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The Problems of Modern Physics
 THE PROBLEMS OF
MODERN PHYSICS

"Quantum physics is the physics of possibilities" (Amit Goswami).

"Quantum physics is the language of nature: the cosmic code" (Heinz Pagels).

"The foundation of quantum physics is something that is neither material nor immaterial and is called a quantum function or quantum field" (Fred Alan Wolf)



The Quantum Enigma

The materialistic view of reality of classical physics has been called into question by the discoveries of quantum physics. It is paradoxical that it is precisely physics that has overthrown the materialistic vision, although it is a profound physics, a physics that we can say is not physics, because it transcends matter, space and time. The world of quantum physics has discovered, paradoxically, a metaphysical, disconcerting world that defies common sense, the traditional vision of reality and the classical conception of science. Quantum physics is not just another theory of physics, it is the foundation of modern science and new electronic technologies, such as the laser, the transistor and magnetic resonance. Even cosmological theories are also based on quantum physics.

Quantum theory was born in 1900 with Planck's discovery of action quanta, a theory that was later formalized by Heisenberg (matrices and corpuscles), Schrödinger (waves and wave function) and Dirac (who unified the two theories). Quantum theory has been the most successful and fruitful attempt to understand the physical world. But the theory has several peculiarities that defy conventional science, logic and common sense:


The wave-corpuscle duality

A quantum entity has a dual nature. Sometimes it behaves as a wave and sometimes as a corpuscle (or particle).

In Thomas Young's famous early experiment (1801) a beam of light was thrown against a plate with two parallel slits close together and an interference pattern was recorded on a detector screen, proving that light was a wave phenomenon, a wave.

This result contradicted Newton's conception that light was made up of tiny elastic material particles traveling in a straight line at high speed and bouncing off a mirror. They behaved according to the universal laws of motion.

The conception of light as a wave was endorsed at the practical level by Faraday, and at the theoretical level by Maxwell when he stated that light was electromagnetic radiation. Later Hertz produced radio waves (a type of electromagnetic radiation) of a frequency lower than that of light.

Einstein, in 1905, in order to explain the phenomenon of the photoelectric effect −the detachment of electrons from a metal plate when a beam of light is projected onto it, a phenomenon discovered by Hertz in 1887−, postulated that light was made up of corpuscles, the so-called "photons", the "atoms" of light. For this theory of the photoelectric effect, Einstein received the Nobel Prize in 1923.

Louis de Broglie had a great insight when he hypothesized that the opposite was also true: that particles such as electrons could also exhibit wave-like behavior: a particle of mass m and velocity v behaves like a wave of length h/mv, with h being Planck's constant. The larger the mass m, the smaller the wavelength. For this simple (and brilliant) idea −proposed in his famous 1920 doctoral thesis of only 6 pages−, he received the Nobel Prize in 1929.

Today Young's experiment is usually performed by launching photons one at a time against the two-slit plate to analyze the phenomenon in detail. What happens is surprising, for it defies logic: In 1978, John Wheeler proposed a slight modification to the double-slit experiment, the delayed choice experiment: What would happen if we decided to observe the photon once it had passed the plate with the two slits and before it hit the screen? The result was the two-slit pattern. Apparently, the photon, feeling "observed", went back in time to change the way it had passed through the two-slit plate: from being a wave it went back in time to become a particle.

According to Niels Bohr's so-called "principle of complementarity", a quantum entity behaves either as a corpuscle or as a wave, but not both at the same time. These two behaviors are mutually exclusive.

According to Richard Feynman, the double-slit experiment and its interpretation are at the heart of quantum physics.


The superposition of states and the measurement problem

A quantum entity, as a wave, appears to be in several places at once. The same entity, as a corpuscle, is located only in one place.

An isolated, unobserved quantum entity exists in a superposition of a set of states. But as soon as it is observed (by making a measurement), the wave is "collapsed" (or projected), i.e., it is forced to adopt only one state among all possible ones and the quantum entity becomes or transforms into a corpuscle. This is the so-called "Copenhagen interpretation" (circa 1927), so called because Niels Bohr (pioneer of quantum physics) and his team worked in that city.

According to this philosophy, the world is not real except when a measurement or observation is made. A quantum entity is different, depending on whether it is observed or unobserved. When unobserved, it is just a wave of possibility, represented mathematically as a "wave function"; it is not a "thing," since it has no definite attributes. When it is observed, the wave function "collapses" and only one of the possibilities passes to the status of real, it manifests itself with definite attributes. and the other possibilities vanish. It passes from the possible to the concrete and specific. A "quantum leap" takes place. What actually happens in this quantum leap is a mystery and seems to be governed by chance.

