3.3.1.

Doppler Effect

CTF represents the “preferred and stationary reference frame” for our universe, like Lorentz-ether. Since all atoms and molecules are diverse assemblies of various torus of this CTF, any emerging light pulse in the CTF will suffer Doppler frequency shift due to the “absolute” source velocity with respect to the stationary CTF-frame. This light pulse will then keep propagating with the velocity “c” across the entire universe, preserving its Doppler shifted frequency. The original quantum transition frequency is now modified into a permanent and real Doppler frequency shift due to the source-only movement. If a set of detecting atoms with different relative velocities w.r.t. CTF, receive this Doppler shifted wave, the perceived frequencies will be different for different atoms [see Ch.10 in 3]. The original Doppler Effect was expressed this way. We use this original formalism due to Doppler when we analyze frequencies of waves generated in the tension fields of material media like pressure tension field (sound waves), surface tension field (water waves), etc. It should not be any different for EM waves propagating as oscillation of CTF.

3.3.2.

Cosmological Redshift

The above discussion automatically leads us to the Cosmological Redshift originally discovered by Hubble. Is it really due to Doppler Effect, or some other physical phenomenon? This controversy already exists in the literature. We believe this shift is due to very slow, linear distance dependent energy loss of all EM waves as they propagate through cosmic “cloud” permeated CTF [8].

3.3.3.

CMBR

The Cosmological Microwave Background is another observed fact. However, acceptance of the stationary CTF and the unchanging rules of operation behind the interaction processes in the cosmic system faces logical contradictions with the hypothesis of expanding universe. Expanding universe implies that the field CTF is expanding and, consequently, its intrinsic tension values ε₀ & μ₀, which determine all the intrinsic characteristics of particles and the fixed velocity of EM waves, would also have been changing with time. Note that particle rest mass m₀ = E / c² = Eε₀μ₀ should also change if space is expanding. There are no such validating observations. Further, this line of argument that the enormous expansion of the early-epoch-space has dilated the wavelength of the EM waves has at least one more serious problem. In the quantum world, in the atomic and molecular emissions, the frequency is the primary physical parameter dictated by the quantum transition characteristics. This original quantum frequency of light remains unchanged as it propagates through different media of different refractive indices, even though the wavelength changes. We believe that CMBR is a pure simple Blackbody Radiation, which is in thermal equilibrium with the thinly spread cosmic dust and molecules. In our laboratory Blackbody, the thermal equilibrium is attained due to innumerable scattering and reflections from of EM waves from the molecules of the inner surface of an enclosed “blackbody” surface maintained at some adjustable thermal equilibrium. In the gigantic cosmic space, the thermal equilibrium is established due to innumerable absorption and re-emission of the radiation by the cosmic dust, which are at 2.7°K. Of course, the stars in galaxies are at much higher temperature. Their coronas also closely follow the rules of Blackbody radiation.

4.1.1.

Measurement Problem (Ensemble Interpretation)

The founders of QM correctly identified that our measurement has some fundamental problems. One is wave-particle duality and the other is uncertainty. The Copenhagen Interpretation has apparently resolved the problems by accepting the wave-particle duality as our new confirmed knowledge without finding any deeper knowledge behind the structures of photons and electrons. The uncertainty is considered to have been resolved mathematically and by assigning it to nature’s inherent mode of operation. Even though this assignment creates consistent causality violation in the micro universe. Again, we have been taking this as our confirmed new knowledge. This is a surprising approach in science because all of our mathematical equation for physics theories are constructed as hard-core causal representation of equating measurable effect with the presumed or hypothesized cause(s). We have been accepting these built-in contradictions as our new mode of thinking. Then the intellectual and collective social skills to interpret elegant equations become the driving force behind the design of new experiments to extract the desired evidences. Naturally, we experience persistent confusion due to the diversity of subjective interpretations we find in books. The way out is to challenge ourselves to visualize the causal (ontological) physical processes that are being executed by nature.

