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Questions and Answers
What is the speed of light in a vacuum according to the theory of relativity?
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.
The general theory of relativity is concerned with inertial reference frames.
False (B)
Who developed the special theory of relativity?
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 ______.
Inertia states that an object at rest will stay at rest unless acted upon by a ______.
Match the following types of frames of reference with their properties:
Match the following types of frames of reference with their properties:
Which of the following statements is true regarding inertial frames?
Which of the following statements is true regarding inertial frames?
All bodies and places in motion are considered to have external forces acting on them.
All bodies and places in motion are considered to have external forces acting on them.
What does the special theory of relativity concern itself with?
What does the special theory of relativity concern itself with?
What happens to the time interval measured by a clock in motion compared to one at rest?
What happens to the time interval measured by a clock in motion compared to one at rest?
The proper time is determined by events that occur at different locations within an observer's frame of reference.
The proper time is determined by events that occur at different locations within an observer's frame of reference.
What is the term for the time interval that is shorter and occurs in a moving spacecraft?
What is the term for the time interval that is shorter and occurs in a moving spacecraft?
The duration $t$ of events in motion is __________ compared to the proper time $t_0$.
The duration $t$ of events in motion is __________ compared to the proper time $t_0$.
Match the terms with their descriptions:
Match the terms with their descriptions:
In the equation $t_0 = \frac{2L_0}{c}$, what does $L_0$ represent?
In the equation $t_0 = \frac{2L_0}{c}$, what does $L_0$ represent?
The light pulse in the moving clock follows a straight path as seen from the ground.
The light pulse in the moving clock follows a straight path as seen from the ground.
How does an observer on the ground perceive the ticking of the moving clock?
How does an observer on the ground perceive the ticking of the moving clock?
What is the total time Dick experiences for his roundtrip voyage to the star?
What is the total time Dick experiences for his roundtrip voyage to the star?
Dick receives a total of 50 signals from Jane during his voyage.
Dick receives a total of 50 signals from Jane during his voyage.
What is the formula to calculate the Lorentz factor used in Dick's voyage regarding length contraction?
What is the formula to calculate the Lorentz factor used in Dick's voyage regarding length contraction?
When traveling at 0.8c, the distance L for Dick’s trip is shortened to _____ light-years.
When traveling at 0.8c, the distance L for Dick’s trip is shortened to _____ light-years.
Match the following terms with their descriptions:
Match the following terms with their descriptions:
How many years does Jane wait for Dick's return?
How many years does Jane wait for Dick's return?
Jane is 70 years old at the end of Dick's voyage.
Jane is 70 years old at the end of Dick's voyage.
What is the rate at which Dick and Jane are separated during the outward trip?
What is the rate at which Dick and Jane are separated during the outward trip?
What is the relationship between velocity components measured in the S frame and the S' frame according to the Galilean transformation?
What is the relationship between velocity components measured in the S frame and the S' frame according to the Galilean transformation?
The speed of light is the same in both the S and S' frames according to the Galilean transformation.
The speed of light is the same in both the S and S' frames according to the Galilean transformation.
What is the term that represents the factor in the Lorentz transformation equations?
What is the term that represents the factor in the Lorentz transformation equations?
In the Lorentz transformation, the equation relating x and x' is given by x' = _____ (x - vt).
In the Lorentz transformation, the equation relating x and x' is given by x' = _____ (x - vt).
Match the variables with their meanings in the context of the Lorentz transformation:
Match the variables with their meanings in the context of the Lorentz transformation:
What happens to the time coordinates t and t' in the context of the Lorentz transformation?
What happens to the time coordinates t and t' in the context of the Lorentz transformation?
In the Galilean transformation, the component vy' is equal to vy.
In the Galilean transformation, the component vy' is equal to vy.
What does the Lorentz transformation fulfill in special relativity?
What does the Lorentz transformation fulfill in special relativity?
What does the symbol $L_0$ represent in the context of the equations provided?
What does the symbol $L_0$ represent in the context of the equations provided?
An observer on the ground considers that the moving clock in the spacecraft ticks faster than the stationary clock.
An observer on the ground considers that the moving clock in the spacecraft ticks faster than the stationary clock.
What is the meaning of the symbol $t_0$ in the equations discussed?
What is the meaning of the symbol $t_0$ in the equations discussed?