An unobserved quantum entity is nowhere, but potentially everywhere. Its attributes or properties dwell in an existential limbo, halfway between the world of ideas and the physical world.

Quantum entities are not "things" (as Heisenberg said). They are waves of possibility that "collapse" into corpuscles when observed. Quantum entities are said to lose coherence.

In general, when a quantum entity has several possible states, they are in superposition. For example, the quantum spin is in superposition of two states (up and down), and collapses into one of the two states when making an observation.

A quantum system exists simultaneously in all its possible states. Only when a measurement is made does one of those states appear or manifest itself. The superpositions (the possibility waves) we never observe; we can only observe the interferences. For example, when a photon passing through two slits interferes with itself.

Therefore, the results of experiments are not predetermined. A quantum entity does not possess definite properties until it is measured.

The possibility wave of a quantum entity propagates rapidly (the wavelength is large). In contrast, the possibility wave of a macroscopic object is very slow, propagates and expands slowly (the wavelength is very small), so it is very difficult to measure or observe. The larger an object is, the larger are its connections, the smaller are its possible states and the smaller is the wavelength.

When an observer contemplates a chair, and then another observer contemplates the same chair, they do not actually see the same chair because the possibility wave collapses at a different, though very close, position. The two observers share a similar experience that makes them infer that the chair is "outside" both of them, in the external world.


Discontinuity

Physical reality, at a deep level, is discontinuous. Max Plank, in 1900, discovered the "quantum" (quantum), the smallest unit of energy, by studying black body radiation. Einstein was inspired by Planck's discovery of the black body to explain the photoelectric phenomenon. He deduced that light was made up of corpuscles. Light has a discontinuous structure formed by photons or light corpuscles. The energy of a quantum is proportional to the radiation frequency.

Bohr introduced the discontinuity into Rutherford's model of the atom (a miniature solar system). In turn, Bohr's model made it possible to explain the spectrum lines, the radiations of precise frequencies emitted by different bodies.

In Bohr's atomic model, when an electron passes from one orbital or energy level to a lower one (emitting a photon), it does so instantaneously and without passing through the intermediate space. It is a quantum leap (quantum leap), discontinuous, discrete.

Another example of instantaneous quantum leap is the phenomenon of quantum tunneling, which is observed for example in transistors. It is the ability of an electron to jump a potential energy barrier. The barrier cannot be crossed by the electron because its kinetic energy is less than the potential energy of the barrier. However, the electron disappears from one side of the barrier and reappears on the other side without crossing it spatially, i.e. without passing through the intervening space.

The tunnel effect is a consequence of the wave-corpuscle duality of quantum entities and of the superposition phenomenon. It was born with the discovery of natural radioactivity by Henri Becquerel in 1896.


Non-locality (quantum entanglement)

At the quantum level space and time seem to be transcended. One quantum entity can interact instantaneously with another, regardless of their physical separation. This occurs with the phenomenon called "entanglement", a concept and term introduced by Scrödinger in 1935. For example, two entangled quantum entities (like a pair of particles emitted by a radioactive element) and which are separated by a great distance, when the possibility wave of one of them collapses (by making an observation), the other one collapses automatically and simultaneously as well. In fact, what is interpreted is that the two particles share the same wave.

In 1935, Einstein, Podolsky and Rosen devised a theoretical experiment −which is often called "EPR experiment" after the initials of its authors− to demonstrate the impossibility of nonlocality, "the ghostly phenomenon at a distance", as Einstein said. According to these authors, the phenomenon of quantum entanglement, which violates the theory of special relativity (the limit of the speed of light), should be explained deterministically, so there must be hidden variables and, therefore, quantum mechanics is incomplete.

In 1964, John Bell showed that no physical theory with local hidden variables can reproduce all the phenomena of quantum mechanics. He also devised a formula (an inequality) to discern whether a quantum phenomenon was local or nonlocal. If the inequality was experimentally satisfied, then the phenomenon was local. If it did not, then the phenomenon was nonlocal.

In 1982, Alain Aspect experimentally demonstrated nonlocality with a pair of entangled photons (an atom laser-irradiated two photons in opposite directions). The particles remained connected at a level that transcended space and time. Aspect showed that there is a metaphysical level in the quantum world.

In the quantum world everything seems to be connected at the spatial and temporal level. There are no classical cause-effect relationships. Cause and effect are confused. Present, past and future are the same thing, they are unified.


