A.5 Galilean and special relativity

The spacetime diagram shows an inertial reference frame S and a second inertial frame S’ that is moving relative to S.

The origins of the frames coincide when the clocks in both frames show zero.

Event $\text{X}$ is shown for the S reference frame.

Which event occurs at the same position in the S’ reference frame as $\text{X}$?

The spacetime diagram shows an inertial reference frame S and a second inertial frame S’ that is moving relative to S.

The origins of the frames coincide when the clocks in both frames show zero.

Event $\text{X}$ is shown for the S reference frame.

Which event occurs at the same position in the S’ reference frame as $\text{X}$?

The spacetime diagram shows coordinate axes of reference frames of Earth (x, ct) and of a spaceship (x', ct'). Three events P, Q and R are plotted.

Which statement is correct about the order of the events according to an observer on the spaceship?

A.  P and Q are simultaneous, R happens later.

B.  Q and R are simultaneous, P happens earlier.

C.  Q and R are simultaneous, P happens later.

D.  P and R are simultaneous, Q happens earlier.

The spacetime diagram shows coordinate axes of reference frames of Earth (x, ct) and of a spaceship (x', ct'). Three events P, Q and R are plotted.

Which statement is correct about the order of the events according to an observer on the spaceship?

A.  P and Q are simultaneous, R happens later.

B.  Q and R are simultaneous, P happens earlier.

C.  Q and R are simultaneous, P happens later.

D.  P and R are simultaneous, Q happens earlier.

Two spaceships, X and Y move in opposite directions away from a space station. The speeds of the spaceships relative to the space station are $u$ and $v$.

What is the speed of Y in the reference frame of X?

A.  $\frac{u-v}{1-{\displaystyle \frac{uv}{c^2}}}$

B.  $\frac{u-v}{1+{\displaystyle \frac{uv}{c^2}}}$

C.  $\frac{u+v}{1-{\displaystyle \frac{uv}{c^2}}}$

D.  $\frac{u+v}{1+{\displaystyle \frac{uv}{c^2}}}$

Two spaceships, X and Y move in opposite directions away from a space station. The speeds of the spaceships relative to the space station are $u$ and $v$.

What is the speed of Y in the reference frame of X?

A.  $\frac{u-v}{1-{\displaystyle \frac{uv}{c^2}}}$

B.  $\frac{u-v}{1+{\displaystyle \frac{uv}{c^2}}}$

C.  $\frac{u+v}{1-{\displaystyle \frac{uv}{c^2}}}$

D.  $\frac{u+v}{1+{\displaystyle \frac{uv}{c^2}}}$

Draw lines to indicate R on the diagram.

Draw lines to indicate R on the diagram.

Draw lines to indicate R on the diagram.

Draw lines to indicate R on the diagram.

Determine, using the diagram or otherwise, the space coordinate $x$′ of event R in S′.

Determine, using the diagram or otherwise, the space coordinate $x$′ of event R in S′.

Determine, using the diagram or otherwise, the space coordinate $x$′ of event R in S′.

Determine, using the diagram or otherwise, the space coordinate $x$′ of event R in S′.

An event has coordinates $x$ = 0 and ct = 0.60 ly in S. Show, using a Lorentz transformation, that the time coordinate of this event in S′ is ct′ = 1.00 ly .

An event has coordinates $x$ = 0 and ct = 0.60 ly in S. Show, using a Lorentz transformation, that the time coordinate of this event in S′ is ct′ = 1.00 ly .

An event has coordinates $x$ = 0 and ct = 0.60 ly in S. Show, using a Lorentz transformation, that the time coordinate of this event in S′ is ct′ = 1.00 ly .

An event has coordinates $x$ = 0 and ct = 0.60 ly in S. Show, using a Lorentz transformation, that the time coordinate of this event in S′ is ct′ = 1.00 ly .

Determine the time coordinate ct′ when the flash of light reaches the spaceship, according to an observer at rest in the spaceship.

Determine the time coordinate ct′ when the flash of light reaches the spaceship, according to an observer at rest in the spaceship.

