Quantum Field Enigma I

Posted on by toomajj

In a previous post titled What is Quantum Physics I introduced the subject and its principles: Quantum Physics, or Quantum Mechanics, is the theory that explains the motion of microscopic objects such as molecules, atoms, nuclei, and all the elementary particles of nature. This is the story of its creation: Before the beginning of the twentieth century physicists were able to discover almost all the laws that governed the observable phenomena at the macroscopic level. These laws, expressed in mathematical form, explained the two main realms of nature: 1) The motion of masses and the gravitational force that is exchanged between them. 2) The behavior of charged particles and the electromagnetic forces exchanged between these charges.

The first set of laws governing gravity and dynamics of masses is known as Classical Mechanics explained by Newton’s Laws of Motion. The second set of laws governing electricity and magnetism is known as Electromagnetism obeying Maxwell’s Equations. All natural phenomena such as heat, waves, etc. could be understood within these two theoretical frameworks. These two frameworks along with Einstein’s Theory of Relativity, which deals with objects moving with high velocities, are together known as Classical Physics. The important point is that in classical physics we are dealing with two distinct types of objects whose collective behaviors determines natural phenomena: Waves and particles. Sound and light are examples of wave phenomena; masses and point-charges are examples of particle phenomena.

As a result of technological advancements of late 19th and early 20th centuries experimental chemists and physicists were able to probe into the microscopic world of molecules and atoms. Scientists expected to find particles obeying Newton’s laws of motion; however, it turned out they were wrong, and in fact they saw that the concepts of classical physics were hopelessly inadequate in capturing the reality of the microscopic world. Let me give you just one example: Experimental findings gave a model of an atom, which is neutral, consisting of a very heavy, positively charged, nucleus concentrated in a very small region of space, within a length of about 10-14 meters. The negatively charged electrons rotate around this nucleus, hence keeping the whole atom neutral (This model is similar to our solar system though we will see that the underlying reality is totally different.) However, this kind of motion for electrons violates the most important tenet of electromagnetism: According to electromagnetism an accelerating charged particle, such as electron, radiates energy in the form of light, hence it keeps losing its energy as long as it is in accelerating motion. We also know from classical mechanics that rotation is an accelerating motion. This means that electrons rotating around the nucleus should radiate light and hence lose their energy until they fall onto the nucleus. But experiments have shown that nothing of the sort happens. Atoms, at least most of them, are stable structures; their electrons revolve the nucleus without radiating light; these electrons emit, or absorb, light only when they jump from one orbit to another orbit, and these orbits are not arbitrary; electrons can only occupy certain allowed orbits with discrete energies. Also, their jumps between orbits are not jumps through space; when an electron jumps from, say, orbit 2 with energy 20 to orbit 1 with energy 10 it does not fly through the space in between orbits; neither does it incrementally decrease its energy from 20 to 10 passing through 19, 18, …. This energy loss is radiated away in the form of electromagnetic radiation, photon. Electron’s jump is instantaneous and doesn’t take any time whatsoever: The electron is in one orbit and then suddenly shows up in another orbit. This inexplicable kind of jump is known as electronic transition or Quantum Jump. This example was one among the many experimental findings that needed a new physics in order to make sense.

Quantum Mechanics which was developed between 1900 to 1927 by the collaboration many physicists is the theory that explains the motion of microscopic objects. In other words, quantum theory was developed as a mathematical tool to make sense of and organize the strange experimental findings in the first decades of twentieth century. Double Slit Experiment is the cornerstone of quantum phenomena and it contains almost all the bizarre features of the quantum world. Quantum Mechanics is considered to be the most successful intellectual achievement of mankind since it has been able to explain all microscopic phenomena, and it is also the most experimentally verified theory in the history of science.

