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Conservation Property of Standing Wave

Eric Su

Published Jun 1, 2020• 0 citations
OpenAlex

Abstract

The standing wave exists in a microwave resonator if the length of the resonator cavity is equal to multiple half-wavelengths of microwave. The stationary interference of standing wave will travel in another inertial reference frame. The vibrating pattern of the standing wave is conserved. The existence of nodes in all reference frames requires the wavelength of the microwave to be conserved in all inertial reference frames. The angular frequency of microwave is different in every reference frame. Hence, the apparent velocity of the microwave depends on the choice of reference frame while the elapsed time remains invariant in all reference frames.

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Journal of the Optical Society of America B•Apr 1, 1991•45 citations
The standing wave exists in a microwave resonator if the length of the resonator cavity is equal to multiple half-wavelengths of microwave. The stationary interference of standing wave will travel in another inertial reference frame. The vibrating pattern of the standing wave is conserved. The existence of nodes in all reference frames requires the wavelength of the microwave to be conserved in all inertial reference frames. The angular frequency of microwave is different in every reference frame. Hence, the apparent velocity of the microwave depends on the choice of reference frame while the elapsed time remains invariant in all reference frames.
A standing wave can be formed in a microwave resonator if the length of the resonator cavity is equal to multiple half wavelengths. The stationary standing wave becomes a moving standing wave in another inertial reference frame. The covariance property of the moving standing wave verifies that the frequencies of two microwaves forming the standing wave become different in the new reference frame while the wavelengths remain identical. Hence, the apparent speed of the microwave appears to be different in a different inertial reference frame.
The double-slit interference shows that the product of the wavelength and the distance from the slit plate to the projection screen is conserved in all inertial reference frames. This conservation ensures that the observed wavelength in any inertial reference frame is identical to the original wavelength in the rest frame of the light source. According to the Doppler effect, the observed frequency depends on the choice of inertial reference frame. With the same wavelength but different frequency, the speed of light is different in a different inertial reference frame.
This paper thinks that the conclusion will disagree with the Bohr angular momentum quantized condition,if the standing wave condition of linear string vibration is used directly to deal with angular momentum of the motion of electron going round nucleus in a circle in the textbook.The paper holds that if one employs the character of the standing wave and the symmetry satisfied by standing wave condition of circinal string vibration,he can reach that the condition of the standing wave of circinal string vibration is just the circumference of the circle equal to even times of half of the wavelength.Through that condition,one can obtain the quantized angular momentum consistent with the stationary state of Bohr Theory.At the end of the paper the authors explain the quantized angular momentum and the quantized energy with the character of the standing wave.
The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light always remains the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterwards, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames.
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 EP , 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.
We compare the scattering of an atom by two different quantized standing-wave configurations. The first one is established in a cavity by a pair of fixed mirrors. The other consists of two independent counterpropagating traveling waves, as could occur in a ring configuration. We show that in the quantum regime (of small photon numbers) atoms are scattered differently by a true standing wave than by a superposition of two counterpropagating waves of equal amplitudes and opposite directions. This behavior is a manifestation of momentum conservation. In the case of traveling waves each wave depletes its momentum independently, whereas the standing wave that is fixed in space acts as a potentially infinite sink or source for momentum.