Uncertainty (the problem of measurement)

According to Heisenberg's indeterminacy principle, it is impossible to know of a quantum particle at the same time a pair of complementary or dual observable quantities, m1 and m2, one static and the other dynamic, verifying the relation Δm1. Δm2h (Planck's constant). This indeterminacy is not an external, measurement problem, but an intrinsic property of every quantum entity.

For example, it is impossible to know both position and momentum (mass×velocity) at the same time. It is also impossible to simultaneously measure the energy of a particle and the time interval it has been existing.

Quantum entities do not occupy a fixed space or exist for a fixed time. They manifest themselves diffuse, with discontinuous, random and unpredictable motions. Quantum entities are really potential entities, ambiguous, undefined, capable of manifesting themselves in many possible ways. Quantum entities are on the borderline between being and non-being.

The indistinguishability of identical quantum particles.

In classical physics, particles of the same mass are perfectly distinguishable from each other, by their positions in space, their trajectories, their possible collisions with other particles, and so on.

In quantum physics, if for example two identical particles collide, it is impossible to distinguish them after the collision. The principle of indistinguishability of quantum particles states that in a system with identical particles, there are only those states that do not change by permuting the positions of any two identical particles.


The coexistence of wave and corpuscle. The Afshar experiment

According to Bohr's principle of complementarity, a quantum entity behaves either as a corpuscle or as a wave, but not both at the same time. But physicist Shahriar Afshar performed an experiment in 2001, which was a modified version of Young's famous two-slit experiment of 1801 (i.e., exactly, 200 years later), in which he demonstrated two important things:
  1. The two aspects of light (wave and corpuscle) occur simultaneously.
  2. Of the two aspects of light, the fundamental one is the wave one.
According to the Copenhagen interpretation, the wave of a quantum entity is transformed or converted into a corpuscle by making an observation. The mechanism of this collapse is not known. The Schrödinger wave function does not contemplate such a collapse. But there is no such conversion, since the wave continues to exist. The fact that a corpuscle is detected does not imply that the wave disappears. According to Afshar, the Copenhagen interpretation is false.

This experiment has been repeated by other researchers and its results have been confirmed, although its interpretation is controversial.


The intention. Mandel's experiment

Leonard Mandel (University of Rochester) was one of the founders of quantum optics (the study of the behavior of photons and their use in the transmission of information). In his laboratory he was able to test the most remarkable phenomena predicted by quantum theory, and made new discoveries. His experiments were a model of simplicity and clarity: But Mandel's most important discovery was the following. Observation or measurement requires direct physical intervention. But an experiment by him and his team showed that a photon can be forced to change behavior (as a wave or as a corpuscle) by something more subtle than direct physical intervention. The interference patterns disappear (i.e., there is corpuscular behavior) when a detector is installed, even though the detector has not been activated. The mere possibility of using the detector to find out through which slit the photon is going to pass causes the interference pattern not to appear. The interference pattern also disappears when the photons to be detected are selected for the path they will take, even with the detector placed non-locally. By launching distinguishable photons no interference occurs.

The conclusions of Mandel's experiment were:
Subjective reality

In classical physics reality is objective, it is the same for different observers. In quantum physics reality is subjective, it depends on the observer, so it is necessary to include the observer in the description of the physical world. The idea that reality is created by observation goes back to Vedic philosophy. Berkeley (considered the father of idealism) asserted that "to be is to be perceived" (esse est percipi), i.e., the only reality is the inner, the mental, what we perceive. Things are not in a certain way (objective) but things are perceived in a certain way (subjective). It is an empiricist epistemology.


The relativistic question

The laws governing the universe on a microphysical scale (established by quantum theory) are different from the laws governing the universe on a macrophysical scale (established by relativity theory). Both theories (quantum and relativistic) were born and evolved independently. And both theories have been verified. In particular, all predictions of Einstein's theory have been fulfilled, including the existence of gravitational waves (recently discovered).

All physicists agree that the two theories need to be unified. Since quantum theory is more general than relativistic theory, the natural path is to extend or generalize quantum theory to encompass relativistic theory.

An important step toward unification was taken by Dirac in 1928, who worked out a quantum theory that included the principle of special relativity. The Dirac equation is the relativistic version of the wave equation of quantum mechanics and takes into account relativistic effects. What is missing is a quantum theory that includes gravity or the quantum theory of gravity.

