Relativity Foundations Quiz

Covers: speed-of-light, time-dilation, length-contraction, spacetime, light-cones

Why is the speed of light the same for all observers? Because light is special among physical phenomena Because our instruments aren't precise enough to detect the difference Because c is the speed of causality — the maximum rate at which any cause can produce any effect — and the laws of physics are the same in all inertial frames Because the luminiferous ether carries light at a fixed speed

The constancy of c is not about light specifically. It is about the structure of spacetime: c is the maximum speed at which causal influence can propagate. Light travels at c because photons are massless, but the speed limit exists independently of light. The Michelson-Morley experiment ruled out the ether, and Einstein's postulates — constant c plus identical physics in all inertial frames — produce all of special relativity.

GPS satellites must correct for relativistic time dilation. What would happen to position accuracy without this correction? Positions would be slightly off by a few centimeters Positions would drift by roughly 10 kilometers per day due to a 38-microsecond daily clock discrepancy GPS would still work because the errors cancel between satellites Only altitude measurements would be affected

GPS satellites experience two relativistic effects: their speed causes clocks to run slow (special relativity, -7 microseconds/day), and their weaker gravitational field causes clocks to run fast (general relativity, +45 microseconds/day). The net effect is +38 microseconds/day. Since GPS determines position by timing signals at the speed of light, and light travels about 11 km in 38 microseconds, uncorrected positions would drift by roughly 10 km daily.

Two data centers receive writes X and Y within the speed-of-light propagation delay between them. Data center A sees X first; data center B sees Y first. What does relativity tell us about this situation? One data center has a faulty clock and the disagreement is a bug The true order could be determined with better clock synchronization The writes are causally related but the causal order is hidden by network latency The writes are spacelike-separated — there is no objective ordering, and both data centers are correct

Events within the propagation delay are spacelike-separated: no signal at or below c can connect them. Relativity of simultaneity means different observers (data centers) can legitimately disagree about the order of spacelike-separated events. This is not a clock synchronization problem — it is a structural fact about spacetime. Lamport timestamps and CRDTs are engineering responses to this physical reality: establish causal order where it exists and handle unordered events explicitly.

What is the spacetime interval, and why is it significant? The spatial distance between two events, which all observers agree on The time difference between two events, which all observers agree on A quantity combining spatial and temporal separation (ds^2 = -c^2*dt^2 + dx^2 + dy^2 + dz^2) that is invariant across all reference frames, even though space and time separately are relative The speed of light, which is constant for all observers

Space is relative (length contraction). Time is relative (time dilation). But the spacetime interval — which combines both with a crucial minus sign — is invariant. All observers in all reference frames compute the same interval between any two events. The interval can be timelike (causal connection possible), lightlike (connected by a light ray), or spacelike (no causal connection possible). It is the geometric invariant that anchors all of relativity, analogous to how causal structure is the invariant in distributed systems.

What does spacelike separation between two events mean for causality? The events can influence each other, but only through gravitational waves The events cannot influence each other yet, but eventually will The events are causally related but the direction of causation is ambiguous The events cannot be causally connected by any signal at or below the speed of light — no influence is possible, and their temporal order is frame-dependent

Spacelike-separated events are outside each other's light cones. No signal at or below c can connect them, so neither can cause the other. Their temporal order depends on the observer's reference frame — some frames see event A first, others see event B first, and all are equally valid. This is not about ignorance; there is no objective ordering. In distributed systems, this corresponds to concurrent events at different nodes within the propagation delay — fundamentally unordered, which is why CRDTs and causal consistency models exist.