Journal of Modern Physics, 2012, 3, 13571368 http://dx.doi.org/10.4236/jmp.2012.310173 Published Online October 2012 (http://www.SciRP.org/journal/jmp) Next Frontier in Physics—Space as a Complex Tension Field Chandrasekhar Roychoudhuri Femto Macro Continuum & Physics Department, University of Connecticut, Storrs, USA Email: chandra@phys.uconn.edu Received July 26, 2012; revised September 3, 2012; accepted September 12, 2012 ABSTRACT We hypothesize that 100% of the energy of our cosmic system is held by a physically real Complex Tension Field (CTF). We are using an old methodology of thinking used by our forefather engineers long before the advent of modern scientific thinking. We call it Interaction Process Mapping Epistemology or IPME. We apply this IPME on to the prevailing Measurable Data Modeling Epistemology or MDME. This approach helped us analyze the “Measurement Problem”, recognized during the rise of quantum mechanics (QM), and helped us recover a universal property of all linear waves, that they do not interact, or interfere, with each other. This NonInteraction of Waves, or the NIWprop erty, should be obvious through daily observations and through the HuygensFresnel diffraction integral and through critical evaluation of contradictory hypotheses we have been assigning to photons through ages. This implicates that the timefrequency Fourier theorem, although mathematically correct, and is used universally in all branches of science; does not map the real physical interaction processes for most optical phenomena. Accordingly, we present the necessary modifications for a few selected phenomena in classical and quantum optics to validate the NIWproperty. In the proc ess we find that accepting photons as noninteracting, but diffractively propagating linear wave packets crossing the entire cosmic space, requires CTF as a physical medium. Then we develop logical arguments in support of stable ele mentary particles as nonlinear but resonant vortexlike undulations of this same CTF. These vortexlike particles im pose various secondary potential gradients around themselves giving rise to the four forces we know. Thus, CTF can serve as the cosmic substrate to develop a unified field theory without the need of dark matter and dark energy. In the process, we demonstrate a path to add ontologic thinking on our biologically successful epistemic thinking. Keywords: NonInteraction of Waves; Cosmic Tension Field; Dark Energy and Matter; Platform for Unified Field Theory 1. Introduction The paper establishes that photons are noninteracting classical wave packets. This requires the cosmic vacuum to be a real physical Complex Tension Field (CTF) to sustain and facilitate such linear waves to propagate across the entire cosmic volume. We then postulate that CTF holds 100% of the cosmic energy. Then we ac commodate particles as vortexlike nonlinear spacefinite oscillations. The oscillations are selfresonant for their stability giving rise to the quantumness in the micro uni verse. Our approach is to “stand on the shoulders of the giants”, a la Newton, who is rightly considered as the father of modern physics. However, our novel approach helps remove a large number of ad hoc hypotheses from many of the modern theories. That the foundational hy potheses behind the working theories of physics need to be revisited is obvious from a large number of recent books and papers [113]. We hope our effort in this paper will add further impetus to put vigorous efforts in devel oping unified field theories in many new ways by ques tioning the foundational hypotheses of the current work ing theories [8,9,1214]. Accordingly, we have put ef forts to differentiate between epistemic and ontologic thinking [13,15] by tracing back to our evolutionary suc cesses. Sustainably evolving within the bounds of the laws of nature is being successfully practiced by all single and multicellular species, including humans, since ancient times. We are the first species to accelerate our rate of evolution, better than the others, by being able to articu late and pass on to the following generations such under standings in various forms, instead of relying only upon genomic transfer and genetic mutations available to all other species. Human ambitions have now been extended, beyond survival, to understand meanings, purposes and roles we can play in the vast cosmic system, beyond the earthly biosphere. A critical review of the records of hu man understandings, validated through quantitative ex C opyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1358 perimentations, reveal that all the physical processes behind cosmological and biospheric phenomena, can be modeled (theorized) fairly closely as long as our funda mental assumption is that all the laws behind the cosmo logical evolution are perfectly logical, rather than or dained ad hoc by some spiritual force. Unfortunately, we do not have direct access to the cosmic logics. So, through ages, we have refined our theorizing approach as an iteratively advancing process, which can continue through ages. We have been first developing a set of hy pothesis logics to bring conceptual continuity among a diverse set of related observations by imposing some logical congruence; and then structure them into a rigor ous theory by imposing on them even more restrictive set of humaninvented mathematical logics [11] with the explicit desire to capture the real set of operational cos mic logics. Even though microbes and ancient humans did not understand the cosmic logics directly, they have remained close to them by virtue of their intuitive capac ity (or, unarticulated biological intelligence) to emulate the natureallowed physical processes in modified forms to better adapt to their environment. We humans have identified this emulation of nature allowed physical processes as technology invention, which is now accel erating at almost an exponential rate as we have entered the Knowledge Age, leveraging the Internet empowered communication technologies. The point is that our primitive forefather human engi neers, inspite of not being scientists in the modern sense of the word, have successfully assured our sustainable evolution by emulating nature allowed processes. They could not visualize the physical process of tilted earth spinning on its axis and revolving around the Sun, yet they succeeded in developing the fundamentals of sea sonally dependent agricultural technologies, critical for us being here today in such large numbers. Lifelong meticulous recording of data on the positions of planets and stars by Tyco Brahe and Johannes Kepler, followed by empirical formulation of the planetary laws of motion by Kepler, finally inspired Newton, the discoverer of differential calculus, to enunciate the universal inverse square law of gravitational attraction. Today, we can mentally or digitally visualize the planetary motions, even though the Voyager (now traveling beyond the solar system) has not recorded and sent back timelapsed vid eos of the planetary motions around the Sun! But, today’s advanced technology behind precision Doppler velocimetry shows that further the stars are from the center of any galaxy, more their velocity deviate from Newton’s law of gravity; so it cannot be all that universal! Neither Newton’s law of gravity, nor Einstein’s General Relativity (GR), models such velocity variation data without ad hoc modifications [16]. Further, it is getting closer to almost a century that we have been trying to develop a unified field theory, first initiated by Einstein, to understand and visualize the evolution of the entire cosmic system; but we have not succeeded yet. We be lieve that this is because we are extremely reluctant to accept space as a real physical field, even though most of the successful working mathematical theories indicate that space is full of physical properties. 