We propose a way out of this dilemma by first recognizing that we cannot overcome the measurement problem by using elegant mathematics and/or interpretations. Second, the data in any instrument emerges as some quantifiable number due to some physical changes in our chosen interactants, none of whose properties is ever known completely by us. Further, we can never claim that our instruments have 100% fidelity. Thus, the real issue is that we have a perpetual Information Retrieval Problem (IRP), not just a measurement problem. We cannot resolve the issues behind IRP by elegant mathematics alone. We have to continue our hard work iteratively by developing newer theories, while developing more and more refined measuring instruments. The approach will be further empowered by iterative approach to unification of theories, while explicitly paying attention to visualize the invisible interaction processes that give rise to the measurable data. However, during each iteration, we must develop improved and integrative new set of basic postulates that combines all the theories to be unified. Attempts to preserve all the basic postulates of each individual working theories will only generate persistent bottlenecks. Because each working theory is a logically closed-system to explain a small set of phenomena, which the theory was constructed to explain. Let us appreciate that all working theories are necessarily incomplete, as they are formulated based upon insufficient knowledge of the universe we are trying to model. In this context, theoretically oriented people should ponder on Gödel’s Incompleteness Theorem. This is only a brief discussion on the measurement problem. This is to facilitate the discussions on quantum optics related issues in the following section.

4.1.2.

Hybrid Photon

Photons as “indivisible light quanta” has been continuing since 1905. It has only contributed to confused interpretations that violate causality. No optical scientist or engineer propagate “indivisible light quanta”. They propagate light waves using Huygens-Fresnel diffraction integral (or its different mathematical variations) along with Maxwell’s wave equations when the intervening material properties are being modified by the wave. Further, the independent “indivisible light quanta” have never been successfully localized. Yet, the QM formalism correctly models the emission properties of “photons”; and the classical optical-wave propagating formalism correctly predicts the instrumental data. Accordingly, it is necessary to resolve the wave particle duality by defining a hybrid photon.

Spontaneous emission, on classical spectroscopic measurements, show Lorentzian line width, as if light beam out of atomic dipole consists of exponential pulses of a finite temporal duration [see Ch.5 in 3]. Some of the measured spectral line widths are in the domain of GHz, implicating temporal duration of the order of nanoseconds. Doppler-free tunable laser spectrometry has successfully measured v_mn in the domain of MHz [13]. These and other observations, give us confidence that at the moment of quantum transition, an atoms or a molecule, does release a quantum of energy given by E_mn = hv_mn. Now to conform to the staggering successes of classical optics and engineering, riding on Huygens principle, it is quite rational to assume that this energy quanta hv_mn must immediately evolve into a quasi-exponential classical wave pulse and propagate out diffractively oscillating at the quantum-transition frequency ν_mn. This model easily accommodates the generation of Doppler frequency shift due to the source velocity and detector velocity with respect to the stationary CTF.

Figure.2.

Hybrid photon model. At the instant of emission from atoms or molecules, the photon of energy hν is a quantum entity, which then triggers the emergence of a classical wave packet the same energy with a quasi-exponential temporal envelope and the QM-predicted carrier frequency ν.

4.1.3.

Superposition Effects with Hybrid Photons without Duality

This sub-section gives the summary of an experiment carried out by the author [14] using a well-known Mach-Zehnder interferometer (MZ) to demonstrate that superposition effect, to become manifest, require physical superposition of the real physical signals that we write down in the superposition Eq. 1. For a two-beam superposition experiment, we have two amplitudes along with their respective phase information. A single stable elementary particle cannot carry these four parameters, as a single quantum photon is claimed to do. A stable elementary particle, by definition, cannot be multivalued at the same moment in the same space. Accordingly, the “indivisible single photon interference” is an erroneous interpretation. When our electronic counter registers a “click”, it is a highly amplified current pulse consisting of, most likely, hundreds of millions of electrons, triggered by the release of the original photoelectron, bound quantum mechanically within the assembly of the detector molecules. Discreteness and quantumness lies with the bound electron, not with the EM waves. Further, quantum transitions do not always require a quantized donor. Mechanical energy of striking stones produces spark and light through quantum ionizations and downward transitions. This quantum process was at the root behind the discovery of controlled fire generation by our very distant ancestors. This was much before they invented any language with grammar. We should recognize that mathematical theories did not guide the most critical phase of early human evolution.

