The title of Project 1 is “Time and Space”.
This project is divided into three parts:
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Time and Space
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General Solution for Einstein’s Relativity.
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Limits of Applicability of the Doppler Theory.
Short review of Project 1.
1. The first part was prepared in 2012 by Dennis Durandin for presentation at the SUNY Stony Brook school student conference called the “Flame Challenge”. The topic of the conference was: “What is time?” In the following years this project was slightly reworked. Some definitions were reformulated, but the main ideas as well as the mathematical expressions are still the same. The first part of this project introduced the definition of TIME and SPACE. The first part includes both historical and dialectical analyses of physical, philosophical and methodological aspects of terminology and non-controversial application of space and time definitions in Applied and Theoretical physics. In Part 1, we’ve demonstrated that in the Optical System of Coordinates there is no difference between Galileo’s and Einstein’s Relativities. The values of time in Galileo’s and Einstein’s Relativity become equivalent, if the time is measured in the units of wave periods. The values of space for Galileo’s and Einstein’s Relativity also become equivalent, if the distance is measured in the units of wavelength. We’ve named such a system – an Optical Coordinate System.
Part 1 of this project brings us to the main conclusion: the general formula for the Relativistic time transformations and the general formula for the Doppler Effect must be identical, because they both describe the same physical phenomenon.
2. In the second part of this project, we’ve explained major errors both theoretical and experimental, which brought Einstein to the creation of his Theory of Relativity. The second part includes analyses of both Poincare and Einstein’s approach to resolving contradictions, created by the results of Michelson’s experiments. We’ve confirmed and agreed with Poincare’s statement that the Lorentz transformations do not represent the general solution of the Maxwell equations. We’ve presented our general solution of Maxwell’s equations for two relativistic inertial systems as:
$\beta=\frac{1}{\sqrt{1 +{ v^2\over c^2} -2 {v\over c}{\cos\delta}}}$.
3. Our new Relativistic beta appeared to be not equivalent to the Doppler formula, which brought us to the third part of this project. In Part 3, we’ve demonstrated the limitations of the Doppler approach. We’ve found general solutions for the Doppler Effect both for linear and for spherical waves. We’ve proved experimentally that the general solution for the Doppler Effect for spherical electromagnetic waves, as well as for other types of spherical waves is described by our formula:
$f_{obs}=f_0 { \ }{\sqrt{1 +{ v^2\over c^2} -2 {v\over c}{\cos\delta}}}$
Our solution for the Doppler Effect should be used in application for spherical and circular waves. This formula is also the general solution for the Maxwell equations of electromagnetic waves.
Parameters in these equations have a similar meaning both to the parameters in the Theory of Relativity and the Doppler Effect. The relativistic $\beta$ becomes a function of angle $\delta$ between the speed of light $c$ and the speed difference $v$ between two inertial systems.
Frequency $f_{obs}$ is measured in the moving system and $f_0$ is measured in the system at rest. The new letter for the angle in the Doppler Effect is introduced, because the definition of the angle $\delta$ is slightly different from old definition of angle $\theta$.
Conclusion:
In Project 1 we’ve demonstrated that the Theory of Relativity and the Doppler Effect describe the same physical phenomenon. The mathematical expression for both the Doppler Effect and Einstein’s Relativity are identical.
This result also means that the conclusion, made by Dennis Durandin in 2012 about the equivalence of Galileo Relativity and Einstein’s Relativity, is now proven.
This result also means that the conclusion, made by Dennis Durandin in 2012 about the equivalence of Galileo Relativity and Einstein’s Relativity, is now proven.
The difference between classic Galileo Relativity and Einstein’s Relativity is a result of the bad choice of light interference as the method for both Einstein’s imaginary experiment and for Michelson’s real experiment.
The paradox of Einstein’s Theory of Relativity is now resolved. There is no more contradictions with Galileo Relativity. The future version of Michelson’s experiment performed with the non-linear detection, using for example, the method described in the Pope, Durandin patent, could finally help to determine the speed of our Solar System in the Universe.
The paradox of Einstein’s Theory of Relativity is now resolved. There is no more contradictions with Galileo Relativity. The future version of Michelson’s experiment performed with the non-linear detection, using for example, the method described in the Pope, Durandin patent, could finally help to determine the speed of our Solar System in the Universe.
For students and young scientists, one of the most important aspects of this presentation is the demonstration of the difference between remembering a theory and understanding one. Many educated people remember the Doppler formula, but there has been no scientist or engineer, who understood the concept well enough to try to prove the validity of the Doppler formula for spherical waves.
It is impossible to prove, because the Doppler formula is incorrect for spherical or circular waves.