1) Gravitational law [17] requires that space has gravity related property G as in G·mM/r2; 2) Maxwell’s wave equation demands the same space to have electric and magnetic properties, 0 and 0 , because the velocity of light [18] in free space is always 00 c; 3) General Relativity defines gravitational force as a curvature of the space; 4) all versions of quantum mechanics find space to be full of “zero point energy”, “quantum foam”, “background fluctuations”, etc. Further, the recent discovery of Higgs’ Boson has not really succeeded in bringing uniform con fidence that the prevailing epistemology of physics is in the right direction [19]. Yet, we have been religiously reluctant to renew our efforts to develop theories from the new foundation that space constitutes a real physical field! Instead, we have been successfully imposing around the globe the view that the foundation of the edi fice of physics has already been laid and they must not be challenged any further! This directly contradicts our long trend of historical evolution of scientific theories. Clas sical theories were consecutively challenged by Relativ ity Theories (RT) and Quantum Mechanics (QM) and they have eventually prevailed. Over almost a century, these theories have provided us with enormously useful and practical guidance. Today our knowledge behind the workings of the micro and the macro universe is unde niably impressive. Yet, we have become collectively reluctant to accept the fundamental tenet of scientific thinking: We are not yet wise enough to ask the ultimate questions about the universe and construct the final the ory! Hence, all theories must be iteratively corrected and enhanced as our measurement technologies keep on ad vancing and makes us wiser. Any and all human organ ized bodies of knowledge are necessarily incomplete, because they have been constructed based upon insuffi cient knowledge and understanding of the deeply inter related and inseparable cosmic system. 1/2 Serious human epistemology should be guided by the enduring need for consciously constructing an evolving path for our sustainable and collective evolution. So the purpose of successful theory building should be explic itly directed towards visualizing the invisible interaction processes behind all phenomena. This will facilitate all engineers to become more inventive towards our contin ued future technological needs. Science cannot continue to flourish without consciously being aware of its re sponsibility to directly facilitate our sustainable evolu tion, while working with the engineers hand in hand. Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1359 Let us define the necessary approach [13] as the Inter action Process Mapping Epistemology (IPME), which should be added on to our currently successful approach, defined here as the Measurable Data Modeling Episte mology (MDME). Our biological brains have evolved as epistemic thinking tools. So, forcing ourselves to con sciously visualize the invisible but ontological processes should train us to become better ontologic thinkers. RT and QM are enormously successful in validating wide ranges of measurable data. But both fail to provide us with visualizable maps for the interaction processes in macro and micro domains [10,20], even though they are successful in predicting the measurable data. In fact, the Copenhagen Interpretation explicitly advices us not to waste time in trying to visualize precise paths of elec trons in stable atoms [21,22]. As a result, more than a century after indivisible photon hypothesis and more than 80 years of continued successes of QM, we are still liv ing with diverse and selfcontradictory metaphysical ex planations for single photon and single particle interfer ence [22]. Yet, we still have not succeeded in mathe matically localizing indivisible photons. The photon as a Fourier mode of the vacuum is inconsistent with our ob servations and classical model for ultrashort laser pulses [23,24]. Besides, Fourier summation of wave amplitudes is inconsistent with the universal property of waves in the linear domain—they do not interact (or interfere) with each other to create new field energy distribution in the absence of some interacting medium. We call this Non Interaction of Waves as the NIWproperty [2527], which we have been neglecting to explicitly recognize for centuries because MDME has kept us satisfied without enquiring any deeper about the invisible interac tion processes between the superposed waves and the detector. It is the recognition of this hitherto neglected NIW property that has inspired us to explore the shortcoming of the prevailing scientific epistemology, which we have characterized as MDME. Our attempts to map the po tential physical processes behind the NIWproperty has helped us to reduce the number of ad hoc hypotheses, a la Occam’s razor, necessary to explain a wide range of classical and quantum optical phenomena wherever the superposition effects play key roles [27]. 2. “Measurement Problem” as an “Information Retrieval Problem” Data we record through instruments are complex emer gent phenomena [8], essentially invisible to direct view ing. This is not a simple measurement problem to be solved by elegant mathematical theorems [2931]. 1) Measurables as transformations: We can measure only physical transformations in an instrument. 2) Preceded by energy exchange: There are no trans formations without energy exchange. 3) Guided by forces of interaction: Energy exchange, and consequent transformations, must be guided by some allowed force(s) of interaction. 4) Must experience physical superposition: Interac tants must be within each other’s sphere of physical in fluence to be able to interact under the guidance of an allowed force to exchange energy and undergo transfor mations. Thus, all interaction produced transformations must be local in the sense that the interactants must be within each other’s sphere of physical influence. 5) Through some physical interaction process: Al though invisible, all transformations are preceded by some real physical interaction process. Our conscious and systematic attempts to understand & visualize these invisible interaction processes provide us with some ex tra referent logical tools to explore cosmic logics (reality). IPME is a key tool that can connect our biological epis temic thinking with the necessary ontologic thinking. 6) Always requires a finite duration: Transforma tions in the interactants from one specific state into an other requires a “compatibility sensing period” [32] be tween them before the interactants can acknowledge the force of interaction and then exchange energy and then undergo the measurable transformation (transition). 