Lesson 2 — Continuous Transport
What Does Continuous Mean?
Transport should not make a state suddenly jump from one position to another. Continuous transport means that every small change follows smoothly from the previous one.
Why Continuity Matters
Small continuous changes can accumulate into a large change. The state does not disappear from one position and reappear somewhere else. Every new position follows smoothly from the position immediately before it.
Changing the speed changes how quickly the state moves, not whether the movement is continuous.
Every intermediate position is included.
The point passes through every position on the way, so the path can be followed and the trail stays connected.
What Does t Mean Here?
In the mathematical derivation, t labels the continuous one-parameter family of transport transformations. It can later acquire the interpretation associated with quantum evolution, but the derivation itself only requires a continuous transport parameter.
Pause and Observe
Pause the motion and use the step buttons. Notice that each new position is only a small change from the one before it. Many small changes together create the full journey around the circle.
QM2 Assumption D1
Can You Spot the Continuous Motion?
Select every example that shows continuous motion.
What You Have Learned
Continuous transport does not make a state suddenly jump. Every small change follows smoothly from the previous one. This allows evolution to remain connected and predictable.
Large changes can be built from many small, continuous changes.