Let us get back to our demonstration experiment. We arranged the two equal-energy incident beams in the output beam-combiner of the MZ from the opposite sides in such a way that the Poynting vectors for the two pairs of output beams are exactly coincident and collinear. Then the classical energy conservation demands that all the energy of the two beams will go to only one direction or the other as the relative phase difference between the two beams is arranged to vary from zero to pi. This is a simple and old classical boundary-value problem. There is a pi-phase shift for “external reflection” compared to the “internal reflection” from the two sides of the beam combiner. Therefore, for zero or pi relative phase delay, all the energy from both the beams will be directed into one or the other direction.

It is correct that classical light pulses are generated by atoms through quantum processes. The classical boundary conditions of a beam splitter arise as bulk properties out of the assembly of quantum atoms. However, the attempt to develop the novel interpretation of EM waves consisting of “indivisible photons” represents logically inconsistent physics. We should not encourage the introduction of complex and non-causal quantum interpretation just by reducing the photoelectric counts to a very low rate. Light always propagates as diffractive wave packets and follows classical boundary conditions. There is no need for wave-particle duality. The next sub-section explains that even for particle diffraction, the wave-particle duality is unnecessary.

Another major and fundamental interpretational problem behind “single photon interference” lies with the assumption that no energy (“photon”) arrives at the dark fringe locations. In reality, at the dark fringe locations, the resultant E-vector stimulation of the detecting dipole is zero. Un-stimulated detecting dipole cannot absorb any energy out of the fields passing-by. Surprisingly, our mathematics clearly tells us that the location of dark fringes are defined by the zero resultant electric field value as experienced by the detecting dipoles (see Eq. 2). Data can be generated in a detecting instrument only after some physical transformation is experienced by the detecting element (or material). This physical transformation require energy absorption from an incident EM field. For light-matter interaction, the dipolar polarizability (χ) of the detecting molecule will determine the resultant strength of the stimulation. For multiple incident waves, the Superposition Principle (SP) determines the degree of stimulation (Eq. 1) and the measurable Superposition Effect (SE), Eq. 2 determines quantity of energy transfer:

In Eq. 2 whenever the factor 2πντ (τ being the relative delay between the two beams) becomes an odd multiple of π, the detected signal will be zero, and specifically under the condition a₁ = a₂ = a. This is because the two stimulating signals are out of phase and cancel each other’s stimulation on the detecting dipole. The location of the unstimulated detector remains dark. It is not because no signal, or no photon, arrived there. The EM waves simply passes through the detecting molecule without being able to stimulate it and share part of their energy with that detecting element. This the causal interpretation dictated by our causal mathematical equation. We just need to pay close attention to the physical interaction processes that generate data. Eq. 1 & 2 are derived heuristically without directly modeling quantum transition, which is embedded in χ. Lamb and Scully [15] has derived proper semi-classical formulation for photoelectric effect.

4.1.4.

Photoelectric Effect due to random superposition of many wave packets

Einstein derived the photoelectric equation using the simple Measurable Data Modeling Epistemology (MDM-E). It was an energy balancing equation. It did not explicitly model the underlying physical amplitude stimulation of the bound electrons within the material before their release through energy absorption (see Eq. 1 & 2). Electrons are quantized particles and they are always bound quantum mechanically in atoms, molecules and solids. However, this detailed knowledge was not available to Einstein during very early 1900. Einstein’s brilliance was in in recognizing the quantumness in the photoelectric data, a cut-off frequency for electron release. He was right in postulating ΔE = hv for bound electrons. However, had he correctly assigned the quantumness to electron, rather than to light waves, he would have invented Quantum Mechanics some twenty years earlier [16]

4.1.5.

