What happens to the stripes when a muscle shortens? The figure moves the sarcomere length slowly back and forth.
The spacing stretches and shrinks. The lighter streak in the middle of each dark band narrows as the muscle shortens, and eventually disappears.
There is one thing worth checking here. Is the width of the dark band itself changing?
Here is the same motion drawn as a diagram. The Z lines at each end move together and apart.
The thick filament sits in the middle and does not move. The thin filaments travel with the Z lines, sliding in and out over the thick filament.
So what shortens is the sarcomere, not the filaments. Neither kind of filament changes its length.
Now the same motion with the bands labelled. The bracket below is the A band, and the I bands are on either side of it.
The A band never leaves 1.60 µm. It is the length of the thick filament itself, so it stays the same whether the sarcomere is stretched or squeezed.
Only the I band and the H zone change. Both measure how much of the thin filament is not overlapping the thick one, so they narrow as the overlap grows and widen as it shrinks.
On the left is a shortened sarcomere, on the right a stretched one, drawn at the same scale.
Check with your own eye that the A band is the same width in both. If the filaments themselves were shortening, the A band would have narrowed too.
If the width stays fixed while only the overlap changes, there is no other conclusion: the two kinds of filament are sliding past each other. This is the sliding filament theory, proposed from exactly this observation in 1954.