15.6 Special Relativity

• What does special relativity describe the relationship between?

  Space and time
• The Principle of Relativity states that the laws of physics are the same for all observers in uniform motion
• The speed of light in a vacuum is the same for all observers regardless of their motion relative to the light source.


  True
• 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 formula for mass-energy equivalence in special relativity?

  $E =$$mc^{2}$
• The Principle of Relativity states that the laws of physics are the same for all observers in uniform motion
• What is the second postulate of special relativity regarding the speed of light?

  Constant speed of light
• Time and space are absolute and universal in special relativity.

  False
• The Principle of Relativity states that the laws of physics are the same for all observers in uniform motion
• 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
• What is the phenomenon called where time appears to slow down for a moving observer relative to a stationary observer?

  Time dilation
• The formula for time dilation is t' = t_{0} / \gamma</latex>, where $t'$ is the time measured by the moving observer
• Time is considered absolute and universal in classical mechanics.


  True
• Arrange the following variables in the time dilation formula from left to right:

  1️⃣ $t'$

  2️⃣ $t_{0}$

  3️⃣ $\gamma$
• Match the time dilation concept with its description:

  Classical Mechanics ↔️ Absolute and universal

  Special Relativity ↔️ Relative and depends on observer motion
• 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
• What is the formula for the Lorentz factor?

  $\gamma =$$1 / \sqrt{1 - v^{2} / c^{2}}$
• In classical mechanics, time is considered absolute
• 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
• What is special relativity primarily concerned with?

  Space and time
• 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
• In special relativity, velocities do not add linearly
• In special relativity, mass increases with velocity.

  True
• What is the relationship between mass and energy according to special relativity?

  E = mc^2</latex>
• 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
• Arrange the features of classical mechanics and special relativity in contrasting pairs:

  1️⃣ Velocity Addition: Speeds add linearly (Classical Mechanics) ||| Velocity Addition: Speeds do not add linearly (Special Relativity)

  2️⃣ Time: Absolute and universal (Classical Mechanics) ||| Time: Relative and varies with observer motion (Special Relativity)

  3️⃣ Space: Absolute and universal (Classical Mechanics) ||| Space: Relative and contracts with observer motion (Special Relativity)

  4️⃣ Mass: Constant (Classical Mechanics) ||| Mass: Increases with velocity (Special Relativity)

  5️⃣ Energy: Separate from mass (Classical Mechanics) ||| Energy: Mass and energy are interchangeable (Special Relativity)
• What does the Principle of Relativity state?

  Laws of physics are invariant
• The Constant Speed of Light postulate states that the speed of light in a vacuum is the same for all observers
• The postulates of special relativity challenge the classical assumptions about the absolute nature of space, time, and other physical quantities.


  True
• What is the formula for time dilation in special relativity?

  $t' =$$t_{0} / \gamma$
• In the time dilation formula, $\gamma$ represents the Lorentz factor
• If a spaceship travels at 0.8c, time aboard appears slower to an Earth observer by a factor of approximately 1.67.


  True
• What is the phenomenon called where the length of a moving object appears to shorten?

  Length contraction
• 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
• In special relativity, length is absolute and universal.

  False
• What is length contraction in special relativity?

  Shortening of moving object
• The formula for length contraction is L' = $L_{0} \sqrt{1 - \frac{v^{2}}{c^{2}}}$
• What does $L'$ represent in the length contraction formula?


  Length measured by moving observer
• What does $L_{0}$ represent in the length contraction formula?


  Length measured by stationary observer
• Length is absolute and universal in classical mechanics.

  True