Superposition Effects due to particles without duality

Very similar equations, Eq. 1 & 2, can also be used to explain Superposition Effect due to particle beams. The origin of the harmonic phase oscillations for EM wave is the “waving” or oscillation of the electric vector. However, the particles do not propagate as waves. Their stability derives from their localized self-looped torus-like harmonic oscillations, exp[i2πf_int], which is also a Schrodinger representation of a free particle. However, the inertial particles stay put unless acted upon by some external force, which is a potential gradient around them, in the CTF, generated by some other particles or their assembly nearby. This is why de Broglie introduced his particles possessing some characteristic wavelength, for its kinetic motion λ = h / mv, without defining what is “waving”. This de Broglie relation also has some inherent mathematical problem. This relation becomes divergent when the velocity of the particle becomes zero. However, superposition effect with particle beams is very well established. Accordingly, we need to introduce a different kind of harmonic oscillation of particles exp[i2πf_ktt], which is always generated when they are given some kinetic energy, hf_kt = mv² / 2. Use of this exponential phase factor in Eq. 1 and 2 will generate the particle superposition effect without conceptual struggle as to what is “waving” with the localized particles. In addition, as far as the “wave-particle duality” is concerned, the same set of arguments, as in sub-section 4.1.3, can be extended that there is no need to invoke duality. Particles are always particles and waves are always waves. Energy exchange between them, or inter-conversions can happen only when they interact.

We are assuming that when we attempt to detect the superposition effect due to particle beams, a normal dipolar quantum detector can become excited and then absorb the energy out of the impinging particles as the square modulus of the non-zero resultant amplitude stimulation and display a “bright fringe”. The “dark-fringe” locations are where the sum total resultant induced amplitude stimulation is zero due to multiple particles carrying different kinetic phase-oscillations. We have expressed this same physical model for superposition effects due to light beams having electricvector oscillations. The approach automatically implies that the dark fringe locations do receive the superposed particles arriving, say, from a double-slit set up, but could not stimulate and deliver their energies as they were mutually out of phase with each other and could not stimulate the detecting molecule. The null stimulation leaves the detecting molecules “unexposed”. Accordingly, we have proposed several experiments using Rb-atom beam to validate this causal approach to particle superposition effect [3,12]. If one uses a thick AgBr holographic plate to detect the fringes of superposition, then after the normal development of the plate and then its observation in white light will show the expected dark/bright fringes. However, illumination with a Rb-resonance light beam of 780 nm would show Gaussian-like distribution of scattered Rb-atoms. Atoms and particles do not diffract like Huygens secondary wavelets, as EM waves do. Once these proposed experiments are validated, we will have a causal model for particle superposition effect consistent with that due to light beams. Neither of them need to use the non-causal model of wave-particle duality.

4.1.6.

Entanglement, Bell’s Theorem & Ensemble Interpretation (in view of hard causality)

Let us first clarify the broad meaning of the word “entanglement”. Our firm position is that the universe is evolving through diverse kinds of interactions between different entities following strictly causal rules of operations; we have been trying to discover. Our successes in understanding most of the observations in the universe through repeated experiments and modeling using causal mathematical rules underscores that the universe is following causal rules. It is counter-productive to assign non-causality on nature to hide our deeper ignorance. However, the universe is a very complex and entangled system, depending upon the various ranges of the different forces. All the galaxies and the stars are influencing each other. The stars are holding the planets. Nevertheless, the ranges of the weak and the strong nuclear forces do not extend much beyond Femto meters.

The concept of entanglement in Quantum Mechanics (QM) without the necessity of some physical force of interaction between a set of entities arises due to one unnecessary assumption and one erroneous assumption in QM. First, let us underscore the unnecessary assumption. We have been trying to adhere to “wave particle duality” in interpreting superposition effects due to EM waves and particles. This “duality” arise only if we keep rejecting all possible causal interpretations. We have presented such a causal interpretation in sub-sections 4.1.3 for EM waves and 4.1.5 for particles. We just need to appreciate that there exist some causal interaction process consistent with our successful causal mathematics.

