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Questions

  • What is the book “Newton and Relativity” about? – answer
  • What are the main findings presented in “Newton and Relativity”? – answer
  • What makes the approach in “Newton and Relativity” different from traditional methods? – answer
  • How does the book “Newton and Relativity” simplify the Theory of Relativity? – answer
  • How does the book “Newton and Relativity” use Newton’s Second Law to derive relativistic equations? – answer
  • How does the book “Newton and Relativity” derive mass-energy equivalence using classical physics? – answer
  • Can you explain how Newton’s Second Law is used to derive relativistic mass relations? – answer
  • How does the book “Newton and Relativity” derive relativistic energy? – answer
  • How does the book “Newton and Relativity” derive relativistic acceleration? – answer
  • How does the book “Newton and Relativity” derive relativistic Doppler effect? – answer
  • How does the book “Newton and Relativity” derive relativistic length contraction? – answer
  • Can you explain how the book “Newton and Relativity” proves the Relativistic addition of velocities? – answer
  • What is the significance of the relativistic velocity addition formula in “Newton and Relativity”? – answer
  • Can you explain how the book “Newton and Relativity” proves the constancy of the speed of light? – answer

Answers

What is the book “Newton and Relativity” about?

The book Newton and Relativity by Francesco Cester presents an alternative approach to understanding the Theory of Relativity, aiming to simplify complex concepts typically associated with Einstein’s theories. Cester’s methodology is rooted in Newtonian mechanics but introduces the idea of variable mass, which allows for a more intuitive derivation of relativistic equations without relying on traditional postulates like the constancy of the speed of light or Lorentz transformations.

Key Concepts of the Book

Alternative Derivation Approach

  • Cester begins with the Equivalence Principle of Mass and Energy, utilizing Einstein’s famous equation E=mc² alongside Newton’s Second Law of Motion. This combination leads to a derivation of relativistic mass relations that express how an object’s inertia changes with its velocity.
  • The book asserts that it is possible to derive important relativistic formulas, including those related to energy, momentum, and even the constancy of the speed of light, through straightforward principles such as conservation laws rather than complex mathematical transformations.

Intuitive Understanding

  • One of the primary goals of Newton and Relativity is to make the concepts of relativity more accessible. Cester emphasizes that concepts like length contraction and time dilation should not be prerequisites but rather outcomes of understanding the relationship between mass, energy, and motion.
  • The author argues for a reunification of classical and relativistic mechanics, suggesting that relativity can be viewed as an extension of Newtonian principles rather than a complete departure from them.

Structure and Content

The book systematically builds on these ideas by presenting a series of proofs that lead from classical mechanics to relativistic mechanics. It covers:

  • Mass-Energy Equivalence E=mc² from classical physics
  • Relativistic mass relation
  • Relativistic theorem of total and kinetic energy
  • Electromagnetic frequency at high speeds
  • Dependence of acceleration on speed
  • Relativistic length contraction
  • Relativistic velocity addition formula
  • Constancy of the speed of light

Cester’s work is positioned as a means to bridge the gap between classical physics and modern theoretical frameworks, making it suitable for readers who may find traditional treatments of relativity daunting.

Overall, Newton and Relativity offers a fresh perspective on fundamental physics, aiming to clarify how Newtonian principles can coexist with and inform our understanding of relativity. This approach is particularly appealing for those seeking a more intuitive grasp of these complex topics without delving deeply into advanced mathematics.

The book is available in English[1], German[2] and Italian[3], published by Books on Demand, and consists of 144 pages.

Back to the questions

What are the main findings presented in “Newton and Relativity”?

The book “Newton and Relativity” by Francesco Cester presents an alternative approach to deriving the special theory of relativity using Newtonian mechanics with variable mass. The main findings presented in the book are:

Key Concepts

  1. Combination of Newton’s Law and E=mc²: The book demonstrates that Newton’s law, combined with the energy-mass equivalence (E=mc²) derived from classical physics, can introduce the theory of relativity in a simple and intuitive way[2].
  2. Validity of Newton’s Law: It shows that the Second Law of Motion remains generally valid even under relativistic conditions, allowing for a direct transition from Newtonian to relativistic mechanics[2].

