Waves need a media to travel and carry energy. A standing wave is an oscillation pattern with a stationary outline (envelope) that results either from the superposition of two identical waves travelling opposite directions or from an inner equilibrium vibration . A given particle that is bound ( confined ) in a certain region of space is a standing wave and vibrates within the constraints of the envelope function y = 2A.sin(kx).cos.(wt) . Light as Force is acting on zero area wavelength as Normal stress and thus measured as linear Momentum (since Stationary energy becomes Kinetic) and Work becomes travelling Energy .This property of energy to be converted into , velocity in wavelength as background media is the reason that doesn`t collapse by radiating away its or their energy . Work as Vibration is confined in its wavelength as a Damper , absorber , and is retained unchanged when travelling . The Why , When and the How is widely analyzed .Since also a stationary wave consists of two transverse waves then is not interpreted as an equal mixture of the two, but an inner equilibrium on monad . It was shown that the Energy-Space universe ( the beyond Planck`s length , Gravity`s and Spaces` levels ) is [PNS] and Space Anti-Space as work [38-39] , which is the cause of Spaces existence , with the only two quantized magnitudes wavelength ,λ , consisting the{MFMF = Background medium Field } and the Gravity force as momentum ,Λ, on Monads as the Gravity force . Momentum as velocity is the cross product of two velocity vectors v1,v2 which form with the two side-by-side Medium breakages ( The Electric E Magnetic P, following the cycloid motion ) and which is the Intrinsic and Stationary Electromagnetic Field of gravity`s in Medium . Breakages and Particles with velocity ,v, being the units of matter with Electric charge ,q, as their physical property is, when placed in prior referred Electromagnetic Field EP , where like charges repel and unlike charges attract , experience a force as Lorentz force , and this is called Gravity-Force , while Background-medium , is the Gravity-Field in the medium , i.e. the Quantized-Space is the medium (ds) which is also Quantized-Energy of two (±) breakages forming dipole, on which is exerted a Thrust as Velocity ,v, which is decomposed into the two equal velocity vectors ,v1,v2, and moving on two transverse cycloid trajectories which create an Intrinsic Stationary Electromagnetic wave E,P,→ the Gravity field,{ into where motion (E,P) and spin is balanced from the anti- cycloidal motion (evolute) of the Anti -Quantized-Space (-ds) }. Gravity force is exerted on breakages which are [The Material points forming dipoles] as velocity vector ,v, which is decomposed into two reverse velocities following the cycloidal motion , and consisting the intrinsic Stationary Electro-magnetic Wave of gravity, and which is binding the points of this Rest and mass-less nature Field .The infinite tiny volumes caves [Spaces of inner Electromagnetic field of particles] are the tanks in where Energy of dark points and dark fringes of two interference waves, is conserved .This is the Space-Energy unification Universe in Inertial systems consisted of this [MFMF] Field and Gravity`s inner Displacement current force and consist the Absolute frames in nature . So the immense confusion in the basic ideas regarding the Quantized Energy-Space , The Quanta , vanishes.