The erroneous assumption is due to our forceful attempt to make a single quantum entity exist simultaneously in two or its entire set of quantum mechanically allowed states at the same time. The hard causality demands that a well defined and a stable quantum entity, when excited, can exist in one and only one of its allowed set of excited states at a time. Only an ensemble of similarly prepared particles will have a population distribution over the entire set of allowed states. In fact, this is why Boltzmann’s classical statistical relation has become so useful in representing the population distributions in QM also. Now, let us note that both the wave equations of Maxwell’s and of Schrodinger’s accept the linear superposition (sum) of all of their allowed solutions. This is the common origin of the Superposition Principle (SP) in classical and quantum physics. In classical optics, as per extended Huygens Principle of NIW, the physical meaning of classical SP is that the propagating waves can co-propagate and cross-propagate through the same volume at the same time without influencing each other’s intrinsic propagation behavior in the absence of interacting material. However, particles do interact to alter their intrinsic identities in multiple possible ways, besides elastic and inelastic scattering. Since particles exist as space-finite entities, they normally cannot occupy precisely the same micro-volume either. Therefore, even though the particles executing various forms of harmonic oscillations to display phase properties, the NIW-property is not applicable for them. Therefore, physical process wise, the Schrodinger’s SP is, different from Maxwell’s SP. However, the causality must reign supreme in nature.

The early developers of QM have succeeded in initiating the culture that QM rigorously apply to a single particle, even though real experimental validations always require collecting data from an ensemble of similarly prepared system of particles. Howevere, they assumed that QM SP implicates that the same particle can exist in the normalized superposition of multiple allowed states. Consider the case of only two allowed states for a single particle, instead of n. This is introductory QM [17].

Now, to make it valid for only one particle over all space ψ·ψ must be normalized, meaning that ∫ ψ·ψdx = 1

Then the mathematical logic proceeds as follows. Since both ψ₁ and ψ₂ represent the same single particle, they are already normalized; further E₂ ≠ E₁ to assure the existence of two distinct solutions (states). We now need to enforce the following two conditions to assure that Ψ is normalized and the same single particle occupies both the states (entangled?):

The integral in Eq. 5 implies that ψ₁ and ψ₂ should have been mathematically prepared as ψ₁ / a₁ and ψ₂ / a₂ to achieve the normalization (single-particle). This, I believe, is the approach in quantum computing when they write entangled states. However, the integral of Eq. 5 is also worth pondering. It means that ψ₁ and ψ₂ are orthonormal to each other; they do not interfere or interact with each other. How can they? It would imply self-interference. The particle is in a superposition state in a magical, un-real world. Thus, Eq. 4 is a mathematically correct construction, but does not represent physically valid interaction process in nature. Therefore, we should not give too much physics credence on the various interpretations generated out of these two mathematical equations. Let us compare Eq. 1 and Eq. 3. The “+” operator sign in Eq. 1 is executed by a detector by virtue of the presence of polarizability χ. There are no physical entity to execute the “+” operation in Eq. 3. It is a correct and elegant mathematical statement without any reality in the physical world. In reality, if we can literally isolate one particle that can be excited to the allowed states of either E₁ or E₂, E₁ ≠ E₂ from the standpoint of energy conservation, it can never be in a superposition of both the states at the same instant because of conservation of energy. Accepting statistical ensemble interpretation of the quantum theory is a causal approach.

Similarly, the inequality condition of the elegant mathematical Bell’s Theorem [18] has been formulated without any relevance to real physical experiment, without incorporating any interaction parameter with some experimental detector. It is elegant mathematics but without representing any causal physical interaction taking place in nature of nature.