Derivations and Proofs

The book provides a sequence of comprehensible derivations to prove various aspects of special relativity:

  1. Relativistic Mass Relation: Using E=mc² and Newton’s Second Law of Motion, the book derives the dependence of a physical body’s inertia on its velocity[5].
  2. Fundamental Relativistic Formulas: From the relativistic mass relation, the book derives:
  • The relativistic theorem of total and kinetic energy
  • The expression of electromagnetic frequency at high speeds
  • The dependence of acceleration on speed
  • Relativistic length contraction
  • The relativistic velocity addition formula[5]
  1. Constancy of Light Speed: As a consequence of the relativistic velocity addition formula, the book demonstrates the constancy of the speed of light, regardless of the motion of the emitting light source[5].

Implications

  1. Unification of Classical and Relativistic Mechanics: The approach suggests that classical mechanics should not be viewed as a special case of relativistic mechanics. Instead, the theory of relativity can be interpreted as a logical extension of Newtonian mechanics[2].
  2. Simplified Introduction to Relativity: The book aims to provide a simple introduction to the Theory of Relativity, avoiding difficult concepts at the outset and presenting them as the goal of the alternative approach[2].
  3. Theoretical Proof: The constancy of the speed of light is presented as a demonstrable principle in a purely theoretical way, without relying on experiments[5].

This alternative approach offers a more intuitive method for understanding and deriving the special theory of relativity, bridging the gap between Newtonian mechanics and Einstein’s groundbreaking work[2][5].

Citations:
[1] https://pages.uoregon.edu/jschombe/cosmo/lectures/lec06.html
[2] https://newton-relativity.com
[3] https://www.iop.org/explore-physics/big-ideas-physics/relativity
[4] https://theconversation.com/from-newton-to-einstein-the-origins-of-general-relativity-50013
[5] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/the-book-newton-and-relativity
[6] https://physics.stackexchange.com/questions/123243/link-between-special-relativity-and-newtons-gravitational-law
[7] https://phys.org/news/2015-11-newton-einsteinthe-relativity.html
[8] https://en.wikipedia.org/wiki/Theory_of_Relativity
[9] https://www.britannica.com/science/relativity/General-relativity
[10] https://imagine.gsfc.nasa.gov/educators/programs/cosmictimes/educators/workshops/docs/InquiringIntoNatureUniverse/Newton_Einstein_FactCards.pdf

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What makes the approach in “Newton and Relativity” different from traditional methods?

The approach in “Newton and Relativity” by Francesco Cester differs from traditional methods in several key ways:

  1. It derives relativistic equations without postulating the constancy of the speed of light or using Lorentz transformations[1].
  2. The book starts with Newton’s Second Law of Motion, incorporating variable mass, and combines it with the energy-mass equivalence (E=mc²)[1].
  3. It demonstrates that classical mechanics can be logically extended to encompass relativistic mechanics, rather than treating classical mechanics as a special case of relativity[1].
  4. The Lorentz factor is derived without using Lorentz transformations, which is a significant departure from traditional approaches[1].
  5. It uses principles of conservation of energy and momentum to derive important relativistic formulas, including the relativistic theorem of total and kinetic energy, electromagnetic frequency at high speeds, and relativistic length contraction[1].
  6. The book shows that the Second Law of Motion remains valid even under relativistic conditions, allowing for a direct transition from Newtonian to relativistic mechanics[1].
  7. Concepts such as length contraction, time dilation, and the constancy of the speed of light are presented as goals of this alternative approach rather than prerequisites[1].

This method provides a more intuitive and accessible path to understanding relativistic concepts by building upon familiar Newtonian principles, potentially making the Theory of Relativity more approachable for readers with a background in classical physics[1].

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How does the book “Newton and Relativity” simplify the Theory of Relativity?

The book “Newton and Relativity” by Francesco Cester presents an alternative, simplified approach to deriving the Theory of Relativity[4][7]. This approach makes the theory more accessible and intuitive, especially for readers unfamiliar with the subject. Key aspects of this simplified method include:

