Relativity of Work Let's say there is a man pushing a wall with a force of $-1 \text N$, and moving it $0 \text m$. Since $W = F \cdot d$, he has done $0\text J$ of work on the wall. Another man is pushing a duck with $1 N$ of force and moving it $1 \text m$. He has done $1 \text J$ on the duck. At least this is what someone on the ground saw.
Someone on a train saw it like this. A main pushing  a wall with a force of $-1 \text N$ moved it $-1 m$. He has done $1 J$ of work. Another man pushes on a duck with $1 \text N$ of force but moves it $0 m$, and has done $0 \text J$ of work.
Why is that?


*

*Is work relative? This would seem to imply though the man pushing on the wall could do infinite work.

*Is the force relative? This doesn't seem to make sense, as for nonzero net forces $F = ma$, where both mass (for the most part) and acceleration are nonrelative (for inertial reference frames.)

*Something else?
 A: You are right. In Newtonian physics, work depends on reference frame. Force does not.
Let's start with a book sitting on a table. The table exerts a normal force on the book, but it does no work because there's no motion.
Next, imagine that the table is in an elevator and the elevator is going up at constant speed. The force between the book and table is exactly the same as before, but now the table is doing work on the book because there is motion, so the work is force * distance.
In one regard, this makes perfect sense. The book is moving upward, gaining gravitational energy, so work is being done on it. That seems pretty intuitive to me.
What's unintuitive is that the table has no energy to give away. The table is doing work on the book, so energy is going from the table to the book, but the table is just a table. It has no muscles or motors or anything, so it should have no energy to give the book.
That's actually not a problem because the table is touching the floor of the elevator. The elevator does work on the table. Some of that energy flows through the table and into the book. The elevator gets the energy from a cable attached to the elevator. The cable gets the energy from a motor, which gets energy from a power plant. So a table in an elevator can do work on a book because it gets energy from a power plant.
How about wall, then? Let's stick to an inanimate object pushing on the wall - a board that has been propped up against the wall and is resting against it at an angle, pushing on the wall with $1N$ of force. From the ground's point of view, there is no motion here so no work is being done.
From the view of a train moving past, you're right, there is a force from the board on the wall and the wall is moving, so the board is doing work on the wall. The further the board and wall move (from the train's point of view), the more work the board does on the wall. If the wall is the wall of a spaceship and the board is inside the spaceship and the whole thing floats past you in deep space, you could watch it disappear off into the very far distance with the board doing an enormous amount of work on the wall over the course of lightyears of travel.
But the board is just a board. It has nowhere to get energy from this time because there is no motor or anything, just a ship drifting unpowered through deep space. Where does the energy come from?
The answer is that the board does work on the wall, putting energy into the wall. However, that energy flows through the wall into the floor, then back into the board. Let's say the board is pushing on the wall in the direction to the right. Then the wall pushes back in the direction to the left. The board is not accelerating, so the net force on it is zero, meaning that the floor underneath the board must be pushing it to the right with a force exactly the same as the force between the board and the wall. That point of contact between the floor and the board is also moving to the right, so the floor does just as much work on the board as the board does on the wall. Energy flows out of the board, into the wall, and completes a loop back into the bottom of the board. It flows up the board and into the wall again.
The lesson is that the change in the amount of energy something has is not equal to the flux of energy into it. It depends instead on the divergence of the flux of energy. In the stationary frame, the flux is zero between the board and wall so the divergence is also zero. In the moving frame, the flux is non-zero, but the divergence of the flux is still zero, so there's no physical difference.
As for the duck, you are correct again. If you push the duck away $1m$ at constant speed with a force of $1N$, you did $1J$ of work on it. But the thing is, how did you push the duck at constant speed? You were putting force on it. It should be accelerating. If it moved at constant speed, there must have been some other force canceling you out. Thus, in this frame the duck is stationary and has zero net force on it; it's no different from viewing the board from different frames.
If you push on the duck with $1N$ of force and it accelerates as it travels $1m$, then viewed in a moving frame the duck will still accelerate because acceleration is the same between inertial frames. So again the mystery goes away.
The takeaway is that work does depend on frame, but the change in energy something has depends on all the things doing work on it, so when something isn't gaining energy but there's a force doing work on it, there's another force there that you haven't accounted for yet draining the same amount of energy away.
