Define a reference frame .

A reference frame is defined as a set of coordinates to record the position and time of events.

True or False? A reference frame is the point of view at which an object located at a specific coordinate is at rest.

True. A reference frame is the point of view at which an object located at a specific coordinate is at rest.

Define the term inertial reference frame .

An inertial reference frame is defined as a reference frame that is non-accelerating .

True or False? All inertial reference frames are moving at a constant velocity with respect to each other.

True. All inertial reference frames are moving at a constant velocity with respect to each other.

True or False? All locations within the Universe are moving relative to each other.

True. All locations within the Universe are moving relative to each other.

A person on one side of the road sees a car moving to the left. In which direction does a person on the opposite side of the road see the car moving?

The person on the opposite side of the road will see the car moving to the right from their frame of reference.

A person on a train platform sees a person on a moving train as moving. Who is moving from the frame of reference of the person on the train?

The person on the train sees themselves as stationary, so from their frame of reference, the person on the platform is moving relative to them.

Define the term Galilean relativity .

Galilean relativity is when Newton's laws of motion are the same in all inertial reference frames.

True or False? In Galilean relativity, the same laws of physics apply, regardless of the frame of reference, as long as the reference frame is moving in a straight line at a constant velocity.

True. In Galilean relativity , the same laws of physics apply, regardless of the frame of reference, as long as the reference frame is moving in a straight line at a constant velocity .

True or False? In Galilean relativity, an object moving with a constant velocity in one reference frame will have a constant velocity in another reference frame.

True. In Galilean relativity, an object moving with a constant velocity in one reference frame will have a constant velocity in another reference frame, although the magnitude of its velocity will be different .

What are the Galilean transform equations used for?

The Galilean transform equations are used to convert velocity, position, and time between reference frames.

State Einstein's two postulates of special relativity.

Einstein's two postulates of special relativity are: the laws of physics are the same in all inertial reference frames the speed of light in a vacuum is the same in all inertial reference frames

What is the condition for special relativity to apply?

Special relativity applies when objects are travelling close to the speed of light when time and space are also relative to the frame of reference.

True or False? Two different observers will always measure the speed of light to be the same value in their own reference frames.

True. Two different observers will always measure the speed of light to be the same value in their own reference frames.

True or False? Velocity addition only works at speeds much lower than the speed of light.

True. Velocity addition, or the Galilean transformation for the velocity of an object moving within the moving reference frame, only works at speeds much lower than the speed of light.

True or False? Galilean transformations predict that objects can travel faster than the speed of light.

True. Galilean transformations predict that objects can travel faster than the speed of light, but this cannot be the case, so for objects travelling at speeds close to the speed of light, Lorentz transformations must be used to correct this.

What are the Lorentz transformations ?

The Lorentz transformations are corrections to the Galilean transformations used when objects are travelling close to the speed of light.

True or False? The Lorentz factor for any moving object will always be less than 1.

False. The Lorentz factor for any moving object will always be greater than 1. This is because the speed of any moving object will always be less than the speed of light.

When should the Lorentz velocity addition transformations be used?

The Lorentz velocity addition transformations should be used when an object is moving both the object and the moving reference frame are travelling close to the speed of light

Define the term invariant quantity .

Invariant quantities are quantities that are the same in all inertial reference frames.

Name three invariant quantities.

The invariant quantities are: proper time proper length space-time interval speed of light in a vacuum

Define proper length .

Proper length is the length of an object measured in a reference frame where the object is at rest relative to the observer.

Proper time is the time interval between two events measured in the reference frame where the events occur in the same place. Proper time is measured by an observer within their own rest frame.

True or False? The units of the space-time interval are metres.

True. The units of the space-time interval are metres.

Define time dilation .

Time dilation is the apparent slowing of time for an object moving at close to the speed of light as measured by a stationary observer.

True or False? For a spaceship travelling at close to the speed of light, time slows down on the spaceship from the reference frame of a stationary observer on Earth.

True. For a spaceship travelling at close to the speed of light, time slows down on the spaceship from the reference frame of a stationary observer on Earth.

True or False? For a spaceship travelling at close to the speed of light, time slows down on Earth from the reference frame of the spaceship.

True. For a spaceship travelling at close to the speed of light, time slows down on Earth from the reference frame of the spaceship because the spaceship is stationary in its own reference frame and Earth is moving at close to the speed of light relative to them.

