Chapter 4. Improved Relativity Theory (IRT)

Transcription

1 Chapter 4 Improved Relativity Theory (IRT) In 1904 Hendrik Lorentz ormulated his Lorentz Ether Theory (LET) by introducing the Lorentz Transormations (the LT). The math o LET is based on the ollowing assumptions: 1. There exists an immobile ether occupying space. 2. Every LET observer assumes the rest rame o this immobile ether to derive the LT. 3. Absolute Motion o an object in this immobile ether should be detectle. Numerous experiments were perormed to detect the solute motion o an object in this immobile ether and they were all ailures. Most noticele o these was the Michelson Morley experiment (the MMX). The null results o the MMX appears to rule out the existence o the ether. However, Lorentz and George rancis itzgerald came up with the concept o physical length contraction to save the LET. They envisaged that the arms o the MMX contracted physically by the right amount in the direction o the Absolute Motion to give the MMX null results. Einstein ormulated his theory o Special Relativity Theory (SRT or SR) in 1905 based on the ollowing postulates: 1. The Laws o Physics are the same or observers in all inertial reerence rames. 2. The speed o light in a vacuum has the same value c in all directions and in all inertial reerence rames. Einstein derived the same LT as LET rom these two postulates. The concept o lexible time and geometric projected length contraction were introduced to explain the LT equations. 54

2 Model Mechanics: The inal Theory 55 However, the idea o lexible time and projected length contraction gives rise to many paradoxes and the most amous o these is the amiliar twin paradox. Instead o two identical human twin I will explain the paradox using two identical clocks A and B. A remains on earth and B accelerated away to a distant star and return. Upon returning, the traveling B clock will accumulated less clock seconds (younger) than the stay at home A clock. But according to SRT B can claim that A is moving away rom him return and thus A should accumulate less clock seconds than B. This is the essence o the twin paradox. Physicists explain the twin paradox by pointing out that when B experienced the initial acceleration and at the turn-around the symmetry between A and B is broken. That s why B accumulated less clock seconds than A when they meet again. The relevant question at this juncture is: why does LET and SRT have the same math? The answer to this question is surprisingly simple. The two SRT postulates can be reworded as the ether rame postulates as ollows: 1. The Laws o Physics are the same in all locations in the immobile ether. 2. The speed o light in the immobile ether is a constant c as measured in all locations in the immobile ether. These two ether rame postulates can use the same derivation procedure as SRT to derive the same LT equations. That s why LET and SRT have the same math and they are summarized as ollows: Clock Time Retardation (LET) or Time Dilation (SRT): t = γ t Physical Length Contraction (LET) or Projected Length Contraction (SRT):

3 56 Improved Relativity Theory L = L γ Lorentz Transormation Equations rom the Primed rame: x = γ( x + v t ) t = γ( t + v x /c 2 ) Lorentz Transormation Equations rom the Unprimed rame x = γ( x v t). 4.5 t = γ( t v x/c 2 ) 4.6 These SRT and LET Transormation Equations are used by every SRT and LET observer. They assume that the unprimed rame is in a state o rest and that the primed rame is moving in the unprimed coordinate system. These assumptions are the reason why every SRT observer claims that clock moving with respect to him runs slow and thus gives rise to the dubious concept o mutual time dilation. Improved Relativity Theory (IRT) The Model Mechanics description o the current universe is summarized as ollows: All o the pure-space in our universe is occupied by a substance called the E-Matrix. Subsequently, the E-Matrix is perceived by us as space. The E-Matrix, in turn, is composed o E-Strings. The diameter o an E-String is not known. It is probly in the region o Planck length that is deined by current physics as the smallest length that has any meaning and its value is in the region o cm. The length o an E-String is not known. It could be a big loop and in that case the diameter o the loop is not known. Away rom matter, E-Strings are oriented randomly in all directions, but near matter, E-Strings are more organized: some emanate rom the matter, and the number o these passing through a unit area at a

