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Special Theory of Relativity

Interpret motion between different objects that are moving at constant speeds relative to each other.

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Credit: Robert Lopez
Source: CK-12 Foundation
License: CC BY-NC 3.0

Probably the most famous equation in physics, Albert Einstein’s equation shows that energy and mass are just different forms of the same thing.

Amazing But True

  • Mass-energy equivalence is the physics concept that the mass of an object is the measure of its energy content. Another way of saying this is that there exists a constant, proportional relationship between the mass in a system and the energy in a system. This relationship is given by


where \begin{align*}E\end{align*} is the energy, \begin{align*}m\end{align*} is the mass and \begin{align*}c\end{align*} \begin{align*}(3\times 10^8 m/s)\end{align*} is the speed of light.

  • The above equation is also known as the rest energy and \begin{align*}m\end{align*}, sometimes written as \begin{align*}m_0\end{align*}, is known as the rest mass. When an object has momentum, the above equation is still a really good approximation until the speed approaches a fraction of the speed of light. When an object is moving with a velocity that is at a fraction of the speed of light, the energy-mass equivalence equation must be rewritten to include the momentum

\begin{align*}E=(m_0c^2)^2 + (pc)^2\end{align*}

where \begin{align*}m_0\end{align*} is the rest mass and \begin{align*}p\end{align*} is the momentum.

  • View One Form of the Derivation of The Mass-Energy Equation at the video below: 


  • See How The Full Equation Comes Into Being at the video below: 


Show What You Know

Using the information provided above, answer the following questions.

  1. If a classmate tells you that a photon breaks the mass energy equation, how you would explain to them that they were wrong? 
  2. How is it that no matter how hard you try, any object with mass will never reach the speed of light \begin{align*}c\end{align*}?
  3. Are there any cases where light can travel faster than \begin{align*}c\end{align*}?

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Image Attributions

  1. [1]^ Credit: Robert Lopez; Source: CK-12 Foundation; License: CC BY-NC 3.0

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