A passenger on a train travelling close to the speed of light watches time pass on a clock onboard the train. A stationary observer on a platform sees the train clock as the train hurtles through the station. Which observer measures proper time?

The observer measuring proper time in this situation is the passenger on the train . The clock being used to measure the time in both reference frames is the clock on the train. Therefore, proper time is the time measured by the clock on the train in its own rest frame .

A passenger on a train travelling close to the speed of light watches time pass on a platform clock as the train hurtles through the station. An observer on the platform is also watching the same clock. Which observer measures proper time?

The observer who measures proper time in this situation is the person on the platform . The clock being used to measure the time in both reference frames is the clock on the platform. Therefore, proper time is the time being measured by the clock on the platform in its own rest frame .

Define length contraction .

Length contraction is the apparent shortening of the length of an object moving at close to the speed of light as measured by a stationary observer.

True or False? For a spaceship travelling at close to the speed of light, the length of an object on the spaceship appears shorter from the reference frame of a stationary observer on Earth.

True. For a spaceship travelling at close to the speed of light, the length of an object on the spaceship appears shorter from the reference frame of a stationary observer on Earth.

True or False? For a spaceship travelling at close to the speed of light, the length of an object on Earth appears shorter from the reference frame of the spaceship.

True. For a spaceship travelling at close to the speed of light, the length of an object on Earth appears shorter from the reference frame of the spaceship. This is because the spaceship is stationary in its own reference frame and Earth is moving at close to the speed of light relative to them.

True or False? Length measurements for length dilation calculations are assumed to be taken with a ruler within each observer's reference frame.

True. Length measurements for length dilation calculations are assumed to be taken with a ruler within each observer's reference frame. This is because the stationary observer would also see the moving ruler contract as well as the object it is measuring.

True or False? Length measurements in length contraction calculations are assumed to be taken at the same time in each reference frame.

True. Length measurements in length contraction calculations are assumed to be taken at the same time in each reference frame.

A passenger on a train travelling close to the speed of light measures the length of the train using a tape measure onboard the train. A stationary observer on a platform measures the length of the train as it passes through the station using their own tape measure. Which observer measures proper length?

The observer measuring proper length in this situation is the passenger on the train . Moving objects contract along their direction of motion. Therefore, proper length is the length measured from the measured object's rest frame. The contracted length is measured by the observer at rest to the moving object.

A passenger on a train travelling close to the speed of light measures the length of the train station sign as they hurtle through the station. A stationary observer on the platform also measures the length of the train station sign using their own tape measure. Which observer measures proper length?

The observer measuring proper length in this situation is the person on the platform . Moving objects contract along their direction of motion. Therefore, proper length is the length measured from the measured object's rest frame. The contracted length is measured by the observer at rest to the moving object; for the person on the train, the platform is moving relative to them.

Define the term relativity of simultaneity .

Relativity of simultaneity refers to the fact that two spatially simultaneous events do not necessarily occur at the same time, depending on the observer's reference frame.

True or False? According to special relativity, two events that occur simultaneously in one reference frame may not occur simultaneously in another reference frame.

True. According to special relativity, two events that occur simultaneously in one reference frame may not occur simultaneously in another reference frame. This is also referred to as the relativity of simultaneity.

True or False? In Galilean relativity, simultaneity is absolute.

True. In Galilean relativity, simultaneity is absolute . If two events occur at the same time in one reference frame, then they also occur at the same time in other reference frames.

True or False? On a spacetime diagram, the dimensions of time and space both have units of metres.

True. On a spacetime diagram, the dimensions of time and space both have units of metres.

What is the name of a line on a spacetime graph?

A line on a spacetime digram is known as a world line .

True or False? On a spacetime diagram, the steeper the gradient, the slower the motion of the object through spacetime.

True. On a spacetime diagram, the steeper the gradient, the slower the motion of the object through spacetime.

State the relativistic phenomena that can be shown on a spacetime diagram.

The relativistic phenomena that can be shown on a spacetime diagram are: multiple reference frames simultaneity time dilation length contraction

State an experiment that provides evidence for time dilation and length contraction.

The muon lifetime experiment provides evidence for time dilation and length contraction.

In the muon lifetime experiment, one reference frame is that of the muon, and another reference frame is that of an observer on Earth. Who measures the proper time?

In the muon lifetime experiment, the muon measures proper time , and the observer on Earth measures dilated time.

