Explain heat-pump analogy of kinetic energy transfer

Question

Many questions on this site revolve around the seeming paradox of different reference frames for kinetic energy. A good example is this one about how walking on a moving platform contributes tons of energy to the walker when seen from the stationary frame. It is often demonstrated that the additional energy gained by the person equals that lost by the platform. Another answer describes this using a heat-pump analogy - burning fuel or muscle energy is used to 'transfer' energy from one object to another.

However, I haven't noticed an explanation of the actual mechanism of transfer. To reduce the problem to a very simple form, suppose two electrons are trapped in a box in close proximity and repel each other via Columb force. If the box is now fixed some large object and accelerated, and we allow an electron to escape, it will gain more kinetic energy than it would have if released while 'stationary'. We would say that the excess energy 'comes' from that lost by the rest of the system. What mediates this transfer?

To be clear, I understand that kinetic energy is frame-relative, but the question is posed from the perspective of the 'stationary' frame that observes the Columb force transferring (as it were) energy from the rest-of-system to the ejected electron: how is that effected?

Answer 1

Kinetic energy (KE) is frame dependent. Suppose your mass is 100kg. If you stand on the street, you have zero KE. To someone walking past you at 1m/s, you have a KE of 50J. From the perspective of a car travelling past you at 10m/s, you have a KE of 5,000J. A helicopter passing you at 100m/s would see your KE as 500,000J. The point is that your KE is arbitrary, depending upon the frame in which it is calculated.

If you start to walk down the street at 1m/s, the force imparted by your legs gives you an increase in KE of 50J relative to the street, but the increase in KE can take any value you like depending on the reference frame from which you view it.

To take the case of your ejected electron, its gain in KE will depend entirely on the frame of reference from which it is viewed- indeed from some frames the electron will appear to be slowing, so that it will lose KE.

The mechanism that causes a change in KE is a force. In the case of your ejected electron, it is the Coulomb force between it and the other electron. The work done by a force is again frame dependent, since it is the product of force by the distance moved, where the distance is frame dependent. If you start to push a broken-down car one metre along the street, the work you do (and the KE you impart to the car) will seem to be much greater from the frame of a passing aeroplane.

So in summary, the application of a force to a body changes its KE. The value of the change depends upon the relative speed between the body and the frame of reference in which the change is determined.

This can lead to all sorts of apparent contradictions (often raised on this site) about conservation of energy. Where the KE gained by an object is increased by a change of reference frame, that is not a violation of energy conservation- there is always some other overlooked object or objects whose energy has been decreased by the change in frame, the gains and reductions cancelling out.

Answer 2

To reduce the problem to a very simple form, suppose two electrons are trapped in a box in close proximity and repel each other via Coulumb force. If the box is now fixed some large object and accelerated, and we allow an electron to escape, it will gain more kinetic energy than it would have if released while 'stationary'. We would say that the excess energy 'comes' from that lost by the rest of the system. What mediates this transfer?

Electric field mediates the transfer. Electric field pushes one electron, which moves to the direction of the push. We say electric field does work on the electron, where work w is force time distance. W=F*d

The same electric field also pushes another electron, which is moving to the opposite direction of the push. Electric field does negative work on the electron. W=-F*d.

In other words electric field sucks energy out of one electron and gives energy to other electron.

Well that kind of answers the question, but I would like to use another example:

There is a wall, a floor, and Bob. Wall is nailed onto the floor, which is massive.

Bob is standing on the floor and pushing the wall, Bob is not doing work because the wall is not moving.

Same from another frame: Bob is doing work on the wall because the wall is moving. The floor that Bob stands on is doing work on Bob because the floor is pushing Bob who is moving. And the wall is doing work on the floor.

Now a sledge hammer hits the wall causing it to be released from the floor. That causes the wall to stop doing work on the floor. Which causes the wall starting to gain energy at rapid rate. Floor is now losing energy because it is pushing Bob, while the wall has stopped pulling the floor.

That may sound dumb, but it's important in this case: https://en.wikipedia.org/wiki/Trouton%E2%80%93Noble_experiment#Laue_current