According to quantum theory the basic constituents of nature are neither wave nor particle. However, depending on the measuring instrument they can manifest either as wave or as a particle but not both at once, see The Complementarity Principle. Prior to the act of measurement the quantum system (particle is a misnomer but we have no better word) is neither a wave nor a particle, and it is also nothing else: It has no characteristics, no form and no properties, no position and no velocity in space. In fact, it is not a thing or entity anymore; it is a no-thing, a no-entity. Nothing can be said about it except saying that if we perform such and such a measurement on this no-thing there is such and such a probability to get such and such a numerical value for what is being measured. This bizarre feature of quantum phenomena is called stochastic behavior, that is the microscopic world is inherently indeterminate, see The Uncertainty Principle.

This indeterminacy is a matter of principle and not of the our ignorance nor of the inefficiency of our equipment. It is not that we don’t know the position of the “particle” in space; the particle has no position, or any dynamical property for that matter, prior to the act of measurement; the measurement process creates the very position that is to be measured. This means that the quantum world and the quantum objects cannot be thought or imagined in any possible way. Even the much used statement that “in quantum world a particle is in many places at once” is a false way of putting it because in the quantum world there is no such thing as particle; it is meaningless to speak of here and there, let alone of everywhere. Place has no place in the quantum realm.

The objection may rise, as it did for myself for quite a while, that this lack of knowledge about the nature of quantum objects is a lack on our part; perhaps the particle itself contains all this missing information but it is us who cannot access it, whether due to our state of knowledge at the present time or because nature somehow doesn’t like us to have that information!

But that is not true, for if it were our everyday world would not look like what it does. It is proven and experimentally verified that the quantum “particle” could not possibly have a position prior to measurement; if it did, whether we know that information or not, then we would not observe phenomena such as waves, colors of a soap bubble, etc. These phenomena can occur and be observed if and only if the underlying constituents do not have inherent properties such as a determinate positions or velocities. In other words, the missing information about the exact properties of quantum objects is not missing at all; it does not, and cannot, exist or else we would not be seeing what we are seeing right here right now. In other words, our observation of the form of appearances is possible only if that which appears is itself formless: Form is formlessness conditioned and partitioned. The set of experiments that have consistently proven this results are known as Bell Experiments and the theory that underlie them is known as Bell’s Theorem.

In the microscopic world what determines the place and status of quantum objects is the act of observation. To avoid mystical mis-interpretations I must add that observation here is not meant seeing with eyes or anything like that, anything depending on the consciousness of the experimenter. Observation in quantum mechanics refers to a complex process in which a macroscopic machine interacts with a microscopic object. Whether or not our consciousness is there in the room, whether or not we read the display of the machine that contains the result of measurement, it is always the internal mechanism of the instrument that by itself determines the state of quantum system and the possible outcome of the measurement. Human consciousness does not create reality, for it is itself already part of a created reality.

In future posts I will continue this subject and introduce you to Quantum Field Theory, QFT for short, in which the quantum world is no more seen as a collection of isolated particles and waves but as a field spread in space-time. In QFT particles are in fact the vibrations of the field. Quantum Field Theory was created by combining Quantum Theory and Einstein’s Theory of Special Relativity.

Quantum Physics & Nonduality

Posted on by toomajj

Nondual Perspectives on Quantum Physics reveals the common thread running through science, philosophy, and spirituality, the main three paths aiming at a knowledge of ultimate reality. Introducing the most advanced representatives of these disciplines in non-technical language I show how they all point to one and the same underlying principle:

The manifest arises from the vibrations of the umanifest.

Quantum Physics from modern science, Transcendental Phenomenology from modern philosophy, and Advaita Vedanta from traditional metaphysics are the three representatives introduced in my book as having a common ground that is essentially transcendental and nondual.

The book has three chapters: In chapter 1 I introduce quantum physics and its philosophical implications. In chapter 2 I introduce the concept of nonduality along with one traditional and one modern example, namely Advaita Vedanta and Transcendental Phenomenology. In chapter 3 I highlight the interconnections between these three disciplines and expose the common ground upon which they are standing and the ultimate reality to which they are pointing.