Determine the time coordinate ct′ when the flash of light reaches the spaceship, according to an observer at rest in the spaceship.

Determine the time coordinate ct′ when the flash of light reaches the spaceship, according to an observer at rest in the spaceship.

Label, on the diagram with the letter P, the point on the ct′ axis whose ct′ coordinate is 1.00 ly.

Label, on the diagram with the letter P, the point on the ct′ axis whose ct′ coordinate is 1.00 ly.

Label, on the diagram with the letter P, the point on the ct′ axis whose ct′ coordinate is 1.00 ly.

Label, on the diagram with the letter P, the point on the ct′ axis whose ct′ coordinate is 1.00 ly.

According to laboratory observers $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}=\frac{1}{2}$.

Calculate D.

According to laboratory observers $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}=\frac{1}{2}$.

Calculate D.

According to laboratory observers $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}=\frac{1}{2}$.

Calculate D.

According to laboratory observers $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}=\frac{1}{2}$.

Calculate D.

show that the distance travelled by the detector when it meets the muon source is 405 m.

show that the distance travelled by the detector when it meets the muon source is 405 m.

show that the distance travelled by the detector when it meets the muon source is 405 m.

show that the distance travelled by the detector when it meets the muon source is 405 m.

Calculate, using the answers to (b)(i) and (b)(ii) the ratio $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}$ in S.

Calculate, using the answers to (b)(i) and (b)(ii) the ratio $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}$ in S.

Calculate, using the answers to (b)(i) and (b)(ii) the ratio $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}$ in S.

Calculate, using the answers to (b)(i) and (b)(ii) the ratio $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}$ in S.

determine the time taken for the detector to reach the muon source.

determine the time taken for the detector to reach the muon source.

determine the time taken for the detector to reach the muon source.

determine the time taken for the detector to reach the muon source.

Show that the speed of shuttle S relative to observer P is approximately 0.6c.

Show that the speed of shuttle S relative to observer P is approximately 0.6c.

Show that the speed of shuttle S relative to observer P is approximately 0.6c.

Show that the speed of shuttle S relative to observer P is approximately 0.6c.

Calculate the distance between star A and star B relative to observer P.

Calculate the distance between star A and star B relative to observer P.

Calculate the distance between star A and star B relative to observer P.

Calculate the distance between star A and star B relative to observer P.

Calculate the time, according to observer P, that the shuttle S takes to travel from star A to star B.

Calculate the time, according to observer P, that the shuttle S takes to travel from star A to star B.

Calculate the time, according to observer P, that the shuttle S takes to travel from star A to star B.

Calculate the time, according to observer P, that the shuttle S takes to travel from star A to star B.

Estimate, using the spacetime diagram, the time in seconds when the flash of light reaches the spaceship according to the Earth observer.

Estimate, using the spacetime diagram, the time in seconds when the flash of light reaches the spaceship according to the Earth observer.

Estimate, using the spacetime diagram, the time in seconds when the flash of light reaches the spaceship according to the Earth observer.

Estimate, using the spacetime diagram, the time in seconds when the flash of light reaches the spaceship according to the Earth observer.

Calculate $\gamma$ for a speed of 0.80c.

Calculate $\gamma$ for a speed of 0.80c.

Calculate $\gamma$ for a speed of 0.80c.

Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.

Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.

An event has coordinates $x$ = 0 and ct = 0.60 ly in S. Show, using a Lorentz transformation, that the time coordinate of this event in S′ is ct′ = 1.00 ly .

An event has coordinates $x$ = 0 and ct = 0.60 ly in S. Show, using a Lorentz transformation, that the time coordinate of this event in S′ is ct′ = 1.00 ly .

An event has coordinates $x$ = 0 and ct = 0.60 ly in S. Show, using a Lorentz transformation, that the time coordinate of this event in S′ is ct′ = 1.00 ly .

An event has coordinates $x$ = 0 and ct = 0.60 ly in S. Show, using a Lorentz transformation, that the time coordinate of this event in S′ is ct′ = 1.00 ly .

Label, on the diagram with the letter P, the point on the ct′ axis whose ct′ coordinate is 1.00 ly.

