Quantum Field Enigma I

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

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/

A Visual Account of Quantum Strangeness

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

[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

Metaphysics Reflected in Physics

Mass is trapped energy   

(E=mc2)

Man is trapped consciousness

(I am Brahman)

*The photo shows physicist Werner Heisenberg on the left, the founder of Quantum Mechanics, and philosopher Martin Heidegger on the right, the founder of nothing in particular.