The Table of Contents

Chapter One: Quantum Physics

The Physics

The Philosophy

Chapter Two: Nonduality

The Idea

Advaita Vedanta

Transcendental Phenomenology

Chapter Three: Unity

Common Ground

Common Language

Quantum Reality

Nondual Reality

Unity  

Nondual Perspectives on Quantum Physics is available also at Goodreads.

http://www.amazon.com/dp/B00N5DL1R0/

What is Quantum Physics

Posted on by toomajj

There is no field in modern science that is misunderstood or misinterpreted more than any other. Two reasons should be mentioned: First, quantum physics deals with the microscopic world, atoms and subatomic particles; it is a world inaccessible to our direct perceptions, to human experience as such. And as much as we like to but our logic and commonsense which are derived from shared human experiences cannot be extended to the realm of atomic phenomena. Even the physicist cannot imagine what an atom looks like. The second reason that has led to much misinterpretation is the desperation of modern man to find meaning, excitement, mystery and surreal phenomena to compensate for the lack of essence in his/her life. Thus, the field is open to people like Deepak Chopra who are the kind to take advantage of the mystery and stick exotic words such as quantum next to whatever it is they sell so to make it sound both cool and healing. But if we are really after knowing the mystery, then wouldn’t we be fooling ourselves if we sufficed to superficial interpretations or one night stands with what may be a glimpse of an ultimate reality!

Of quantum mechanics (or quantum physics) it is said “Quantum physics is not something to understand; it is something to do.” Physicists do quantum mechanics all the time; in fact, almost all electronic equipment owe their lives to the quantum physics done by physicists; doing it involves solving equations and calculating probabilities; but this doesn’t entail a deep understanding of the meaning of these equations. Rarely can physicists say that they have truly understood quantum physics. We may even define quantum physics as the subject that when we think we have understood it we suddenly realize we haven’t. This is not because we are stupid or quantum physics is too hard; both are true to some extent, but the problem has to do with what it is that we call understanding.

To understand is to reduce something new to something that we already understand, and to do so until we arrive at simple, elementary facts that are self-evident from experience. But if the subject matter is one which is altogether alien to experience as such, then understanding, in the sense we know it, is not possible. In light of an understanding of understanding we can say that quantum physics is only understood in terms of abstract mathematics; the only elementary concepts to which the object of the quantum world can be reduced are abstract mathematical objects. But I have developed a new way of introducing quantum physics which involves reflections on why we cannot understand it. In short, we can indirectly understand the quantum world by understanding what it is not rather than what it is. Now let us try.

Physics is an attempt at understanding the natural order. It used to be part of what is known as natural philosophy. The natural order, the object of inquiry, is the world that know through experience. In this experience we encounter different kinds of phenomena: Some are mechanical; they have to do with motion of massive objects, like projectiles, motion of the stars and planets. Some are electromagnetic in nature, like light, electricity, magnets, etc. Some others are thermodynamic in nature, dealing with phenomena such as heat and cold and transfer of energy. Three main sub-fields of physics were developed to study these phenomena: Mechanics, Electromagnetism, and Thermodynamics.

As experimental technologies advanced scientists focused on the study of the origin of phenomena such as electricity, magnetism, and heat. The guiding idea here, and in all of modern science, was that the behavior of the whole is exclusively determined by the behavior of the parts. This is the assumption behind all modern sciences, the assumption that broke in quantum physics. Thus, physicists started studying the smaller constituents of the macroscopic phenomena. Eventually they arrived at elementary particles such as electrons and photons, but they noticed that in the new realm of microscopic phenomena things are very strange. Our everyday logic does not hold anymore. Below I mention a few of the new mysteries.

1. Particles of matter which were expected to be point-like stuff confined in space strangely appear to be in many places at once.

2. It turned out that material particles can sometime behave as point-like particles and sometimes as waves spread in space, depending on where we put them.

3. Wave phenomena, such as light, can sometimes behave as point-like material particles.

4. Particles seem to know a way of communication that transcends space and time.

5. It is possible to have two distinct particles each at opposite ends of our universe that are intrinsically correlated in their behavior. No matter how far apart we put them they still remain, and behave as, one whole system and not two separate things.

