Theory of Relativity Quiz
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Questions and Answers

What is the speed of light in a vacuum according to the theory of relativity?

  • 3 × 10^4 m/s
  • 3 × 10^8 m/s (correct)
  • 3 × 10^6 m/s
  • 3 × 10^10 m/s

    • The general theory of relativity is concerned with inertial reference frames.

    False

    Who developed the special theory of relativity?

    Albert Einstein

    Inertia states that an object at rest will stay at rest unless acted upon by a ______.

    <p>force</p> Signup and view all the answers

    Match the following types of frames of reference with their properties:

    <p>Inertial Frame = Constant velocity Non-Inertial Frame = Accelerating Special Theory = Non-universal frame General Theory = Gravity and acceleration</p> Signup and view all the answers

    Which of the following statements is true regarding inertial frames?

    <p>An inertial frame moves with constant velocity.</p> Signup and view all the answers

    All bodies and places in motion are considered to have external forces acting on them.

    <p>False</p> Signup and view all the answers

    What does the special theory of relativity concern itself with?

    <p>Comparison of measurements in different inertial frames</p> Signup and view all the answers

    What happens to the time interval measured by a clock in motion compared to one at rest?

    <p>It ticks slower than the rest clock.</p> Signup and view all the answers

    The proper time is determined by events that occur at different locations within an observer's frame of reference.

    <p>False</p> Signup and view all the answers

    What is the term for the time interval that is shorter and occurs in a moving spacecraft?

    <p>proper time</p> Signup and view all the answers

    The duration $t$ of events in motion is __________ compared to the proper time $t_0$.

    <p>longer</p> Signup and view all the answers

    Match the terms with their descriptions:

    <p>Proper time = Time measured in a moving frame Time dilation = The phenomenon where time intervals appear longer for moving observers Rest clock = Clock that remains stationary relative to an observer Light pulse = Signal that marks the time interval in a clock</p> Signup and view all the answers

    In the equation $t_0 = \frac{2L_0}{c}$, what does $L_0$ represent?

    <p>The distance between the mirrors</p> Signup and view all the answers

    The light pulse in the moving clock follows a straight path as seen from the ground.

    <p>False</p> Signup and view all the answers

    How does an observer on the ground perceive the ticking of the moving clock?

    <p>Slower than the rest clock</p> Signup and view all the answers

    What is the total time Dick experiences for his roundtrip voyage to the star?

    <p>30 years</p> Signup and view all the answers

    Dick receives a total of 50 signals from Jane during his voyage.

    <p>True</p> Signup and view all the answers

    What is the formula to calculate the Lorentz factor used in Dick's voyage regarding length contraction?

    <p>L = L0 √(1 - v²/c²)</p> Signup and view all the answers

    When traveling at 0.8c, the distance L for Dick’s trip is shortened to _____ light-years.

    <p>12</p> Signup and view all the answers

    Match the following terms with their descriptions:

    <p>Lorentz factor = Used to calculate time dilation and length contraction Time dilation = The phenomenon of time appearing to pass at different rates Length contraction = The shortening of distance traveled at high speed Doppler effect = Change in frequency of signals due to relative motion</p> Signup and view all the answers

    How many years does Jane wait for Dick's return?

    <p>50 years</p> Signup and view all the answers

    Jane is 70 years old at the end of Dick's voyage.

    <p>True</p> Signup and view all the answers

    What is the rate at which Dick and Jane are separated during the outward trip?

    <p>0.8c</p> Signup and view all the answers

    What is the relationship between velocity components measured in the S frame and the S' frame according to the Galilean transformation?

    <p>Velocity in S' depends on the velocities from S.</p> Signup and view all the answers

    The speed of light is the same in both the S and S' frames according to the Galilean transformation.

    <p>False</p> Signup and view all the answers

    What is the term that represents the factor in the Lorentz transformation equations?

    <p>gamma (γ)</p> Signup and view all the answers

    In the Lorentz transformation, the equation relating x and x' is given by x' = _____ (x - vt).

    <p>γ</p> Signup and view all the answers

    Match the variables with their meanings in the context of the Lorentz transformation:

    <p>x = Position in S frame x' = Position in S' frame t = Time in S frame t' = Time in S' frame</p> Signup and view all the answers

    What happens to the time coordinates t and t' in the context of the Lorentz transformation?

    <p>They can differ.</p> Signup and view all the answers

    In the Galilean transformation, the component vy' is equal to vy.

    <p>True</p> Signup and view all the answers

    What does the Lorentz transformation fulfill in special relativity?

    <p>The first postulate of special relativity.</p> Signup and view all the answers

    What does the symbol $L_0$ represent in the context of the equations provided?

    <p>Vertical distance between the mirrors</p> Signup and view all the answers

    An observer on the ground considers that the moving clock in the spacecraft ticks faster than the stationary clock.