Waves need a media to travel and carry energy. A standing wave is an oscillation pattern with a stationary outline (envelope) that results either from the superposition of two identical waves travelling opposite directions or from an inner equilibrium vibration . A given particle that is bound ( confined ) in a certain region of space is a standing wave and vibrates within the constraints of the envelope function y = 2A.sin(kx).cos.(wt) . Light as Force is acting on zero area wavelength as Normal stress and thus measured as linear Momentum (since Stationary energy becomes Kinetic) and Work becomes travelling Energy .This property of energy to be converted into , velocity in wavelength as background media is the reason that doesnt collapse by radiating away its or their energy . Work as Vibration is confined in its wavelength as a Damper , absorber , and is retained unchanged when travelling . The Why , When and the How is widely analyzed .Since also a stationary wave consists of two transverse waves then is not interpreted as an equal mixture of the two, but an inner equilibrium on monad . It was shown that the Energy-Space universe ( the beyond Plancks length , Gravitys and Spaces levels ) is [PNS] and Space Anti-Space as work [38-39] , which is the cause of Spaces existence , with the only two quantized magnitudes wavelength ,λ , consisting the{MFMF = Background medium Field } and the Gravity force as momentum ,Λ, on Monads as the Gravity force . Momentum as velocity is the cross product of two velocity vectors v1,v2 which form with the two side-by-side Medium breakages ( The Electric E Magnetic P, following the cycloid motion ) and which is the Intrinsic and Stationary Electromagnetic Field of gravitys in Medium . Breakages and Particles with velocity ,v, being the units of matter with Electric charge ,q, as their physical property is, when placed in prior referred Electromagnetic Field EP , where like charges repel and unlike charges attract , experience a force as Lorentz force , and this is called Gravity-Force , while Background-medium , is the Gravity-Field in the medium , i.e. the Quantized-Space is the medium (ds) which is also Quantized-Energy of two (±) breakages forming dipole, on which is exerted a Thrust as Velocity ,v, which is decomposed into the two equal velocity vectors ,v1,v2, and moving on two transverse cycloid trajectories which create an Intrinsic Stationary Electromagnetic wave E,P,→ the Gravity field,{ into where motion (E,P) and spin is balanced from the anti- cycloidal motion (evolute) of the Anti -Quantized-Space (-ds) }. Gravity force is exerted on breakages which are [The Material points forming dipoles] as velocity vector ,v, which is decomposed into two reverse velocities following the cycloidal motion , and consisting the intrinsic Stationary Electro-magnetic Wave of gravity, and which is binding the points of this Rest and mass-less nature Field .The infinite tiny volumes caves [Spaces of inner Electromagnetic field of particles] are the tanks in where Energy of dark points and dark fringes of two interference waves, is conserved .This is the Space-Energy unification Universe in Inertial systems consisted of this [MFMF] Field and Gravitys inner Displacement current force and consist the Absolute frames in nature . So the immense confusion in the basic ideas regarding the Quantized Energy-Space , The Quanta , vanishes.
The puzzles of quantum mechanics are: 1. What is the medium for the photon and for the electron wave? i.e. what is waving? 2. How can a particle have an interference pattern 3. Observer effect. 4. Entanglement. In Quantum Erasure and Double-Slit experiments, how does the emitter know to direct the photon two both slits or only to one slit? And how does the detector know where to detect the photons to form an interference pattern and not a bell-shaped (Gaussian) pattern or vice versa? This paper proposes that the hint in the mystery of light waves without a medium (ether) is contained in the Planck’s relation itself: E = hf. It is shown that Planck’s relation itself hints on the mystery of light waves without medium, and is a consequence or manifestation of non-existence of a medium for light propagation. The subtle law of nature that has eluded physicists so far is that the photon energy density ( amplitude of electric and magnetic fields) at a given point in the spatial dimensions of the photon is directly related to the rate of change of the electric and magnetic fields at that point. The higher the frequency of the photon, the higher the rate of change of the fields at every point for that photon, compared to a photon of lower frequency. The higher the rate of change of the fields at a given point, the higher the amplitude of oscillation of the electric and magnetic fields at that point. It follows that the higher the frequency of the photon and the higher the amplitude of the electric and magnetic fields, which results in high intensity of vibration of the photon, the more localized it will be. A high frequency photon will spread less in space than a lower frequency photon of equal envelope amplitude because, if the high frequency photon spreads out, there would be high rates of change over a wider region of space, and the total energy would be greater than the finite photon energy. The photon energy will always be concentrated at regions of high rate of change of electric and magnetic fields. This theory explains how electric and magnetic fields can be their own ‘medium’ , 'dragging' of the electromagnetic energy by the wave, hence eliminating the need for any medium. Since the electromagnetic wave (the photon) is a traveling disturbance of electric and magnetic fields, the rate of change of the fields at a point in space will create the intensity (amplitude) of the fields at that point. Likewise, the electron wave is a travelling disturbance of the electron mass density wave on the electron ‘sea’. The higher the frequency of mass density variation of the electron at a given point of space, the higher the mass density of the electron at that point. This will make the electron ( the electron ‘sea’) its own medium of propagation. i.e. the electron ‘sea’ is the medium of propagation for the electron wave. This means that the electron wave 'drags' the electron with itself. The other theory proposed in this paper is the predetermination of interference fringes in double-slit experiments and predetermination of which slit the photon takes in which-way or quantum erasure experiments. We propose a fundamental law of nature that an electron, an atom or any source of electromagnetic waves will always emit a weak, continuous electromagnetic energy even when not excited, which implies that electrons and atoms are always in continuous, fundamental, weak vibrations (accelerations). Therefore, in double-slit experiments and in quantum erasure or which-way experiments, the atom (electron) of the light source is always emitting weak, continuous electromagnetic waves, even before the atom is excited. Therefore, even before the atom/the electron of the light source starts emitting a photon, a weak electromagnetic (light) wave exists as an entity, extending all the way from the light source (the atom) to the slits and to the detecting screen. This ‘precursor’ wave serves as the 'highway' for the propagation of the main photon energy packet, both of which are coherent and exist as an entity. When the atom is excited, it will just emit a photon that is coherent with the weak wave it had already been emitting continuously. Therefore, even before the atom is excited, a weak wave interference pattern already exists on the screen. The photon emitted after excitation simply follows the path already created by the weak ‘precursor’ wave and will land on the screen according to the predetermined interference pattern, collapsing to the point of detection at the instant of detection. The path to be taken by the photon is predetermined in which-way or quantum erasure experiments. The same theory explains quantum entanglement: the polarization of two entangled photons is predetermined even before the excitation of the atoms emitting the photons.
The formidable problem with double-slit experiments is: if electrons and photons exhibit wave properties (seen as interference patterns), then what is waving? What is the medium for transmission of ‘electron waves’? Such a medium has been disproved experimentally, in the case of the photon, and not even conceivable for the electron. Erwin Schrodinger was on the right track with his view of the electron as a ‘smeared’ object, rather than as a point particle. Then how is a wave possible without a medium? How can a wave property and a particle property co-exist in a single physical entity (wave- particle duality)? Nature uses a simple and subtle trick : the average electron mass density at a given region of space is directly proportional to the root mean square (RMS) intensity of oscillation (velocity) of the electron (the electron wave) in that region. The instantaneous mass density of the electron at a given point is directly proportional to the instantaneous magnitude of vibrational velocity of the electron at that point. The average photon energy density in a given region of space is directly proportional to the root mean square of rate of change of the electric and magnetic fields in that region. The instantaneous energy density of the photon at a given point of space and time is directly proportional to the magnitude of rate of change of the electric and magnetic fields at that point. The rate of change of electric and magnetic fields in turn depends on the frequency, amplitude and phase of the wave. The electron mass and photon energy will always be concentrated at regions of high wave amplitude. This means that the electron and the photon are dragged by their respective waves. The new theory provides a hint on the mystery behind Planck’s relation: E=h.f. Higher frequency photons have higher energy than lower frequency photons just because higher frequency photons also have higher amplitudes of electric and magnetic field oscillations. If we assume that ordinary waves also have the same fundamental properties as electron waves, then we may be able to explain the lack of backward propagation in Huygens’ principle. We may be able to explain why the bouncing oil droplet in the Couder-Fort oil bath experiment starts to go in the direction of the wave propagation.
The double-slit experiment is usually taken as evidence that a particle is also a wave. We show by simulation that a definite particle, moving through a physical medium and guided by its own wave, produces the same interference pattern, with no constant fitted to the pattern. Space is modeled as a compressible particle medium with a short-range stiffness. A particle set in motion disturbs it once. The disturbance disperses, and the particle carries with it the part of the wave whose group velocity matches its own speed, so the wavelength at the particle is fixed by its speed alone, λ ∝ 1/v, with no oscillator and no continued pushing. That wave passes through two slits and interferes as any wave does. The particle passes through one slit, keeps its speed, and takes its direction from the flow of the wave around it. It lands where the wave is bright. Hundreds of particles, sent one at a time, reproduce the wave's own pattern: at three speeds and two slit spacings, up to nine bright lanes with empty dark bands between them, lane spacing that scales with the wavelength of the wave it carries, the same pattern for a stream of particles as for one, and no lanes when one slit is closed. The rule that steers the particle has no strength, no frequency, and no free constant, and it is the same rule at every scale because each particle's wave is sized to itself. The result depends on one condition: that the particle's launch point lie well beyond the near-field distance of the slit pair, which laboratory sources satisfy. We record the rules that were tried and failed and the numerical pitfalls, and we state what remains open: the silent coast is a postulate, the mass dependence of the wavelength is untested, and the work is two-dimensional.
