The Postulates of Special Relativity and the Loss of Simultaneity
All inertial frames share the same physical laws and vacuum light speed. Frames in relative motion can disagree about the simultaneity of separated events. Events connected by a causal signal keep their order.
What a learner can do afterwards
- States both postulates and identifies what counts as an inertial frame
- Uses a light-signal argument to show that simultaneity depends on the observer
- Explains why a fixed speed of light is incompatible with adding velocities the ordinary way
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An inertial frame does not accelerate or rotate. Free particles, with no net force, remain at rest or move at constant velocity. Special relativity has two postulates: the physical laws are the same in all inertial frames, and vacuum light travels at speed c in every direction in each inertial frame, independently of source motion.
Each frame uses clocks at rest in that frame, synchronized by assigning equal times to outward and return light travel. An event's time is its local clock reading, not when distant light reaches your eye. Correct signal-travel delays before comparing events. If flashes at unequal distances send light to a stationary detector together, the farther flash was emitted earlier.
An ideal train moves at constant speed toward its front. Its midpoint emits light in both directions through vacuum. Train clocks record both doors being lit together: the stationary doors are equally far away and both pulses travel at c. Platform clocks record the rear door being lit first. In that frame, the rear moves toward its pulse and the front moves away. These are door illumination times, not signal-arrival times at someone's eyes.
Clocks synchronized at different positions on the train are not synchronized according to platform coordinates. The reverse also holds. Different inertial frames can therefore assign different times to separated events even when all clocks work correctly. There is no universal simultaneity shared by every inertial frame.
Ordinary forward velocity addition would give a vacuum pulse platform speed c+v when its source moves at speed v. For v=0.1c, that rule gives 1.1c. This conflicts with the second postulate, which gives c. Ordinary addition approximates low-speed motion of material objects, but it does not transform vacuum light speed correctly.
Order can reverse only for spacelike-separated events: light could not cross their separation within their time gap. Events simultaneous at different positions are spacelike; motion along their separation changes their assigned times. If a signal travelling at c or less connects one event to the other, every inertial frame agrees on their causal order.
Changing inertial frames cannot put reception of the same signal before its emission.
An experiment confined to a sealed inertial lab cannot identify absolute rest. Every inertial lab uses the same physical laws. Measuring vacuum light speed c therefore does not select a preferred frame. Comparing the lab with an outside object can still measure their relative motion.
Inertial frames share physical laws and vacuum light speed c. They can disagree on separated events' simultaneity, but they agree on causal signal order.
Lesson, questions and study cards written for this learning dataset. OpenStax relativity chapters were consulted for facts.
Readings and study cards written for this learning dataset. OpenStax chapters were consulted for facts. The linked video is a Khan Academy lesson.
More to read
What an internal experiment can tell you
A laboratory can compare its motion with objects outside. An experiment confined to a sealed inertial laboratory cannot identify an absolute state of rest. Another inertial laboratory uses the same physical laws.
The light-speed postulate makes a specific prediction. Each inertial frame measures vacuum light speed c in every direction, independently of source motion. This does not say that light travels at c through every material.
The postulates concern laws and vacuum light speed. They do not require every frame to assign the same distance or time to an experiment. The train example shows why event timing must be reconsidered.
Testing an inertial frame
Consider particles on which no net force acts. In an inertial frame, they remain at rest or move in straight lines at constant speed. A nonrotating frame moving at constant velocity relative to an inertial frame is also inertial.
A turning vehicle changes direction even if its speed stays fixed. A braking vehicle changes speed. Frames attached to those vehicles are not inertial during those motions.
These postulates compare inertial frames. Special relativity can also describe accelerated particles using inertial coordinates. An accelerating particle and an accelerating coordinate frame are different ideas.
One pulse, two door events
Take an ideal train moving at constant velocity toward its front. A source at its midpoint emits light toward both doors through vacuum.
In train coordinates, the doors are stationary and equally far from the source. Since both pulses have speed c, the doors are illuminated at equal train times.
In platform coordinates, the pulses still have speed c. The rear moves toward its pulse while the front moves away from its pulse. Rear illumination therefore has the earlier platform time.
The compared events are the moments when light reaches the doors. Light from those events may reach a viewer later. Correcting that viewing delay does not remove the difference between train and platform event times.
Receiving light and assigning event times
A frame assigns an event the reading of a synchronized clock at its location. A distant detector receives news of the event later. If light from two flashes arrives together after unequal vacuum journeys, the farther flash must have been emitted earlier in the detector's frame.
Frames in relative motion use different systems of synchronized clocks. Some separated event pairs can therefore change order between frames. Such pairs must be spacelike-separated: their distance is too large for light to cross within their time gap.
Emission and reception of one light pulse do not form such a pair. Every inertial frame places reception after emission. Changing frames cannot reverse a causal order established by a signal travelling at c or less.
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