7) Perpetual information retrieval problem: How do we gather quantitative and accurate information re garding the transformations experienced by our chosen set of interactants in an experiment? We interpret. But, there are four fundamental limitations that always de prive us from gathering complete information about any entities we are studying. a) First, we have not succeeded in constructing any data registering instrument that has 100% fidelity in acquiring all the quantitative data (in formation) it generates through secondary transforma tions induced by the primary transformations experi enced by our chosen interactants; b) Second, we have never succeeded in setting up an experiment where the interactants experience all the four forces that could in troduce various measurable transformations in them, even though all material particles are subject to all of them under different circumstances; c) All interactants are incessantly perturbed by omnipresent cosmic rays and background EM radiations of all frequencies. These effects we usually burry under quantum statistics . d) Finally, it is the human mind that provides the inter pretations based upon whatever incomplete data we gather. And, since human minds have evolved for inter preting information for biological and sociocultural sur vival first, our interpretations are subjective and vary from person to person and from culture to culture. Recall that BohrEinstein debate lasted for decades without res olution. We still do not know what an elementary particle Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1360 is made out of! Physics has never formalized any force of interaction between linear waves. It is the lightmatter interaction process that triggers the transformation we register as interference fringes. So, interference of waves is a mis guided, yet well perpetuated concept, in most books and literature. This NonInteraction of Waves, or the NIW property is known [2527] but we ignore it. We could not be enjoying music or visual sights unless all the neces sary waves were reaching our sensors without being per turbed by other crossing waves. 3. Empowering Mathematical Logics [11] Using IPME It is instructive to find out why our MDME using cur rent representation of the superposition effects perfectly validate the measured data and allows for diverse subjec tive interpretations like: photons and particles 1) display waveparticle duality; 2) display selfinterfere and 3) the superposition effects are nonlocal phenomena; etc. We never see light. We can interpret the presence of EM wave only by inferring from electric current pulses in our detector consisting of billions of electrons. A sili conbased visible light detector fails to alert us about the presence of Xrays even though they possess more en ergy! It is the quantum mechanically allowed physical transformation in a detector, which becomes our meas ured data. So the mathematical equation representing light detection must first model the lightmatter interac tion process. Material molecules are modeled as oscillat ing dipoles in the presence of EM waves by both classi cal physics and QM. If we superpose N coherent waves 2πtnexp i nn Ea n with a periodic phase delay on a detecting dipole, the total stimulated dipolar undulations can be represented by, using as the first order polarizability: nn nn n n E E (1) When is a constant for a narrow band of frequen cies, the mathematical rule allows us to take it out of the sumsymbol as a common factor. Now the physical meaning of the last two mathematical expressions in Eq uation (1) can be interpreted dramatically differently. The expression in the second line of Equation (1) domi nates the prevailing physics: EM fields interact with each other and sum themselves to create a new resultant field distribution; is no more than a mere detector con stant! However, the expression in the first line of Equa tion (1) tells us that the fields are noninteracting, but the detecting dipole executes the joint stimulations imposed on it by all the simultaneously present fields. Thus the superposition effect is a local phenomenon [10,32] car ried out by localized detectors. The recipe for the energy exchange has been given correctly by both the classical and the quantum physics; it is the square modulus of the total complex amplitudes. If we consider the special case of a twobeam Michelson or MachZehnder interferome ter, we get: 2 i2π 2i2π 12 22 2 12 12 22 12 ee 2cos2π 21cos2π;for t t aa aa aa aaaa (2) aa Note that in the real world it is very difficult to ex perimentally arrange absolutely correctly 12 . So a detector registers an oscillatory energy absorption 12 2 2cos2πaa 22 22 aa aa cos 2π riding on a DC bias of 12 . Our mathematics tells us that the detector absorbs energy proportional to the product 12 to display fringe oscil lation. The hypothesis “photons interfere only with itself”, prevails only because we stay focused exclusively on the oscillatory parameter, a E , while ignoring the contribution of energy by both the beams indicated by the factors and a. 1 2 We need to stay alert that the algebraic symbols rep resent actual physical parameters of the entities under study and the operating symbols represent nature allowed interaction process guided by an appropriate force. Con sider again Equation (1). nn E represents n induced physical dipole undulations allowed by the elec tromagnetic force of interaction between the EM wave and the material dipole. So n is not just an abstract mathematical probability amplitude; it is the physical dipolar undulation amplitude. We can eliminate Born’s interpretation for and make QM represent more reality. Summing n E implies that we are visualizing a critical physical process: First, the dipole executes a re sultant undulation by summing all the individual stimula tions and then executes the squaremodulus recipe to absorb energy from all the fields, proportional to the in dividual intensities n a. All the prevailing noncausal interpretations regarding superposition effects and ad hoc hypotheses regarding photons, become unnecessary, in cluding waveparticle duality. Very similar logics apply to superposition phenomena registered by using particle beams [33]. 2 Waveparticle duality implies lack of our knowledge about both particles and waves. If we treat lackof knowledge as an acceptable part of a working theory, we are formalizing lackofknowledge as realknowledge! In the process, we are discouraging critical enquiry of na ture any further at the cost of imposing brakes on the scientific evolution of our minds. Fortunately, no engi neers try to propagate indivisible photons, whether de signing a radiotelescopes or an Xray telescope; they use Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1361 century old HuygensFresnel (HF) diffraction integral. We should not impose waveparticle duality interpreta tion on the highly successful HF integral. HF integral tells us that the farfield divergence angle of all EM waves reaches an asymptotic maximum and is inversely proportional to the frequency of the wave. This accom modates why gammarays behave more like particles than all the other lower frequency waves. Note that e , pair production can happen only when e interacts with some nucleus. Direct interaction in vacuum has remained elusive even today. 