Ψ∂ (4.1) The harmonic trial solution of this equation with respect to a fixed inertial frame ( is given by )tx, ( ) ( ) ( )ctxikectxktx −Ψ=Ψ−Ψ=Ψ 00 orcos, In another inertial frame( ),, tx ′′ considered to be in uniform translational motion with velocity as described by the Galilean transformation (2.13), with respect to the fixed frame, the wave is represented by a wave function ,v ( ) ( ), related to ,x t x′ ′Ψ Ψ t as 2 2i.e., x t x x x t x x x x ′ ′∂Ψ ∂Ψ ∂ ∂Ψ ∂ ∂Ψ ∂ Ψ ∂ Ψ= + = =′ ′ ′ ′∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ and 2 2i.e., 2 x t v v v t x t t t x t x tt x ′ ′∂Ψ ∂Ψ ∂ ∂Ψ ∂ ∂Ψ ∂Ψ ∂ Ψ ∂ Ψ ∂ Ψ ∂ Ψ= + = − + = − +′ ′ ′ ′ ′ ′ ′∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ 2t∂ ∂ ∂ where use has been made of known properties of partial derivatives. It follows that obeys the following wave equation, with respect to the moving inertial frame ( tx ′′Ψ , ) ( ) tx v tx vc ′∂′∂ Ψ∂−′∂ Ψ∂=′∂ Ψ∂− 2 22 2 (4.2) which is obviously different from the wave equation (4.1) that holds in the fixed inertial frame. In other words the electromagnetic wave equation is not invariant with respect to a uniform translation of the inertial frame, using a Galilean transformation. Inserting into Eq.(4.2) harmonic solution written as we obtain 2 2 2 2 2 2( ) ( ) 2 ( ) i.e., orc v k k w v k w w v c w c− − = − − = − ± = ± v (4.3) Hence Galileo's transformation predicts that the velocity of light should be different from c, if measured with respect to a moving inertial frame. We therefore have a choice to make before we can fully understand the electromagnetic phenomena. We can either accept Galileo's principle of relativity which states that all inertial frames are equivalent or the Galilean transformation (2.13). We can sacrifice Galileo's principle of relativity by saying that there is a privileged inertial frame, called the ether, in which it is supposed that the electromagnetic wave velocity is c as given by Maxwell's equations, although they made no essential reference to the ether. A long series of investigations has been carried out, in order to detect some effect of the motion of the earth through the ether, always with negative results. All of the experiments (the best known being that of Michelson-Morley) have indicated that the speed of light is always the same in all directions and is independent of the relative motion of observer, source and transmitting medium. Einstein has reaffirmed Galileo's principle of relativity on the equivalence of all the inertial frames and, in addition, has assumed as a basic postulate the experimental fact that the speed of light is always constant. As a consequence, the Galilean transformation had to be replaced by another, in order to preserve the same speed of light in all systems. Einstein's basic assumptions are known as the postulates of special relativity: 1. The laws of physics take the same form in all inertial systems 2. The speed of light in empty space is a universal constant c and is the same for all observers. It is independent of the state of motion of the emitting body Special relativity is only concerned with transformations between inertial frames, as indicated by the restriction contained in the first postulate. General relativity covers reference frames in arbitrary relative motion, and is based on the principle of equivalence, confirmed experimentally, which unifies gravitational and inertial forces. The first of Einstein's postulates implies that it is only possible, by means of physical measurements, to demonstrate that two gravity-free reference frames are moving relative to each other. There is no physical basis to infer that any such frame is intrinsically at rest or in uniform motion. The notion of absolute rest is not consistent with the first postulate. The second postulate is in contradiction with the Galilean transformation which would preserve the form of Newton's laws of motion, as illustrated by Eq.(4.3). Therefore, we must find a transformation between two frames moving with uniform relative motion, which is consistent with the second postulate. We must then generalize the laws of Newtonian mechanics in a form which is invariant under that transformation, as required by the first postulate. A fundamental requirement of special relativity is that the laws of Newtonian mechanics are valid in the low speed limit and must be obtained as limiting cases of relativistic formulae for .cv << This assumption plays, for special relativity, a role analogous to that of Bohr's correspondence principle in quantum mechanics (see Chapter 28). 