Proper ensemble interpretation of actual quantum phenomena should be able to identify which interpretation of real quantum phenomena are worth perusing to extract better physics out of nature. QM formalism does represent individual atomic or other quantum phenomena. However, the basic QM formalism does not explicitly incorporate the incessant collisions of the QM entities under measurement due to the passing of a wide variety of EM radiation and cosmic rays. The finite lifetime of an excited state automatically implicates that it is sitting on a small energy-well in the energy-space, the depth of which determines the longevity in this state [19]. The statistically random collisions with the fluctuating background radiation can free it out of the mini-energy well to come down to a more stable lower state (level). This is the causal and physical reason behind the statistical behavior of excited quantum entities. In other words, quantum statistics is not a whole lot different from that for classical physics where there are 10²³ molecules within a box of one cubic meter randomly colliding with each other when confined. We cannot write down all the equations for all possible degrees of freedom for10²³ molecules. For the QM world, it is worse. Unfortunately, the QM entities are in the open box of the entire universe; we can never box-out all the background fluctuations, neither have we been able to identify all background fluctuations. This is why, from the standpoint of measurement, the decisive detection of a single “click” can never help us validate any theory. Naturally, QM formalism aptly applies only to statistical ensemble average.

Let us consider an ensemble of stimulated quantum entities in one specific “upper state” that can come down multiple possible separate lower states when left alone. The background fluctuations will be stimulating each one of them randomly but differently to make the various possible downward transitions at different moments. In this physical picture, each one of them is conceptually identifiable, like the 10²³ classical gas molecules in a meter-cubed box, due to the various different, but the specific stimulations they are experiencing. However, we cannot succeed in individually tracking them to identify which one is making which downward transition to which particular allowed lower state (of the allowed many), at least not with the existing technologies we have today. The key epistemological point is that we should not assume that an isolated single excited quantum entity remains in the normalized superposed states until the actual transition takes place. They do not reside in a single superposed state of “amplitude excitation”. From the causality stand point, it is the statistically fluctuating background that triggers any specific transition.

4.2.1.

Superposition Principle (SP) vs Superposition Effect (SE) in light of NIW

Here we want to pay close attention to differentiate between observable parameters that we can measure and correlate with the theories in contrast to the parameters that are not directly measurable, albeit, referring to conceptually important parameters that have been necessary to develop the “correct” theory. For visible light, a.exp[i2πνt], the amplitude a is not directly observable, but a² is, due to the quadratic response of detectors for high frequency EM waves, which is usually a quantum transition in the detecting molecule. In contrast, in the radio wave domain, the conduction electrons in a resonant LCR-circuit can directly respond to the incident oscillatory electromotive force generated across the LCR-circuit. An oscilloscope connected across the resistor in the LCR circuit can dynamically generate an oscillatory voltage signal that is proportional to the “amplitude” of the incident radio wave. Accordingly, when two or more waves are superposed on such a detector with broad resonance, the observable superposition effects are different for radio waves compared to the light waves, even though, the starting mathematical expression for the Superposition Principle (SP) would look identical. However, the expression for the measured Superposition Effect (SE) would be very different. This is one of the key reason for sustained confusion in interpreting the results of SE in the optical domain. The interpretational problem is even more compounded because; optical SE can be generated both (i) classically by a boundary layer of a beam combiner in an interferometer, and (ii) directly by a quantum detector [16].

4.2.2.

Superposition Effects in Diffraction Phenomenon in light of NIW

Fresnel’s mathematical representation of the Huygens Principle automatically incorporates the mathematical SP and NIW for EM waves, which is presented as the summation (integral) of all the Huygens’ secondary wavelets. Young already demonstrated SE for light around 1802. Maxwell presented mathematical physics behind the SP around 1867 through his wave equation for EM waves. The wave equation accepts all linear combinations of harmonic oscillations as its solution. It is an inherent mathematical property of any wave equation. However, to generate the observable (measurable) SE, some physical entity must execute the physical operation of summing the independent amplitudes connected by the summation symbols. The energy transfer then takes place as the square of the resultant amplitude. The necessary critical epistemological discussions are missing in the current physics books even though mathematics is presented correctly. However, Huygens [4] explicitly mentions that his secondary wavelets evolves through each other without perturbing each other, or re-organizing the spatial and temporal energy distribution of each other. The physical meaning of Maxwell’s wave equation is that the waves can co-propagate through each other keeping individual parametric values unperturbed in the absence of interacting materials. Thus, Maxwell’s wave equation validates Huygens’ Principle of secondary wavelets.

