9: Special Relativity
- Page ID
- 30486
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Chapter 9 focuses on Special Relativity, including the effects of time dilation and length contraction, the geometry of spacetime, and the \(E = mc^2\) formula. On the foundation that the speed of light and the laws of physics are the same for all observers, you will learn that moving clocks run slower and moving rulers are shorter. In addition, you will become familiar with spacetime diagrams and the relationship between mass and energy. Several practical and fanciful applications will be explored.
- 9.0: Special Relativity Introduction
- Since human forms of transportation, such as bicycles, automobiles, and trains, do not really travel at the extremely high speeds needed to experience relativistic effects, how do we know these effects really exist? We can observe what happens when much smaller, rapidly moving particles known as cosmic rays move through Earth’s atmosphere.
- 9.1: The Principles of Special Relativity
- You will know that the speed of light is the same for all observers. You will know that the laws of physics are the same for all observers in reference frames moving at constant velocity with respect to each other.
- 9.2: Time Dilation
- You will know that moving clocks are slower. You will be able to correctly use the time dilation formula to compare times in different reference frames.
- 9.3: Length Contraction
- You will know that moving rulers are shorter. You will be able to correctly use the length contraction formula to compare lengths in different reference frames.
- 9.4: The Geometry of Special Relativity - Spacetime
- You will recall the mathematical concepts of coordinate systems and the Pythagorean theorem. You will be able to draw/interpret spacetime diagrams for a variety of scenarios.
- 9.5: Applications of Spacetime
- You will explore aspects of the feasibility of interstellar travel. You will understand that events that are simultaneous in one frame are not necessarily simultaneous in another. You will understand that events are real, that the same events happen in both frames, but that observers in different frames disagree about the spacetime coordinates of the events.
- 9.6: Mass and Energy
- You will be able to calculate rest energy and mass. You will understand that mass and energy are different aspects of the same underlying quantity, and that is the total of mass and energy that is truly conserved. You will know that a tiny amount of matter can release a great deal of energy. You will understand that it is possible to produce a pair of charged particles from an energetic photon, and that the annihilation of a particle-antiparticle pair releases energy.
- 9.7: Faster Than Light?
- You will understand the fundamental reasons why particles cannot travel faster than the speed of light.
- 9.8: Wrapping It Up 9 - A Trip to Alpha Centauri
- You will be able to put everything together to demonstrate your understanding of special relativity, using spacetime diagrams.
- 9.9: Mission Report 9 - A Trip to Alpha Centauri
- You will be able to put everything together to demonstrate your understanding of special relativity, using spacetime diagrams.