4. Improving Classical & Qua n t um Optics Using NIWProperty and IPME Figure 1. Pulse replication by grating and their temporally delayed superposition by a lens L in on a detector at the measurement plane. In this section we demonstrate that recognition of the universal NIWproperty of waves helps us remove sev eral more unnecessary ad hoc hypotheses to explain op tical phenomena, while bringing stringent causality back within the framework of existing theories. We also pre sent causally valid and QMtransition consistent model of photons as noninteracting classical wave packets and hence the QM definition of photon as a Fourier mode of the vacuum is unnecessary. We integrate this for the entire duration of Npulses and get the registered fringe width centered on : 4.1. Improving Classical Optics 1) Spectrometry: Classical theory of spectrometry has been formulated based upon propagating a Fourier mo nochromatic frequency through passive linear spec trometer (grating, FabryPerot, etc.), which match up with most observed data. Unfortunately, Fourier mono chromatic wave is a noncausal proposition as it exists in all space and hence violates the principle of conservation of energy. So, we have developed a causal theory by propagating the carrier frequency of a timefinite pulse [34]. Spectrometers functionally replicate an incident pulse into a train of Nidentical pulses, N being the grating slit number (or the finesses number for a FabryPerot), with a characteristic periodic temporal step delay c mv; where is the physical step delay, and m is the order of interference. So, all spectrometers have a char acteristics time constant 0 N exp i (Figure 1) is required to generate the entire train of N pulses. This physical property of spectrometers has not been formally recog nized by classical spectrometry [35]. The resultant time varying dipolar stimulation of a detector placed at the exit plane of the spectrometer due to an incident pulse 2πtat is: 1 out 0exp i 2π n it Natntn N (3) The temporal rate of energy that can be absorbable is: 2 πtn 21 out 0exp i2 N n i tNatn (4) 22 1 pls 21 2 2 ,cos2π where, dddd()d N pNppp NN ptntmttt (5) Equation (5) yields the classical CW result for a long pulse: 0 22 1 pls 2 1 22 22 2 ., cos2π sin π, sin π N tp cw Lt INpp NN NI N (6) Application of Parseval’s energy conservation theorem on the time integrated Equation (4) can also be expressed as: 2 pls out ,d cw IittIA t (7) The fringe broadening given by Equation (5) is not due to the physical presence of the Fourier frequencies, which is mathematically obtainable from the pulse enve lope. It is due to the partial superposition of the translated stimulating pulses on the detector. Diffraction and reflec tions are almost instantaneous and linear response of gratings and mirrors. They do not have the physical ca pacity to carry out Fourier algorithms and then respond to the Fourier frequencies. Thus, we are proposing a fundamentally important conceptual change in inter preting “what is a spectrum” due to a pulse. Notice that our theory of spectrometry (Equations (3) (7)), has also derived the key classical results under spe cial conditions, which helps remove classical misconcep tions. In the limit of long pulse, 0 , Equation (5) becomes Equation (6) that is equivalent to classical CW Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1362 derivation. This is because the Nreplicated pulses are now effectively almost fully superposed giving p 1 . Next, classical spectrometry assumes that the meas ured fringe broadening due to a pulse is the con volution between its Fourier intensity spectrum at A I and the CW response function cw . We have derived this in Equation (7). The concept of the physical reality of Fourier frequency is a wrong hypothesis perpetuated due to this a mathematical coincidence, supported by the conservation of energy, but only when the entire pulse train is integrated by the detector. The “spectral fringe” due to a nano second pulse through a spectrometer regis tered by a pico second streak camera will show time va rying fringe broadening (Equation (4)). This also implies that the Fourier indeterminacy relation 1vt is not a real resolution limit in our physical world. During quan titative spectrometry, Equation (5) should be treated as the pulse impulse function for the instrument and it should be deconvolved from the recorded fringe function to achieve super resolution. One can also use heterodyne spectrometry [36] using a known reference frequency to determine the unknown carrier frequency . 2) Diffraction: Diffraction theory is a unique example where it started with IPME in mind by Huygens, but once mathematically formulated by Fresnel, the physical model and its implications got lost. Propagation process of waves imply as if every point on the wave front gen erates a new forward moving spherical wave front with a cos reduction in its amplitude from the forward direc tion. So the total field amplitude at a point 0 with a distance 01 due to a field distribution on an ap erture plane is the sum of all the secondary spherical wave fronts arriving at . 0 UP P r 0 P 01 0 d kr UP s 1 exp P 01 i r iU cos (8) The complex amplitude 0 UP at any near or any far distance 01 is given by the same set of evolving spheri cal wave fronts. This clearly implies that the secondary wavelets propagate through each other while evolving, without interacting (or interfering) with each other. Thus HuygensFresnel diffraction principle works because the NIWproperty is automatically built into it [37]. The in tegral allows one to find the sum of the resultant ampli tude and corresponding intensity but only at the plane of observation by placing some suitable detector; in between they are not interacting. It is a subtle but very important point to recognize. r 3) Coherence: Coherence theory is normally pre sented as normalized mathematical autocorrelation t between a pair of replicated and superposed pulses, which also turn out to be equivalent to the measurable fringe visibility [38] V : 12 0 12 12 22 12 00 12 0 12 12 22 12 00 d dd d dd T tTT T TT ata tt V at tatt ata tt attatt (9) By virtue of the NIWproperty, fields cannot correlate with each other. So, the first line in Equation (9) does not represent any physical process. Yet, measured V t is well validated. MDME works, but why? The second line has incorporated IPME by converting all the field amplitudes into a detector’s dipolar amplitude sti mulations by inserting the multiplying factor χ, which is behind the real measurable transformation. Since, ma thematical rule allows us to cancel the common factor χ from the numerator and the denominator; the two expres sions in Equation (9) are mathematically identical, as far as MDME is concerned. However, as per IPME, they represent different physics. The first line represents wrong physics since fieldfield correlation cannot exist. The second line represents correct physics, because di poledipole correlation represents real detection process. This correlation also depends upon the duration of inte gration (intrinsic and circuit imposed). If we can invent an atto second detector with complementary time resolved fringe registration system, any and all light will give very high visibility fringes. So, light, by itself, is neither co herent nor incoherent. Note that even quantum coher ence theory is, unfortunately, built upon the assumption of fieldfield correlation, rather than the correlation of the same dipole stimulated by two different fields. So, we have redefined coherence as correlation properties of detectors, albeit dictated by specific characteristics of light [39] as follows: a) Spectral correlation (light with a frequency variation); b) Temporal correlation (light with temporal amplitude variation); c) Spatial correlation (light with independent multiple emitters); And d) Com plex correlation (mixture of the above cases). 