There is a great article, called commutation cells, which states that you cannot transfer kinetic energy from one container to another immediately, bypassing the potential energy storage. Otherwise, you will loose half of the energy.

They do not explain why, however. Furthermore, I feel that the principle is deeper and universal. It is not limited to switching power electronics. For instance, you wish to save energy by harvesting it from a car that is moving at speed v but ultimately needs to stop and, this, transfer that energy to accelerate a standing car or accelerate itself at a later time. You could spin up a massive rotor inside the car, connecting it to the spinning wheels or hit another car. But, this has are 3 problems

  1. When you connect moving inertial body to another one, there will be explosion, friciton and smoke, the processes known as destruction
  2. which will eat up exactly half of the moving energy $K = mv^2/2$ that you have
  3. and you will stabilize at the half speeds. Both crashed rotors or cars will move at speed v/2 instead of flipping v with 0.

I am telling that half of energy is used to power up the crash or tear down the clutch because two cars at speed v/2 have energy $2\times m(v/2)^2/2 = mv^2/4 = K/2.$

Same happens if you have one glass full and another empty and will make them [communicating][2], despite you want all water from the first to migrate into the second. It actually will for a second, and the swing back and forth until settled. The half of energy is lost again. I mean that the water, standing in the glass, possesses some potential energy (if total height is H then integrating over all layers of water at height h, potential energy $U = \sum_0^H{mgh} = mg\sum_0^H{h} = mgH^2/2$). After splitting into two glasses, the height is 2x shorter and energy is $2 * mg(h/2)^2 / 2 = mg(h/2)^2 = mgh^2/4 = U/2$ -- the half is lost again. The fact that the water will overshoot first time means that in order to flip the glasses at 0 waste of energy you should use intermediate form the energy -- the kinetic energy of the moving water and close the switch as soon all liquid is migrated into another glass. You could do the same with cars, harvesting all kinetic energy of moving car/rotating rotor into a spring or electric accumulator -- into potential energy, save your power equipment from destruction and use this energy to accelerate the vehicle afterwards.

I see that it is related to oscillators and conjugate variables. The capacitor/inductor accumulators are conjugates of each other. My question is should the accumulators be of some conjugate nature in order to non-admit the entropy growth or I can somehow use accumulators of the same nature? How deep is this principle? Is it known in QM?

I notice the same principle in heat transfer also. In order to save energy in ventilation or in all kind of cases where some stream must be first heated (cooled) and then cooled down again, it would be a waste to take cold water/air from the street, heat it up in the room, use, and throw away back to the street, taking more water/air to heat up. There is so called recuperation when you have two thermal liquids, one cold and one hot and want to exchange the temperature. You cannot just take connect them. Result will be the same as above -- the temperatures will equalize. You can do better if you let n-th part of a hot body to heat up the n-th part of the cold one. This will cool down the hot part but it still be warmer than the rest of the cold body parts. So, you can apply it once more to heat up some another cold body part. It will cool down even more but you can still proceed and heat up all cold parts to some extent and get the originally hot part cooled down almost to the temperature of inflow cold stream. The opposite happens to the parts of the cold body. Cooling down the everhotter parts, it will heat up to the hot stream temperature. This way, turning inflow stream with outflow stream, we can exchange the temperatures. We can have warm fresh air in our room at the North Pole for free! We have achieved by connecting our inflow and outflow pipes so that the temperature at every point is the same in both pipes -- it is hot at the room side and cold at the street side. The principle that I see is exactly one stated in the switching power electronics that we can connct two voltage sources only if they have the same voltage.

I remember also Feynman explained in his lectures that we can transport masses for free using a balance if we put the same masses on both of the balance or something like that but I never seen it was declared as a certain principle, likewise principle of least action.

So, do you understand the question, do you feel that there is a general principle, which says that there are two types of energy in physics, kinetic and potential (probably also is third waste/dissipation energy), which are turned into thermal waste if we connect two sources of the same kind, more general than Commutation Cell? Is it related with the fact that physics is reversible at the fundamental level, that it everything can be described in terms of 2-order configuration space, which consists of speeds and positions alone?

I think that there is a poor understanding of this idea even among power engeneers, which leads to anecdotal situations. I would like to raise awareness but I must start with some references.


I see that comments say that the principle cannot be true universally because if we measure energy of capacitors with respect to each other, rather than to the common ground as the article on Commutators explains, we will see that energy drops to 0 after the collision because zero voltage (or zero speed in the comment) means that all energy is dissipated in the collision and the principle total crap if this remark does not change anything. In this case, I want to ask if this invalidates my generalization of the commutation alone or it is Commutation Cell principle which is not universally valid either? Can I go further and imagine a world where energy is not conserved and, thus say that our basic laws of physics, e.g gravity F=m_2 \times m_2/r^2, is not universal on this ground? It seems what the answer does.

closed as unclear what you're asking by John Rennie, user36790, Gert, Kyle Kanos, DilithiumMatrix Nov 30 '15 at 0:16

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  • I do not understand your principle: if two objects of the same mass and speed collide head on, all the kinetic energy is dissipated, how would that agree with your principle? – user83548 Nov 29 '15 at 14:01
  • @brucesmitherson You wanted to say that opposite speeds, where 'opposite' means exactly opposite of the same. I smashed one object against a still one, giving resulting speed v + 0 / 2 = v/2. In your case, resulting is also the average v + (-v) = 0. Half of energy wasted is seen from one of the car observers. No matter how you slice it, you will loose energy when connecting two inertial bodies unless their speeds are exactly the same. Don't you want to say that we need to keep disregarding this great principle just because speeds and the amount of wasted energy depends on the observer? – Valentin Tihomirov Nov 29 '15 at 15:23
  • no, I am not saying anything, just trying to understand it, as I do not believe it is correct. The fact that it depends on the observer does matter, otherwise is not generally valid – user83548 Nov 29 '15 at 15:27
  • In addition, your example of the water would be no longer correct if, say the potential energy were mgh^2 (a different conservative force instead of gravity) instead of mgh – user83548 Nov 29 '15 at 15:29
  • @brucesmitherson So you are not saying it because you are saying it. Please, form a concrete sentence the principle says that but this is not valid for this and this reason. The principle is not about exact amount of energy you waste (I did not compute it for heat transfer at all). It only says that you cannot connect two sources of the same nature, whose value is different. – Valentin Tihomirov Nov 29 '15 at 15:39

Your principle ("you will loose half of the energy,... I feel that the principle is deeper and universal") does not work, and I will show that using a counterexample. Assume a similar example to the one you used with the water, but in this case the potential energy were $mgH^2$ instead of $mgh$. In such a case $U=mgH^3/3$, after splitting the water in two halves you will have $U=2mg(H/2)^3/3=U/4$

  • Please refer to the principle that you refute. I asked you to re-state the principle. You may quote my text. I do not know how realistic your conditions (the principle is supposed to work in this world). Nevertheless, so far, using imaginary world, you have just proven that we have lost some energy. That is, my principle works in your world also. – Valentin Tihomirov Nov 29 '15 at 15:57

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