  1. It avoids postulating the constancy of the speed of light, which is a fundamental assumption in traditional derivations of special relativity[1].
  2. The approach does not rely on Lorentz transformations to derive relativistic equations, making it more accessible to those familiar with classical mechanics[1].
  3. Starting point: The book begins with the Equivalence Principle of Mass and Energy (E = mc²), which can be derived without using relativistic considerations[4].
  4. Fundamental relationship: It uses Newton’s Second Law of Motion combined with E = mc² to derive the relativistic mass relation, showing how a body’s inertia depends on its velocity[4].
  5. The method demonstrates that Newton’s law remains valid under relativistic conditions, allowing for a direct transition from Newtonian to relativistic mechanics[1].
  6. Derivation process: From this fundamental relationship, the book demonstrates important relativistic formulas using only the principles of conservation of energy and momentum[4]. This includes:
  • Relativistic theorem of total and kinetic energy
  • Expression of electromagnetic frequency at high speeds
  • Dependence of acceleration on speed
  • Relativistic length contraction
  • Relativistic velocity addition formula
  1. Constancy of light speed: Instead of using it as a postulate, the book derives the constancy of the speed of light as a consequence of the relativistic velocity addition formula[4].
  2. Avoiding complex concepts: The approach avoids initially introducing difficult concepts like “length contraction,” “time dilation,” and “Lorentz transformation,” making them the goal rather than the starting point of the derivation[1].

By using this alternative method, the book aims to make the Theory of Relativity more understandable and accessible to a wider audience, while still arriving at the same results as the conventional approach[3].

Citations:
[1] https://newton-relativity.com
[2] https://www.space.com/17661-theory-general-relativity.html
[3] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/notice-to-the-reader
[4] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/the-book-newton-and-relativity
[5] https://www.nationalgeographic.com/science/article/einstein-relativity-thought-experime

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How does the book “Newton and Relativity” use Newton’s Second Law to derive relativistic equations?

The book “Newton and Relativity” by Francesco Cester presents an alternative approach to deriving the special theory of relativity using Newton’s Second Law of Motion in conjunction with the principle of mass-energy equivalence (E = mc²). This method offers a more intuitive and transparent way to arrive at relativistic equations without relying on the traditional postulates of special relativity[1][2].

Key Steps in the Derivation

  1. Starting Point: The approach begins with the mass-energy equivalence formula (E = mc²), which can be derived using classical physics without relativistic considerations[1].
  2. Application of Newton’s Second Law: The derivation combines Newton’s Second Law of Motion with the mass-energy equivalence principle. Specifically, it uses the time derivative of momentum, interpreted in light of variable mass[2].
  3. Relativistic Mass Formula: By applying Newton’s Second Law with variable mass and the energy relation dE = mvdv + v²dm, the relativistic mass formula is derived: \[m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}\] This formula also leads to the expression for relativistic momentum[3].
  4. Derivation of Key Relativistic Equations: Using the relativistic mass formula as a foundation, the book proceeds to derive other important relativistic equations:
  • Relativistic velocity addition formula
  • Constancy of the speed of light (as a consequence, not a postulate)
  • Length contraction and time dilation
  • Lorentz transformations
  • Relativistic Doppler effect
  • Formulas for longitudinal and transversal acceleration[3]

Significance of this Approach

This alternative derivation method has several important implications:

  1. Unification of Classical and Relativistic Mechanics: It demonstrates that relativistic mechanics can be seen as a logical extension of Newtonian mechanics, rather than a separate theory[2].
  2. Intuitive Understanding: By starting from familiar classical concepts, this approach provides a more accessible path to understanding relativistic phenomena[1].
  3. Removal of Postulates: The constancy of the speed of light emerges as a demonstrable principle rather than an assumed postulate[3].
  4. Simplified Derivations: Complex relativistic concepts are derived in a more straightforward manner, making them easier to comprehend[2].

This approach showcases that Newton’s Second Law, when properly interpreted and combined with the mass-energy equivalence principle, can lead to the fundamental equations of special relativity. It offers a bridge between classical and relativistic physics, potentially making the theory of relativity more accessible to students and researchers alike[1][2][3].

Citations:
[1] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/the-book-newton-and-relativity
[2] https://newton-relativity.com
[3] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/sequence-of-relativistic-proofs
[4] https://www.gsjournal.net/Science-Journals/Research%20Papers-Quantum%20Theory%20/%20Particle%20Physics/Download/5518
[5] https://books.google.com/books/about/Newton_and_Relativity.html?id=LsCSDwAAQBAJ
[6] https://scholar.harvard.edu/files/david-morin/files/cmchap11.pdf
[7] https://williamsgj.people.charleston.edu/Relativistic%20Mechanics.pdf
[8] https://dec41.user.srcf.net/notes/IA_L/dynamics_and_relativity.pdf
[9] https://api.pageplace.de/preview/DT0400.9783753411149_A41175413/preview-9783753411149_A41175413.pdfDT0400.9783753411149_A41175413/preview-9783753411149_A41175413.pdf

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How does the book “Newton and Relativity” derive mass-energy equivalence using classical physics?

