Explain why high-speed measurements require a frame-dependent account of time and length.
Method and worked examples
An inertial frame is one where an isolated object moves at constant velocity. Frames moving uniformly relative to one another are all inertial; no one is absolute rest. A ball thrown vertically inside a uniformly moving train has horizontal motion in the ground frame. Position, velocity and path descriptions can depend on frame.
Special relativity has two postulates: physical laws are the same in all inertial frames, and all inertial observers measure vacuum light speed c. Do not add observer speed to c. At speeds much smaller than c, Newtonian mechanics is a good approximation. An accelerating turnaround changes inertial frames, so it cannot be treated as uninterrupted coasting in one frame.
Example 1
A train moves at constant speed on a straight track. Are train and ground both candidate inertial frames?
Approximately yes, over a short interval that neglects Earth’s rotation and train acceleration. Neither is a preferred absolute-rest frame.
Example 2
A spacecraft moving toward a light source measures its vacuum light speed. What does the second postulate predict?
It measures c, not c plus the spacecraft speed. The observers can disagree about frequency and time while agreeing on vacuum light speed.
Watch out:Vacuum light speed and physical laws are invariant; measured time intervals, lengths and velocities can depend on the frame.
12. Inertial frames and relativity postulates | Year 12 Physics | Ascent Arcade