Decided to do a search for ya on the net, and this is the basic same answer I found everywhere. Well...... accept for the freaky sites that say it's an omen meaning "someone is going to die". LOL I wouldn't listen to that though - that site had some strange people on it. But here's what I found:
What to do if you are having trouble with a bird such as a robin or a cardinal flying and pecking at your window.
A bird, perhaps a cardinal or a robin, is insistently pecking and flying at one of your windows, starting early in the morning and perhaps continuing intermittently throughout the day. Does this sound familiar? Although this behavior seems odd, it's a very common complaint, especially in the springtime. Don't worry -- the bird is not trying to get into your house nor has it gone entirely crazy.
Male cardinals and robins are most known for this behavior, although females and other species also do it. The bird is seeing its own reflection in the window, and interpreting it as an interloper or competitor in its territory. In springtime, when birds are establishing territories in preparation for nesting and breeding, they have little tolerance for rival birds in the vicinity. They will diligently peck and fly at the "rival" bird they see in the window, in a futile attempt to drive it off. The bird will return again and again, only to find the intruder still there!
The problematic reflection is on the outside surface of the window, so changes made inside the house will be useless. The only way to dissuade the bird is to dull, break up or eliminate the reflection on the exterior surface of the window. Spray the window with glass-wax (fake snow), tape up newspaper, cardboard or similar material over the window, put up screening, or drape half-inch-mesh garden netting in front of the window. Leave the material up for at least two or three weeks. Remember to put the material on the outside of the window.
After a few weeks, the bird should get out of the habit of finding a "rival" at that location. The sooner you eliminate the reflection, the easier it will be to break the habit. If you've noticed the bird using a favorite perch or two while watching the window, try removing those perches, or blocking access to them temporarily. If you have a large house with many wide expanses of plate glass, you are may have a correspondingly large problem - especially if the bird has already developed the habit of going from window to window, finding its reflection at each one. But usually, the bird will have a "favorite" window; try your countermeasures there first.
The bird does not usually injure itself seriously, but may expend a large amount of energy defending against nonexistent intruders. Fortunately, the behavior is usually short-lived, and disappears when the bird begins nesting and caring for young. However, a few stubborn birds persist throughout the spring and summer; it seems to be an individual aberration. You may go years without a problem before a bird suddenly starts acting "bird-brained." It may stop as suddenly as it began.
I know you said you don't think it sees a reflection because there's no sun on the window, but they did say these birds do it all day. Starting from early morning, just as your little finch is doing.