6. When we are not looking at a quantum object it behaves totally different from when we are looking at it (notice that to see something really means to bounce light off of it and see the reflected light.)

7. It appears that observation is not a passive position; it is an active and creative act. By observing a quantum phenomena we actually make it happen. Thus, it is in principle impossible to speak of nature in the absence of observation.

8) The quantum realm is a realm of interconnectedness. There is are only wholes and not parts. There is a deep unity that even the strongest technologies cannot break. Heisenberg Uncertainty Principle, the cornerstone of quantum mechanics, is a mathematical expression of this indestructible unity.

Double Slit Experiment is one the most famous experiments that exposes the strangest features, and hence the deepest principles, of the quantum world.

Werner Heisenberg, the first founder of quantum mechanics, then known as Matrix Mechanics, says in his Physics and Philosophy “What we observe as nature is not nature herself but nature as exposed to our methods of inquiry.” This idea is the juice of quantum physics. Let me encrypt this saying into a more philosophical and concise proposition: The object and the knowledge of object are one and the same. 

I mentioned a few of the strange features of the quantum world but it becomes even stranger than that. In my book Nondual Perspective on Quantum Physics I have explained these features in detail but I will mention some metaphysical implications of it here. It has to do with understanding our commonsense:

Look at a glass of water in front of you. The glass has a distance from you; it has a certain speed (hopefully zero.) It has an apparent size and shape that changes as you move relative to the glass. Though we may view the glass from an infinite number of perspectives, we know that it is one and the same glass. According to our commonsense our perspective changes but the glass does not.

But we have more assumptions: We assume that the glass has an independent shape and size, specific position in space and place in time irrespective of our presence. On the other hand, we know that the color and the lighting by which we see the glass is not a property of the glass itself. Color is understood to be a moment of subjective experience; in reality there are only wavelengths and frequencies which represent different energies; it is our brain that translates these different energies into different colors. In other words, there are certain properties that we attribute to the glass itself and certain others that we attribute to our perceptions. This reflection is crucial in understanding quantum mechanics.

We may speak of primary and secondary qualities: Primary qualities are those that belong (according to our commonsense) to the object itself; they are always present in the object whether we are present or not, whether we experience them or not. Examples are actual shape and size, position and velocity, etc. Secondary qualities are those that arise only when the object is being experienced by a subject; they arise in the subject but only in the presence of the object and only insofar as the object is present. Examples are apparent shape and size, color and shade, etc. For instance, notice that color is not in the glass itself; color of the glass is something that happens during seeing of the glass.To be more precise, the secondary qualities belong to the overlap of object and experience: I won’t see the green glass if I do not look at the green glass and I see it only as long as I am looking at it. 

Having a clear sense of the distinction between the two qualities we can now define the whole of the quantum realm as a realm where some primary qualities are pushed over into the of secondary qualities. If our commonsense breaks in the face of quantum phenomena it is because what we had previously taken to be the primary qualities of natural objects turn out to be their secondary qualities!

Abstract science background electromagnetic radioactive core

To take this understanding to the quantum realm we first have to got back to the glass: One of the most important primary qualities of a glass that was always taken for granted is its state of motion. We know from commonsense that the glass has a fixed position and speed in space and at each moment of time. Even when we not present with the glass we never doubt that it is somewhere, that it has a position in space and a velocity; this is because we take the state of motion to be the primary quality of objects. Consciousness of place is most fundamental to our commonsense and understanding: Everything has a place whether we know of it or not, at least we think. We attribute our lack of knowledge about the place, or position, of an object to our ignorance rather than the object itself. Try to imagine an object that has no place! I do not mean an object that is constantly moving, but an object that has no place at all, whether in real space or imagined space. It is impossible. We cannot imagine or conceive of objects without imagining them in their primary qualities though we may do so dispensing with their secondary qualities.