In the muon lifetime experiment, one reference frame is that of the muon, and another reference frame is that of an observer on Earth. Who measures the proper length?

In the muon lifetime experiment, the observer on Earth measures proper length , and the muon measures contracted length. Proper length is the length measured from the measured object's rest frame. The measured object is the distance between the atmosphere where the muons are produced and the detectors. The rest frame is therefore the stationary observer on Earth.

True or False? Muons are produced in the upper atmosphere as a result of pion decays produced by cosmic rays.

True. Muons are produced in the upper atmosphere as a result of pion decays produced by cosmic rays.

True or False? Muons have an average lifetime of 2.2 μs.

True. Muons have an average lifetime of 2.2μs.

IBPhysicsDPHLFlashcardsSpace, Time & MotionGalilean & Special Relativity

Galilean & Special Relativity (DP IB Physics)

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Define a reference frame.
A reference frame is defined as a set of coordinates to record the position and time of events.
True or False?
A reference frame is the point of view at which an object located at a specific coordinate is at rest.
True.
A reference frame is the point of view at which an object located at a specific coordinate is at rest.
Define the term inertial reference frame.
An inertial reference frame is defined as a reference frame that is non-accelerating.
True or False?
All inertial reference frames are moving at a constant velocity with respect to each other.
True.
All inertial reference frames are moving at a constant velocity with respect to each other.
True or False?
All locations within the Universe are moving relative to each other.
True.
All locations within the Universe are moving relative to each other.
A person on one side of the road sees a car moving to the left.
In which direction does a person on the opposite side of the road see the car moving?
The person on the opposite side of the road will see the car moving to the right from their frame of reference.
A person on a train platform sees a person on a moving train as moving.
Who is moving from the frame of reference of the person on the train?
The person on the train sees themselves as stationary, so from their frame of reference, the person on the platform is moving relative to them.
Define the term Galilean relativity.
Galilean relativity is when Newton's laws of motion are the same in all inertial reference frames.
True or False?
In Galilean relativity, the same laws of physics apply, regardless of the frame of reference, as long as the reference frame is moving in a straight line at a constant velocity.
True.
In Galilean relativity, the same laws of physics apply, regardless of the frame of reference, as long as the reference frame is moving in a straight line at a constant velocity.
True or False?
In Galilean relativity, an object moving with a constant velocity in one reference frame will have a constant velocity in another reference frame.
True.
In Galilean relativity, an object moving with a constant velocity in one reference frame will have a constant velocity in another reference frame, although the magnitude of its velocity will be different.
What are the Galilean transform equations used for?
The Galilean transform equations are used to convert velocity, position, and time between reference frames.
The position and time in reference frame $S$ are denoted as $x$ , $y$ , and $t$ .
State the notation for this time and these positions from reference frame $S'$ .
The position and time in reference frame $S$ are denoted as $x$ , $y$ , and $t$ .
In reference frame $S'$ , these are $x'$ , $y'$ , and $t'$ .
State the Galilean transformation equation from $x$ to $x'$ .
The Galilean transformation equation from $x$ to $x'$ is: $x' = x - v t$
Where:
- $x'$ = $x$ coordinate in the moving reference frame
- $x$ = $x$ coordinate in the stationary reference frame
- $v$ = velocity of the moving reference frame, $S'$ , with respect to the stationary reference frame, $S$
- $t$ = time at which the event occurred
State the Galilean transformation equation from $y$ to $y'$ .
The Galilean transformation equation from $y$ to $y'$ is: $y = y'$
The coordinates of $y$ are the same in both reference frames because the relative motion is only ever considered in the $x$ direction.
State the Galilean transformation equation from $z$ to $z'$ .
The Galilean transformation equation from $z$ to $z'$ is: $z = z'$
The coordinates of $z$ are the same in both reference frames because the relative motion is only ever considered in the $x$ direction.
State the Galilean transformation equation from $t$ to $t'$ .
The Galilean transformation equation from $t$ to $t'$ is: $t = t'$
The coordinates of $t$ are the same in both reference frames because the origin of both reference frames coincide at $t = 0$ . Both observers agree on the time of the event, but disagree on the position that event occurs at.
