15.6 Special Relativity

• What does special relativity describe the relationship between?

  Space and time
• Match the feature with its description in special relativity:

  Velocity Addition ↔️ Speeds do not add linearly

  Time ↔️ Relative and varies with motion

  Space ↔️ Relative and contracts with motion

  Mass ↔️ Increases with velocity
• What is the second postulate of special relativity regarding the speed of light?

  Constant speed of light
• Match the feature with its description in classical mechanics or special relativity:

  Velocity Addition in Classical Mechanics ↔️ Linear addition

  Velocity Addition in Special Relativity ↔️ Relativistic velocity addition
• The formula for time dilation is t' = t_{0} / \gamma</latex>, where $t'$ is the time measured by the moving observer
• Match the time dilation concept with its description:

  Classical Mechanics ↔️ Absolute and universal

  Special Relativity ↔️ Relative and depends on observer motion
• In classical mechanics, time is considered absolute
• Match the postulate of special relativity with its description:

  Principle of Relativity ↔️ The laws of physics are the same for all observers in uniform motion

  Constant Speed of Light ↔️ The speed of light in a vacuum is the same for all observers
• What is the relationship between mass and energy according to special relativity?

  E = mc^2</latex>
• What does the Principle of Relativity state?

  Laws of physics are invariant
• What is the formula for time dilation in special relativity?

  $t' =$$t_{0} / \gamma$
• What is the phenomenon called where the length of a moving object appears to shorten?

  Length contraction
• What is length contraction in special relativity?

  Shortening of moving object
• What does $L_{0}$ represent in the length contraction formula?


  Length measured by stationary observer
• What is the mass-energy equivalence equation in special relativity?

  E = mc^{2}</latex>
• In classical mechanics, mass and energy are considered separate and independent quantities.
• Match the feature with its description in special relativity:

  Velocity Addition ↔️ Speeds do not add linearly

  Time ↔️ Relative and varies with motion

  Energy ↔️ Mass and energy are interchangeable
• Time dilation occurs when the passage of time appears to slow down for a moving observer relative to a stationary observer.
• What is the key prediction of special relativity related to time?

  Time dilation
• If a spaceship is traveling at 0.8c relative to Earth, by what factor will time slow down for the crew?

  $\gamma \approx 1.67$
• What does $L_{0}$ represent in the length contraction formula?


  Length measured by stationary observer
• Length contraction and time dilation are interconnected results of relative motion
• What does 'm' represent in the $E =$$mc^{2}$ equation?


  Mass of the object
• Match the velocity addition formula with its correct theory:

  Classical Mechanics ↔️ $v' =$$v +$$u$

  Special Relativity ↔️ $v' =$$(v + u) / (1 + vu / c^{2})$
• In classical mechanics, space and time are considered interconnected aspects of a single continuum.

  False
• The Principle of Relativity states that the laws of physics are the same for all observers in uniform motion
• What is the formula for mass-energy equivalence in special relativity?

  $E =$$mc^{2}$
• Time and space are absolute and universal in special relativity.

  False
• Time is considered absolute and universal in classical mechanics.


  True
• If a spaceship is traveling at 0.8c, the time measured by the spaceship crew will be slower by a factor of approximately 1.67
• If a spaceship is traveling at 0.8c relative to Earth, the time measured by the spaceship crew will be slower than the time measured by an observer on Earth.

  True
• In special relativity, velocities do not add linearly
• A light beam emitted from a spaceship moving at 0.8c relative to Earth will be measured by Earth observers to travel at 1.8c.

  False
• The Constant Speed of Light postulate states that the speed of light in a vacuum is the same for all observers
• In the time dilation formula, $\gamma$ represents the Lorentz factor
• The formula for length contraction is $L' =$$L_{0} \sqrt{1 - \frac{v^{2}}{c^{2}}}$, where $L'$ is the length measured by the moving
• The formula for length contraction is L' = $L_{0} \sqrt{1 - \frac{v^{2}}{c^{2}}}$
• Length is absolute and universal in classical mechanics.

  True
• Mass and energy are interchangeable according to special relativity.


  True
• What are the two key postulates of special relativity?

  Principle of Relativity and Constant Speed of Light