The book “Newton and Relativity” by Francesco Cester derives the mass-energy equivalence (E=mc²) using classical physics principles through the following steps:

  1. It considers the emission and absorption of radiation between two identical bodies of mass m in an isolated physical system[1].
  2. The proof is based on the fact that a body emitting radiation receives a counter-impulse, causing it to move in the opposite direction[1].
  3. Using the principle of conservation of momentum, it establishes that the momentum of the emitted radiation (E/c) is equal to the momentum of the emitting body[1].
  4. The demonstration considers three key aspects:
  • The time taken for radiation to reach the absorbing body
  • The unchanged position of the center of gravity despite the emitting body’s displacement
  • The conservation of momentum between the radiation and the emitting body[1]
  1. By setting up and solving a system of equations based on these aspects, the relationship Δm = E/c² is derived, establishing the equivalence principle between mass and energy[1].
  2. The book also presents an alternative derivation using the decay of a particle created by electron-positron collision, which results in the emission of two photons in opposite directions[1].

This approach demonstrates that E=mc² can be obtained using only the laws of classical physics, without relying on relativistic axioms. The derivation serves as a connecting link between Newtonian and relativistic mechanics, providing a foundation for further relativistic proofs[1].

Citations:
[1] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/derivation-of-the-mass-energy-equivalence-emc%C2%B2
[2] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/derivation-of-relativistic-energy
[3] https://www.physicsresjournal.com/articles/ijpra-aid1100.php
[4] https://api.pageplace.de/preview/DT0400.9783753411149_A41175413/preview-9783753411149_A41175413.pdf
[5] https://www.researchgate.net/profile/Michael_Schmiechen/publication/206327713_Newton’s_Principia_and_related_’principles’_revisited/links/5db359d24585155e27011456/Newtons-Principia-and-related-principles-revisited.pdf
[6] https://spjnewswire.jrn.columbia.edu/FR/academia/==AVxA3cVFDczJFbaxkWHRnWXRkVWVlM0dVYxI1bVxGZXdVbRpnVUpVYNdlRwp1R4VVZqZlcW1GdP1kVslXUtBHbXtGc2claRhnVWl0dR1GcXNWbnlXWXRXYiZEZaJ2R4l2VthWWWVkWPdVRxcVZFRGaipnRWllaS9WYxQWShVEZPZFMaVUWxY1UNxmS69kVWF2UUZlRZFDcLJ1RWVFVqZ0UUpHbYdVVWdXYxUVP.pd

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Can you explain how Newton’s Second Law is used to derive relativistic mass relations?

Newton’s Second Law can be used to derive relativistic mass relations by incorporating the concept of variable mass and the principle of mass-energy equivalence. Here’s how this derivation works:

  1. Start with Newton’s Second Law in its original form:

\[F = \frac{d(mv)}{dt}\]

  1. Assume that mass can vary with velocity, which is a key difference from classical mechanics[2].
  2. Expand the derivative using the product rule:

\[F = m\frac{dv}{dt} + v\frac{dm}{dt}\]

  1. For motion in the same direction as the force, we can write the work-energy equation:

\[Fds = dE = mvdv + v^2dm\]

  1. Apply the principle of mass-energy equivalence (E = mc²) to replace the energy term:

\[c^2dm = mvdv + v^2dm\]

  1. Rearrange and integrate this differential equation:

\[\int_{m_0}^m \frac{dm}{m} = \int_0^v \frac{vdv}{c^2 – v^2}\]

  1. Solve the integral to obtain the relativistic mass formula:

\[m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}\]

Where m₀ is the rest mass and \[\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\] is the Lorentz factor[2].

This derivation shows that Newton’s Second Law, when applied with the concept of variable mass and mass-energy equivalence, leads directly to the relativistic mass formula. It demonstrates that relativistic mechanics can be viewed as an extension of Newtonian mechanics, rather than a separate theory[2].

This approach provides an alternative to the traditional derivations based on Lorentz transformations, offering a more intuitive understanding of how classical mechanics transitions into relativistic physics at high velocities[1][2].

