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Why is the pitch measured with respect to the horizon and not the ground? How different are the angles between the ground and the horizon? Would it be possible to fly with an attitude indicator that indicated pitch with respect to ground rather than horizon? What does it mean when you have a 0 degree pitch with respect to the horizon? What, exactly, are you flying towards in that case?
I've always had a hard time understanding this. Thanks for your time.
Pitch is measured with respect to a plane orthogonal to the local weight¹ force, which is properly called the horizontal.
That is used because:
It is called simply horizon, presumably because looking at the horizon is the easiest way to find that plane by human senses.
Using ground, which is not flat, as reference wouldn't work. Aircraft need to fly mostly along the equipotential plane, because climbing to a higher one requires adding more energy by the engines and descending below means the aircraft accelerates and needs to dissipate (= waste) the energy. So following terrain would require quite a bit more energy than flying horizontal. Plus it would be very complicated.
¹ By weight I mean the sum of gravity and centrifugal force in the reference frame rotating with Earth.
An airplane needs to be oriented to a frame of reference which does not change depending on altitude or the elevation of the ground, this is so the pilot will be able to judge the angle of the wing through the air flow. If you used angle between the ground and the horizon then it would be constantly changing depending on your height and the elevation of the ground. If the ground level ahead goes up then the angle between ground and horizon decreases, if the ground level stays the same and you increase altitude the angle increases. If you see the angle diminish you would not know whether it was because of a change in attitude, altitude, or ground elevation.
Your question seems to boil down to the following:
Assuming that the earth is a perfect sphere, why does the virtual horizon (i.e., the pitch indicator) point to the horizon? The answer is, it doesn't.
Pitch is determined with gravity, which always 'points' to the center of the earth. The virtual horizon you see on your pitch indicator is always at an angle of 90° (i.e., a straight angle) from that, and only points to the actual horizon in case you were exactly on the ground. This difference is negligible for normal flight (which happens in the very lowest part of the atmosphere). The following is only to demonstrate what is actually happening.
In the above picture, I drew an exaggerated version of what you mean. The red line points to the center of the earth (so, where gravity points), and is the reference of your pitch indicator. The green line is what you will see on your pitch indicator. The blue line is where you actually see the horizon. They don't match up, and that's fine.
A pilot really doesn't care where the horizon is. He cares about maintaining altitude, ascending or descending. Maintaining altitude is done by keeping the airplane level with respect to the center of the Earth, in which case he will make a complete circle around the earth since his velocity vector is always perpendicular to the center of the Earth. Ascending and descending is done by having the pitch above or below this.
From the picture you can see that if the virtual horizon were to point to the actual horizon, you would eventually impact the ground - on a perfectly smooth sphere, it would be a smooth landing too. I guess there's a reason they call it the virtual horizon, eh?
The "horizon" is a fixed reference that will be the same wherever you are flying. It is fairly straightforward to create an instrument for the cockpit that illustrates pitch and roll with respect to this horizon. It also relates to gravity, since gravity will be pointing straight down with respect to the horizon. Pitching up means you are working against gravity, regardless of what the ground below you is like. Humans have a natural sense of "up" and what is "level", which is based on our perception of gravity.
Showing pitch with respect to the ground would be much more chaotic. You would need some way to know what the ground below the aircraft is doing, at any altitude. The relationship of pitch and power would be even more confusing, as pitch would no longer consistently relate to gravity, and therefore no longer consistently relate to power.
Passengers typically like a smooth and level flight. Airliners flying over mountains would have a wildly changing pitch indication, despite flying "straight and level." If an aircraft wanted to fly level with respect to the ground, it would require steep climbs and descents in these areas. Since air density changes with height above sea level, not the ground, the aircraft's performance would continually change as it stays level with the ground.
If a pilot is concerned about hitting the ground, there are many better ways to avoid that. Traditionally, charts and navigation will allow a pilot to avoid terrain. Technology like radar altimeters have also helped, which shows the pilot how high they are above the ground. Newer systems allow things like synthetic vision if the terrain is not clearly visible.