Label, on the diagram with the letter P, the point on the ct′ axis whose ct′ coordinate is 1.00 ly.

Label, on the diagram with the letter P, the point on the ct′ axis whose ct′ coordinate is 1.00 ly.

Label, on the diagram with the letter P, the point on the ct′ axis whose ct′ coordinate is 1.00 ly.

Draw lines to indicate R on the diagram.

Draw lines to indicate R on the diagram.

Draw lines to indicate R on the diagram.

Draw lines to indicate R on the diagram.

Determine, using the diagram or otherwise, the space coordinate $x$′ of event R in S′.

Determine, using the diagram or otherwise, the space coordinate $x$′ of event R in S′.

Determine, using the diagram or otherwise, the space coordinate $x$′ of event R in S′.

Determine, using the diagram or otherwise, the space coordinate $x$′ of event R in S′.

According to laboratory observers $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}=\frac{1}{2}$.

Calculate D.

According to laboratory observers $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}=\frac{1}{2}$.

Calculate D.

According to laboratory observers $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}=\frac{1}{2}$.

Calculate D.

According to laboratory observers $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}=\frac{1}{2}$.

Calculate D.

show that the distance travelled by the detector when it meets the muon source is 405 m.

show that the distance travelled by the detector when it meets the muon source is 405 m.

show that the distance travelled by the detector when it meets the muon source is 405 m.

show that the distance travelled by the detector when it meets the muon source is 405 m.

determine the time taken for the detector to reach the muon source.

determine the time taken for the detector to reach the muon source.

determine the time taken for the detector to reach the muon source.

determine the time taken for the detector to reach the muon source.

Calculate, using the answers to (b)(i) and (b)(ii) the ratio $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}$ in S.

Calculate, using the answers to (b)(i) and (b)(ii) the ratio $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}$ in S.

Calculate, using the answers to (b)(i) and (b)(ii) the ratio $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}$ in S.

Calculate, using the answers to (b)(i) and (b)(ii) the ratio $\frac{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{detected}}{\mathrm{number} \mathrm{of} \mathrm{muons} \mathrm{produced}}$ in S.

Calculate the distance between star A and star B relative to observer P.

Calculate the distance between star A and star B relative to observer P.

Calculate the distance between star A and star B relative to observer P.

Calculate the distance between star A and star B relative to observer P.

Show that the speed of shuttle S relative to observer P is approximately 0.6c.

Show that the speed of shuttle S relative to observer P is approximately 0.6c.

Show that the speed of shuttle S relative to observer P is approximately 0.6c.

Show that the speed of shuttle S relative to observer P is approximately 0.6c.

Calculate the time, according to observer P, that the shuttle S takes to travel from star A to star B.

Calculate the time, according to observer P, that the shuttle S takes to travel from star A to star B.

Calculate the time, according to observer P, that the shuttle S takes to travel from star A to star B.

Calculate the time, according to observer P, that the shuttle S takes to travel from star A to star B.

Estimate, using the spacetime diagram, the time in seconds when the flash of light reaches the spaceship according to the Earth observer.

Estimate, using the spacetime diagram, the time in seconds when the flash of light reaches the spaceship according to the Earth observer.

Estimate, using the spacetime diagram, the time in seconds when the flash of light reaches the spaceship according to the Earth observer.

Estimate, using the spacetime diagram, the time in seconds when the flash of light reaches the spaceship according to the Earth observer.

Determine the time coordinate ct′ when the flash of light reaches the spaceship, according to an observer at rest in the spaceship.

Determine the time coordinate ct′ when the flash of light reaches the spaceship, according to an observer at rest in the spaceship.

Determine the time coordinate ct′ when the flash of light reaches the spaceship, according to an observer at rest in the spaceship.

Determine the time coordinate ct′ when the flash of light reaches the spaceship, according to an observer at rest in the spaceship.

Discuss the ratios in (a) and (c).

Discuss the ratios in (a) and (c).

Discuss the ratios in (a) and (c).

Discuss the ratios in (a) and (c).