Citations:
[1] https://physics.stackexchange.com/questions/586867/relativistic-version-of-newtons-2nd-law
[2] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/derivation-of-the-relativistic-mass-formula
[3] https://www.vaia.com/en-us/textbooks/physics/classical-dynamics-of-particles-and-systems-5-edition/chapter-14/problem-38-show-that-the-relativistic-form-of-newtons-second/
[4] https://www.physicsclassroom.com/class/newtlaws/lesson-3/newton-s-second-law
[5] https://www.vaia.com/en-us/textbooks/physics/university-physics-3-edition/chapter-5/problem-99-show-that-the-relativistic-form-of-newtons-second/
[6] https://en.wikipedia.org/wiki?curid=491022
[7] http://kestrel.nmt.edu/~raymond/classes/ph321/notes/rel_dyn/rel_dyn.pdf
[8] https://www

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How does the book “Newton and Relativity” derive relativistic energy?

The book “Newton and Relativity” by Francesco Cester presents an alternative approach to deriving the relativistic energy formula, using a combination of classical physics principles and the mass-energy equivalence. This derivation is based on two key components:

Mass-Energy Equivalence

The derivation begins with the principle of mass-energy equivalence, expressed as $$E = mc^2$$[1]. This relationship is applied to the relativistic mass formula, which expresses the dependence of a body’s mass on its velocity.

Newton’s Second Law of Motion

The author then employs Newton’s Second Law of Motion, interpreted as the time derivative of momentum, in conjunction with the mass-energy equivalence principle[1].

Derivation Process

The derivation follows these steps:

  1. General Energy Equation: The most general case of the energy-mass equivalence is expressed as: $$E = \frac{m_0c^2}{\sqrt{1-\frac{v^2}{c^2}}}$$ where m0 is the rest mass, v is the velocity, and c is the speed of light[2].
  2. Kinetic Energy: The kinetic energy is derived by subtracting the rest energy from the total energy: $$E_k = \frac{m_0c^2}{\sqrt{1-\frac{v^2}{c^2}}} – m_0c^2$$
  3. Differential Equation: Using Newton’s Second Law for variable masses at high speeds, a differential equation is obtained: $$dE_k = v^2dm + mvdv$$
  4. Integration: By substituting the mass-energy equivalence and relativistic mass relations into this differential equation and integrating, the expression for relativistic kinetic energy is derived[2].

Significance

This derivation demonstrates the compatibility of Newton’s law with the Theory of Relativity and provides a more intuitive approach to understanding relativistic energy. It forms part of a chain of proofs that lead from classical physics to Special Relativity, including the derivation of other important relativistic formulas such as the addition of velocities[1][2].

The book emphasizes that this method allows for a transparent derivation of key relativistic concepts, including the constancy of the speed of light, without relying on postulates but rather demonstrating them theoretically[1].

Citations:
[1] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/the-book-newton-and-relativity
[2] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/derivation-of-relativistic-energy
[3] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/derivation-of-the-relativistic-mass-formula
[4] https://pressbooks.bccampus.ca/collegephysics/chapter/relativistic-energy/
[5] https://philarchive.org/archive/GOYDOC-2
[6] https://www.math.uchicago.edu/~may/VIGRE/VIGRE2010/REUPapers/Tolish.pdf
[7] https://philsci-archive.pitt.edu/18020/7/Derivation-of-mechanics-from-conservation-and-relativity-%5Bcomments-deleted%5D-(27-July-2020).pdf
[8] https://www.damtp.cam.ac.uk/user/tong/em/el4.pdf
[9] https://api.pageplace.de/preview/DT0400.9783753411149_A41175413/preview-9783753411149_A41175413.pdf

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How does the book “Newton and Relativity” derive relativistic acceleration?

The book “Newton and Relativity” presents an alternative approach to deriving relativistic acceleration by starting from Newton’s Second Law and incorporating the principle of mass-energy equivalence (E=mc²). This approach differs from the traditional derivation based on Lorentz transformations and provides a more intuitive understanding of relativistic mechanics.