The fundamental paradigm shift in the case of quantum physics is that the state of motion of a particle which was previously assumed to be a primary quality turns out to be a secondary quality, a property present in the observation rather than in the object itself. The place and the velocity of elementary particles are unknown prior to observation, not because we do not know them, but because they do not have properties such as position and velocity. To speak of the position or velocity of a particle in the absence of observation is like to speak of circular triangle.

When we measure the position of an electron and get a numerical value we do not see the electron hiding somewhere; instead, the very process of measurement forces the electron to take a position in space. In other words, measurement of position creates the measured position. Prior to measurement the electron is described as being present everywhere at once, but the act of measurements makes the electron to instantaneously collapse into a point in space. This instantaneous, atemporal, collapse is known as the collapse of the wave function.

See that we cannot imagine what happens during the measurement process because we cannot imagine the quantum objects under investigation. As I mentioned above, in order to imagine something there must be something that we imagine; but now that all the imaginable properties of quantum objects have turned out to be only secondary properties, properties that do not preexist the observation, then in the absence of observation there is nothing to imagine.

An analogy may help: If I compare the faculty of imagination with the our hands, then trying to imagine the quantum world is like using our hands to listen to music. Sound is not a tactile object; it is something heard and not touched. Thus, no amount of moving or stretching our hands will help us hear a sound. Instead, we must listen. In the same way the quantum realm lies forever beyond imagination because the objects and processes of this realm have more intrinsic properties through which they can be imagined or grasped.

Now I must add that quantum physics is the most experimentally verified scientific theory in the whole history of civilization. It is as solid as it can get, and its best proof is the myriad of tools and devices that we use today on a daily basis, all of which were born out of the findings of quantum physics: Transistors which exist in all electronics, GPS, microwave, your car, cellphone, TV, computer and internet, etc.

There are more details about the mysteries of quantum physics, its philosophical implications, and its astonishing similarities to the world described my mystics. In my book Nondual Perspectives on Quantum Physics I have first introduced the strange features of the quantum world in a non-technical language and then compared it to philosophical and mystical traditions of the East and the West such as Advaita Vedanta Metaphysics and Transcendental Phenomenology. The conclusion is that physics and metaphysics, physicists and mystics, one through discursive thought and the other through direct intuition, have both described a world that appears to be one and the same, and this similarity is more than ever present in our time.

Glowing blue synapses in space

The world of the mystic speaks of One, a nondual ground from which all diversities arise. The world of the physicist is a world fundamentally interconnected and whose fluctuations appears as the multitude of phenomena. The Nondual Perspectives on Quantum Physics finds and recounts the one conclusion at the heart of modern physics and traditional metaphysics:

The manifest arises from the vibrations of the unmanifest

http://www.amazon.com/dp/B00N5DL1R0/

Frontcover

Physics & Metaphysics

Posted on by toomajj

I noticed I write more about metaphysics than physics. I have done so perhaps because metaphysical questions are more relevant to our lives today than abstract questions of modern physics; also because I am much more certain, in fact absolutely certain, of the metaphysical order and its eternal truths than the physical order and its facts. But during decades of working with both disciplines I have come to understand the physical order as an imperfect reflection of the metaphysical order, the mathematical laws of physics as temporal reflections of eternal truths of metaphysics. It cannot be otherwise, for there is only one truth and one fact. The truth is the One, and the fact is the fallen one, man. If man is the fallen spirit, then fact is the fallen truth, physics the fallen metaphysics, and reason the fallen intellect.

The irony of the situation is that after all these years in both fronts I have arrived at one and the same question: “How does the one become the many?”

In the context of metaphysics, I know from direct perception the unity and unicity of the Real, the nondual substance of totality which is beyond being and non-being. I also know the apparent diversity of the phenomena world, that we live in an apparently changing universe. Thus, there is a truth and a fact: The truth is that there is nothing but the One; the fact is that there is an experience of multiplicity. The question is how does that truth appear as this fact? How does the nondual, immutable One at once appear as the changing? I call this the enigma of all enigmas. No doubt the One never really becomes the many; the difference is only apparent, each belonging to different order of reality. But metaphysics is metaphysics and must ground metaphysical questions.

