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LORENTZ TRANSFORMATION PDF

Monday, September 16, 2019


The Lorentz transformation, for which this chapter is named, is the coordinate Lorentz transformation; we will derive it from the Main Postulates of Special. If both coordinate systems are inertial (that is, no relative acceleration), then a particle moving along a straight line in one system must move along a straight line. Lorentz transformations: Einstein's derivation simplified1. Bernhard Rothenstein1 and Stefan Popescu2. 1) Politehnica University of Timisoara, Physics.


Lorentz Transformation Pdf

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Matter-Antimatter annihilation 7 Relativity and Electromagnetism. Magnetic Field due to a Current Lorentz Transformation of . In physics, the Lorentz transformation (or transformations) is named after the Dutch physicist .. (sppn.info~yakovenk/teaching/Lorentz. pdf). In these notes we study rotations in R3 and Lorentz transformations in R4. Let L denote the set of all such Lorentz transformation matrices.

Lorentz transformation equations. Using these Lorentz transformation equations, all other relations of special theory viz.

We also identify the advantage of this approach over the conventional approach. First problem in the theory of light is the invariance of relative speed of light with respect to all stationary and moving observers.

lorentz-transformations.pdf - Derivation of Lorentz

This is because in our common experience with moving matter, relative speed of matter with respect to observer is always seen to be dependant on speed of observer. If the observer moves in same direction as the velocity of moving matter, relative speed decreases assuming velocity of observer is less than velocity of matter and if the observer moves in opposite direction of the velocity of moving matter, relative speed increases. This is true for matter but not for light!

This is because these relativistic formulae are derived using the postulate of invariance of speed of light. So invariance of speed of light i.

This observation of invariance of speed makes the observer feel that the light photon or wave has the knowledge about motion of observer and it adjusts its speed to keep the relative speed with respect to the moving observer constant.

But, the observer then thinks how can the light know about the motion of observer before reaching him and why should it care about it? If there are many observers moving with different speeds, how can the photon of light adjust its speed so that its relative speed with respect to all observers remains same? If we say that light has a dual nature i. If we think about the above stated two problems viz. In this new theory, as there is no motion of light, there will be no place for the previously mentioned paradoxes.

The Light Cone

Physical possibility of this phenomenon from different angles and explanation of other effects of light such as rectilinear motion, refraction, interference, photoelectric effect, Doppler shift etc. As by conventional definition, photon is a packet of energy propagating in free space between the source and absorber and in our theory of reaction-at-a- distance, propagation of energy through intermediate space is ruled out, so the existence of photon must also be ruled out as per the concept of reaction-at-a-distance.

This theory of reaction-at-a-distance is different from the earlier theory of action-at-a- distance proposed by Schwarzschild, Tetrode5, Fokker6, Wheeler and Feynman In their theory of action-at-a-distance, although light is interpreted as a consequence of direct inter- particle interaction between source and observer, information about the energy loss event propagates from the source to observer at the speed of c.

But, in our theory of reaction-at-a- distance, the observer becomes aware of all the past and present events of the universe on its own which is a fundamental property of matter. Even if some matter is created just now say by electron-positron pair production , it gains the knowledge about all the events of the universe as soon as it is born. Thus, nothing comes from the source; observer only reacts to the source based on its own absolute knowledge about the events that have occurred in space- time.

This instantaneous awareness in the theory of reaction-at-a-distance is in someway analogous with the experimentally observed quantum-entanglement effect in which any operation on one member in an entangled pair instantaneously affects the state of other one placed at whatever distance apart.

Consequences of Lorentz transformation notes.

Despite of the proposed reaction time delay of our theory, there should not be any time delay between the events occurring at two members of entangled pair because the members of the pair behave like a single entity. So, both of them react simultaneously to the external agent when any operation is done on any one of the members.

First, awareness is just a knowledge which may be instantaneous, but reaction is a physical event which has to happen in time coordinate as per the priority of the reacting body. This priority is inversely proportional to the distance where the action event has occurred. If two events happen simultaneously at two different distances from a reacting body, the body reacts first to the event that is closer to itself.

Rotations-Lorentz-Transformations.pdf - LORENTZ

Thus time delay appears because of the distance dependant priority of the reacting body. Second argument is that, if there were no reaction time delay i.

Thus all the events of the universe would have been completed within a single instant and there would have been no temporal evolution of nature. As the creation of universe is itself a temporal evolution, universe would not have been created if instantaneous reaction were true.

Thus, the reaction time delay was a requirement for creation of the universe. The above-proposed theory should not be considered outside the limits of science just because of our inability to detect the awareness generated in a material body in response to any event occurring far away we can detect only when that material body reacts to the event.

Here, the concepts of instantaneous awareness and delayed reaction have been brought in to explain in a unified manner the experimental results of Michelson-Morley invariance of speed of light , single photon interference and photoelectric effect wave-particle duality. It is just like the picture in quantum mechanics in which a body is represented by a wave function, but we can not directly detect the wave function. We can only experimentally test the predicted results based on the hypothesis of wave function.

Still, quantum mechanics is science. Similarly, as the hypothesis of instantaneous awareness and delayed reaction correctly predicts the experimental results of Michelson-Morley, single photon interference and photoelectric effect, it is also science. Lorentz transformation, length contraction, time dilation etc. This group contains the proper rotations of R 3 , and also the group of proper, orthochronous Lorentz transformations of R 4. This both gives insight into the structure of Lorentz transformations, and also into charge conjugation.

The latter describes symmetry between spin- 1 2 particles like electrons, protons, neutrons, and quarks and their anti-particles. Contents I.

Lorentz Transformations 1 I. Components of L 2 I. The Components of L 3 II.

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Restricted Lorentz Transformations 5 II. Proper Rotations 5 II.

Pure Lorentz Boost: 5 II.If all these hold, then the coordinate systems are said to be in standard configuration, or synchronized. A notable advantage of this approach is that it is valid for all types of interactions electromagnetic and gravitational between the observer and the body being observed.

If the observer moves in same direction as the velocity of moving matter, relative speed decreases assuming velocity of observer is less than velocity of matter and if the observer moves in opposite direction of the velocity of moving matter, relative speed increases. General theory of relativity agrees with our conclusion as it also predicts the velocity of gravity to be c. Then we focus on one subgroup, the restricted Lorentz transformations.

Using this basic Lorentz transformation, all other conventional relations viz. A notable advantage of this approach is that it is valid for all types of interactions electromagnetic and gravitational between the observer and the body being observed which will be clear during our derivations in the next section.

We also identify the advantage of this approach over the conventional approach. So invariance of speed of light i. Acknowledgement The author is grateful to Dr.