4) Polarization: Consider that we are working with a twobeam MachZehnder interferometer which can gen erate and combine two different coherent beams of dif ferent states of linear polarizations. Then the detector will be simultaneously stimulated by two different Evectors at an angle . Then the standard twobeam cosine fringes cos 2π cos will be multiplied by a visibil ity degrading factor : 2 i2π i2π 12 22 2 12 ee 21coscos2π; cos t t Da a a χχ χχ (10) For the case of π2 , the fringe visibility will be zero. This is well known in physics and we tend to explain Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1363 it by using an ad hoc hypothesis that orthogonally polar ized light beams are incoherent to each other. IPME now guides us to extract, so far, unarticulated physical proc ess—that detecting dipoles cannot simultaneously oscil late in two orthogonal directions and hence fails to absorb energy from both the field simultaneously. Then, can it be true that the introduction of a precise phase delay between the two beams 290˚ will generate a circu larly rotating polarized light, even though light beams do not interact with each other [40]? π2π 5) Fourier transform spectrometry (FTS) and light beating spectrometry (LBS): These two methods of spectrometry experimentally give different information about the frequency content of the light being analyzed in different forms. Consider that we are analyzing the fre quency content of a HeNe laser, running in two fre quencies, 1 and 2 , using a Michelson’s Fourier transform spectrometer where the relative delay be tween the two paths can be varied very slowly. If we use a very fast modern detector at the output, the photo cur rent, normalized by the square of the detector polariza bility factor, can be given by Equation (11). 2 12 1 12 12 1 12 exp i2πexp i2π exp i2πexp i2π 42cos2π2cos2π cos 2πcos 2π 2cos2πcos2π. D tt tt t t 2 2 12 12 2 () t t (11) This photo current appears quite complex because of spatial and temporal beat signals between the modes and their replicated beams. All the timedependent factors in Equation (11) will be reduced to zero if we use a very slow timeintegrating detector. We will be left with terms 242cos2πD12 cos 2π (12) what a normal Fourier transform spectrometer will record, as shown in Equation (12). Note that the original as sumption by Michelson was that different optical fre quencies are incoherent and hence they do not interf er e. It is a wrong hypothesis because EM waves never inter fere. But his mathematical result was correct because he used long time integrating photographic plate for his quantitative work. Michelson recognized that the mathe matical Fourier transform of the oscillatory component of the recorded fringes will give him the actual physical spectrum of the original signal. Then, from Equation (12) we have: We have now eliminated another ad hoc hypothesis in optics, noninterference of different frequencies, and ex plicitly recognize a more important experimental process, the physical role of the integration time of detectors [32]. 4.2. Improvements in Quantum Optics In this paper, we will confine our discussions to those that are directly relevant to the NIWproperty. 1) Are photons indivisible quanta or classical wave packets? One should note that Dirac’s formulation [41] found photons as Fourier modes of the vacuum and they do not interact. This means that Dirac actually discovered the NIWproperty; but to accommodate the mistaken classical assumption that light interferes, he proposed an unnecessary ad hoc hypothesis, “a photon interferes only with itself”. We now know that it is the detector that generates the superposition effect absorbing energy from all the incident (superposed) waves. Regarding Dirac’s “Fourier mode”, we believe that it is an unphysical and noncausal assertion since a Fourier monochromatic mode has to extend over all space and time and would violate the principle of conservation of energy. Again, Dirac was most likely trying to accommodate QM pre dicted single frequency emission mn in an atomic tran sition mn mn Eh E , with the classical assumption, that a single frequency (monochromatic) radiation must be a Fourier monochromatic mode. We are proposing that the emission of the energy packet mn by an atom, either through spontaneous or through stimulated emission process, evolves into a semiexpo nential pulse [42] with the unique carrier frequency mn (see Fi gure 2). Classical Lorentzian emission for a dipole radiation was derived to be an exponential pulse. Preci sion spectrometric measurement also found natural line width to be Lorentzian, which is a Fourier transform of an exponential pulse (recall Equation (7) for sperctrome try). Quantum mechanics also derived natural line width of atomic lines to be Lorentzian. Thus, our spectrometric theory implies that photon wave packets should be very much like an exponential pulse. But it should start from . cos 2π osc FT DFT 12 12 cos 2π (13) Integranted energy underthe envelopemn mn Eh mn Figure 2. Photons are classical wave packets with a unique carrier frequency with a semiexponentially decaying enve lope. The model supports classic a l and QM observations. Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1364 zero value, and very quickly rise to its peak and then die exponentially, while containing the total energy mn h to satisfy the needs of QM. The next question is whether we can replace the 107 years old hypothesis, indivisible quanta, proposed by Einstein, by a better model based on interaction process. Let us first underscore that QM does not demand that a quantum entity can absorb the required quantum of en ergy only if it is delivered as a prequantized packet. In side HeNe laser discharge tubes, Neatoms can undergo transition to its upper lasing quantum level by accepting the desired amount of energy either 1) from a resonantly excited Heatom sharing an exact quantum of energy, or, 2) from an accelerated classical electron as the necessary fraction out of its total kinetic energy. Next we need to appreciate that photo electron stimu lation is a complex process. Einstein genius mind was the first one to recognize that there definitely was some quantumness behind the photoelectric data and the re lated interaction process. Being five years ahead of Bohr’s heuristic quantum theory and 20 years ahead of modern QM, Einstein imposed the quantumness on the photon wave packets, instead of on the electrons. Other wise, he would have invented QM, most likely in a dif ferent format than what we have today! He assumed that the quantum h was directly absorbed to provide for the binding energy , and the rest went to provide the ki netic energy to the emitted electron: 2 1 2vwhm ork function n (14) Today we know that electrons in materials are bound collectively to the matrix of atoms (molecules). Hence, their excitation would require the induction of some form of dipolar stimulations, whose allowed frequency band is set by the quantum mechanics. Equation (14) can be rewritten in terms of dipolar stimulations induced si multaneously by many competing photon wave packets, followed by absorption of energy by the material matrix that facilitates the complete liberation of a photo electron, or its transfer from the valence to the conduction band (m) as photo electric current to be drawn by exter nal circuit: 2 exp i2πgives qqqq q qat mnmn Eh (15) This reformulation helps us better appreciate and model the dependence of photo electron counting statis tics on the fluctuating amplitudes and phases of simulta neously present multiple wave packets, besides the tem poral energy fluctuations due to beat between different frequencies which fall within the allowed quantum band of frequencies. 