Special Relativity Flashcards: Reference Frames, Time, and Length

Question 1

What two kinds of coordinates identify an event in an inertial frame?

Accepted Answer

A position and a time. A camera shutter closing is one event, and the frame gives the coordinates of that closure.

Question 2

An instrument is bolted to a pod that coasts past a lab. Which is the instrument’s rest frame?

Accepted Answer

The pod frame. The instrument stays at a fixed position in that frame.

Question 3

A pod recedes from a lamp in vacuum. What speed does the pod measure for light from the lamp?

Accepted Answer

c, the same speed the lab measures for the light.

Question 4

A beacon flashes and its light reaches a distant camera. Which event does the camera’s detection timestamp give directly?

Accepted Answer

The light’s arrival at the camera. The flash is a separate event at the beacon.

Question 5

Two events occur beside the same clock at rest in a frame. What interval does that clock record between them?

Accepted Answer

The proper time, \Delta	au, between the two events.

Question 6

In one inertial frame, how can two separated events be timed locally and compared?

Accepted Answer

Place a clock at each event location. Keep both clocks at rest and synchronized in the chosen frame, then subtract the event readings.

Question 7

In which frame is the proper length of a rigid calibration bar measured?

Accepted Answer

The bar’s rest frame, where both ends stay at fixed positions.

Question 8

A probe coasts in a straight line at constant speed relative to an inertial lab. Is the frame attached to the coasting probe inertial?

Accepted Answer

Yes. Constant velocity relative to an inertial frame gives another inertial frame.

Question 9

A detector at rest midway between two stationary lamps receives their vacuum flashes together. When were the flashes emitted in the lamps’ frame?

Accepted Answer

At the same time. The paths to the detector have equal length and light travels at the same speed along both.

Question 10

How do you calculate the Lorentz factor \gamma from the relative speed v?

Accepted Answer

\gamma=1/\sqrt{1-(v/c)^2}, where c is the speed of light in vacuum.

Question 11

A rod moves along the lab’s track. Which two lab events give the rod’s length in that frame?

Accepted Answer

Record the front and rear endpoint positions at the same lab time. Their separation at that time is the lab length.

Question 12

Two events happen at different lab stations but both happen beside the same clock on a coasting probe. Which clock gives the proper time?

Accepted Answer

The probe clock. The events occur at its one fixed probe location.

Question 13

A detector at rest in a lab receives a flash at lab time 6\,\mu\mathrm{s}. The light traveled for 2\,\mu\mathrm{s} in the lab frame. When was the flash emitted in that frame?

Accepted Answer

At 4\,\mu\mathrm{s}. Subtract travel time from arrival time in the same frame.

Question 14

What is the Lorentz factor at relative speed 0.60c?

Accepted Answer

1.25. The square root in the denominator is \sqrt{1-0.60^2}=0.80.

Question 15

A lab timed two flashes when they were emitted. Which events should a passing pod use to compare the time interval in its own frame?

Accepted Answer

The same two emissions. The arrival of either flash at a detector is a separate event.

Question 16

A moving rod’s front position is recorded first and its rear position one lab second later. Does the difference between the recorded positions give the lab length?

Accepted Answer

No. Use endpoint positions at one lab time. The rear has moved during that second.

Question 17

A clock coasts past an inertial lab and records proper time \Delta	au between two ticks. What interval \Delta t does the lab assign to those same ticks?

Accepted Answer

\Delta t=\gamma\Delta	au. The lab uses synchronized clocks to time the ticks at different positions.

Question 18

Two flashes at different positions along a test range are simultaneous in the range frame. A pod coasts along the line joining them. Are the emissions simultaneous in the pod frame?

Accepted Answer

No, for a nonzero relative speed along that line. The two frames assign different time differences to the same emissions.

Question 19

If the relative velocity reverses direction without changing speed, what happens to the Lorentz factor?

Accepted Answer

It stays the same. The factor depends on (v/c)^2.

Question 20

A bar coasts past an inertial lab with its length perpendicular to its velocity. How does the length measured in the lab compare with the bar’s rest length?

Accepted Answer

They are equal. The lab records both ends at the same lab time, and their separation is entirely transverse to the motion.

Question 21

A pod coasting at 0.80c relative to the lab records 9\,\mathrm{s} between two ticks of its own clock. How much lab time separates those ticks?

Accepted Answer

15\,\mathrm{s}. The lab interval is (5/3)	imes9\,\mathrm{s}.

Question 22

How do you find the measured length L of an object moving along its length at constant speed, given its proper length L_0?

Accepted Answer

L=L_0/\gamma. Measure both ends at one time in the frame where the object moves.

Question 23

Two lamps and a detector are at rest in the same frame. Their flashes travel directly through vacuum to the detector and arrive together. If one lamp is farther away, which lamp emitted first in that frame?

Accepted Answer

The farther lamp. Both flashes traveled at the same speed, so the longer path took more time.

Question 24

A boom’s endpoints are measured at the same lab time while it moves lengthwise. Does the boom frame assign the same time to those two measurements?

Accepted Answer

No. Simultaneity is frame-dependent for these two events because they occur at different points along the direction of relative motion.

Question 25

Two ticks of a clock coasting at 0.60c relative to the lab are 15\,\mathrm{s} apart in lab time. How much time elapsed on the moving clock?

Accepted Answer

12\,\mathrm{s}. Its proper time is 15\,\mathrm{s}/1.25.

Question 26

A 75\,\mathrm{m} bar in its rest frame moves lengthwise at 0.80c in the lab. What length does the lab measure?

Accepted Answer

45\,\mathrm{m}. Divide 75\,\mathrm{m} by 5/3.

Question 27

Two inertial crews coast past one another and each uses clocks synchronized in its own frame. How can each assign a slower rate to the other crew’s clock?

Accepted Answer

They compare different pairs of ticks. Each times two ticks of the other crew’s clock with separated clocks synchronized in its own frame.

Question 28

The nose of a coasting probe passes two checkpoints at rest in an inertial lab. Which frame gives the proper time between those crossings?

Accepted Answer

The probe frame. Both crossings happen at its nose, where one clock on the probe can time them.

Question 29

Two light pulses reach the same detector at the same instant. Do all inertial frames agree that the pulses arrive together?

Accepted Answer

Yes. They arrive at one place and time, so their arrivals coincide in a single event. Each frame still assigns its own coordinates to that event.

Question 30

A bar moves lengthwise at 0.60c relative to the lab, which measures its length as 52\,\mathrm{m}. What is the bar’s proper length?

Accepted Answer

65\,\mathrm{m}. Multiply the lab length by 1.25.

Special Relativity Flashcards: Reference Frames, Time, and Length

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Special Relativity Flashcards: Reference Frames, Time, and Length

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