For v=0.6c, find the Lorentz factor.
Answer and explanation
1.25
γ=1/sqrt(1−0.6²)=1/0.8.
Subjects
Relativity
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Sample exercises
A clock accumulates proper time 4 s. For γ=1.25, find the corresponding coordinate time.
Answer and explanation
5 s
Δt=γΔτ=5 s.
Which clock measures proper time between two events on its worldline?
- Any remote clock regardless of synchronization
- The clock present at both events
- Only a clock at infinity
- No physical clock
Answer and explanation
The clock present at both events
Proper time belongs to the path joining the events.
In units c=1, events have Δt=5 and Δx=3, with other separations zero. Find s² using +−−−.
Answer and explanation
16
s²=25−9=16, a timelike separation.
For a lightlike interval in vacuum, what is s²?
- Equal to mass
- Zero
- Always negative
- Always positive
Answer and explanation
Zero
Null separations have zero invariant interval.
Explain why a frame-independent statement that distant events occur at the same time is generally invalid.
Answer and explanation
Lorentz transformations mix time with spatial separation. For separated events, simultaneity can differ between inertial frames.
Credit spatial separation and frame transformation.
Study notes
Special relativity and invariant intervals
Special relativity describes inertial-frame transformations with invariant vacuum light speed. It replaces Galilean transformations when relativistic effects matter.
UniversitySpecial relativity and invariant intervals · revision notes
Special relativity describes inertial-frame transformations with invariant vacuum light speed. It replaces Galilean transformations when relativistic effects matter.
UniversityCurved spacetime and the scope of general relativity
General relativity relates spacetime geometry to stress-energy. The metric determines spacetime intervals and causal structure.
Advanced universityCurved spacetime and the scope of general relativity · revision notes
General relativity relates spacetime geometry to stress-energy. The metric determines spacetime intervals and causal structure.
Advanced universityLorentz factor
The speed is subluminal; Newtonian approximations become inaccurate as β increases.
UniversityLorentz factor · formula reference
The speed is subluminal; Newtonian approximations become inaccurate as β increases.
UniversityProper time from coordinate time
The clock moves at a constant speed between the two events; proper time is measured by that clock.
UniversityProper time from coordinate time · formula reference
The clock moves at a constant speed between the two events; proper time is measured by that clock.
UniversityMinkowski interval in one spatial dimension
Use the (+,−) sign convention. A negative result is spacelike, not an arithmetic error.
Advanced universityMinkowski interval in one spatial dimension · formula reference
Use the (+,−) sign convention. A negative result is spacelike, not an arithmetic error.
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