Relativity and measuring events
Введено| English | Значение |
|---|---|
| proper time/ˈprɒpə taɪm/ | собственное время |
| inertial frame/ɪˈnɜːʃl freɪm/ | инерциальная система отсчёта |
What would explain this observation?
- Two observers can assign different times between the same events. A clock reading has meaning only when the frame and events are specified.
Build the model
- In special relativity, inertial observers measure the same vacuum light speed.
- Time dilation compares proper time 固有时间 measured where two events occur at one place with the interval in another inertial frame 惯性参考系.
- proper time: Time between events measured at one location in a frame.
- inertial frame: A frame in which a free body moves at constant velocity.
Where is proper length measured?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Proper length is defined in the frame where the object is at rest; every frame moving relative to the object measures a contracted length. It exists - it is simply tied to one specific frame.
Match each technical term to its precise meaning.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- The Lorentz factor is 1 divided by the square root of 1 minus speed squared over light speed squared.
- Galilean velocity addition is an approximation for speeds much smaller than light speed.
In the lab: Label which frame measures proper time or proper length before substituting. Use event coordinates consistently. Do not combine lengths from one frame with time intervals from another without transformation.
Which two habits make the investigation or model in this case more defensible?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Stating the conditions and assumptions lets others repeat the work exactly, and recording the supporting evidence lets them check the conclusion. Hiding disagreeing results removes the evidence that could challenge a wrong conclusion, and one measurement can never establish a wider claim.
Work from known quantities
- Known: v = 0.60c and proper time is 4.0 microseconds. γ = 1/√(1-v²/c²) = 1/√(1-0.60²) = 1.25. Δt = γΔt₀ = 1.25×4.0 = 5.0 microseconds in the stated second frame.
Your turn: A proper interval is 8 microseconds and gamma is 1.25. Find the other-frame interval.
A proper interval is 8 microseconds and gamma is 1.25. Find the other-frame interval.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
The result is 10 μs. Known: proper interval 8 microseconds; gamma = 1.25. Use time dilation: other-frame interval = gamma x proper interval. Interval = 1.25 x 8 = 10 microseconds. The moving-frame interval is longer, as the worked case at 0.60c also shows.
Check the conclusion and its limits
- Time dilation is not an instrument fault.
- Proper length is measured in the object rest frame; a contracted length is measured in a frame where it moves.
Not true: All inertial observers must measure the same time interval between any two events. Simultaneity and duration are frame-dependent: inertial observers in relative motion generally measure different time intervals between the same two events. Only the proper interval, measured in the rest frame of the events, is shared.
- In special relativity, inertial observers measure the same vacuum light speed.
- The Lorentz factor is 1 divided by the square root of 1 minus speed squared over light speed squared.
- Watch for: time dilation is not an instrument fault.
Write from a dilated interval of 18 microseconds
- A proper interval is 12 microseconds and gamma is 1.5.
- Find the interval in the other frame. Inertial observers need not agree on the duration.
All inertial observers must measure the same time interval between any two events.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Simultaneity and duration are frame-dependent: inertial observers in relative motion generally measure different time intervals between the same two events. Only the proper interval, measured in the rest frame of the events, is shared.
Time between events measured at one location in a frame: write the technical term.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
proper time means Time between events measured at one location in a frame.
A proper time interval is 12 microseconds and gamma is 1.5. What interval does the other frame measure, and why need inertial observers not agree on the duration?
Time dilation multiplies the proper time by gamma. Simultaneity and duration depend on the frame.
What interval does the other frame measure?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
12 times 1.5 is 18 microseconds. Other options — 12 microseconds (the proper interval); 10 microseconds (the lesson example's result for 8 microseconds and gamma 1.25).