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- TL;DR Summary
- Is the Quantum mechanics theory of light easily understood or not? Could a better approach have been used?
Ask any informed man on the street for the quantum mechanics explanation of light and his answer would probably be something like this:
“Light as it travels from point A to point B is not something real, it exists as an abstract mathematical wave function that exists everywhere and nowhere (i.e., is disembodied) . During its passage from point A to point B light travels through multiple dimensions that have no existence, on earth, in our solar system or in the Universe itself. When the light is finally detected at point B the wave function collapses and the light becomes 'real' again. Consequent with the collapse of the wave-function, multiple universes are born”
How accurate is this picture on the quantum mechanics explanation for the propagation of light? To get an answer the question should be dealt with in more detail. How does quantum mechanics explain the propagation of light? It is complicated, to begin with multiple disciplines of quantum mechanics are needed to explain the QM version of the propagation of light, beginning with QFT (Quantum Field Theory) and progressing to (Quantum Electrodynamic Theory). A point of solace is that QM still uses Maxwell’s theory on the propagation of electromagnetic waves as its basis. However, since Maxwell’s is a wave theory, some alterations are needed before it can fit in with quantum mechanics.
Converting Maxwell's equations to a form suitable for quantum mechanics involves a series of processes beginning with First quantization, followed by second quantisation, followed by normalisation and re-normalisation. What do all these processes mean and what is the end result? Here's a brief overview.
First Quantisation: refers to the standard approach of quantizing individual particles, in this case photons. In this framework, particles are described by wavefunctions that evolve according to the Schrödinger equation or the Dirac equation, depending on whether they are non-relativistic or relativistic particles. First quantization deals with the wave-particle duality and the behaviour of individual quantum systems.
(note) Schrodinger’s wave equation works well for single particle situations, however with each additional particle that is considered, three additional dimensions are required. This is a well documented fact, freely admitted by both Max Born and Heisenberg. Though recent proponents argue that it is not dimensions that are involved but multiple degrees of freedoms. This is an evasion rather than an attempt to address the problem. Even a cursory examination of the philosophical implications reveal that it is dimensions that are involved (i.e., actual spatial dimension) and not degrees of freedom.
Second Quantisation: is a different approach used in quantum field theory (QFT) to quantize fields rather than individual particles. Instead of describing particles as discrete entities, second quantization treats particles as excitations of quantum fields that permeate space. This framework allows for the creation and annihilation of particles and provides a more natural description for many-particle systems present in EMR. Quantization of the electromagnetic field, involves imposing commutation relations on the creation and annihilation operators to ensure that the resulting quantum field theory is consistent with the principles of quantum mechanics.
In second quantization, the electric and magnetic fields are represented by creation and annihilation operators. These operators create or destroy particles (quanta) associated with the electromagnetic field. During second quantisation the electromagnetic field is expanded in terms of its Fourier modes, which describe the field in terms of different wavelengths and momenta.
(note) The first question that occurs to anyone, is how does this help in the propagation of light? The answer is fascinating, as the photon propagates, it undergoes spontaneous self-annihilation, the product of this self-annihilation process is the creation of an electron and a positron, these two particles experience mutual annihilation the end product of which is the creation of a photon with identical properties to the original photon before it self-annihilated. This is the way in which EM radiation propagates according to QM, the use of fourier modes and fock states ensures that all wave-lengths and frequencies come under the purview of this theory.
Normalisation, is the cleaning up process used in quantum mechanics to ensure that wavefunctions (or states) are properly normalized. Normalization ensures that the integral of the square of the wavefunction over all space (or some appropriate region) equals 1. This condition guarantees that the probability of finding a particle in any allowed region of space is unity. Normalization is achieved by dividing the wavefunction by a normalization constant, which is determined by integrating the square of the wavefunction and then taking the square root of the result.
Re-normalisation: is a technique used in quantum field theory to handle infinities that arise in certain calculations. In quantum field theory, interactions between particles can lead to divergent quantities, such as infinite values for certain physical quantities. Renormalization involves redefining these quantities in terms of experimentally measurable quantities, effectively absorbing the infinities into the parameters of the theory. Renormalization ensures that physical predictions from the theory remain finite and meaningful. It's a crucial aspect of quantum field theory, particularly in dealing with theories like QED where infinities arise in perturbative calculations.
While going through some of the posts here at Physics Forums involved with the propagation of light, I had noticed that while many of these issues have been raised piece meal, a more complete explanation of what is involved has not been undertaken. It is needless to state that it is a wonderful theory even if one wishes that quantum mechanics would have done better to formulate an original theory rather than piggybacking on Maxwell’ Theory of the propagation of electromagnetic radiation.
