty is desirable for its own essence. If the Exalted (Real) did not manifest in the form of beauty, the World would not have appeared, so the appearance of the World into existence was driven by Passion, and Love is the origin of its movement, and this state is eternal, so the the motion of the World is going without end. If there were anything to which this motion ends, which is called the center, the world would necessarily accumulate over itself and motion would stop, so the World would annihilate and its essence will disappear, but it is not like that. [II.677.12].

It is very clear that Ibn al-Arabi is describing here a singularity or a Black Hole that is the bottom of void with the most extreme density and darkness, which is still continuously receding for ever , but the most important thing to note here is his description that the same abstract four spheres of Nature , , , and  appeared in the physical world and in the imaginable (psychical) world after they were only abstract reasonable concepts (in the spiritual world), which describes how the hyper-symmetry of bosons is lowered to the super-symmetry of fermions with their two orthogonal arrows of time.

Therefore, the Principle of Love leads to the emergence of time, including space, as the containers of motion, as well as the principle of stationary action described above, because the reason why particles move is to re-unite with their partners, which is the abstract cosmological progeny that we shall discuss further in Chapter II.

Motion is associated with time, so it must incorporate some exchange of energy. If the microscopic particles, such as the electrons, and all objects in general, are executing actual motion in real space background, they must loose energy when they move through the medium. Of course, normally this is explained in terms of friction which is considered zero because the medium is vacuum, i.e. empty space, but this does not have any physical sense apart from being a good macroscopic approximation. Nevertheless, we still observe objects and particles moving through this hypothetical vacuum, so what actually happens is that the elementary particles that appear moving in our normal time arrow are actually instantaneously uniting and splitting with their identical partners, or anti-particles, in the conjugate time arrow, thus converting into non-localized energy waves which then re-localize again in new adjacent positions upon each subsequent observation, causing the illusion of motion. In reality, motion is a result of re-creation, and there is no transmutation where the object gradually leaves its place to occupy a new position.

This uniting and splitting is instantaneous in our normal time because it is actually happening in the inner levels of time, in one linear chronological sequence that is nested inside the spatial dimensions as we explained in Chapter V of Volume II, so on the physical level there is no real motion at all, only changes in relative locations.

Luckily, this uniting and splitting is covered by the same mass-energy equivalence relation  that cannot be derived without the Duality of Time postulate, as we shall describe in Chapter III. The process of particle-antiparticle annihilation into energy, and the subsequent splitting of this information or consciousness into the physical and psychical worlds, can also be expressed as: , which means that when Earth and Fire, or absolute mass and energy, are mixed together they produce Water and Air, or particles and antiparticles, or the physical and psychical Worlds, all the same things but in different time arrows. Equally, therefore, we can say that the continuous dimensions of space split into opposite time directions, and vice versa, as also expressed through the equation: , so , ,  and .

Therefore, the Principle of Love, as the primary cause of first creation and all subsequent motion, or re-creation, is the most fundamental principle in Nature, where Love is not only a moral or ethical quality, but a natural physical inclination in all objects and particles for example manifested as positive and negative charges as well as the individual abstract points of space, in this world to unite with their partners in the mirror-world that exists in the reverse time direction, in parallel with our own world that exists in the normal time direction that we encounter. These two parallel worlds are intertwined together, and, because of the sequential creation, when the union is instantly achieved between the two opposite directions of time, they annihilate together to create one dimension of space, or energy, but also instantly separate again to their physical and psychical disconnection, and so on, infinitely. The creation is always perpetually fluctuating between these two states of mass and energy, or particles and waves, or space and time, in our normal three-dimensional space, but also other corresponding dualities in lower, and possibly higher, dimensions.