State the Galilean transformation equation from $x'$ to $x$ .
The Galilean transformation equation from $x'$ to $x$ is: $x = x' + v t$
Where:
- $x$ = $x$ coordinate in the stationary reference frame
- $x'$ = $x$ coordinate in the moving reference frame
- $v$ = velocity of the moving reference frame, $S'$ , with respect to the stationary reference frame, $S$
- $t$ = time at which the event occurred
State the Galilean transformation equation from $u$ to $u'$ .
The Galilean transformation equation from $u$ to $u'$ is: $u' = u - v$
Where:
- $u'$ = velocity of an object, as measured from within the moving reference frame, $S'$
- $u$ = velocity of an object, as measured from the stationary reference frame, $S$
- $v$ = velocity of the moving reference frame, $S'$ , with respect to the stationary reference frame, $S$
State the Galilean transformation equation from $u'$ to $u$ .
The Galilean transformation equation from $u'$ to $u$ is: $u = u' + v$
Where:
- $u$ = velocity of an object, as measured from the stationary reference frame, $S$
- $u'$ = velocity of an object, as measured from within the moving reference frame, $S'$
- $v$ = velocity of the moving reference frame, $S'$ , with respect to the stationary reference frame, $S$
State Einstein's two postulates of special relativity.
Einstein's two postulates of special relativity are:
- the laws of physics are the same in all inertial reference frames
- the speed of light in a vacuum is the same in all inertial reference frames
What is the condition for special relativity to apply?
Special relativity applies when objects are travelling close to the speed of light when time and space are also relative to the frame of reference.
True or False?
Two different observers will always measure the speed of light to be the same value in their own reference frames.
True.
Two different observers will always measure the speed of light to be the same value in their own reference frames.
True or False?
Velocity addition only works at speeds much lower than the speed of light.
True.
Velocity addition, or the Galilean transformation for the velocity of an object moving within the moving reference frame, only works at speeds much lower than the speed of light.
True or False?
Galilean transformations predict that objects can travel faster than the speed of light.
True.
Galilean transformations predict that objects can travel faster than the speed of light, but this cannot be the case, so for objects travelling at speeds close to the speed of light, Lorentz transformations must be used to correct this.
What are the Lorentz transformations?
The Lorentz transformations are corrections to the Galilean transformations used when objects are travelling close to the speed of light.
State the equation for the Lorentz factor.
The equation for the Lorentz factor is $γ = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$
Where:
- $γ$ = Lorentz factor (no units)
- $v$ = velocity of moving object, measured in metres per second (m s^–1)
- $c$ = speed of light in a vacuum, measured in metres per second (m s^–1)
True or False?
The Lorentz factor for any moving object will always be less than 1.
False.
The Lorentz factor for any moving object will always be greater than 1.
This is because the speed of any moving object will always be less than the speed of light.
State the Lorentz transformation equation for $x$ to $x'$ .
The Lorentz transformation equation for $x$ to $x'$ is: $x' = γ (x - v t)$
Where:
- $x'$ = $x$ coordinate as measured from the moving reference frame, $S'$
- $γ$ = Lorentz factor (no units)
- $x$ = $x$ coordinate as measured from the stationary reference frame, $S$
- $v$ = speed of moving reference frame, $S'$ , relative to the stationary reference frame, $S$
- $t$ = time of the event as measured from the stationary reference frame, $S$
State the Lorentz transformation equation for $x'$ to $x$ .
The Lorentz transformation equation for $x'$ to $x$ is: $x = γ (x' - v t')$
Where:
- $x$ = $x$ coordinate as measured from the stationary reference frame, $S$
- $γ$ = Lorentz factor (no units)
- $x'$ = $x$ coordinate as measured from the moving reference frame, $S'$
- $v$ = speed of moving reference frame, $S'$ , relative to the stationary reference frame, $S$
- $t'$ = time of the event as measured from the moving reference frame, $S'$
State the Lorentz transformation equation for $t'$ to $t$ .
The Lorentz transformation equation for $t'$ to $t$ is: $t = γ (t' - \frac{v x'}{c^{2}})$
Where:
- $t$ = time of the event as measured from the stationary reference frame, $S$
- $γ$ = Lorentz factor (no units)
- $t'$ = time of the event as measured from the moving reference frame, $S'$
- $v$ = speed of the moving reference frame, $S'$ , relative to the stationary reference frame, $S$
- $x'$ = $x$ coordinate as measured from the moving reference frame, $S'$
- $c$ = speed of light, constant in both reference frames
State the Lorentz transformation equation for $t$ to $t'$ .
The Lorentz transformation equation for $t$ to $t'$ is: $t' = γ (t - \frac{v x}{c^{2}})$
Where:
