I know that there are a lot of people who believe that the Earth and everything that has mass in the universe has a gravity field and there are others who think that everything in the universe has a gravity well.
No, these aren't two different things. A "well" is just a description of the energy diagram that is associated with a gravitational field. The surface of the earth and the moon are both low points, in the sense that it takes energy from either one to get to a point in the middle, and that an object displaced to either side of the high point will fall, of its own accord, to the surface. So we describe both those surfaces as being in gravity wells.
I found a contradiction.
I think what you found is something you are confused about. Einstein's description of gravity and how it is perceived can't differ substantially from Newton's. Newton's description works very very well, and relativity only adds tiny corrections except in cases of extreme gravity, such as neutron stars or black holes.
I heard in a book about Einstein's theroy of gravity when he said that he either saw someone fall off a building or he heard about someone falling off a building and that person didn't feel his or her own weight.
It would be useful if you could find the original quote. But the fact is that while you are falling you feel "weightless". This is well known. It's how astronauts train. It's how the movie "Apollo 13" was filmed. While in freefall, you do not feel a sensation of weight. That feeling comes from having the ground to press against.
Now if there is a gravity feild pulling down on everybody, then that person would have felt heavier as he or she approached the ground.
Not true. You wouldn't feel heavier as you approached the ground. When you're in free fall, you can't tell if you're on the space shuttle or on an elevator right off the surface of earth. Have you really never been in freefall, never felt that stomach-dropping-out sensation?
How could this happen if Einstein clamied that that person didn't feel his/her own weight?
It wouldn't. There's no such sensation of feeling heavier as you get closer to a massive object. Not in freefall.
There's a contradiction here to the gravity feild theory.
You haven't said what you think the "gravity field theory" is, but the term "gravitational" field simply means that there is a force associated with every point in space. This is what Newton expressed when he wrote F = G M m/r^2, which tells you the
force between to masses M and m, at a distance r.
We believe this to be a pretty accurate description for most of the universe.
Perhaps what's confusing you is the fact that you EXPERIENCE a force, which pulls you more and more as you approach an object, yet you don't FEEL the force. Both of those are true. There's no contradiction. You feel a force when a car is accelerating you, because the back of the car is pushing against you in order to accelerate you. But you don't feel any force when you and your elevator, or your aircraft, are in free fall under the influence of gravity. That's because the walls or the floor aren't pushing you. Everything is falling together. No solid object has to push on you for gravity to accelerate you.