Key Steps in the Derivation

  1. Starting Point: The derivation begins with Newton’s Second Law of Motion, allowing for the possibility of variable mass[1].
  2. Work-Energy Relation: A differential equation for work and energy is derived from the Second Law: $$ Fds = dE = mvdv + v^2dm $$ Here, the term v²dm accounts for the possibility of variable mass at high speeds[1].
  3. Mass-Energy Equivalence: The added kinetic energy dE is replaced with the equivalent mass term c²dm, based on the principle E=mc²[1].
  4. Integration: The resulting differential equation is integrated to obtain the relativistic mass formula: $$ m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} $$ where m₀ is the rest mass and the denominator is the Lorentz factor[1].
  5. Relativistic Acceleration: The relativistic acceleration can be derived from this mass formula and Newton’s Second Law. The relationship between the 3-acceleration in the instantaneous rest frame (proper acceleration $$\vec{a}_0$$) and the 3-acceleration in the lab frame ($$\vec{a}$$) is given by: $$ \vec{a} = \frac{1}{\gamma^2} \left( \vec{a}_0 – \frac{\gamma-1}{\gamma} \frac{(\vec{v} \cdot \vec{a}_0)}{v^2} \vec{v} \right) $$ where γ is the Lorentz factor[2].

Implications and Insights

  • Compatibility with Relativity: This derivation demonstrates that Newton’s Second Law of Motion is compatible with Special Relativity when using the relativistic mass formula[1].
  • Logical Extension: The approach shows that Special Relativity can be viewed as a logical extension of Newtonian mechanics, rather than a separate theory[1][3].
  • Intuitive Understanding: By deriving relativistic effects from familiar Newtonian concepts, this method provides a more intuitive grasp of relativistic mechanics[1][3].
  • Unified Approach: This derivation suggests a way to reunify classical and relativistic mechanics into a single scientific discipline[3].

By using this alternative derivation, the book “Newton and Relativity” aims to provide a simpler and more accessible introduction to the Theory of Relativity, avoiding complex concepts like length contraction and time dilation at the outset[3].

Citations:
[1] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/derivation-of-the-relativistic-mass-formula
[2] https://download.itp3.uni-stuttgart.de/rt2324/Lecture_10.pdf
[3] https://newton-relativity.com
[4] http://scipp.ucsc.edu/~haber/webpage/avector.pdf
[5] https://api.pageplace.de/preview/DT0400.9783753411149_A41175413/preview-9783753411149_A41175413.pdf
[6] https://www.researchgate.net/publication/254235022_Derivations_of_Relativistic_Force_Transformation_Equations

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How does the book “Newton and Relativity” derive relativistic Doppler effect?

The website “Newton and Relativity” derives the relativistic Doppler effect using an alternative approach based on classical physics principles. The derivation follows these key steps:

  1. It starts with the mass-energy equivalence formula E = mc², which is obtained using only classical physics[3][4].
  2. The relativistic mass formula is then derived by combining Newton’s Second Law of Motion with the mass-energy equivalence principle[4].
  3. Using the relativistic mass formula and the principles of conservation of energy and momentum, the website derives the relativistic formula for the frequency of electromagnetic radiation[6]:

$$f_1 = f\sqrt{\frac{c+v}{c-v}} \quad ; \quad f_2 = f\sqrt{\frac{c-v}{c+v}}$$

This formula represents the relativistic Doppler effect, where f₁ is the frequency when the source is moving towards the observer, and f₂ is the frequency when the source is moving away from the observer[6].

The website emphasizes that this approach allows for a more intuitive understanding of relativistic concepts, deriving them from classical physics principles rather than relying on postulates or the Lorentz transformations[4][6].

Citations:
[1] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/the-book-newton-and-relativity
[2] https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-Optics_and_Modern_Physics(OpenStax)/05:__Relativity/5.08:_Doppler_Effect_for_Light
[3] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/derivation-of-the-mass-energy-equivalence-emc%C2%B2
[4] https://newton-relativity.com
[5] https://cupcakephysics.com/relativity/2015/06/07/the-relativistic-doppler-shift.html
[6] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/sequence-of-relativistic-proofs
[7] https://seko-online.de/shop/item/9783752683288
[8] https://www.youtube.com/watch?v=d6ieu0Z8gAo
[9] https://physics.stackexchange.com/questions/61946/relativistic-doppler-effect-derivation
[10] https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

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How does the book “Newton and Relativity” derive relativistic length contraction?