4 Model Mechanics: The inal Theory 57 distance r rom the matter is inversely proportional to r 2. Matter particles will ollow the local geometry o the E-Strings as they travel in the E-Matrix. In turn, the motions o matter particles in the E-Matrix will distort the geometry o the E-Strings locally. These provisions are responsible or the peculiar properties o the gravitational orce. Also, it explains why the propagation o light and gravity obeys the inverse square law. The E-Strings exert a repulsive orce on each other. This orce is undamental. This means that there is a compacting orce that is compacting the E-Strings together to orm the E-Matrix and this compacting orce is also undamental. The compacting orce and the repulsive orce between the E-Strings are in a delicate equilibrium and this equilibrium is sel-restoring when it is disturbed by the motion o particles in the E-Matrix The ove Model Mechanics description o the current state o our universe gives rise to the ollowing unique properties and these unique properties enled me to ormulate a new theory o relativity called Improved Relativity Theory (IRT). The assumptions o IRT are as ollows: 1. A photon is a wave-packet in neighboring E-Strings. 2. The speed o light is isotropic in all rames o reerence. 3. Motions o objects in the E-Matrix are unimpeded. 4. Every object in our universe is in a state o solute motion in the E-Matrix. This means that every IRT observer must include the possibility that he is in a higher state o solute motion than the observed object (the observed rame). 5. Wavelength o an elementary source is a universal constant. 6. Absolute time is the only time that exists. Clock time (a clock second) in the rame o the clock represents a speciic interval o solute time. The amount o solute time

5 58 Improved Relativity Theory contained in a clock second is dependent on the state o solute motion o the clock. 7. The speed o light is not a universal constant. 8. Material length o a meter stick is a universal constant. 9. The light-path length o a moving meter stick is observer dependent. 10. The light-path length o the observer s meter stick is assumed to be its material length. IRT eliminates the SRT constant light speed postulate in all inertial rames. This, in turn, eliminates all the paradoxes derived rom this postulates. The equations o IRT are valid in all environments, including gravity. Thereore IRT can be used to replace GRT in all applications. The IRT Postulates: 1. Every object in our universe is in a state o individual solute motion in the E-Matrix. There is no rest rame or any observer. 2. Relative motion between two objects in the E-Matrix is the vector dierence o their solute motions along the line joining them. 3. The measured wavelength o a standard elementary source is a universal constant in all rames o reerence. 4. The speed o light in the rame o the standard elementary source is isotropic. The Consequences o the IRT Postulates: 1. The local speed o light is the product o the local measured requency o the standard elementary source and its measured universal wavelength. 2. Light rom a source moving with respect to the observer becomes a new light source in the observer s rame. The arriving speed o incoming light rom a moving elementary

6 Model Mechanics: The inal Theory 59 source is the product o its measured incoming requency and its universal wavelength. 3. There is no physical (material) length contraction. The physical (material) length o a meter stick remains the same length in all rames o reerence. However, the light path length o a moving meter stick is observer dependent. 4. The rate o a clock is dependent on the state o solute motion o the clock. The higher is the state o solute motion the slower is its clock rate. 5. Absolute time exists. The relationship between clock time and solute time is as ollows: A clock second will contain a dierent amount o solute time in dierent states o solute motion (dierent rames o reerence). The higher is the state o solute motion o the clock the higher is the solute time content or a clock second. There is no solute time dilation. The observed clock time dilation is the result o a clock second contains a dierent amount o solute time in dierent rames. 6. Simultaneity is solute. I two events are simultaneous in one rame, identical events will also be simultaneous in dierent rames. However the solute time interval or the simultaneity o identical events to occur will be dierent in dierent rames. This is due to that dierent rames are in dierent states o solute motion. 7. The postulates o IRT allow that the rate o a clock moving with respect to the observer can be running at a slower or aster rate compared to the observer s clock. Also the light path length o a meter stick moving with respect to the observer can be longer or shorter compared to the light path length o the observer s meter stick which is assumed to be the physical (material) length o the meter stick. These consequences lead to two equations or the time rate o an observed clock and two equations or the light-path length o a meter stick moving with respect to the IRT observer. Also they lead to two sets o

7 60 Improved Relativity Theory transormation equations rom observer A s rame to the observed B rame. It turns out that i the observed rame is in a higher state o solute motion than the observer all the IRT predictions will be identical to the SRT and LET predictions. That s why the math o SRT and LET is a subset o the math o IRT. The Math o IRT: The existing SRT and LET equations are converted to IRT equations when the observed rame B is in a higher state o solute motion than the IRT observer A. New IRT equations are developed when the observed rame is in a lower state o solute motion than the IRT observer. The conversion actors rom observer A s point o view are as ollows: Relative Velocity v a c a Local speed o light c ' a Incoming speed o light c = c{ a = a } Incoming speed o light 1 a = Wavelength o the standard elementary light source used as measured in observer A s rame. = Transverse wavelength o the standard elementary light source in B s rame as measured by A. = Instantaneous requency measurement o A s standard elementary light source as measured by A. = Instantaneous requency measurement o B s standard elementary light source as measured by A. (x)