- $t'$ = time of the event as measured from the moving reference frame, $S'$
- $t$ = time of the event as measured from the stationary reference frame, $S$
- $γ$ = Lorentz factor (no units)
- $t$ = time of the event as measured from the stationary reference frame, $S$
- $v$ = speed of the moving reference frame, $S'$ , relative to the stationary reference frame, $S$
- $x$ = $x$ coordinate as measured from the stationary reference frame, $S$
- $c$ = speed of light, constant in both reference frames
State the Lorentz transformation equation from $y$ to $y'$ .
The Lorentz transformation equation from $y$ to $y'$ is: $y = y'$
The coordinates of $y$ are the same in both reference frames because the relative motion is only ever considered in the $x$ direction.
State the Lorentz transformation equation from $z$ to $z'$ .
The Lorentz transformation equation from $z$ to $z'$ is: $z = z'$
The coordinates of $z$ are the same in both reference frames because the relative motion is only ever considered in the $x$ direction.
State the Lorentz velocity addition equation for $u$ to $u'$ .
The Lorentz velocity addition equation for $u$ to $u'$ is: $u' = \frac{u - v}{1 - \frac{u v}{c^{2}}}$
Where:
- $u'$ = velocity of an object, as measured from the moving reference frame, $S'$
- $u$ = velocity of an object, as measured from the stationary reference frame, $S$
- $v$ = velocity of moving reference frame, $S'$ , relative to the stationary reference frame, $S$
- $c$ = speed of light, constant in both reference frames
State the Lorentz velocity addition equation for $u'$ to $u$ .
The Lorentz velocity addition equation for $u'$ to $u$ is: $u = \frac{u' - v}{1 + \frac{u' v}{c^{2}}}$
Where:
- $u$ = velocity of an object, as measured from the stationary reference frame, $S$
- $u'$ = velocity of an object, as measured from the moving reference frame, $S'$
- $v$ = velocity of moving reference frame, $S'$ , relative to the stationary reference frame, $S$
- $c$ = speed of light, constant in both reference frames
When should the Lorentz velocity addition transformations be used?
The Lorentz velocity addition transformations should be used when
- an object is moving
- both the object and the moving reference frame are travelling close to the speed of light
A rocket ship travelling close to the speed of light launches a probe, which also travels close to the speed of light. A stationary observer on a nearby planet witnesses the launch of the probe.
Assign the correct terms $u$ , $u'$ , $v$ , $S$ and $S'$ to this situation.
A rocket ship travelling close to the speed of light launches a probe, which also travels close to the speed of light. A stationary observer on a nearby planet witnesses the launch of the probe.
- $u$ = the velocity of the probe as measured by the stationary observer on the nearby planet
- $u'$ = the velocity of the probe as measured by an observer in the moving rocket ship
- $v$ = the velocity of the moving space rocket relative to the stationary observer on the nearby planet
- $S$ = the stationary reference frame of the observer on the nearby planet
- $S'$ = the moving reference frame of the observer on the moving rocket ship
A rocket ship travelling at $0.8 c$ launches a probe, which travels at $0.6 c$ as measured by the pilot of the rocket ship. A stationary observer on a nearby planet witnesses the launch of the probe.
What is the speed of the probe as measured by the stationary observer?
The speed of the probe as measured by a stationary observer on a nearby planet is $u = 0.9 c (1 s . f .)$
A rocket ship travelling at $v = 0.8 c$ launches a probe, which travels at $u' = 0.6 c$ as measured by the pilot of the rocket ship, $S'$ . A stationary observer, $S$ , on a nearby planet witnesses the launch of the probe.
- $u = \frac{u' + v}{1 + \frac{u' v}{c^{2}}} = \frac{0.6 c + 0.8 c}{1 + \frac{0.6 c \times 0.8 c}{c^{2}}} = \frac{1.4 c}{1.48} = 0.9 c$
Define the term invariant quantity.
Invariant quantities are quantities that are the same in all inertial reference frames.
Name three invariant quantities.
The invariant quantities are:
- proper time
- proper length
- space-time interval
- speed of light in a vacuum
Define the space-time interval.
The space-time interval is the change in space-time between two events as represented on a four-dimensional coordinate system ( $x$ , $y$ , $z$ , $t$ ) in special relativity. The space-time interval is an invariant quantity that is the same in all inertial reference frames.
State the equation for the space-time interval.
The equation for the space-time interval is ${(∆ s)}^{2} = {(c ∆ t)}^{2} - {(∆ x)}^{2}$
Where:
- $∆ s$ = space-time interval, measured in metres (m)
- $c$ = speed of light in a vacuum, measured in metres per second (m s^-1)
- $∆ t$ = temporal separation, measured in seconds (s)
- $∆ s$ = spatial separation, measured in metres (m)
Define proper length.
Proper length is the length of an object measured in a reference frame where the object is at rest relative to the observer.
Define proper time.