The website “Newton and Relativity” derives the relativistic length contraction using an alternative approach based on the law of conservation of energy, without relying on the Lorentz transformation[1]. The derivation involves the following key steps:

  1. A thought experiment is set up involving the collision of an electron and a positron, creating a new particle.
  2. Two observers are considered: one at rest (O) and one moving vertically (O’) at the same speed as the electron and positron.
  3. For observer O, the energy balance before and after the collision is expressed as: $$m_0c^2 = \frac{2m_{0e}c^2}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$
  4. For observer O’, the particle formed after the collision moves downwards along the Y axis at speed v.
  5. Applying the principle of energy conservation from O’s perspective and using the relation from step 3, the following equation is derived after algebraic manipulations: $$l’=l\sqrt{1-\frac{v^2}{c^2}}$$

This final equation expresses the relativistic contraction of lengths as a function of speed[1]. The website claims that this derivation demonstrates that the Lorentz transformation and Special Relativity can be interpreted as logical extensions of Newtonian mechanics.

Citations:
[1] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/derivation-of-length-contraction
[2] https://www.youtube.com/watch?v=mMXa0OwFzWQ
[3] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/sequence-of-relativistic-proofs
[4] https://www.savemyexams.com/a-level/physics/aqa/17/revision-notes/12-turning-points-in-physics/12-3-special-relativity/12-3-7-length-contraction/
[5] https://courses.lumenlearning.com/suny-physics/chapter/28-3-length-contraction/
[6] https://www.researchgate.net/post/Twin_effect_from_relativity_of_simultaneity_alone_provides_a_totally_wrong_prediction_Is_somebody_aware_of_it/2
[7] http://www.newtonphysics.on.ca/kinetic/
[8] https://www.youtube.com/watch?v=wJ9mHwHWinQ
[9] https://physics.stackexchange.com/questions/188043/derivation-of-length-contraction-from-lorentz-transforms

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Can you explain how the book “Newton and Relativity” proves the Relativistic addition of velocities?

The book “Newton and Relativity” by Francesco Cester presents an alternative approach to deriving the relativistic addition of velocities formula, which differs from the traditional method based on Lorentz transformations. This approach relies on fundamental principles of physics and follows a more intuitive path[1][7].

Key Steps in the Derivation

  1. Mass-Energy Equivalence: The derivation begins with Einstein’s famous equation E = mc², which can be obtained without using relativistic considerations[7].
  2. Newton’s Second Law: The author interprets Newton’s Second Law of Motion as the time derivative of momentum, combining it with the mass-energy equivalence principle[7].
  3. Relativistic Mass Relation: Using these principles, the book derives the relativistic mass relation, which expresses how the inertia of a physical body depends on its velocity[7].
  4. Conservation Principles: The derivation then employs the principles of conservation of energy and momentum to proceed further[1].

The Derivation Process

The book describes a chain of proofs leading from classical physics to Special Relativity. The derivation of the relativistic addition of velocities is the fourth link in this chain, following the derivations of:

  1. The mass-energy equivalence principle (E = mc²)
  2. The relativistic mass formula
  3. The relativistic energy equation[1]

For the specific derivation of the relativistic addition of velocities, the book considers a central collision of two particles resulting in the creation of a new particle. Two observers, moving relative to each other, examine this experiment independently, applying the principles of conservation of energy and momentum[1].

Final Expression

The final expression for the relative velocity as a function of the velocities of the individual particles is given as:

\[ v_{12} = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}} \]

This formula represents the relativistic addition of velocities[1].

Significance of the Approach

This alternative derivation is noteworthy because it arrives at the Lorentz factor without using the Lorentz transformations. It provides a more intuitive understanding of relativistic effects by relating them to the inertia of mass associated with the kinetic energy of moving bodies, in accordance with the Mass-Energy Equivalence principle[7].

By using this method, the book demonstrates that the constancy of the speed of light can be derived as a consequence rather than being assumed as a postulate. This approach offers a new perspective on the Theory of Relativity, making it more accessible and intuitively understandable[7].

Citations:
[1] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/relativistic-addition-of-velocities
[2] https://jwu.pressbooks.pub/collegephysics/chapter/relativistic-addition-of-velocities/
[3] https://openstax.org/books/college-physics-2e/pages/28-4-relativistic-addition-of-velocities
[4] https://en.wikipedia.org/wiki/Relativistic_addition_of_velocities_formula
[5] https://www.researchgate.net/publication/312938573_The_Velocity_Addition_Formula_According_to_Special_Relativity_-_The_Most_Unsustainable_Formula_in_All_Physics
[6] https://galileo-unbound.blog/2023/10/18/relativistic-velocity-addition-einsteins-crucial-insight/
[7] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/the-book-newton-and-relativity
[8] https://www.cantorsparadise.com/relativistic-velocity-addition-c5349ad07907?gi=991d4ce13c85

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What is the significance of the relativistic velocity addition formula in “Newton and Relativity”?

