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A.3 – Spacetime diagrams
Description
Nature of science:
Visualization of models: The visualization of the description of events in terms of spacetime diagrams is an enormous advance in understanding the concept of spacetime. (1.10)
Understandings:
- Spacetime diagrams
- Worldlines
- The twin paradox
Applications and skills:
- Representing events on a spacetime diagram as points
- Representing the positions of a moving particle on a spacetime diagram by a curve (the worldline)
- Representing more than one inertial reference frame on the same spacetime diagram
- Determining the angle between a worldline for specific speed and the time axis on a spacetime diagram
- Solving problems on simultaneity and kinematics using spacetime diagrams
- Representing time dilation and length contraction on spacetime diagrams
- Describing the twin paradox
- Resolving of the twin paradox through spacetime diagrams
Guidance:
- Examination questions will refer to spacetime diagrams; these are also known as Minkowski diagrams
- Quantitative questions involving spacetime diagrams will be limited to constant velocity
- Spacetime diagrams can have t or ct on the vertical axis
- Examination questions may use units in which c = 1
Data booklet reference:
Theory of knowledge:
- Can paradoxes be solved by reason alone, or do they require the utilization of other ways of knowing?
Aims:
- Aim 4: spacetime diagrams allow one to analyse problems in relativity more reliably
Directly related questions
- 17N.3.SL.TZ0.6c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
- 17N.3.SL.TZ0.6c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
- 17N.3.SL.TZ0.c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
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17N.3.SL.TZ0.6d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
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17N.3.SL.TZ0.6d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
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17N.3.SL.TZ0.d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
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18M.3.SL.TZ1.5a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
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18M.3.SL.TZ1.5a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
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18M.3.SL.TZ1.a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
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18M.3.SL.TZ2.4d.i:
Construct event A and event B on the spacetime diagram.
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18M.3.SL.TZ2.4d.i:
Construct event A and event B on the spacetime diagram.
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18M.3.SL.TZ2.d.i:
Construct event A and event B on the spacetime diagram.
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18M.3.SL.TZ2.4d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
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18M.3.SL.TZ2.4d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
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18M.3.SL.TZ2.d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
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18N.3.SL.TZ0.5b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
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18N.3.SL.TZ0.5b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
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18N.3.SL.TZ0.b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
- 19N.3.SL.TZ0.4c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
- 19N.3.SL.TZ0.4c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
- 19N.3.SL.TZ0.c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
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19N.3.SL.TZ0.4c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis '.
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19N.3.SL.TZ0.4c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis '.
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19N.3.SL.TZ0.c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis '.
- 17N.3.SL.TZ0.6b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
- 17N.3.SL.TZ0.6b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
- 17N.3.SL.TZ0.b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
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18M.3.SL.TZ1.5b:
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
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18M.3.SL.TZ1.5b:
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
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18M.3.SL.TZ1.b:
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
- 18N.3.SL.TZ0.5b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the...
- 18N.3.SL.TZ0.5b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the...
- 18N.3.SL.TZ0.b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the...
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19M.3.SL.TZ2.7a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
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19M.3.SL.TZ2.7a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
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19M.3.SL.TZ2.a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
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19M.3.SL.TZ2.7b:
Label, with the letter E, the event of the spaceship going past the planet.
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19M.3.SL.TZ2.7b:
Label, with the letter E, the event of the spaceship going past the planet.
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19M.3.SL.TZ2.b:
Label, with the letter E, the event of the spaceship going past the planet.
- 19M.3.SL.TZ2.7d: On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to...
- 19M.3.SL.TZ2.7d: On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to...
- 19M.3.SL.TZ2.d: On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to...
- 19M.3.SL.TZ1.5a: Plot, on the axes, the point corresponding to event 2.
- 19M.3.SL.TZ1.5a: Plot, on the axes, the point corresponding to event 2.
- 19M.3.SL.TZ1.a: Plot, on the axes, the point corresponding to event 2.
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19M.3.SL.TZ1.5b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
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19M.3.SL.TZ1.5b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
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19M.3.SL.TZ1.b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
- 19M.3.SL.TZ1.5d.i: An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart....
- 19M.3.SL.TZ1.5d.i: An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart....
- 19M.3.SL.TZ1.d.i: An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart....
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19M.3.SL.TZ1.5d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
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19M.3.SL.TZ1.5d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
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19M.3.SL.TZ1.d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
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19M.3.SL.TZ1.5e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
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19M.3.SL.TZ1.5e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
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19M.3.SL.TZ1.e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
- 19N.3.SL.TZ0.4c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
- 19N.3.SL.TZ0.4c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
- 19N.3.SL.TZ0.c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
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20N.3.SL.TZ0.5a(i):
Calculate in terms of the velocity of spaceship A relative to observer O.
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20N.3.SL.TZ0.5a(i):
Calculate in terms of the velocity of spaceship A relative to observer O.
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20N.3.SL.TZ0.a(i):
Calculate in terms of the velocity of spaceship A relative to observer O.
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20N.3.SL.TZ0.5a(ii):
Draw the axis for the reference frame of spaceship A.
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20N.3.SL.TZ0.5a(ii):
Draw the axis for the reference frame of spaceship A.
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20N.3.SL.TZ0.a(ii):
Draw the axis for the reference frame of spaceship A.
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20N.3.SL.TZ0.5b(i):
Plot the event E on the spacetime diagram and label it E.
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20N.3.SL.TZ0.5b(i):
Plot the event E on the spacetime diagram and label it E.
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20N.3.SL.TZ0.b(i):
Plot the event E on the spacetime diagram and label it E.
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20N.3.SL.TZ0.5b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
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20N.3.SL.TZ0.5b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
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20N.3.SL.TZ0.b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.