2) Relevancy of Bell’s inequality theorem: Bell’s theorem assumes photons are indivisible quanta and that single photons interfere by themselves. Since we have more confidence on our causal NIWproperty, we believe that Bell’s nogo theorem is irrelevant in experimental observation of superposition effects, which, in reality, is functionally determined by the detectors and not by the photons themselves! 3) Can photons be entangled? If an isolated quantum entity emits a pair of photon wave packets, the quantum nature of the light emitting process will clearly impose all the necessary conservation laws and the emitted pho ton wave packets will acquire complementary properties during the emission process. So, one can describe them to be entang led during their birthing process as conjoined twins due to having, say, orthogonal polarizations. These two energy packets, after emission, keep on evolving as diffractively propagating and spreading wave packets as linear undulations of CTF. These spatially separated li nearly undulating wave packets neither can interact, nor can influence each other [2527]; even though they re main corelated as orthogonally polarized entities. In fact, if one folds one of the wave packets back on to the other, one using a mirror, they would not even perceive each other’s presence because of the NIWproperty. We be lieve that the use of the word entangled is unfortunate. 5. Space as a Complex Tension Field (CTF) 5.1. How Does EM Waves Move Perpetually through Free Space? We know that emitting atoms or molecules do not add kinetic velocity to EM waves. To be selfconsistent with our model for photon as a 1) classical wave packet, 2) which can traverse through the entire length and breadth of the cosmic system, 3) with the same staggeringly high velocity 12 c 00, 4) obeying HF integral and as a solution of Maxwell’s wave equation, we need the space to be a tension field with intrinsic EM properties 0 and 0 . This is similar to the ether of nineteenth century, but conceptually modified to be a massless physical tension filed, rather than some novel substance. Let us very briefly review how waves propagate, which was visualized by Huygens some 300 years earlier. Sound waves are undulation of the pressure tension of air. Water waves are undulations of the surface and gravita tional tensions of water. String waves are due to undula tion of a string under mechanical tension. Within the linear domain, a perturbed point of a tension field tries to come back to its original state of equilibrium by pushing away the perturbation energy to its surroundings, which is then repeated by the consecutive disturbed points. This persistent restoration tendency of every point of the ten sion field is the root cause behind the perpetual sinusoi dal movement of a perturbation as a group of linear sim Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1365 ple harmonic wave. HF diffraction integral models this physical process very well and hence it is so successful in modeling diffractive propagation of all waves. One should carefully note that waves do not really “carry” energy. The group of propagating undulating waves makes the energy of the local tension field available, wherever the wave packets are, to be absorbed if a suit able absorber is present (resonance helps). Let us now attempt to assign tensionfield oriented physical meaning on to 0 and 0 of CTF, beyond just the traditional definition of dielectric permittivity and magnetic permeability of the free space. We repro duce the wave equation for a stretched string [43] and then rewrite Maxwell’s wave equation, but in terms of the vector potential [44] A to accommodate both electric and magnetic potential in the same equation, while emu lating the string equation and then compare the two. 22 2 22 ,, v yzt yzt tz 2 2 ,yzt T z (16) 22 2 22 ,, 2 1 0 2 0 , ztA zt c tz A zt z 1 (17) We see that 0 can be treated as the potential elec tric tension triggered in the CTF, which then generates 0 as the restoring magnetic resistance. In this simple model of undulations of CTF, photon wave packets, most likely, do not possess properties like spin, angular momentum etc. It is the detecting mole cules while absorbing energy from one or more polarized superposed waves, display modifications in their own such properties that they possess. We should not assign response characteristics of atoms and molecules on to EM waves. 5.2. Accommodating Massless Localized Particles in CTF CTF to be a valid physical hypothesis, it must also ac commodate particles that form the material universe. So, let us now assume that CTF also possess some intrinsic dynamic properties that allows it to sustain localized vortexlike nonlinear but harmonic spinning undulations, some of which could acquire resonant stability within its surroundings giving rise to all the stable and semistable particles. We underscore this vortex motion as nonlinear, which is beyond the linear restoration capability of CTF. So, vortices are locally confined and cannot move auto matically like the EM waves. Further, the linear pertur bations, induced by dipoles, not only move perpetually away from its location of generation, they also pass through each other unperturbed as long as the sum total perturbations at any local point do not exceed the linear restoration capacity of CTF (the intrinsic NIWproperty). In contrast, vortices being nonlinear in origin, they can neither move by themselves, nor can pass through each other. This is the root of solidness in the material world. One can hypothesize that the spin quantization is one of the required properties to provide resonant stability to the vortex that will always have a preferred axis within the 3D CTF. Under the dynamic vortexlike motions of CTF, its intrinsic properties, 0 1 and 0 , possibly be come manifest as charge and magnetic moments, the critical properties of all particles [1,45] The resonant (long lived) and semiresonant (short lived) particles should possess a set of quantized energy values defined by some of the intrinsic properties of CTF. In fact, the energy values of most of the particles have recently been actually found [46] to possess an integer relation Z which equals to the product of , the fine structure constant, multiplied by two times the ratio of the particletoelec tron energy (not mass): 12 2 elctrn.0 0 2; 2mmZe h 1 (18) This implies that the electronic charge e and the Planck’s constant h are also two intrinsic properties of CTF under vortexlike undulation, which play key roles in bringing out the quantumness in the material universe. The unit of quantum h being “erg.sec”, it supports the hypothesis that the energy and the undulation periods of vortexlike resonant oscillations are inseparably related Our model of particles as vortexlike motion of the field CTF automatically implies that they cannot possess any Newtonian property like mass. Thus we do not need to find how the particles acquire mass. They are stable in the CTF as local vortices hence they should naturally display inertia against any attempt to move them. In oth er words, we need to hypothesize the origin of the forces between particles to move them. We hypothesize that the nonlinear vortexlike motion of CTF creates four different kinds of secondary poten tial gradients around themselves, so the stable vortices naturally fall into (or pushed away by) each other due to these potential gradients depending upon their mutual manifest properties. Gravitational force can be visualized as purely a mechanical depression, like negative poten tial gradient, imposed