In the context of physics, we know that though there appears to be an infinite number of particles in the universe, their behavior is as if there were only one particle, a scenario called the One Electron Universe by John Wheeler. The question arises: How can one electron appear as the many at once being at many places? This question is the focus of my academic research as a physicist and I call it the quantum enigma.

Seeing that there is one question at the bottom of both quests I felt that insight into one may lead to insight into another. I am much more clear about the metaphysical aspect of the question but like to know its bearing on the physical plane.

For these reasons I feel I need to write something in the area of my expertise, quantum physics, in a simplified language which may interest others as it interests me; the goal is to see the astonishing similarities between the world of the mystic and the world of the modern physics. I will do so in the upcoming post(s).

A Visual Account of Quantum Strangeness

Posted on by toomajj

The strangeness of the microscopic world, aka the quantum world, is best captured in a famous experiment known as The Double Slit Experiment. It is a simple experiment that shows how our intuitive ideas of matter and reality don’t hold anymore. This experiment shows the essence of quantum mechanics and why it is so strange and counter-intuitive. The following video is the best and the most accurate description of this experiment I have found so far. I hope you enjoy it.

From Quantum Physics to Advaita Vedanta Metaphysics

Posted on by toomajj

[The wave image below depicts a wave packet, the wave aspect of a particle; but unlike the physical particle this wave packet is not in physical space; it is a vibration in an abstract mathematical space known as Hilbert Space. The only physical significance of this vibration is that it is related to the probability of finding the physical particle within a given volume of physical space.]

WavePacket

Quantum mechanics is the physics of microscopic phenomena. Newtonian physics which is known as classical physics describes all natural phenomena in the scales observable by humans, namely the macroscopic world. But when we enter the world of atoms Newtonian mechanics breaks down. Atomic phenomena cannot be explained or understood in terms of laws of physics postulated by Isaac Newton. Physicists of the 20th century had to find new laws and postulates that could explain and predict atomic phenomena. This new physics which applies to small scales is known as Quantum Physics, or Quantum Mechanics. It has been shown that all the laws of Newton and classical physics can be derived from the laws of quantum mechanics. In fact, the laws of quantum mechanics are the fundamental laws from which Newtonian physics is derived as an approximation or a special case. In other words, our world is essentially quantum mechanical and not Newtonian, though we perceive only the Newtonian aspect of it at human scales: World is Newtonian when you look at it, but it is quantum mechanical when we are not looking at it. But this itself is a prediction of quantum mechanics: According to the principles of quantum mechanics the world at human scale must appear classical and Newtonian.

What distinguishes quantum mechanics from classical mechanics is the wave-particle duality. It is possible to explain all the strange phenomena of atomic realm by reference to the dual nature of elementary particles. Here I state and restate the fundamental features of quantum mechanics all of which are based on the wave-particle quality. The fundamental constituents of nature have a particle aspect and a wave aspect, and above all their particles aspect is entangled to their wave aspect which is the source of all the strangeness of quantum phenomena. Below I present the deep physical and philosophical implications of foundations. If it is too technical at certain points it is because their omission would damage our purpose. (FE=Fundamental Entanglement)

1) There is a fundamental entanglement between certain physical variables. The most important of these are position, momentum, energy, and time: Position x is fundamentally entangled with momentum p. Energy E is fundamentally entangled with time t.

2) The product of these fundamentally entangled variables is always of the dimension of classical action which has the dimension of angular momentum. [xp] = [Et]

3) Due to this FE there is always an uncertainty relation between any pair of fundamentally entangled variables whose products have the dimension of action. Thus, the uncertainty relations involve Planck’s constant h.