The standard model of quantum physics is incomplete because it does not account for gravitation. A hypothetical particle, the graviton, has been postulated as responsible for the gravitational force. Modern string theory promises to be able to describe and explain all physical phenomena, including the gravitational force. According to this theory, different particles are the result of different modes of vibration of a string.

And at the level of cosmology we still know little. For example, we do not know the true nature of dark energy and dark matter. Dark energy is a hypothetical energy responsible for the expansion of the universe. Dark matter is a hypothetical invisible form of matter that would explain why galaxies do not disperse in their rotational motion.


Interpretations of Quantum Physics

The phenomena of quantum physics have been interpreted in many ways: with the existence of a transcendent level of reality, with consciousness, with information, with mathematical abstraction, with probability, and so on. At present there is no consensus on the interpretation of quantum phenomena. The quantum enigma remains unsolved. Some physicists propose a complete reworking of quantum theory. Others prefer simply to stick to the superficial, to the equations, without searching for their deeper meaning. The most important interpretations are described below.


Mathematical abstraction

The mathematical interpretation of quantum physics, based on Bohr's initial conception, the Copenhagen interpretation, can be summarized as follows: This interpretation refers to the description and manipulation of mathematical objects, and have no objective physical correlate. At a deep level, physics disappears and we contact the abstract universe of mathematics. This conception of quantum physics has been challenged:
The transcendent level of reality: the Akasha

According to the transcendental interpretation, the possible states of a quantum entity do not belong to the physical world. They belong to another level of reality, an unmanifest, diffuse, indeterminate and inaccessible level of reality. Heisenberg was the first to intuit that the possibility waves of quantum entities reside in a transcendent domain, beyond space, time and matter.

In the two-slit experiment, quantum entities apparently have a schizophrenic behavior, for sometimes they behave as waves, and sometimes as particles. But the explanation lies in the fact that the possibility waves of quantum entities belong to a non-physical dimension, a dimension that transcends space, time and matter. This non-physical (or metaphysical) space is often referred to as hyperspace, metaspace, deep space, ether or Akasha. Akasha is a concept from Hindu Vedic philosophy and is a Sanskrit term meaning "heaven, space or ether".

The characteristics of the Akasha are as follows: The Akasha explains quantum entanglement, since at the deepest level there is no space and no time. It also explains Wheeler's delayed choice experiment because since at the deepest level there is no time, the behavior of a photon is independent of the time at which the observation is made.

The Akasha is identified with the so-called "Zero Point Field", the quantum vacuum field, a deep space filled with energy.

According to David Bohm, reality is an indivisible whole in which everything is connected at a deep level, the "implicate order", a transcendent level, a "folded" world, a physical world beyond space and time. From the implicate order emerges or emanates the "explicate order", the "unfolded" world. Bohm's implicate order can be identified with the Akasha. Bohm's theory of the nature of reality gave rise to the holographic theory of the universe, which was applied by Karl Pribram to postulate the holographic theory of the brain.


The many worlds theory

Hugh Everett, in the 1950s, disagreed with the Copenhagen interpretation. He considered it incomplete because the Scrödinger equation only applies to the microscopic world and does not refer to the macroscopic world we call "real". The equation describes how the wave function evolves with time, an evolution that is continuous and deterministic. But the equation does not contemplate what happens in an observation: that the wave function collapses into a single element of the superposition and the other elements vanish, thus introducing the discontinuity. This approach privileges the observer, placing him in a classical realm distinct from the quantum realm.

Everett's idea −expounded in his April 1957 doctoral thesis "Universal Wave Function Theory", and republished three months later under the title "Relative State Formulation of Quantum Mechanics"− was to interpret the wave function literally, considering that every element of the superposition was real, that all possibilities are realities, and that none is more real than the rest: For example, if a photon can be transmitted or reflected in a medium, the universe is divided into two, one in which the photon is transmitted and one in which the photon is reflected.

Everett merged the microscopic and macroscopic worlds by introducing an integrated (or universal) wave function that encompassed the observer and the quantum system. This integrated wave function would bifurcate at every interaction between the observer and the system in superposition of states. Everett's goal was for the wave function to serve the entire universe.

For example, if we have a quantum system with two states i>>A and B in superposition, there is a wave function describing this system. If an observer appears, a new wave function is created that encompasses the system and the observer. When the observer makes a measurement, there are two possible branches: one branch with the observer and the state >A, and another branch with the observer and the state >B. These two branches are independent of each other and each follows a different future.

