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Questions and Answers
According to the concept of length contraction, how does the length of an object appear to an observer when the object is in motion relative to the observer?
According to the concept of length contraction, how does the length of an object appear to an observer when the object is in motion relative to the observer?
- Longer than its proper length.
- Shorter than its proper length. (correct)
- Wider than its proper length.
- The same as its proper length.
What is 'proper length' in the context of length contraction?
What is 'proper length' in the context of length contraction?
- The length of an object measured by an observer in relative motion.
- The length of an object measured when it is at rest. (correct)
- The length of an object when it is accelerating.
- The average length of an object in motion.
A spaceship is traveling at a significant fraction of the speed of light. Which dimension of the spaceship will appear contracted to a stationary observer?
A spaceship is traveling at a significant fraction of the speed of light. Which dimension of the spaceship will appear contracted to a stationary observer?
- Only the width of the spaceship.
- The dimension parallel to the direction of motion. (correct)
- The dimensions perpendicular to the direction of motion.
- Only the height of the spaceship.
Imagine two observers, one stationary on Earth and another inside a spaceship moving at 0.8c relative to Earth. They both observe a meter stick oriented along the direction of the spaceship's motion. Which observer measures the proper length of the meter stick?
Imagine two observers, one stationary on Earth and another inside a spaceship moving at 0.8c relative to Earth. They both observe a meter stick oriented along the direction of the spaceship's motion. Which observer measures the proper length of the meter stick?
A meter stick is moving parallel to its length at a velocity v relative to an observer. If the observer measures the length of the stick to be 0.5 meters, what happens to the measured length if the velocity v increases?
A meter stick is moving parallel to its length at a velocity v relative to an observer. If the observer measures the length of the stick to be 0.5 meters, what happens to the measured length if the velocity v increases?
A spacecraft of proper length 100 m is observed to have a length of 80 m as it passes by Earth. What can be inferred about the spacecraft's velocity?
A spacecraft of proper length 100 m is observed to have a length of 80 m as it passes by Earth. What can be inferred about the spacecraft's velocity?
A muon has a certain lifetime when measured at rest. If the same muon is observed moving at a speed close to the speed of light, what happens to its observed lifetime?
A muon has a certain lifetime when measured at rest. If the same muon is observed moving at a speed close to the speed of light, what happens to its observed lifetime?
What is 'proper time' in the context of time dilation?
What is 'proper time' in the context of time dilation?
A clock is moving at a speed v relative to an observer. According to time dilation, how does the rate of the moving clock appear to the observer, compared to an identical clock at rest?
A clock is moving at a speed v relative to an observer. According to time dilation, how does the rate of the moving clock appear to the observer, compared to an identical clock at rest?
If a spaceship travels at 50% the speed of light, how will time passage on the spaceship appear to an observer on Earth?
If a spaceship travels at 50% the speed of light, how will time passage on the spaceship appear to an observer on Earth?
Two observers, one on Earth and another on a spaceship moving at a relativistic speed, each have identical clocks. If both observe the Earth for one hour according to their own clocks, which observer measures a longer time interval for the observation of the Earth?
Two observers, one on Earth and another on a spaceship moving at a relativistic speed, each have identical clocks. If both observe the Earth for one hour according to their own clocks, which observer measures a longer time interval for the observation of the Earth?
A certain particle has a lifetime of 10 nanoseconds when at rest. If it is accelerated to a speed of 0.9c, what is its observed lifetime according to a stationary observer?
A certain particle has a lifetime of 10 nanoseconds when at rest. If it is accelerated to a speed of 0.9c, what is its observed lifetime according to a stationary observer?
A spaceship is traveling at a constant velocity past Earth. If an astronaut on the spaceship shines a light beam in the direction of the spaceship's motion, how is the speed of light observed by someone on Earth, according to the principle of the constancy of the speed of light?
A spaceship is traveling at a constant velocity past Earth. If an astronaut on the spaceship shines a light beam in the direction of the spaceship's motion, how is the speed of light observed by someone on Earth, according to the principle of the constancy of the speed of light?