4) This FE is expressed in De Broglie equation which is also the expression of wave-particle duality:

Pλ = h

De Broglie’s equations tie the particle aspect to the wave aspect, the product of which has the dimension of action again: P stands for the momentum of the particle; landa stands for the associated wavelength, and h is Planck’s constant. De Broglie’s equation is also equivalent to the two following equations:

P=ɦk     E=ɦω

Here P stands for the momentum of the particle; k known as wave-number stands for a wave aspect related to wavelength; E is energy, and omega is the angular frequency. In both these formulas the left hand side is related to the corporeal aspect, and the right hand side is related to the wave aspect. The relation, the FE, is mediated by Planck’s constant.

5) Considering the classical relations for the phase of a wave, kx-ωt, if we replace the wave number and the angular frequency with their quantum mechanical counterparts we arrive at the following which relates the phase to action:

px-Et=ɦΦ

6) Beginning with only the De Broglie relation we arrive at quantum mechanics when we consider the wave phase above to be the phase of an abstract wave which is obtained by replacing the above formulate with the one in classical waves:     kx-ωt =(px-Et)/ɦ

In the classical case we generally write wave as following:

Ψ(x,t)=ei(kx-ωt)

Now insert the phase relation above to obtain the equivalent wave formula:

Ψ(x,t)=ei(kx-ωt) = ei(px-Et)/ɦ

The above which is obtained from imposing the De Broglie relation on classical waves is nothing but the quantum mechanical wave function, the solution to the Schrodinger equation which plays the role of Newton laws in the microscopic realm.

If here we define the action S to be: S = S(x,t) = px-Et, then we can write the wave function as following:

Ψ(x,t)=eiS(x,t)/ɦ

This is the most general form of quantum mechanical wave function as the solution to Schrodinger equation. As a matter of fact, this wave is the solution to Hamilton-Jacobi equation in classical physics. If we differentiate the above wave function with respect to time, and replacing E with the Hamiltonian H, then we derive the following non-linear partial differential equation:

H + \frac{\partial S}{\partial t}=0

This is none other than the famous Hamilton-Jacobi equation from which we can derive the Schrodinger equation:

i \hbar \frac{\partial}{\partial t}\Psi = \hat H \Psi

This is the wave equation for quantum particles. The peculiar fact of wave-particle duality is that the particle aspect is related to a wavelength of a non-physical wave. The wave aspect of phenomena, which is related to vibrations, is not a physical wave; it is a wave in an abstract Hilbert Space, and hence not observable. In other words, the observable aspect of phenomena is associated with the vibrations of a non-observable wave. This is the wave-particle duality that is behind all strangeness of quantum mechanical world. We can express the De Broglie formula of wave-particle duality in a more philosophical way:

The manifest is associated with the vibrations of the unmanifest.

This expression, though still different from saying that “the manifest is the vibration of the unmanifest,” is a restatement of Advaita Vedanta metaphysics. But it is also the very definition of string theory.

More details about this subject can be found in my book Nondual Perspectives on Quantum Physics.

http://www.amazon.com/dp/B00N5DL1R0/

Frontcover

A Non-Dual Perspective on The Big Bang

Posted on by toomajj

Existence As The Grand Illusion 

The similarities between Quantum Physics and Plato’s theory of Forms is so astonishing that one may even view quantum theory as a mathematical formulation of Plato’s theory of Forms.

Plato’s fundamental forms are regular solids of Euclidean Geometry. The fundamental forms of quantum physics are elementary particles which are not physical objects at all; elementary particles are mathematical objects; what we perceive in the form of matter is only the manifestation of these ideal-mathematical objects.

Plato considers our world to be the imperfect shadow of an ideal, perfect world of pure forms. It is not that Plato’s Pure Forms or Ideas are mental objects or subjective constructs. Plato’s Forms have existence of their own and are in fact the sole reality that exists. Only these Forms are real; what we experience as reality is the imperfect shadow of the world of pure forms. Thus, Plato’s Pure Forms are not physical entities existing in space and time; they are ideal-and in Plato’s view mathematical-entities existing beyond space and time.