4.2. THE LORENTZ TRANSFORMATION Einstein's procedure is to locate an event in a reference frame by its spatial Cartesian coordinates x, y and z and a temporal coordinate t. Consider two frames S and S' moving with uniform relative motion, such that the Cartesian axis system in coincides with that in S, Oxyz, at time ,S ′ zyxO ′′′′ .0==′ tt As illustrated in Figure 4.1, the x and axes are parallel to the direction of relative motion: in moves in the x direction with velocity v, and in x′ , the frameS ′S S, the frameS ′ moves with velocity in the direction. A pulse of light emitted from O at time v− x′ 0=t spreads as a spherical wave travelling with speed c, so that the equation of the wave front in S, at a time t will be (4.4) 22222 tczyx =++ 0 0' z' y' x,x' z y Figure 4.1. Cartesian axes of two inertial frames in uniform relative motion The second postulate requires that the wave front in S ′ can be represented by (4.5) 22222 tczyx ′=′+′+′ In other words an observer in also sees a spherical wave travelling from its origin if not, any change of the wave front could be used to infer that the system is moving uniformly instead of being at rest. The invariance of the expression S ′ ,O′ S ′ (4.6) 2222222222 tczyxtczyx ′−′+′+′=−++ is a basic requirement that the transformation between the two systems must satisfy. The Galilean transformation (2.13), which in our case reads ttzzyyvtxx =′=′=′−=′ ,,, is not consistent with the invariance property (4.6), as it gives xvttvtczyxtczyx 2222222222222 −+−++=′−′+′+′ The first postulate brings some simplification to the possible form of the desired transformation. Since a uniform rectilinear motion in S must go over into a uniform rectilinear motion in S', the transformation must be linear. A nonlinear transformation would predict acceleration in S' even if the velocity were constant in S. The choice of the origins in space and time has avoided constant terms, and the transformation will be homogenous. The directions perpendicular to the relative motion, which are effectively at rest, must be left unchanged by the transformation. We then take the general form BtAxx +=′ yy =′ (4.7) zz =′ FtDxt +=′ Further simplification comes from the argument that the origin O', which has the coordinate moves along the x axis with velocity ,0=′x ,/ vdtdx = that is ABvBtAx /or0 −=+= while the origin O, with coordinate ,0=x moves along x-axis with velocity Recalling that when , we can write .'/' vdtdx −= 0=x 0=t 00 ort D B Bx A B t v F F F ′ − ⋅′ ′= ⋅ + = − = so that Inserting now Eqs.(4.7) into Eq.(4.5), we obtain the equation .FA = ( ) ( ) 02 22222222222222222 =−+⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ −−++−=′−′+′+′ DcBAxt c BAtczyxDcAtczyx The identity (4.6) requires that 2222 =−=−=− DcB c BADcA Since ,B vA= we obtain 2222 /1 /, /1 , /1 cv cvD cv vB cv A − −= − −= − = (4.8) so that Eqs.(4.7) now read 22 /1 cv vtxx − −=′ yy =′ (4.9) zz =′ /1 / cv cvxtt − −=′ The four equations (4.9) are known as the Lorentz transformation, which in this case applies to the relative motion of inertial frames along the x-axis. It is a straightforward matter to show that Eqs.(4.9) are consistent with the invariance relation (4.6), which is thus a sufficient as well as a necessary condition for the Lorentz transformation. With the usual abbreviations ( )1 /1 1, 222 ≥ − = − == γ β γβ cvc v (4.10) the Lorentz transformation simplifies to ( ) ( )x x ct x x ctγ β γ β′ ′= − = + ′ a) yyyy ′==′ or b) (4.11) zzzz ′==′ c) ⎟⎠ ⎞⎜⎝ ⎛ ′+′=⎟⎠ ⎞⎜⎝ ⎛ −=′ x c ttx c tt βγβγ d) The right hand side shows the inverse transformations where the primed and unprimed quantities are interchanged and the sign of the relative velocity is reversed, because its direction is the only difference between the systems S and S'. In the low velocity limit the Lorentz transformation reduces to the Galilean transformation since the only difference consists in the presence of the factor γ and the term ,1< that, in Eq.(4.11a), γ indicates a change of measuring stick length and in Eq.