The entire universe behaves like a tree that divides and subdivides into multiple branches at every fraction of time. Each new universe created has a different history, corresponding to the succession of universes that have led to that particular universe. An observer following a particular path never perceives this phenomenon of division or partition. Since we perceive nothing but the universe we observe, these universes must be separated from each other. The universe is composed of a quantum superposition of many (possibly infinite) worlds, increasingly divergent, parallel and non-communicating with each other.

In short, Everett's theory holds that everything that can happen, really happens; all possibilities occur, even if we are only aware of one of them. Given a set of possibilities, the universe subdivides into as many universes as there are possibilities. Therefore, there are infinitely many possible universes.

Positive aspects of the theory are: Negative aspects are: Everett's theory was ignored for a decade after its publication. It has subsequently been the subject of great controversy for years, but is gaining increasing acceptance, to the point of surpassing even the Copenhagen interpretation. Bryce De Witt was responsible for its popularization and the originator of the term "many worlds". Today, Everett's theory is interpreted seriously, although not entirely in its original form. The modern version is that each branch represents a classical or macroscopic reality, the result of a "quantum decoherence". Quantum computing is based precisely on this interpretation.

Richard Feynman formulated a different version. Instead of many worlds he spoke of many histories or multiple histories or parallel histories. When a particle travels from point P to point Q (in phase space) there are multiple trajectories (or histories), each with its associated probability. The complete trajectory integrates all the individual trajectories. When one trajectory is observed, the others pass into parallel universes.


Bohm's interpretation

Postulated by David Bohm in 1952 −inspired by Louis de Broglie's pilot wave theory, which he presented in 1927−, David Bohm's theory is called "pilot wave theory" or "causal interpretation". In this theory, each particle has a well-defined trajectory and passes through only one of the slits, but at the global level a "pilot wave" is generated that guides the particles so that together they form an interference pattern. Using a simple mathematical formalization, Bohm deduced that there is a "quantum force" (or quantum potential) acting on each particle to produce a global wave behavior. The quantum force on a particle is a function (at each instant) of the positions of the other particles.

The measurement problem is interpreted as a consequence of the interaction of the particles with the detector, which alters the pilot wave. In the observation, there is no collapse of the wave function and the unobservable part of the wave function does not disappear.

Bohm's theory describes an objective and fully deterministic real world. The wave function is physically real. This theory makes the same predictions as the probabilistic interpretation of the Copenhagen interpretation, in a simpler way and solves the riddle of wave-corpuscle duality.

Bohm believed in universal connectivity, which he describes in his work ">The Undivided Universe" [1995]. Bohm's theory inspired Bell to formulate his famous theorem for determining whether or not a quantum phenomenon was local.


The theory of consistent histories

This theory is a generalization of the Copenhagen interpretation. It consists in assigning probabilities to the possible histories of a quantum system, such that these probabilities obey the rules of classical probability while being consistent with the Schrödinger equation. A consistent history (also called a "decoherent history") is a sequence of quantum events (wave functions) at successive times.

This theory does not consider the measurement issue fundamental, unlike the Copenhagen interpretation. Measurements produce consistent probabilistic-type histories. The histories are used to describe how a particle interacts with the measuring apparatus.

This theory resolves the paradoxes of quantum physics. It has the advantage of being more accurate, quantum physics is local and consistent with special relativity. Classical physics emerges as a useful approach to quantum physics. The logic is quantum, but in the macroscopic world it becomes classical logic.

The theory of consistent histories was proposed by David Griffiths in 1984 and further developed by Roland Omnès in 1988, as well as by Murray Gell-Man and James Hartle, who used the term "decoherent histories" in 1990.


The interpretation of pregeometry

John Wheeler postulated that, beyond the usual geometry we conceive of the universe, there is something deeper which he called "pregeometry." Pregeometry is a deep structure from which geometry emerges. Space-time is an emergent reality from an underlying pregeometric reality.

This concept was introduced by Wheeler as a possible explanation of quantum gravity (the union of quantum physics and the theory of general relativity). While geometry allows describing the surface properties of physical objects, pregeometry allows expressing the deep laws of physics.

Today pregeometry (deep geometry, which we can also call "transgeometry", meta-geometry, "transcendental geometry" or "quantum geometry") can be identified with the geometry of the ether. The ether, which used to be considered a kind of subtle matter that filled absolute space (and in which light was a vibration of the ether), is today considered to be the deep space that connects all known (surface) space with each other, like the Hindu Akasha.

Precisely, one of the great challenges of physics today is the discovery of the true nature of space.