The relativistic velocity addition formula plays a crucial role in the book “Newton and Relativity” by Francesco Cester, serving as a key component in the alternative approach to deriving special relativity. Its significance can be summarized in several points:

  1. It is derived without using Lorentz transformations or postulating the constancy of the speed of light, which is a departure from traditional methods[1].
  2. The formula is obtained using only the principles of conservation of energy and momentum, building upon classical physics concepts[1].
  3. It serves as the fourth link in a chain of proofs leading from classical physics to Special Relativity, following the derivations of mass-energy equivalence, relativistic mass, and relativistic energy[1].
  4. The velocity addition formula is crucial for demonstrating the constancy of the speed of light. By applying this formula, the book shows that the speed of light remains constant for any inertial frame, regardless of the velocity of the light source[1][2].
  5. This derivation challenges the historical belief that Newtonian physics was incompatible with the constancy of the speed of light, providing a bridge between classical and relativistic physics[2].
  6. The formula is expressed as: \[v_{12} = \frac{v_1 + v_2}{1 + \frac{v_1v_2}{c^2}}\] where v12 is the relative velocity between two particles, and v1 and v2 are their individual velocities[1].

By deriving this formula and using it to prove the constancy of the speed of light, the book offers a more intuitive path from Newtonian mechanics to relativistic concepts, potentially making the Theory of Relativity more accessible to those familiar with classical physics[2].

Citations:
[1] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/relativistic-addition-of-velocities
[2] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/the-book-newton-and-relativity
[3] https://www.physicsresjournal.com/articles/ijpra-aid1100.php
[4] https://api.pageplace.de/preview/DT0400.9783753411149_A41175413/preview-9783753411149_A41175413.pdf
[5] https://www.researchgate.net/publication/385344163_Precessional_Motion_Emerging_from_Relativistic_Component_of_External

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Can you explain how the book “Newton and Relativity” proves the constancy of the speed of light?

The book “Newton and Relativity” by Francesco Cester presents an alternative approach to proving the constancy of the speed of light without relying on it as a postulate. The proof follows these key steps:

  1. It starts with the mass-energy equivalence principle (E = mc²), which can be derived using classical physics[1][2].
  2. The Second Law of Motion with variable mass is combined with the mass-energy equivalence[2].
  3. This combination leads to the derivation of the relativistic mass relation, expressing how a body’s inertia depends on its velocity[3].
  4. Using conservation of energy and momentum, various relativistic formulas are derived, including the relativistic velocity addition formula[3].
  5. The constancy of the speed of light is then proved using the relativistic velocity addition formula[1].

The final step involves considering a light source moving relative to an observer. By substituting the speed of the light source and the speed of light emitted by a stationary source into the velocity addition formula, it is shown that the resulting speed of light remains constant (c) for any velocity of the light source[1].

This theoretical proof demonstrates that the speed of light is the same for any inertial frame, regardless of its velocity, without relying on experimental results or postulating the constancy of light speed as an axiom[1][2].

Citations:
[1] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/derivation-constancy-of-speed-of-light
[2] https://newton-relativity.com
[3] https://newton-relativity.com/alternative-approach-to-theory-of-relativity/the-book-newton-and-relativity
[4] https://www.researchgate.net/post/Twin_effect_from_relativity_of_simultaneity_alone_provides_a_totally_wrong_prediction_Is_somebody_aware_of_it/2
[5] https://www.raabcollection.com/literary-autographs/einstein-newton
[6] https://api.pageplace.de/preview/DT0400.9783753411149_A41175413/preview-9783753411149_A41175413.pdf
[7] https://www.bod.de/booksample?json=http%3A%2F%2Fwww.bod.de%2Fgetjson.php%3Fobjk_id%3D2640311%26hash%3Db911fb8f8bdb5bb698c6ac7c00c09077
[8] http://www.claudemercier.com/download/the%20speed%20of%20light%20may%20not%20be%20constant%20de.php

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