Theory of Relativity Quiz

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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 (B)

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. (C)</p> Signup and view all the answers

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

<p>False (B)</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. (B)</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 (B)</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 (B)</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 (B)</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 (D)</p> Signup and view all the answers

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

<p>True (A)</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 (A)</p> Signup and view all the answers

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

<p>True (A)</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. (B)</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 (B)</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. (D)</p> Signup and view all the answers

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

<p>True (A)</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 (C)</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 (B)</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>$t &gt; t_0$ (C)</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 (B)</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. (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 (B)</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 $u_z'$. (D)</p> Signup and view all the answers

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

<p>False (B)</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

Flashcards

Proper Time

The time interval between two events that occur at the same place in an observer's frame of reference.

Time Dilation

The phenomenon where a clock moving relative to an observer ticks slower than a stationary clock.

Proper Time (𝑡0)

The time measured by a clock at rest.

Time (𝑡)

The time measured by a clock in motion relative to an observer.

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Mirror Separation (𝐿0)

The distance between two mirrors in a clock.

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Speed of Light (𝑐)

The speed of light in a vacuum.

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Time Interval (𝑡)

The duration of a time interval, measured by an observer in a different frame of reference than the proper time.

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Speed of the Clock (𝑣)

The speed of a clock relative to an observer.

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Modern Physics' Genesis

The beginning of modern physics is marked by Planck's discovery of energy quantization in blackbody radiation and Einstein's theories of relativity and light's quantum nature.

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Theory of Relativity

The theory of relativity, proposed by Albert Einstein, deals with the motion of objects moving at speeds close to the speed of light. It states that all motion is relative.

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Special Relativity

The special theory of relativity, developed in 1905, focuses on comparing measurements made in different frames of reference moving at constant velocities relative to each other.

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General Relativity

The general theory of relativity, developed around 1916, deals with accelerated frames of reference and the concept of gravity.

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Frame of Reference

A frame of reference is a location where an observer can make measurements and observe events.

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Inertial Frame

A frame of reference that moves with a constant velocity relative to another inertial frame is also an inertial frame.

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Non-Inertial Frame

Frames of reference that accelerate with respect to inertial frames are non-inertial frames and do not follow the law of inertia.

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Equivalence of Inertial Frames

All inertial frames are equally valid, and there's no absolute or universal frame of reference. The observer's motion influences their perception of events.

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Proper Time (t0)

The time interval measured by an observer at rest relative to a clock.

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Time Interval (t)

The time interval measured by an observer who is moving relative to a clock.

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Relative Speed (v)

The speed of an object relative to an observer.

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Speed of Light (c)

The speed of light in a vacuum, a constant value.

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Lorentz Factor (γ)

The ratio of the time dilation between two observers.

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Time Dilation Equation

The formula used to calculate time dilation.

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Principle of Relativity

The principle that all inertial observers observe the same laws of physics.

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Length Contraction

The apparent shortening of the distance between two points when an object moves at speeds close to the speed of light.

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Time Dilation (Relativistic Doppler Effect)

The time it takes for a signal to be received by an observer moving at relativistic speed. It is time dilated or slowed compared to the time interval measured in the observer's rest frame.

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The Speed of Light (c)

The speed of light in a vacuum, approximately 299,792,458 meters per second.

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Rest Frame

A reference frame in which an object is at rest.

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Moving Frame

A frame of reference in which an object is moving relative to the observer.

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Proper Length (L0)

The length of an object as measured by an observer in the object's rest frame.

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Apparent Length (L)

The length of an object as measured by an observer in a moving frame.

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ux

The component of an object's velocity along the x-axis as measured by an observer in frame S.

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ux'

The component of an object's velocity along the x-axis as measured by an observer in frame S'.

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uy

The component of an object's velocity along the y-axis as measured by an observer in frame S.

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uy'

The component of an object's velocity along the y-axis as measured by an observer in frame S'.

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uz

The component of an object's velocity along the z-axis as measured by an observer in frame S.

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uz'

The component of an object's velocity along the z-axis as measured by an observer in frame S'.

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Galilean Transformation of Velocity

In a stationary frame (S) an object moves with velocity v, in another frame (S') moving with velocity v relative to S, the object's velocity, according to Galilean transformation, is simply the difference between the velocities in S and S', which is v - v.

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Second Postulate of Special Relativity

The principle of special relativity stating that the speed of light in vacuum is constant irrespective of the observer's motion or the source's motion.

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Lorentz Transformation

The transformation between coordinates of two inertial frames of reference that moves at a constant velocity relative to each other, according to special relativity.

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γ (Lorentz Factor)

A factor in the Lorentz transformation that relates time and space coordinates in different inertial frames of reference, it depends on the relative velocity between the frames.

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Lorentz Transformation of Position

The relationship between the spatial coordinates of an event in one frame of reference (S) and another frame (S') moving at a constant velocity, according to the Lorentz transformation.

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Lorentz Transformation of Time

The relationship between the time coordinates of an event in one frame of reference (S) and another frame (S') moving at a constant velocity, according to the Lorentz transformation.

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First Postulate of Special Relativity

The first postulate of special relativity states that the laws of physics are the same in all inertial frames of reference.

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Lorentz Transformation - Consistency with Principles of Special Relativity

The Lorentz transformation is a coordinate transformation that fulfills the first postulate of special relativity, meaning, the laws of physics are the same for all observers in inertial frames. It also explains the second postulate of special relativity, the constancy of speed of light.

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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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