Proper time is the time interval between two events measured in the reference frame where the events occur in the same place. Proper time is measured by an observer within their own rest frame.
True or False?
Motion can be described as spanning both time and space.
True.
Motion can be described as spanning both time and space using a 4D coordinate system ( $x$ , $y$ , $z$ , $t$ ); this is the space-time interval.
True or False?
The units of the space-time interval are metres.
True.
The units of the space-time interval are metres.
Define time dilation.
Time dilation is the apparent slowing of time for an object moving at close to the speed of light as measured by a stationary observer.
State the equation for time dilation.
The equation for time dilation is $∆ t = γ ∆ t_{0}$
Where:
- $∆ t$ = dilated time interval, as measured by an observer moving relative to the clock being used to measure proper time
- $γ$ = Lorentz factor
- $∆ t_{0}$ = proper time interval, as measured by the clock in its own rest frame
True or False?
For a spaceship travelling at close to the speed of light, time slows down on the spaceship from the reference frame of a stationary observer on Earth.
True.
For a spaceship travelling at close to the speed of light, time slows down on the spaceship from the reference frame of a stationary observer on Earth.
True or False?
For a spaceship travelling at close to the speed of light, time slows down on Earth from the reference frame of the spaceship.
True.
For a spaceship travelling at close to the speed of light, time slows down on Earth from the reference frame of the spaceship because the spaceship is stationary in its own reference frame and Earth is moving at close to the speed of light relative to them.
A passenger on a train travelling close to the speed of light watches time pass on a clock onboard the train. A stationary observer on a platform sees the train clock as the train hurtles through the station.
Which observer measures proper time?
The observer measuring proper time in this situation is the passenger on the train. The clock being used to measure the time in both reference frames is the clock on the train.
Therefore, proper time is the time measured by the clock on the train in its own rest frame.
A passenger on a train travelling close to the speed of light watches time pass on a platform clock as the train hurtles through the station. An observer on the platform is also watching the same clock.
Which observer measures proper time?
The observer who measures proper time in this situation is the person on the platform. The clock being used to measure the time in both reference frames is the clock on the platform.
Therefore, proper time is the time being measured by the clock on the platform in its own rest frame.
Define length contraction.
Length contraction is the apparent shortening of the length of an object moving at close to the speed of light as measured by a stationary observer.
State the equation for length contraction.
The equation for length contraction is $L = \frac{L_{0}}{γ}$
Where:
- $L$ = contracted length, as measured by an observer moving relative to the object being measured
- $γ$ = Lorentz factor
- $L_{0}$ = proper length, as measured in the object's own rest frame
True or False?
For a spaceship travelling at close to the speed of light, the length of an object on the spaceship appears shorter from the reference frame of a stationary observer on Earth.
True.
For a spaceship travelling at close to the speed of light, the length of an object on the spaceship appears shorter from the reference frame of a stationary observer on Earth.
True or False?
For a spaceship travelling at close to the speed of light, the length of an object on Earth appears shorter from the reference frame of the spaceship.
True.
For a spaceship travelling at close to the speed of light, the length of an object on Earth appears shorter from the reference frame of the spaceship.
This is because the spaceship is stationary in its own reference frame and Earth is moving at close to the speed of light relative to them.
True or False?
Length measurements for length dilation calculations are assumed to be taken with a ruler within each observer's reference frame.
True.
Length measurements for length dilation calculations are assumed to be taken with a ruler within each observer's reference frame.
This is because the stationary observer would also see the moving ruler contract as well as the object it is measuring.
True or False?
Length measurements in length contraction calculations are assumed to be taken at the same time in each reference frame.
True.
Length measurements in length contraction calculations are assumed to be taken at the same time in each reference frame.
A passenger on a train travelling close to the speed of light measures the length of the train using a tape measure onboard the train. A stationary observer on a platform measures the length of the train as it passes through the station using their own tape measure.
Which observer measures proper length?