8 Model Mechanics: The inal Theory 61 = requency o a standard elementary light source in A's rame as measured by A. = Transverse Doppler requency o an identical standard elementary light source in B's rame as measured by A. The behavior o clocks A and B in relative motion: T ' T (4.7) This equation applies when the observed clock B is in a higher state o solute motion than observer A s clock. It shows that the passage o an interval o clock time T on the observed B clock corresponds to the passage o T on observer A s clock. However, both o these clock time intervals represent the same amount o solute time. This means that the rate o passage o solute time is independent o the solute motion o the clock. T " T (4.8) This equation applies when the observed clock B is in a lower state o solute motion than clock A. It shows that the passage o a clock time T on the observed B clock corresponds to the passage o clock time interval o T on observer A s clock. However, both clock time intervals represent the same amount o solute time. This means that the rate o passage o solute time is independent o the relative or solute motions o the clocks. It is noted that only one o these two equations is valid or any pair o clocks in relative motion. I the observed clock B s solute motion is higher than the observer A s clock then Eq. (1) is used and i the observed clock B s solute motion is lower than observer A s clock then Eq. (2) is used. In accelerator design applications Eq. (1) is used exclusively. The reason is that acceleration will increase the state o solute motion o the accelerated particle.

9 62 Improved Relativity Theory Light path length o a moving meter stick: The light path length o observer A s meter stick is deined to be its physical or material length. The ollowing equations predict the light path lengths o B s meter stick. The ollowing equation (4.9) is used to predict the light path length o B s meter stick when B is in a higher state o solute motion than A. L ' L (4.9) When B is in a lower state o solute motion than A the ollowing Eq. (4.10) is used to predict the light path length. o B s meter stick. L " L (4.10) It is noted that the physical or material length o a meter stick is a universal constant in all rames o reerence. However the light path length o a meter stick moving with respect to the observer is observer dependent. Also it is noted that only one o these two equations will provide the correct prediction. I the state o solute motion o B compare to A is not known then both calculations are made and the result that agrees with observation is chosen. IRT Transormation Equations: Equations (4.11) and (4.12) are used when the observed rame B is in a higher state o solute motion than observer A. ' x x a t (4.11) ' t t x (4.12) 2 a Equations (4.13) and (4.14) are used when the observed rame B is in a lower state o solute motion than observer A.

10 Model Mechanics: The inal Theory 63 x " x a " t t 2 a x t (4.13) (4.14) Momentum o an object: o a p M (4.15) Kinetic energy o an object: 2 2 K M 1 o a (4.160 Energy o a single particle: E M o (4.17) 2 a 2 Gravitational red shit: 1 (4.18) 1 (4.19) Gravitational time dilation: T T 1 (4.19) T = T 1 (4.20)

11 64 Improved Relativity Theory The IRT procedure or determining the perihelion recession o Mercury without recourse to GRT is: a. Set up a coordinate system or the Sun and Mercury. b. Use the IRT coordinates transormation equations to predict the uture positions o the Sun and Mercury. c. The perihelion shit o Mercury will be revealed when these uture positions are plotted against time. The value o the shit can be determined rom the plot. The IRT Concept or Gravity Lensing and Gravity Bending o Light: The E-Strings surrounding a massive body are curved. Thereore light rom distant stars will ollow these curved E-Strings on its way to the earth to give the observed lensing eect. Similarly, the E-Strings surrounding the Sun are curved. Thereore light rom distant stars will appear to be bended around the Sun as it reaches the earth. IRT math includes SRT and LET math as subsets when the observed rame is in a higher state o solute motion than the observer. IRT math includes the possibility that the observer is in a higher state o solute motion than the observed rame. Thereore dierent math were developed to include this possibility. This IRT interpretation eliminated all the paradoxes encounter by SRT. In addition IRT provides physical explanation or dark matter, dark energy and the observed accelerated expansion o the universe. There is no GRT explanation or these observations. The equations o IRT have an unlimited domain o applicility and thereore they are valid or use to replace GRT in all cosmological applications.