4.2.3.

Superposition Effects in Interference Phenomenon in light of NIW

Because of the NIW property of EM waves, we should not be representing the superposition as direct summation of the waving field amplitudes as is customarily done in all books and literature. We need to apply the Interaction Process Mapping Epistemology (IPM-E) mentioned earlier. In this section, we will differentiate the generation of heterodyne beat signal due to the superposition of two waves with two different frequencies and underscore that observed SE differs based upon the detector’s physics properties.

Let us consider the case of superposition of two EM waves with closely similar but different frequencies [20]. When a frequency resonant detector can simultaneously respond to both the stimulating waves, the enforced oscillation of an LCR circuit, or of a photo detecting dipole, can execute the resultant amplitude oscillation. Therefore, the detector’s physical response characteristics to the impinged fields determines the properties of the measurable (observable) data. First, consider two EM waves of closely similar frequencies, ν₁ and ν₂, in the radio frequency domain simultaneously stimulates a resonant LCR circuit, whose resonance breadth is wider than(ν₁ – ν₂). If the circuit response-figure is η, then one can measure an oscillatory current i_total (t) through the resistor of the LCR circuit as a two-term Fourier sum-like current (Eq. 6). The measurable current oscillates at a high frequency of (ν₁ + ν₂) / 2, which is enveloped by a slower oscillatory current of (ν₁ – ν₂) / 2. This is because the conduction electrons in the LCR circuit can directly respond to the resultant electromotive force (potential difference across the circuit) and follow the radio frequency. This is an AC current.

However, if the EM wave is in the optical frequency domain, the detectors that can respond to this high frequency are quantum detectors that are atomic, molecular or their assembly, through quantum level transition. Such quantum dipolar excitations are normally expressed as complex functions, ψ_1,2 = χa exp[–i2πν_1,2t], where χ is the linear dipolar polarizability of the quantum detector’s dipole element. Here also we are assuming that the resonant response breadth of the dipole is wider than (ν₁ – ν₂) around the mean frequency. The observed photoelectric current is oscillatory at the

difference frequency only (Eq. 7). However, it is a DC current, not an AC current as it is for the radio wave and the LCR-circuit detector. This is because, inside a photo detector with broad energy bands, electrons are undergoing one-way upper level transition at this oscillatory rate and an externally applied voltage draws them out through an external LCR circuit as the oscillatory DC current. Of course, to display faithfully this oscillatory current, the response time constant of the external circuit of the photo detector electronics must be faster than the optical difference frequency (ν₁ – ν₂). If it is much slower, the photo current will again be a steady DC current proportional to the sum total intensity of the waves, 2χ²a². We just need to recognize that our math must faithfully model the physical interaction processes that generate the measurable data. Only an appropriate responsive physical detector can execute the operation “+” in the above equations and its response characteristics determine the measurable superposition effect.

For the case of optical quantum detector, one can use real, instead of complex mathematical representation. However, the mathematical steps to derive the final result require taking a time averaging integration over a couple of cycles to derive the same result, as is in Eq. 8. Nature’s logics do not really follow human invented math, especially, the complex representation.

Then the physical meaning of Eq. 8, most likely, is that a quantum detector does not undergo any instantaneous quantum transition. It needs a couple cycles-equivalent time period to assess whether the stimulating signal is resonant for its quantum transition. We may call it a “quantum compatibility sensing period” [20].

4.2.4.