on the CTF around particles and their assemblies. So gravitation is universally attractive; where G is the intrinsic property of CTF that becomes manifest as the potential gradient. In contrast, the elec tromagnetic force, originating out as positive or negative potential gradients imposed on the CTF out of 0 and 0 properties. What kind of antisymmetric motion in a vortex give rise to positive and negative chargelike gra dients, still remains to be imagined and visualized. These two forces are long range and hence the gradients extend far out from the particle vortices. The two nuclear forces have been found to be very short range and quite com Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1366 plex by Quantum Chromodynamics [1]. In this present heuristic paper, we will not venture into presenting any detailed map for these two forces. However, we think these forces are also emergent properties onto CTF. They are complex short range positive and negative gradients generated out of vortexlike churning of some of the in trinsic properties of the stationary CTF. 5.3. Resolving WaveParticle Duality for Particles [33] Albeit nonlinear, the harmonic undulation of the vortex of energy E has been captured by Schrodinger for a free particle as: expi expiEt 2π; ftE hf (19) If we assume the particle of energy E has vortex fre quency f, then we have particles as nonlinear harmonic oscillators. We can now rewrite the Equation (18), using Equation (19), in terms of restfrequency ratio of parti clestoelectrons as: 0,p ff 0,el 2Z (20) The rest frequency for an electron can be computed from as Ehf0,el . This also appears to be in the range of highest frequency gamma rays that can be converted into electronpositron pair while being scattered by some nucleon. For CTF, this appears to be the possible boundary between linearly pushable gam ma wavefrequency and localized nonlinear resonant vortex like oscillations as electrons. 1.23 20f The rest frequency 0, for any particle will increase to v, as the standard restenergy have been found to follow when it is forced to move under some potential gradient (force) with a velocity v: 12 2 v, v, 2 0,0, 0 v 11 pp v pp fhfm fhfm c 12 2 00 v 1 (21) We measure this excess energy as kinetic energy of the particle. One can now appreciate that the heuristic con cept of de Broglie wave or “pilot wave” is unnecessary. But its internal vortexlike frequency has to increase to achieve higher velocity to overcome the inertial resis tance due to 0 and 0 of CTF. It is better to refer to them rather than c to appreciate that we are dealing with physical properties of free space and they can be changed (as per General Relativity, through bending of star light by the Sun’s gravity). Since particleparticle interactions are also driven by two steps, phase sensitive complex fieldfield stimula tions as , followed by energy exchange through the recipe , we can now appreciate superposition ef fects due to particle beams as localized interactions be tween harmonically oscillating multiple particles simul taneously stimulating the same detecting molecule and trying to transfer some of their kinetic energy, which mathematically appear to be like wavewave interactions [33,47]. Thus by imposing IPME to visualize particles as vortexlike undulations, we find that QM has more realities built into it than the Copenhagen Interpretation has allowed us to imagine [48]. Thus, our hypothesis, particles as vortexlike localized oscillators, removes the waveparticle duality for particles. 5.4. Time Dilatation and Ether (CTF) Drag Does CTF need to be four dimensional? A deeper en quiry of the measurement process behind time [30,4951] reveals that there are no physical objects that have t as one of its real physical parameters. What we really meas ure is the physical frequency f of some suitable oscillator. Then invert it to define an element of time interval, 1tf tNt. We get longer measured duration by counting N times the number of oscillations. We should not assign any fundamental physical behavior on nature what is not a valid physical parameter of some thing in nature. Let us recognize that one can success fully model a small subset of a very large complex sys tem by hypothesizing some rules, none of which may precisely coincide with the original fundamental rules behind the entire complex system. What about observation of extended life time of muons? It is safe to hypothesize that the life time of an offresonant vortex oscillation is enhanced due to its higher kinetic velocity, somewhat like the extra stability enjoyed by a speeding bike rider. Muon’s internal physi cal oscillation frequency may have altered, but its clock has not changed, because it does not have one. If CTF is a space filling 3D field, then the old “ether drag” question is brought out again. To propagating EM waves, CTF is stationary. Is it the same for vortexlike particles, or their assembly (planets and stars)? A high energy laser beams can be focused through a pinhole without distorting any of the fundamental properties of the beam. This implies that strong Evector amplitude is not physically extended in 3D space. Then a stronger Evector oscillation must be due to a stronger field gra dient oscillation, rather than a spatial size of oscillation. If we extend this understanding to particles, vortex oscil lations may also be purely temporal oscillatory gradients of different physical properties of CTF. Then the move ment of particles under the influence of secondary gra dients (forces) does not require dragging the CTF; only the complex set of gradients moves spatially. This is consistent with the following famous observations: 1) Bradley telescope parallax for stars due to earth’s motion, 2) MichelsonMorley null experiments to detect earth’s motion around the Sun. However, stationary CTF does Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI 1367 not explain 3) positive and null [12] Fresnel drag ex periments for moving and nonmoving medium, respec tively, within an interferometer. Some people believe that Fresnel positive drag is an EM phenomenon within a moving medium [52] and that it is not due to ether drag. Hence, further research is called for and the author has initiated a project to study this. 6. Conclusions We believe that our proposition of space as a physical Complex Tension Field (CTF), in some form or another, does represent a potentially viable new approach to de velop a unified field theory, especially utilizing the pos tulate that all the four forces are different kinds of poten tial gradients imposed on the same CTF by the particles. The strength of CTF comes from its capability to accept most of the tenets of the existing theories, while at the same time; it helps clean up much confusion in current physics by simply eliminating the need for quite a few selfcontradictory hypotheses, waveparticle duality be ing the most important one. Most of the cited papers by this author can be found at this website [53]. 