    <p>False</p> Signup and view all the answers

    What is the meaning of the symbol $t_0$ in the equations discussed?

    <p>Time interval on clock at rest relative to an observer</p> Signup and view all the answers

    The equation relating time dilation can be expressed as $t = rac{t_0}{ ext{______}}$

    <p>$ ext{√(1 - v²/c²)}$</p> Signup and view all the answers

    Match the variables with their correct meanings:

    <p>$t$ = Time interval on clock in motion $t_0$ = Time interval on clock at rest $v$ = Speed of relative motion $c$ = Speed of light</p> Signup and view all the answers

    In the provided equations, which inequality is always true for a moving object?

    <p>$t &gt; t_0$</p> Signup and view all the answers

    The path of the light pulse from the ground clock is considered a straight line in the spacecraft's reference frame.

    <p>False</p> Signup and view all the answers

    What occurs to the time interval as observed by every observer on clocks in motion?

    <p>Clocks in motion tick more slowly than clocks at rest.</p> Signup and view all the answers

    What is the relation of the velocity components between an observer in S and an observer in S' according to the Lorentz transformation?

    <p>They transform based on the velocity v and the speed of light c.</p> Signup and view all the answers

    An observer in frame S will measure a speed of light emitted from frame S' as less than c.

    <p>False</p> Signup and view all the answers

    Write the equation that relates the velocity component $u_x$ in frame S and $u_x'$ in frame S'.

    <p>u_x = (u_x' + v) / (1 + (vu_x'/c^2))</p> Signup and view all the answers

    If the spacecraft is moving at 0.9c with respect to the earth, the observer on earth measures the speed as _____ c.

    <p>0.9</p> Signup and view all the answers

    Which statement describes $u_y$ in frame S?

    <p>It transforms independently of $u_x'$ and $u_z'$.</p> Signup and view all the answers

    The inverse Lorentz transformation equations do not consider the speed of light c.

    <p>False</p> Signup and view all the answers

    What will a stationary observer measure if light is emitted in the direction of motion of S'?

    <p>The speed of light as c.</p> Signup and view all the answers

    Study Notes

    Special Relativity

    • Modern physics began in 1900 with Max Planck's discovery of quantized energy in blackbody radiation.
    • Albert Einstein's theory of relativity describes motion at speeds close to the speed of light (c = 3 × 108 m/s).
    • Einstein's theory of relativity affects the measurement of time and space when comparing different frames of reference.
    • Special relativity considers inertial frames (constant velocity) while general relativity deals with accelerated frames and gravity.

    Frames of Reference

    • A frame of reference is a place where an observer makes measurements.
    • Inertial frame: A frame moving at a constant velocity relative to an inertial frame itself is also an inertial frame. This concept is described by Newton's first law (law of inertia).
    • Non-inertial frame: A frame accelerating relative to an inertial frame where Newton's first law doesn't hold true.

    Postulates of Special Relativity

    • Postulate 1: The laws of physics are the same in all inertial frames of reference.
    • Postulate 2: The speed of light in a vacuum has the same value in all inertial frames of reference (c = 3 × 108 m/s).

    Michelson-Morley Experiment

    • The Michelson-Morley experiment aimed to detect the ether (a hypothetical medium for light propagation).
    • The negative result of the experiment disproved the existence of ether and supported the idea that the speed of light is constant in all directions, independent of the motion of the observer.

    Time Dilation

    • A moving clock ticks slower than a stationary clock, relative to a stationary observer.
    • The time interval measured by a stationary observer is longer than the proper time interval measured by an observer in motion with the clock.

    Length Contraction

    • An object moving relative to an observer appears shorter in the direction of motion than its proper length (length when at rest).
    • The length of the moving object is contracted along the direction of motion.

    Twin Paradox

    • The twin paradox describes a thought experiment where one twin travels at a high speed and returns to find the other twin older.
    • Time dilation and length contraction explain this apparent paradox.

    Doppler Effect in Light

    • The Doppler effect in light involves a change in the observed frequency of light waves depending on the relative motion between the source and the observer.
    • The observed frequency of light is affected by the relative motion between the source and the observer (either approaching or receding).

    Relativistic Momentum

    • The classical definition of linear momentum (p = mv) is modified in special relativity, incorporating relativistic mass, which is the mass as measured in a particular frame of reference.

    Relativistic Energy

    • The total energy of an object (E) is given by E = mc² + KE.
    • The rest energy of an object is given by E₀ = mc².

    Lorentz Transformation

    • The Lorentz transformation is used to relate measurements of space and time between two inertial frames of reference moving relative to each other in uniform motion.
    • These formulas show how coordinates and time change between two moving frames.

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    Modern Physics, Chapter 1: Special Relativity (2024-2025) PDF

    Description

    Test your knowledge about key concepts in the theory of relativity, including inertial frames, proper time, and the speed of light in a vacuum. This quiz will challenge your understanding of how motion affects time and reference frames.

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