The observer measuring proper length in this situation is the passenger on the train.
Moving objects contract along their direction of motion. Therefore, proper length is the length measured from the measured object's rest frame. The contracted length is measured by the observer at rest to the moving object.
A passenger on a train travelling close to the speed of light measures the length of the train station sign as they hurtle through the station. A stationary observer on the platform also measures the length of the train station sign using their own tape measure.
Which observer measures proper length?
The observer measuring proper length in this situation is the person on the platform.
Moving objects contract along their direction of motion. Therefore, proper length is the length measured from the measured object's rest frame. The contracted length is measured by the observer at rest to the moving object; for the person on the train, the platform is moving relative to them.
Define the term relativity of simultaneity.
Relativity of simultaneity refers to the fact that two spatially simultaneous events do not necessarily occur at the same time, depending on the observer's reference frame.
True or False?
According to special relativity, two events that occur simultaneously in one reference frame may not occur simultaneously in another reference frame.
True.
According to special relativity, two events that occur simultaneously in one reference frame may not occur simultaneously in another reference frame. This is also referred to as the relativity of simultaneity.
True or False?
In Galilean relativity, simultaneity is absolute.
True.
In Galilean relativity, simultaneity is absolute. If two events occur at the same time in one reference frame, then they also occur at the same time in other reference frames.
True or False?
On a spacetime diagram, the three dimensions of space are collapsed into one $x$ dimension.
True.
On a spacetime diagram, the three dimensions of space are collapsed into one $x$ dimension.
True or False?
On a spacetime diagram, the dimensions of time and space both have units of metres.
True.
On a spacetime diagram, the dimensions of time and space both have units of metres.
True or False?
On a spacetime diagram, the time axis is labelled as $c t$ .
True.
On a spacetime diagram, the time axis is labelled as $c t$ .
What is the name of a line on a spacetime graph?
A line on a spacetime digram is known as a world line.
True or False?
On a spacetime diagram, the steeper the gradient, the slower the motion of the object through spacetime.
True.
On a spacetime diagram, the steeper the gradient, the slower the motion of the object through spacetime.
What does the gradient of a worldline represent?
The gradient of a world line represents the velocity of the object.
- $gradient = \frac{c ∆ t}{∆ x} = \frac{c}{v}$
Describe the motion of object Y in this spacetime diagram.
Object Y is at rest in this spacetime diagram. It moves through time ( $c t$ ) with no change in its position ( $x$ ).
Which object, Y or Z, is travelling at the fastest speed on this spacetime diagram?
The fastest object is that with the shallowest gradient, so Object Z has the fastest speed.
Why is the motion of the object in this spacetime diagram not permitted?
The fastest speed an object can have is the speed of light. $v = c$ when the worldline is at a 45° angle from the axes. Any gradient shallower than 1 is not possible.
State the relativistic phenomena that can be shown on a spacetime diagram.
The relativistic phenomena that can be shown on a spacetime diagram are:
- multiple reference frames
- simultaneity
- time dilation
- length contraction
State an experiment that provides evidence for time dilation and length contraction.
The muon lifetime experiment provides evidence for time dilation and length contraction.
In the muon lifetime experiment, one reference frame is that of the muon, and another reference frame is that of an observer on Earth.
Who measures the proper time?
In the muon lifetime experiment, the muon measures proper time, and the observer on Earth measures dilated time.
In the muon lifetime experiment, one reference frame is that of the muon, and another reference frame is that of an observer on Earth.
Who measures the proper length?
In the muon lifetime experiment, the observer on Earth measures proper length, and the muon measures contracted length.
Proper length is the length measured from the measured object's rest frame. The measured object is the distance between the atmosphere where the muons are produced and the detectors. The rest frame is therefore the stationary observer on Earth.
True or False?
Muons are produced in the upper atmosphere as a result of pion decays produced by cosmic rays.
True.
Muons are produced in the upper atmosphere as a result of pion decays produced by cosmic rays.
True or False?
Muons travel at an average speed of $0.98 c$ .
True.
Muons travel at an average speed of $0.98 c$ .
True or False?
Muons have an average lifetime of 2.2 μs.
True.
Muons have an average lifetime of 2.2μs.