Why doesn't characteristic impedance depend on track length?

Whether the wire or trace is 10mm long or a mile long the characteristic impedance remains the same provided there is no change in the geometry.

Resistance increases as wire gets longer, but in PCB calculators the impedance depends only on track geometry and distance from the plane. The characteristic impedance is not the same as the lumped resistance of the wire. They just happen to have the same units.

Take for example an amplifier with current as input and voltage as output.

The gain of this amp will be I/V with a unit of ohms. But the gain of the amplifier does not have anything in common with the resistor. They just happen to have the same unit as a resistor. Similar thing happens with characteristic impedance.

The characteristic impedance is a ratio of the current and voltage waves.

This makes sense technically, but let’s try to understand this with an analogy. Imagine you are a wave and your steps are wave cycles, assume your steps are the same and this will be your wavelength. On a normal day, you are walking fine and say this is low impedance.

Now you take the same steps in a loose desert sands, your movement will be impeded more than in previous cases. This case is of high impedance. Your energy left for sure will depend on how long you walk.

Characteristic impedance is the impedance felt on taking one step.