(4.11d) a change in the clock rate in the Lorentz transformation. The term ( )xc/β− in Eq.(4.11d) shows that the time is dependent on the position of a given event. Therefore, the immediate consequences of the Lorentz transformation require the revision of the usual concepts of simultaneity, time and length. Simultaneity Consider two events occuring at the same time ttt == 21 at two different positions and in the unprimed system S. According to Eqs.(4.11) the events are recorded in the primed system S' at different times 1x 2x / /, 1 1 t x c t xt t cβ ββ β − −′ ′= = − − so that the apparent time interval in S' is given by ( ) 0 1 / 2 21 12 ≠− −=′−′=′∆ β β cxx ttt (4.12) and hence, it is a function of the relative velocity v. The events will not appear as simultaneous to observers in S'. We are then forced to abandon the intuitive idea of absolute simultaneity, which is based on our experience with objects of low velocity, and accept the relativity of simultaneity, which depends on the coordinate system and applies in the domain of high velocities. Length contraction Consider a rod at rest in the primed system S' lying along the x-axis and having the length 12 xx ′−′=λ given by the distance between its ends 21 and xx ′′ measured at the same instant of time t'. The length in an inertial frame in which the rod is at rest is called its proper length. To define length in a frame S in which the rod is moving, an observer must locate the position of both end points, 21 and xx ′′ , at the same time From the inverse equations (4.11) we obtain 1 2 .t t t= = 1 1 2 1 x ct x ct x xx x x xβ ββ β β − −′ ′ ′ ′= = − = − − − − so that the apparent length 12 xxl −= is 21 βλ −=l (4.13) This equation is known as the Lorentz contraction and states that a rod parallel to the direction of its motion is shortened by the factor .1 2β− It results from the fact that simultaneous events in the rest frame of one rod are not simultaneous in the rest frame of the other. A rod transverse to its direction of motion is unchanged in length. The proper length λ is independent of the orientation of the rod, as a manifestation of the isotropy of inertial rest frame S'. If the orientation of a rod is neither longitudinal nor transverse to the direction of relative motion, both the length and the inclination are changed in the laboratory frame S, as an effect of a contraction in the direction of the relative motion with no change of transverse dimensions.
Momentum and Kinetic Energy equations are developed from the hypothesis that oppositely directed components of harmonically oscillating pseudo standing waves pass through a quantum particle center and can be represented by Longitudinal Matter Waves that carry the particle’s momentum and energy. The Doppler effect on the component wave lengths allows the net forward momentum and kinetic energy to increase with speed well beyond classical values. De Broglie (1925) issues with stationary wavelength and moving pulse rate are resolved in a different manner. Because a quantum particle is considered to be nothing more than the sum of “in” and “out” matter waves focused through its center, whatever happens to these matter waves determines the future location of that center. This opens the door to physical explanations for gravity, interference, and the slowdown of light in transparent mediums. Gravity, for example, is shown in section 6, to possibly be caused by the local gradient in matter wave speed near a large body like earth.
We set up the classical wave equation for a particle formed of an oscillatory zero-rest-mass charge together with its resulting electromagnetic waves, traveling in a potential field V in a susceptible vacuum. The waves are Doppler-displaced upon the source motion, and superpose into a total, traveling- and in turn a standing- beat wave, or de Broglie phase wave, described by a corresponding total classical wave equation. By back-substitution of the explicitly known total, standing beat wave function and upon appropriate reductions at classic-velocity limit, we separate out from the total a component wave equation describing the kinetic motion of particle, which is equivalent to the Schrödinger equation. The Schrödinger wave function follows to be the envelope function of the standing beat wave at classic-velocity limit.