7. Acknowledgements The author would like to acknowledge the help of critical reading of the manuscript by A. Ambroselli. REFERENCES [1] F. Wilczek, “The Lightness of Being: Mass, Ether, and the Unification of Forces,” Basic Books, New York, 2010. [2] T. Silverman, “Philosophical Solutions: In Physics, Ma thematics and the Science of Sentience,” International In stitute for Advanced Studies, BadenBaden, 2010. [3] L. Smolin, “Trouble with Physics,” Houghton Mifflin, Boston, 2006. [4] R. Laughlin, “A Different Universe: Reinventing Physics from the Bottom Down,” Basic Books, New York, 2006. [5] R. Penrose, “Road to Reality,” Alfred Knopf, New York, 2005. [6] N. C. Panda, “Maya in Physics,” Motilal Banarsidass Publishers, Delhi, 1999. [7] L. Smolin, “A Real Ensemble Interpretation of Quantum Mechanics,” Foundations of Physics, Vol. 42, No. 10, 2012, pp. 12391261. doi:10.1007/s1070101296664 [8] P. W. Anderson, “More and Different: Notes from A Thoughtful Curmudgeon,” World Scientific, Singapore City, 2011. doi:10.1142/8141 [9] L. Susskind, “String Theory,” Foundations of Physics, 2011. doi:10.1007/s107010119620x [10] H. P. Stapp, “Quantum Locality?” Foundations of Phys ics, Vol. 42, No. 5, 2012, pp. 647655. doi:10.1007/s1070101296321 [11] R. Omnès, “Wigner’s ‘Unreasonable Effectiveness of Mathematics’, Revisited,” Foundations of Physics, Vol. 41, 2011, pp. 17291739. doi:10.1007/s1070101195877 [12] C. Roychoudhuri, “The Constancy of ‘c’ Everywhere Requires the Cosmic Space to Be a Stationary and Com plex Tension Field,” Proceedings of SPIE, Vol. 8121, 2011, p. 23. [13] C. Roychoudhuri, “Appreciation of the Nature of Light Demands Enhancement over the Prevailing Scientific Epistemology,” Proceedings of SPIE, Vol. 8121, 2011, p. 58. [14] G. S. Sandhu, “Fundamental Nature of Matter and Fields,” 2009. http://www.amazon.com/FundamentalNatureMatterFiel dsSandhu/dp/1440136564/ref=sr_1_4?s=books&ie=UTF 8&qid=1316629764&sr=14 [15] M. Pauri, “Epistemic Primacy vs Ontological Elusiveness of Spatial Extension: Is There an Evolutionary Role for the Quantum?” Foundations of Physics, Vol. 41, No. 11, 2011, pp. 16771702. doi:10.1007/s1070101195810 [16] P. D. Mannheim, “Why Do We Believe in Dark Matter and Dark Energy—And Do We Have to?” In: M. D’Onofrio and C. Burigana, Eds., Questions of Modern Cosmology—Galileo’s Legacy, Springer Publishing Com pany, Heidelberg, 2009. [17] F. Lassiaille, “Gravitational Model of the Three Elements Theory,” Journal of Modern Physics, Vol. 3, No. 5, 2012, pp. 388397. doi:10.4236/jmp.2012.35054 [18] P. Smeulders, “Why the Speed of Light Is Not a Con stant,” Journal of Modern Physics, Vol. 3, No. 4, 2012, pp. 345349. doi:10.4236/jmp.2012.34047 [19] Inside Science News Service, “Physicists Detect New Heavy Particle,” 2012. http://www.insidescience.org/?q=content/physicistsdetec tnewheavyparticle/724&track=AW [20] A. Kent, “Real World Interpretations of Quantum The ory,” Foundations of Physics, Vol. 42, 2012, pp. 421435. [21] P. Grujic and N. Simonovic, “Insights from the Classical Atom,” Physics Today, Vol. 65, No. 5, 2012, pp. 4146. [22] G. Greenstein and A. G. Zajonc, “The Quantum Chal lenge,” Jones & Bartlett, Boston, 2006. [23] C. Roychoudhuri and N. Prasad, “Discerning Comb and Fourier Mean Frequency from a fs Laser, Based on the Principle of NonInteraction of Waves,” Proceedings of SPIE, Vol. 8236, 2012. [24] C. Roychoudhuri, “Various Ambiguities in Generating and Reconstructing Laser Pulse Parameters,” In: F. J. Duarte, Ed., Laser Pulse Phenomena and Applications, InTech, Morn Hill, 2010. [25] D. Lee and C. Roychoudhuri, “Measuring Properties of Superposed Light Beams Carrying Different Frequen cies,” Optics Express, Vol. 11, No. 8, 2003, pp. 944951 doi:10.1364/OE.11.000944 [26] C. Roychoudhuri, “Principle of NonInteraction of Waves,” Journal of Nanophotonics, Vol. 4, No. 1, 2010, Article ID: 043512. doi:10.1117/1.3467504 Copyright © 2012 SciRes. JMP
C. ROYCHOUDHURI Copyright © 2012 SciRes. JMP 1368 [27] C. Roychoudhuri, “Why We Need to Continue the ‘What Is a Photon?’ Conference? To ReVitalize Classical and Quantum Optics,” SPIE Proceedings, Vol. 7421, 2009, p. 28. doi:10.1117/12.828193 [28] J. Leibovitz, “Dark Energy as a Property of Dark Matter,” Journal of Modern Physics, Vol. 2, No. 1, 2011, pp. 14701479. doi:10.4236/jmp.2011.212181 [29] B. Tamir and S. Masis, “Weak Measurement and Weak Information,” Foundations of Physics, Vol. 42, 2012, pp. 531543. [30] C. Roychoudhuri, “Measurement Epistemology and Time Frequency Conjugate Spaces,” AIP Conference Proceed ings, Vol. 1232, 2009, pp. 143152. [31] C. Roychoudhuri, “Inevitable Incompleteness of All Theories: An Epistemology to Continuously Refine Hu man Logics towards Cosmic Logics,” In: C. Roychoud huri, A. F. Kracklauer and K. Creath, Eds., The Nature of Light: What Is a Photon? CRC/Taylor & Francis, Boca Raton, 2008. [32] C. Roychoudhuri, “Locality of Superposition Principle Is Dictated by Detection Processesm,” Physics Essays, Vol. 19, No. 3, 2006, p. 333. [33] C. Roychoudhuri and C. V. Seaver, “Are Dark Fringe Locations Devoid of Energy of Superposed Fields?” SPIE Proceedings, Vol. 6285, 2006. doi:10.1117/12.684613 [34] C. Roychoudhuri, “Propagating Fourier Frequencies vs Carrier Frequency of a Pulse through Spectrometers and Other Media,” SPIE Proceedings, Vol. 5531, 2004, pp. 450461. doi:10.1117/12.580700 [35] C. Roychoudhuri, “Response of FabryPerot Interferome ters to Light Pulses of Very Short Duration,” Journal of Optical Society of America, Vol. 65, No. 12, 1975, p. 1418. doi:10.1364/JOSA.65.001418 [36] C. Roychoudhuri and M. Tayahi, “Spectral SuperReso lution by Understanding Superposition Principle & De tection Processes,” International Journal of Microwave and Optics Technology, July 2006. [37] C. Roychoudhuri, “Exploring LightMatter Interaction Processes to Appreciate Various Successes behind the Fourier Theorem!” SPIE Proceedings, Vol. 8122, 2011. [38] M. Born and E. Wolf, “Principles of Optics,” Cambridge University Press, Cambridge, 1980. [39] C. Roychoudhuri, “ReInterpreting Coherence in Light of NonInteraction of Waves, or the NIWPrinciple,” SPIE Proceedings, Vol. 8121, 2011, p. 44. [40] C. Roychoudhuri and A. M. Barootkoob, “Generalized Quantitative Approach to TwoBeam Fringe Visibility (Coherence) with Different Polarizations and Frequen cies,” SPIE Proceedings, Vol. 7063, 2008. doi:10.1117/12.793747 [41] P. A. M. Dirac, “The Principles of Quantum Mechanics,” Oxford University Press, Oxford, 1974. [42] N. Tirfessa and C. Roychoudhuri, “Analysis of Spectro metric Data and Detection Processes Corroborate Photons as Diffractively Evolving Wave Packets,” SPIE Proceed ings, Vol. 8121, 2011, p. 33. [43] D. H. Goldstein, “Polarized Light,” 3rd Edition, CRC Press, Boca Raton, 2011. [44] J. D. Jackson, “Classical Electromagnetism,” John Wiley, Hoboken, 1999. [45] R. T. Hammond, “Spin, the Classical Theory,” Journal of Modern Physics, Vol. 3, No. 1, 2012, pp. 18. doi:10.4236/jmp.2012.31001 [46] K. O. Greulich, “Calculation of the Masses of All Fun damental Elementary Particles with an Accuracy of Ap prox. 1%,” Journal of Modern Physics, Vol. 1, No. 5, 2010, pp. 300302. [47] V. Konushko, “Stability of Atoms, Causality in Elemen tary Processes and the Mystery of Interference and Hyro scope,” Journal of Modern Physics, Vol. 3, No. 3, 2012, pp. 224232. doi:10.4236/jmp.2012.33032 [48] A. I. Arbabl and F. A. Yassein, “A New Formulation of Quantum Mechanics,” Journal of Modern Physics, Vol. 3, No. 2, 2012, pp. 163169. doi:10.4236/jmp.2012.32022 [49] V. Balasubramanian, “What We Don’t Know about Time,” Foundations of Physics, 2011. doi:10.1007/s107010119591y [50] T. Filk, “Temporal NonLocality,” Foundations of Phys ics, 2012. doi:10.1007/s1070101296717 [51] S. Gryb and K. Thébault, “The Role of Time in Relational Quantum Theories, Foundations of Physics, Vol. 42, No. 9, 2012, pp. 12101238. doi:10.1007/s1070101296655 [52] R. T. Cahill and D. Brotherton, Progress in Physics, Vol. 1, No. 43, 2011. [53] C. Roychoudhuri. http://www.phys.uconn.edu/people/faculty/storrs/roychou dhuri/