Superposition Effects in Spectrometry

Classical formulation of spectrometer response function is derived by propagating a Fourier monochromatic mode through the spectrometer. Such a signal cannot exist in nature, as that would violate the law of conservation of energy. Besides, the present classical formulation misses several important physical characteristics of spectrometers. We have derived [Ch.5 in 3] a causal formulation of spectrometer response function by propagating a finite classical light pulse with a single carrier frequency and of finite width, Δt to obtain a generic spectrometer pulse-response function. Under the condition of Δt > τ₀, where τ₀=Nτ. Here τ=mλ/c is the spectrometer step delay and N is number of actual superposed beams on the detector; m is the order of diffraction (for gratings), or the order of interference for Fabry-Perots. Note also that, by virtue of NIW, simple superposition of Fourier amplitude modes cannot generate new re-distribution of wave energy. Only a quadratic process can create energy re-distribution. These causal facts should be properly underscored to avoid any confusion in interpreting physical E-vector oscillation frequency content vs the spectrometer broadened impulse function. Further, spectrometers being memoryless linear optical beam replicators, they cannot carry out complex mathematical Fourier transform algorithms to determine the Fourier monochromatic frequencies that could be mathematically contained in a pulse envelope.

4.2.5.

Superposition Effects in Coherence Phenomenon in light of NIW

Traditionally, we define the degree of coherence, or the visibility of fringes, for any light beam through an autocorrelation integral. The integrated energy, detected due to the superposition of a pair of replicated and temporally translated pulses, provides the measured value of the degree of coherence. This well-defined approach to characterize light beams has been extremely valuable. In reality, the joint stimulation of a quadratic response of a detector due to the distribution of different amplitudes and different phases determine the recorded fringe visibility. Therefore, the fringe visibility is a joint property of a quadratic detector and the amplitude/phase distribution in the light beam. So, the measured fringe visibility should not be characterized as the coherence property of the light beam alone.

We should note that neither a linear optical system, nor a simple quadratic optical detector without any built-in memory, could execute Fourier transform algorithm. However, in the traditional coherence theory, mathematical Fourier frequency and the source generated physical frequencies are used in mathematical formalism interchangeably. We have underscored this logical inconsistency in Ch.6 of ref. 3.

4.2.6.

Superposition Effects in Laser Mode-Lock Phenomenon in light of NIW

The traditional books on optics and lasers present the mode-locking phenomenon as direct sum of cavity longitudinal mode amplitudes and the required temporal phases are stabilized by the intra-cavity mode-locker. The implication is that a Fourier summation is executed by the wave amplitudes themselves within the cavity to generate the temporal oscillation of the cavity energy. By virtue of the NIW-property of waves, this approach fails to represent the deeper active roles that are played by the intra-cavity mode-locking materials. The actual energy reorganization happens due to the cyclic temporal-gating property of the intra-cavity phase-locking devices, which is a quadratic process. As per Fourier theory, all the in-phase longitudinal modes should collapse into a single central optical frequency in the output. However, we already know the various engineering use of the frequency comb (all the longitudinal cavity modes) contained in each of the pulses coming out of mode-locked lasers [Ch.7 in 3].

4.2.7.

Superposition Effects in Material Dispersion Phenomenon in light of NIW

The group velocity has been one of the key property taught through every books on material dispersion. The derivation is by summing two phase-steady CW waves with two different frequencies. This is again counter to the NIW-property of waves. While the two waves are co-propagating with parallel Poynting vectors, they still preserve their independent oscillations. This is why wavelength multiplexed signals can be sent through many kilometers of single mode fiber and fully recovered by a spectrometer at the output. Thus, the concept of group velocity is not a good physical parameter to characterize multi-frequency wave propagation [Ch.8 in 3].

4.2.8.

Superposition Effects in Polarization Phenomenon in light of NIW

We are taught that light beams of orthogonal polarization do not interfere. However, we have started this paper by underscoring the NIW-property of all waves, whether polarized orthogonal or parallel. It is the dipolar properties of dielectric material boundaries and detecting molecules whose joint oscillatory response characteristic is restricted to only one polarizable axis in isotropic media at a time. Anisotropic media show two orthogonally fixed directions of polarizability and consequent behavior. Thus, the response of material to multiple incident waves of different polarization will be always resolved into one or the other axial vibration. For an isotropic detector, receiving multiple polarized beams, it will first accept amplitude stimulation from the multiple waves as their vectorial cosine projections, and then absorb energy proportional to the square modulus of the vectorial sum of the projected amplitudes [Ch.9 in 3]. This is congruent with the analysis presented by Jones’ matrix method.