Doppler Phenomenon for Electromagnetic Waves and New Equations for Quantum Relativity

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1 Doppler Phenomenon or Eletromagneti Waes and New Equations or Quantum Relatiity Mohammadreza Tabatabaei What is the Doppler eet? Beause o the Doppler phenomenons importane in osmology, it is neessary to hae a short reision. Doppler phenomenon is onsidered in lassi physi as hanges in the requeny o a soure o sound. Aording to this eet, wheneer an obserer is moing ompared to a soure o sound, he will reeie a dierent requeny than emitted by that soure. For example, i an ambulane with a gien speed is moing toward us, its sound waes hange beause o its motion, and a higher requeny and shorter waelength results. When it passes us and reedes in the distane, the sound hanges beause o lower requeny and longer waelength. The Doppler Eet applies to light, where the spetrum will hange rom red to blue depending on its diretion and speed. The behaior o light waes diers rom that o sound and must be desribed by Speial relatiity. Based on a relatiisti uniiation o physial rules in all inertia reerene rames, the existene o any supreme reerene rame in the unierse is disallowed. Beause o this, a soure moing towards an obserer or an obserer moing toward a soure gies the same result. In either ase, there will be a displaement towards the blue spetrum. This is gien by the ollowing equation: 0 e Wher 0 is the reeied wae length, and e is waelength that is emitted by the light soure. It is lear that in this situation, the waelength reeied is shorter than it is when sent. I the soure is

2 moing away with an inrease in the reeied light waelength, there will be a displaement in absorption or emission as ollows: 0 e The display will dier under lassi mehani, relatiity and quantum mehanis: In the piture below, the soure o the green spetrum (entral irle) is the spotted harmoni. Its waelength and requeny are: C is light speed, is the waelength, and is the requeny o the eletromagneti wae. Now i the soure o the green spetrum is displaed by the speed, we hae:

3 ) ) ( ) ( ) ( ) ( ) s ( ) is the reeied waelength, is the speed o the soure, is the waelength at soure, is soure requeny and is the reeied requeny. In the last equation, is the speed o the wae or example sound and Vs is wae or sound soure speed. The aboe equations are reerred to as the lassi equations or the Doppler Eet. For example, a polie ar is dispathing a wae with a requeny o 4000 Hz and moing along with an obserer at a 7km/hour speed. At a onsiderable distane rom another obserer, what is the sound requeny? The speed o sound in air is 340m/s: 4000Hz s 7km / h 0m / s 340m / s? & 450Hz & But as we know, by inreasing the speed o the light soure, time will slow and length will ontrat, so the obserer beside the light soure wont register the dierene in requeny and waelength and also will determine the preious result in light speed measurement. But in the iew o the other obserer not moing with the light soure, the greater the inrease in speed, the slower in time passes and length is shortened, giing a derease in requeny o the spetrum. This means moing towards the yellow spetrum rom the green spetrum requiring hanges in the measurement units o length and time. This spetrum is understood by obserations based on the Fitzgerald-Lorentz ontration. The lassi equation will hange to the ollowing equation where is the requeny o the soure spetrum moing with V speed.

4 As we know the units o requeny is yle per seond and by slowing time, the requeny o the soure spetrum will be dereased or obserers in relatie motion. This means: ( ) t t t is time, t is slowed time, and " is requeny o on the moing soure. Its ease and adantage ompared to the old ormula is that we just hange a sign in the numerator o the equation whih simpliies its meaning and appliation.

5 The aboe ure shows a shortening in waelength by inreasing the speed o the approahing soure (blue tendeny) and the upper ure shows lengthening o the waelength by inreasing speed o a soure moing away rom an obserer (red tendeny). Now we ompare the results o the new and old ormulas: V0 V0.5 V0.5 V

6 ( ) ( ) ( ) ( ) As it is lear, the results are same and now assuming the auray o the equation, try to merge these equations with the equations in quantum mehanis to reate new ormulas: The aboe equation shows the requeny o the reeied eletromagneti waes rom a soure whih is moing away rom the obserer. That is soure requeny and is reeied requeny by the obserer.

7 The upper ure shows requeny inrease by inreasing the speed o the soure approahing the obserer (blue tendeny) and the ure below shows a requeny derease by inreasing the speed o soure moing away rom the obserer (red tendeny). E h E h Lim h 0 E is the photon energy and h is Planks onstant. The aboe equation and limit shows the energy o eletromagneti wae rom a moeing soure. As it is lear by approahing light speed, the energy o the radiant wae is dereased by the soure, and this will ause a balane in the soure and preent explosion and mass onersion to energy. In at by approahing light speed, the temperature will approah absolute zero whih will be disussed in another paper. E E h h This is the general and inal equation to show the energy o eletromagneti waes reeied by a ixed obserer. The general onlusion is that energy in some leels o spae time is quantized. Beause the unit o requeny in Planks ormula is yles per seond, this means eletromagneti energy is quantized and pakaged in time and its unit is the seond and length is measured in meters

8 We an onsider this pakage as mehanial; a bit like a photon or a string o.t length where t whih will be disussed later.

Classical Electromagnetic Doppler Effect Redefined. Copyright 2014 Joseph A. Rybczyk

Classical Electromagnetic Doppler Effect Redefined. Copyright 2014 Joseph A. Rybczyk Classial Eletromagneti Doppler Effet Redefined Copyright 04 Joseph A. Rybzyk Abstrat The lassial Doppler Effet formula for eletromagneti waves is redefined to agree with the fundamental sientifi priniples