Which of the following scenarios demonstrates the concept of relativistic velocity addition?
Which of the following scenarios demonstrates the concept of relativistic velocity addition?
A spaceship is moving at a velocity of 0.6c relative to Earth. It launches a probe in the same direction at a velocity of 0.8c relative to the spaceship. What is the velocity of the probe relative to Earth?
A spaceship is moving at a velocity of 0.6c relative to Earth. It launches a probe in the same direction at a velocity of 0.8c relative to the spaceship. What is the velocity of the probe relative to Earth?
A spaceship moving at 0.5c relative to an observer on Earth launches a probe directly towards the Earth at a speed of 0.5c relative to the spaceship. What is the speed of the probe as observed from Earth?
A spaceship moving at 0.5c relative to an observer on Earth launches a probe directly towards the Earth at a speed of 0.5c relative to the spaceship. What is the speed of the probe as observed from Earth?
What is the main difference between Galilean and relativistic velocity addition?
What is the main difference between Galilean and relativistic velocity addition?
What is the significance of the Lorentz transformation in special relativity?
What is the significance of the Lorentz transformation in special relativity?
Which of the following is a key difference between the Galilean transformation and the Lorentz transformation?
Which of the following is a key difference between the Galilean transformation and the Lorentz transformation?
In the context of simultaneity, what does it mean for two events to be simultaneous?
In the context of simultaneity, what does it mean for two events to be simultaneous?
According to the principle of relativity of simultaneity, do two events that are simultaneous in one frame of reference have to be simultaneous in all other frames of reference?
According to the principle of relativity of simultaneity, do two events that are simultaneous in one frame of reference have to be simultaneous in all other frames of reference?
Imagine a spaceship moving at a relativistic speed past an observer on Earth. Inside the spaceship, two lights at opposite ends flash simultaneously. According to the observer on Earth, which light flashes first?
Imagine a spaceship moving at a relativistic speed past an observer on Earth. Inside the spaceship, two lights at opposite ends flash simultaneously. According to the observer on Earth, which light flashes first?
Two observers are in relative motion. Observer A sees two events occur at the same time but at different locations. How will Observer B, who is moving relative to Observer A, perceive these events?
Two observers are in relative motion. Observer A sees two events occur at the same time but at different locations. How will Observer B, who is moving relative to Observer A, perceive these events?
A train is moving at a constant velocity. A light flashes simultaneously at the front and back of the train, according to an observer on the train. How will an observer standing on the ground next to the tracks perceive the flashes?
A train is moving at a constant velocity. A light flashes simultaneously at the front and back of the train, according to an observer on the train. How will an observer standing on the ground next to the tracks perceive the flashes?
What is the relationship between space and time intervals as viewed by different observers in relative motion, according to special relativity?
What is the relationship between space and time intervals as viewed by different observers in relative motion, according to special relativity?
An observer on Earth measures a spaceship moving at a significant fraction of the speed of light. The observer notes the length of the ship and the time it takes to pass a certain point. How would these measurements compare to those made by an astronaut on the spaceship?
An observer on Earth measures a spaceship moving at a significant fraction of the speed of light. The observer notes the length of the ship and the time it takes to pass a certain point. How would these measurements compare to those made by an astronaut on the spaceship?
Consider two events that occur at the same location in a certain inertial frame. Which of the following statements is true about the time interval between these events as measured in a different inertial frame moving at a constant velocity relative to the first?
Consider two events that occur at the same location in a certain inertial frame. Which of the following statements is true about the time interval between these events as measured in a different inertial frame moving at a constant velocity relative to the first?
Imagine two spaceships, A and B. Ship A is equipped with a laser pointed towards ship B. Both are moving at significant fractions of the speed of light, but at different velocities relative to a stationary observer. How does the speed of the laser light emitted from ship A appear to the observer in ship B?
Imagine two spaceships, A and B. Ship A is equipped with a laser pointed towards ship B. Both are moving at significant fractions of the speed of light, but at different velocities relative to a stationary observer. How does the speed of the laser light emitted from ship A appear to the observer in ship B?
