A.2 – Lorentz transformations

Identify the terms in the formula.

u′ = $\frac{u-v}{1-\frac{uv}{c^2}}$

Identify the terms in the formula.

u′ = $\frac{u-v}{1-\frac{uv}{c^2}}$

Identify the terms in the formula.

u′ = $\frac{u-v}{1-\frac{uv}{c^2}}$

Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.

Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.

Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.

Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.

Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.

Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.

Calculate the velocity of the spaceship relative to the Earth.

Calculate the velocity of the spaceship relative to the Earth.

Calculate the velocity of the spaceship relative to the Earth.

Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.

Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.

Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.

The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.

The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.

The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.

Outline why the observed times are different for A and B.

Outline why the observed times are different for A and B.

Outline why the observed times are different for A and B.

ct′ = –1.1 m.

ct′ = –1.1 m.

ct′ = –1.1 m.

Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.

Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.

Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.

x′ = 1.5 m.

x′ = 1.5 m.

x′ = 1.5 m.

Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.

Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.

Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.

The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.

The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.

The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.

Calculate, for observer A, the length L_A of the bridge

Calculate, for observer A, the length L_A of the bridge

Calculate, for observer A, the length L_A of the bridge

Calculate, for observer A, the time taken to cross the bridge.

Calculate, for observer A, the time taken to cross the bridge.

Calculate, for observer A, the time taken to cross the bridge.

Explain how the force in part (b)(ii) arises.

Explain how the force in part (b)(ii) arises.

Explain how the force in part (b)(ii) arises.

Determine, according to an observer in A, the velocity of B.

Determine, according to an observer in A, the velocity of B.

Determine, according to an observer in A, the velocity of B.

Determine, according to an observer in A, the time taken for B to meet A.

Determine, according to an observer in A, the time taken for B to meet A.

Determine, according to an observer in A, the time taken for B to meet A.

Discuss the change in d according to observer Y.

Discuss the change in d according to observer Y.

Discuss the change in d according to observer Y.

Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.

Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.

Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.

Calculate the velocity of rocket B relative to rocket A.

Calculate the velocity of rocket B relative to rocket A.

Calculate the velocity of rocket B relative to rocket A.

Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.

Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.

Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.

As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.

As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.

As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.

Explain what is meant by the statement that the spacetime interval is an invariant quantity.

Explain what is meant by the statement that the spacetime interval is an invariant quantity.

Explain what is meant by the statement that the spacetime interval is an invariant quantity.

calculate the spacetime interval.

calculate the spacetime interval.

calculate the spacetime interval.

determine the time between them according to observer B.

determine the time between them according to observer B.

determine the time between them according to observer B.

Calculate the speed of the probe relative to the ground.

Calculate the speed of the probe relative to the ground.

Calculate the speed of the probe relative to the ground.

Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).

Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).

Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).

Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².

Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².

Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².

Determine the time, according to observer A, between X and Y.

Determine the time, according to observer A, between X and Y.

Determine the time, according to observer A, between X and Y.

Deduce the length of the probe as measured by an observer in the spaceship.

Deduce the length of the probe as measured by an observer in the spaceship.

Deduce the length of the probe as measured by an observer in the spaceship.

Explain which of the lengths is the proper length.

Explain which of the lengths is the proper length.

Explain which of the lengths is the proper length.

Calculate the speed of the probe in terms of $c$, relative to Earth.

Calculate the speed of the probe in terms of $c$, relative to Earth.

Calculate the speed of the probe in terms of $c$, relative to Earth.

Calculate the speed of the probe in terms of $c$, relative to Earth.

Calculate the speed of the probe in terms of $c$, relative to Earth.

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.

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.