Now take a look at a sentence from Werner Heisenberg, the German physicist and Nobel Laureate who was one the founders of quantum mechanics. He says in his Physics and Philosophy:

“What we observe is not nature itself, but nature exposed to our methods of questioning.”

From the point of view of Quantum Physics what we regard as physical reality is only the projection of an ideal, non-physical reality. According to quantum physics the underlying reality is beyond space and time, and that is why we observe phenomena such as interference and entanglement. A purely physical reality existing in space-time could not possibly produce these phenomena which are observed and experimentally confirmed.

The universe as we know it, as this physical object, has no real, physical existence; it is a mere shadow of something that lies outside space and time, something essentially non-dual. In fact the non-existence of universe as an independent reality is an immediate consequence of the postulates of quantum physics:

An isolated quantum system remains forever in a superposition state (state of pure potentiality) until it is observed or disturbed by something outside the system itself.

Now if we take the quantum system to include our universe and all other possible universes, namely if we take our quantum system to coincide with the totality of what is, then there is no way for this system to ever leave the state of pure potentiality and become actual. Even if we posit the existence of some conscious agent outside totality, like god or whatever, which can make the universe into actuality the problem remains intact; we can now define the quantum system to include that agent as well, thus making it a pure potentiality rather than something actual that can produce any effects. Though this may sound pretty abstract or strange it was common sense for the non-dual Vedantist who knows that none of this has ever happened.

According to the principles of quantum physics universe cannot possibly exist; it cannot possibly be real. Though most physicists avoid this aspect of the theory, it is interesting to know that this conclusion of modern physics is identical to the central principle of Advaita Vedanta Metaphysics. The details of this similarity is discussed in my book “Non-Dual Perspective on Quantum Physics” to which I would provide a link at the end of this essay.

Now, what is even more striking when it comes to the similarity between Plato’s Forms and Quantum Physics is the idea that “the observable reality is an imperfect shadow of a transcendent reality.” Here is the source of awe:

In quantum theory the underlying reality is described by this mathematical object called “state vector” which is a more abstract form of wave function. The whole of quantum theory and its description of reality is built upon mathematical objects called vectors and operators.

The quantum system described by a state vector naturally dwells in Hilbert Space which is an abstract mathematical space lying beyond space-time. Hilbert Space in which superposition states exist is the space of pure potentiality where the formless, non-dual reality dwells. Hilbert Space is NOT inside our familiar space and time; it is more like the void that contains our space-time in pure, formless potentiality.

In quantum physics observation corresponds to the action of operators on state vectors. The operators corresponding to the act of observation are called Projection Operators. What projection operator does is to project what is in Hilbert Space onto our familiar space-time. A quantum system which is originally in superposition state inside Hilbert Space (space of pure potentiality) in thrown into actuality by the action of the Projection Operator.

The Projection Operator is defined in a graduate textbook of quantum physics as follows:

“The action of Projection Operator gives the shadow of any state vector on a subspace.”

Through the act of observation it is not the reality that we experience but a mere shadow of it; the true reality, including our own real selves, lies beyond space and time. According to quantum physics what is observed is a mere shadow of a transcendent reality.

Considering this precise meaning of observation and experience and also the fact that our universe could not have possibly been thrown into actuality, we see that the reality described by quantum physics is somewhat identical to the reality described by Plato’s Theory of Forms. Both agree that what is real is not what is observed: Observation is a mere shadow, a pure appearance, having no reality of its own.

The only thing that ever existed is the state of pure potentiality which can never be actualized. What we experience as actual reality is more like a dream: The apparent actuality must be a cosmic illusion, a Noema, a Maya, namely a Noemaya.

It is interesting to see that cosmologists have caught some clues about this idea since a lot of them are coming to the conclusion that our universe behaves more like a hologram, a theory known as the Holographic Universe.”

I have explained in detail the non-dual aspects of quantum physics and its similarities to esoteric traditions such as Advaita Vedanta in the following book:

http://www.amazon.com/dp/B00N5DL1R0/