Two lightning bolts strike the front and back of a moving train simultaneously, as measured by a platform observer equidistant from both strikes. What does an observer sitting at the exact center of the moving train measure?
AThe strikes as simultaneous — the passenger's position at the midpoint guarantees both light signals arrive together
BThe front strike as occurring first, because the train observer is moving toward the front and light from that strike covers less distance to reach them
CThe rear strike as occurring first, because the train's velocity compresses the effective distance to the rear
DNeither as occurring first — the relativity of simultaneity applies to clocks but not to physical events like lightning strikes
The platform observer is at rest and equidistant from both strikes — equal distances, same speed c, simultaneous arrival. The train observer is moving toward the front strike and away from the rear strike. The second postulate requires light to travel at speed c in all directions for all observers, so the forward light covers a shorter distance to the moving observer and arrives first. The train observer correctly concludes the front strike happened earlier. Both observers are right in their own frames — the disagreement about simultaneity is physically real, not a measurement artifact.
Question 2 Multiple Choice
Two events occur simultaneously (Δt = 0) but at different locations (Δx ≠ 0) in frame S. Using the Lorentz transformation Δt' = γ(Δt − vΔx/c²), what does a frame S' moving at velocity v relative to S measure?
AΔt' = 0 — simultaneous events in any inertial frame are simultaneous in all inertial frames
BΔt' = γΔt = 0, since Δt = 0 makes the time-dilation term vanish entirely
CΔt' = −γvΔx/c² ≠ 0, since the spatial separation term survives even when Δt = 0
DΔt' cannot be determined without knowing whether the events are causally connected
With Δt = 0, the Lorentz transformation reduces to Δt' = −γvΔx/c². Since v ≠ 0 and Δx ≠ 0, this is nonzero. The spatial separation between events, combined with relative motion between frames, generates a time difference. This is the precise mathematical statement that simultaneity is relative: events at different locations that are simultaneous in one frame are non-simultaneous in any frame in relative motion. Only if Δx = 0 (same location) does Δt = 0 guarantee Δt' = 0.
Question 3 True / False
Two events that are simultaneous in one inertial reference frame are simultaneous in most inertial reference frames.
TTrue
FFalse
Answer: False
This is exactly what special relativity denies. Absolute simultaneity — a universal 'now' shared by all observers — is incompatible with the constancy of the speed of light. The Lorentz transformation shows that Δt' depends on both Δt and Δx: even when Δt = 0, spatially separated events (Δx ≠ 0) are non-simultaneous in any frame with v ≠ 0. Only events at the same spatial location maintain their simultaneity across all frames.
Question 4 True / False
The relativity of simultaneity implies that observers in different inertial frames could disagree about whether a cause preceded its effect, opening the door to causal paradoxes.
TTrue
FFalse
Answer: False
Causally connected events have timelike separation: one event can send a signal to the other at or below the speed of light. For such events, the time ordering is invariant across all inertial frames — every observer agrees which event came first. Only spacelike-separated events — which cannot causally influence each other (no signal can travel between them without exceeding c) — can have their time ordering reversed between frames. Because they are causally disconnected, swapping their order creates no causal paradox. The structure of spacetime preserves causality even while permitting frame-dependent simultaneity.
Question 5 Short Answer
Why does the constancy of the speed of light force simultaneity to be relative? Use the train thought experiment to explain the core logical step.
Think about your answer, then reveal below.
Model answer: The platform observer is equidistant from both lightning strikes and at rest — light from each strike travels the same distance at speed c, arriving simultaneously, so both strikes are simultaneous in the platform frame. The train observer at the center of the train is moving toward the front strike. In Newtonian mechanics, we could restore simultaneity by noting that the observer's motion adds to or subtracts from the effective light speed. But the second postulate forbids this: light travels at speed c regardless of the observer's motion. So the forward light still travels at c but covers less distance to reach the moving observer; it arrives first. The train observer must conclude the front strike happened earlier. The constancy of c removes the only adjustment that could preserve absolute simultaneity, making time itself frame-dependent.
The key step is that the second postulate eliminates the escape valve that Newtonian mechanics would have provided. In Newtonian physics, you could restore simultaneity by adding the observer's velocity to the light's speed. Relativity forbids this, so the different distances light must travel to reach different observers translate directly into different measured time orderings — simultaneity becomes relative.