The interpretation of information

John Wheeler también elaboró una teoría que denominó “>it from bit”, una teoría de explicación inmaterial del mundo físico: Vlatko Vedral argues in his work "Decoding Reality" [2010] that the universe at its most fundamental level is information. Information is the origin of everything that exists. Information creates reality. Before matter or energy existed, information existed. Information is the thread that connects all phenomena. Reality is made of information. In the wave function there is no information, but when it collapses, information is generated.

This Vedral interpretation of quantum physics explains that a system has several states at the same time: because there is no information available to know in which state it is. The laws of quantum physics are a consequence of the restrictions linked to the acquisition, representation and transmission of information. The information paradigm is linked to the so-called "digital physics": the universe is describable by information and is therefore computable. The universe is a process carried out by a computer program or by a computational device.


The Akashic Field theory

The unified theory of the Akashic field has been proposed by Ervin Laszlo in his book "Science and the Akashic Field. An Integral Theory of Everything" [2004] and "The Un-Formed Universe" [2007]. This theory combines the Hindu Akasha theory and information theory. In it he proposes a new unifying paradigm: all things in the universe are interconnected through an information field, which he calls "Akashic", following the ancient Hindu Akasha philosophy:
The explanation of mind and consciousness

According to John von Neumann and Eugene Wigner, quantum theory is incomplete because it needs consciousness to be complete. According to the von Neumann-Wigner interpretation, consciousness causes the collapse of the wave function. According to Amit Goswami [see Bibliography], there are close connections or analogies between mind and consciousness with the quantum world:

Addendum

The Schrödinger equation

The wave equation developed by Erwin Schrödinger in 1925, describes the time evolution of a quantum entity in an abstract space, the Hilbert space, a generalized Euclidean space of infinite dimensions.

This equation plays in quantum physics a role analogous to Newton's second law of classical mechanics. It is the new universal law of motion, valid for the microscopic and macroscopic world. Schrödinger was inspired by de Broglie's "matter waves". Just as Newton's laws of motion are deterministic, so is the Scrödinger equation. This equation is not proved, it is a postulate: The Schrödinger wave equation has several remarkable features:
  1. indicates possibility. The wave function is interpreted as the superposition of each and every one of the infinite possible states of the quantum entity. The wave is a superposition of possibilities. When the wave function collapses, it is reduced to only one of the possibilities it describes. This reduction of the wave function takes place instantaneously and without energy consumption.

  2. It is imaginary. It connects with the imaginary world, as they appear:

    The imaginary unit i (i.e., i2 = −1).

    The derivative, which is based on infinitesimals, which are imaginary expressions (the infinitesimal ε is defined as ε2 = 0).

    Infinity, expressed in the wave function |Ψ(t)⟩, which has infinite components.

    The wave function is a complex variable function, something abstract. Max Born gave it a probabilistic interpretation: the square of its amplitude is a measure of the probability of finding the particle at a certain position in space and at a certain instant. This interpretation was rejected by Schrödinger himself.

  3. It is multimodal or polymorphic. If you perform one operation on the wave function, you get the position (or its probability); if you perform another, you get the energy (or its probability), etc. Despite being a complex function, the result is always a real number.

  4. It is simple. The equation introduces a simpler formalism than the one previously introduced by Heisenberg, which was based on the discrete nature of the quantum entity (it used matrices). The Schrödinger equation refers to a wave. Schrödinger showed that both formalisms were equivalent. Schrödinger's formalism being simpler and more synthetic, Heisenberg's was relegated.

  5. It is profound. The wave belongs to a deeper level of reality than the particle. Moreover, simplicity and depth are concepts that go together. These two aspects (wave - corpuscle) are dual and correspond to the two basic modes of consciousness.

  6. It is abstract. It is expressed in mathematical language. And it is, paradoxically, also physical reality. At a deep level, reality is abstract. The Heisenberg uncertainty principle can also be derived from the Scrödinger equation.

  7. It is universal. It is valid for all kinds of objects. The whole universe also evolves according to the Schrödinger equation (the equation is being applied to study the Big Bang). But it is not relativistic, i.e., it is not valid for velocities close to light. For large objects, the equation becomes Newton's equation of motion.

Imágenes gestalt

The term ">gestalt" means whole, configuration, totality or form. The >gestalt philosophy interprets phenomena as organized units, with a high level of structural cohesion, rather than a simple aggregate of parts. Images >gestalt contain several interwoven forms, each with different meaning, from which our consciousness chooses only one of them in the act of perception. Here are 4 examples:
Bibliography