Question

Your friend flies from Los Angeles to New York. She carries an accurate stopwatch with her to measure the flight time. You and your assistants on the ground also measure the flight time.

a. Identify the two events associated with this measurement.

b. Who, if anyone, measures the proper time?

c. Who, if anyone, measures the shorter flight time?

Short answer

a. First event will be friend will leaves the Los Angeles and the second event will be friend will reach the New York.

b. The friend in the flight will measure the proper time.

c. Your friend will measure the shorter time.

Step-by-step solution

Part (a) Step 1: Given information

We have given that your friend will travel from the Los Angeles to New York by flight.

We have to find the events.

Simplify

Here we can see to things is happens firstly your friend levees the Los Angeles and other is Reaches the New York.

then,

Event 1: Your friend take off from the Los Angles.

Event 2: Your friend land on the New York.

Part (b) Step 1: Given information

We have given, that your friend will travel from the LOs Angeles to New York by flight.

We have to find the who will measure the proper time.

Simplify

Using Lorentz Transformation,

$\mathrm{t}=\mathrm{\gamma }(\mathrm{t}\text{'}-\frac{\mathrm{vx}}{{\mathrm{c}}^2})$

Where,

t= time for the assistance

t'= time for your friend

v= velocity of flight

x= distance between the two cities.

Let us consider ${\mathrm{t}}_1$and ${\mathrm{t}}_2$as time of leaving flight and time of landing of flight for assistance and ${\mathrm{t}}_1^{\text{'}}$and ${\mathrm{t}}_2^{\text{'}}$as time of leaving and landing the flight for your friend

$({\mathrm{t}}_1-{\mathrm{t}}_2)=\mathrm{\gamma }({\mathrm{t}}_1^{\text{'}}-{\mathrm{t}}_2^{\text{'}})$.

then,

Since the proper time is$({\mathrm{t}}_1^{\text{'}}-{\mathrm{t}}_2^{\text{'}})$ in frame of your friend then it will measure the proper time.

Part (c) Step 1: Given information

We have given, that your friend will travel from the Los Angeles to New York by flight.

We have to find the who will measure the shorter time.

Simplify

Using Lorentz transformation,

$({\mathrm{t}}_1-{\mathrm{t}}_2)=\mathrm{\gamma }({\mathrm{t}}_1^{\text{'}}-{\mathrm{t}}_2^{\text{'}})$

Then the time observe by the assistance is equal to the time will observer by your friend with some multiple factor.

Then we can say that the time of your friend is less then the time for the your assistance since the value of the factor will be always greater then 0.

localid="1649816704619" $\mathrm{\gamma }>0.$