Which of the following is a direct consequence of the principle of relativity of simultaneity?
Which of the following is a direct consequence of the principle of relativity of simultaneity?
Flashcards
Length Contraction
Length Contraction
The apparent shortening of moving objects along the direction of motion.
Improper Length
Improper Length
Length measured by an observer in relative motion to the moving object.
Proper Length
Proper Length
Length measured when the object is at rest relative to the observer.
Length of spacecraft (at rest)
Length of spacecraft (at rest)
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Moving Observer's Length
Moving Observer's Length
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Direction of Contraction
Direction of Contraction
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Time Dilation
Time Dilation
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Proper Time
Proper Time
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Improper Time
Improper Time
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Velocity in Moving Frame (v')
Velocity in Moving Frame (v')
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Velocity on Earth (vx)
Velocity on Earth (vx)
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Relative Velocity (u)
Relative Velocity (u)
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Lorentz Transformation
Lorentz Transformation
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Relativity of Simultaneity
Relativity of Simultaneity
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Study Notes
- Modern Physics deals with length contraction, time dilation and the relativity of simultaneity
Length Contraction
- Moving objects appear shorter to an observer
- Length is measured when an object is at rest, otherwise known as proper length
- The length measured by an observer in relative motion to the moving object is the improper length
- Length contraction can be calculated: $l_v = l_0\sqrt{1 - \frac{v^2}{c^2}}$
- $l_0$ is the length of the object in the rest frame (m)
- $l_v$ is the length of the object observed from a different frame in relative motion (m)
- $v$ is the velocity of the frame of reference relative to the rest frame ($ms^{-1}$)
- $c$ is the speed of light ($3 \times 10^8 ms^{-1}$)
- Length contraction only occurs in the direction parallel to the relative motion between the observer and the object
Time Dilation
- Moving clocks tick slower
- Time dilation is the time interval between two events as recorded by a stationary clock versus a moving clock
- Time dilation can be calculated as: $t = \frac{t_0}{\sqrt{1 - \frac{v^2}{c^2}}}$
- It is the time interval between two events measured by the same clock
- The time interval between two events in a moving frame is measured by an observer on the ground
- Proper time is measured by clocks at rest in a reference frame in which the two events occur at the same coordinates
Relativistic Velocity Addition
- Calculates that the speed of the moving object according to observer on Earth S
- Moving frame according to observer in spaceship S'
- Relative velocity between S and S'
- Since observer S is at rest, then u is equal to the velocity of S' - velocity of spaceship
- Relativistic velocity addition can be calculated as: $ v_x = \frac{v'_x + u}{1+ \frac{uv'_x}{c^2}}$
Lorentz Transformation
- Transformation from one reference frame to another
- Coordinates for the moving frame:
- $x' = \frac{x - ut}{\sqrt{1 - u^2/c^2}} = \gamma(x - ut)$
- $y' = y$
- $z' = z$
- $t' = \frac{t - ux/c^2}{\sqrt{1 - u^2/c^2}}$
- Coordinates for the fixed frame:
- $x = \frac{x'+ut'}{\sqrt{1 - u^2/c^2}}$
- $y = y'$
- $z = z'$
- $t = \frac{t'+(u/c^2)x'}{\sqrt{1 - u^2/c^2}}$
Relativity of Simultaneity
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Events that are simultaneous in one reference frame may not be simultaneous in another
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According to the observer in the spaceship, two events occur at the same time but different locations
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Two events happen at different locations according to S'
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According to the observer on Earth, the two events occur at different locations at different points in time
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Transforming to the moving frame equations becomes:
- $x'_2 -x'_1 = \frac{(x_2 -x_1) + v(t_2 -t_1)}{\sqrt{1 - (v^2/c^2)}}$
- $t'_2 -t'_1= \frac{(t_2 -t_1) + \frac{v}{c^2}(x_2 -x_1)}{\sqrt{1 - (v^2/c^2)}}$
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