The equation relating time dilation can be expressed as $t = rac{t_0}{ ext{______}}$
The equation relating time dilation can be expressed as $t = rac{t_0}{ ext{______}}$
Match the variables with their correct meanings:
Match the variables with their correct meanings:
In the provided equations, which inequality is always true for a moving object?
In the provided equations, which inequality is always true for a moving object?
The path of the light pulse from the ground clock is considered a straight line in the spacecraft's reference frame.
The path of the light pulse from the ground clock is considered a straight line in the spacecraft's reference frame.
What occurs to the time interval as observed by every observer on clocks in motion?
What occurs to the time interval as observed by every observer on clocks in motion?
What is the relation of the velocity components between an observer in S and an observer in S' according to the Lorentz transformation?
What is the relation of the velocity components between an observer in S and an observer in S' according to the Lorentz transformation?
An observer in frame S will measure a speed of light emitted from frame S' as less than c.
An observer in frame S will measure a speed of light emitted from frame S' as less than c.
Write the equation that relates the velocity component $u_x$ in frame S and $u_x'$ in frame S'.
Write the equation that relates the velocity component $u_x$ in frame S and $u_x'$ in frame S'.
If the spacecraft is moving at 0.9c with respect to the earth, the observer on earth measures the speed as _____ c.
If the spacecraft is moving at 0.9c with respect to the earth, the observer on earth measures the speed as _____ c.
Which statement describes $u_y$ in frame S?
Which statement describes $u_y$ in frame S?
The inverse Lorentz transformation equations do not consider the speed of light c.
The inverse Lorentz transformation equations do not consider the speed of light c.
What will a stationary observer measure if light is emitted in the direction of motion of S'?
What will a stationary observer measure if light is emitted in the direction of motion of S'?
Flashcards
Proper Time
Proper Time
The time interval between two events that occur at the same place in an observer's frame of reference.
Time Dilation
Time Dilation
The phenomenon where a clock moving relative to an observer ticks slower than a stationary clock.
Proper Time (𝑡0)
Proper Time (𝑡0)
The time measured by a clock at rest.
Time (𝑡)
Time (𝑡)
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Mirror Separation (𝐿0)
Mirror Separation (𝐿0)
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Speed of Light (𝑐)
Speed of Light (𝑐)
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Time Interval (𝑡)
Time Interval (𝑡)
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Speed of the Clock (𝑣)
Speed of the Clock (𝑣)
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Modern Physics' Genesis
Modern Physics' Genesis
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Theory of Relativity
Theory of Relativity
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Special Relativity
Special Relativity
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General Relativity
General Relativity
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Frame of Reference
Frame of Reference
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Inertial Frame
Inertial Frame
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Non-Inertial Frame
Non-Inertial Frame
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Equivalence of Inertial Frames
Equivalence of Inertial Frames
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Proper Time (t0)
Proper Time (t0)
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Time Interval (t)
Time Interval (t)
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Relative Speed (v)
Relative Speed (v)
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Speed of Light (c)
Speed of Light (c)
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Lorentz Factor (γ)
Lorentz Factor (γ)
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Time Dilation Equation
Time Dilation Equation
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Principle of Relativity
Principle of Relativity
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Length Contraction
Length Contraction
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Time Dilation (Relativistic Doppler Effect)
Time Dilation (Relativistic Doppler Effect)
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The Speed of Light (c)
The Speed of Light (c)
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Rest Frame
Rest Frame
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Moving Frame
Moving Frame
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Proper Length (L0)
Proper Length (L0)
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Apparent Length (L)
Apparent Length (L)
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ux
ux
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ux'
ux'
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uy
uy
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uy'
uy'
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uz
uz
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uz'
uz'
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Galilean Transformation of Velocity
Galilean Transformation of Velocity
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Second Postulate of Special Relativity
Second Postulate of Special Relativity
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Lorentz Transformation
Lorentz Transformation
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γ (Lorentz Factor)
γ (Lorentz Factor)
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Lorentz Transformation of Position
Lorentz Transformation of Position
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Lorentz Transformation of Time
Lorentz Transformation of Time
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First Postulate of Special Relativity
First Postulate of Special Relativity
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Lorentz Transformation - Consistency with Principles of Special Relativity
Lorentz Transformation - Consistency with Principles of Special Relativity
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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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