“Light as it travels from point A to point B is not something real, it exists as an abstract mathematical wave function that exists everywhere and nowhere (i.e., is disembodied) . During its passage from point A to point B light travels through multiple dimensions that have no existence, on earth, in our solar system or in the Universe itself. When the light is finally detected at point B the wave function collapses and the light becomes 'real' again. Consequent with the collapse of the wave-function, multiple universes are born”
How accurate is this picture on the quantum mechanics explanation for the propagation of light? To get an answer the question should be dealt with in more detail. How does quantum mechanics explain the propagation of light? It is complicated, to begin with multiple disciplines of quantum mechanics are needed to explain the QM version of the propagation of light, beginning with QFT (Quantum Field Theory) and progressing to (Quantum Electrodynamic Theory). A point of solace is that QM still uses Maxwell’s theory on the propagation of electromagnetic waves as its basis. However, since Maxwell’s is a wave theory, some alterations are needed before it can fit in with quantum mechanics.
Converting Maxwell's equations to a form suitable for quantum mechanics involves a series of processes beginning with First quantization, followed by second quantisation, followed by normalisation and re-normalisation. What do all these processes mean and what is the end result? Here's a brief overview.
First Quantisation: refers to the standard approach of quantizing individual particles, in this case photons. In this framework, particles are described by wavefunctions that evolve according to the Schrödinger equation or the Dirac equation, depending on whether they are non-relativistic or relativistic particles. First quantization deals with the wave-particle duality and the behaviour of individual quantum systems.
(note) Schrodinger’s wave equation works well for single particle situations, however with each additional particle that is considered, three additional dimensions are required. This is a well documented fact, freely admitted by both Max Born and Heisenberg. Though recent proponents argue that it is not dimensions that are involved but multiple degrees of freedoms. This is an evasion rather than an attempt to address the problem. Even a cursory examination of the philosophical implications reveal that it is dimensions that are involved (i.e., actual spatial dimension) and not degrees of freedom.
Second Quantisation: is a different approach used in quantum field theory (QFT) to quantize fields rather than individual particles. Instead of describing particles as discrete entities, second quantization treats particles as excitations of quantum fields that permeate space. This framework allows for the creation and annihilation of particles and provides a more natural description for many-particle systems present in EMR. Quantization of the electromagnetic field, involves imposing commutation relations on the creation and annihilation operators to ensure that the resulting quantum field theory is consistent with the principles of quantum mechanics.
In second quantization, the electric and magnetic fields are represented by creation and annihilation operators. These operators create or destroy particles (quanta) associated with the electromagnetic field. During second quantisation the electromagnetic field is expanded in terms of its Fourier modes, which describe the field in terms of different wavelengths and momenta.
(note) The first question that occurs to anyone, is how does this help in the propagation of light? The answer is fascinating, as the photon propagates, it undergoes spontaneous self-annihilation, the product of this self-annihilation process is the creation of an electron and a positron, these two particles experience mutual annihilation the end product of which is the creation of a photon with identical properties to the original photon before it self-annihilated. This is the way in which EM radiation propagates according to QM, the use of fourier modes and fock states ensures that all wave-lengths and frequencies come under the purview of this theory.
Normalisation, is the cleaning up process used in quantum mechanics to ensure that wavefunctions (or states) are properly normalized. Normalization ensures that the integral of the square of the wavefunction over all space (or some appropriate region) equals 1. This condition guarantees that the probability of finding a particle in any allowed region of space is unity. Normalization is achieved by dividing the wavefunction by a normalization constant, which is determined by integrating the square of the wavefunction and then taking the square root of the result.
Re-normalisation: is a technique used in quantum field theory to handle infinities that arise in certain calculations. In quantum field theory, interactions between particles can lead to divergent quantities, such as infinite values for certain physical quantities. Renormalization involves redefining these quantities in terms of experimentally measurable quantities, effectively absorbing the infinities into the parameters of the theory. Renormalization ensures that physical predictions from the theory remain finite and meaningful. It's a crucial aspect of quantum field theory, particularly in dealing with theories like QED where infinities arise in perturbative calculations.
While going through some of the posts here at Physics Forums involved with the propagation of light, I had noticed that while many of these issues have been raised piece meal, a more complete explanation of what is involved has not been undertaken. It is needless to state that it is a wonderful theory even if one wishes that quantum mechanics would have done better to formulate an original theory rather than piggybacking on Maxwell’ Theory of the propagation of electromagnetic radiation.