## Tuesday, July 9, 2013

### Why only two energy types in the nature: potential and kinetic (aka position and speed)?

There is only two kind of state (energy) in physics: potential and kinetic. In mechanics you have a spring that accumulates potential energy. Once you release it, the strain will accelerate the mass and the potential energy flows into the kinetic energy - the momentum of moving mass. Once all energy is migrated into the kinetic form, mass keeps moving further, behind the spring equilibrium point, and if you do not detach it from the spring, spring starts deaccelerating the mass, turning energy back into the potential form. Potential energy is transformed into kinetic, kinetic into potential. Forth and back, harmonically. This is called "a pendulum" or "harmonic oscillations".

The measure of how much energy is transferred between kinetic and potential form every unit of time is called power. Power is energy transferred over instant of time. I do not want to stop at the power. I just want to highlight that it quantifies the flow of energy between kinetic an potential forms. I want to highlight that the flow of energy exist. You never have one spring transferring energy to another spring directly, bypassing the kinetic form of moving mass. Nor, you ever can transfer energy from one moving body to another immediately. Suppose, you have a moving car, which must stop (at the traffic light) and you want to harvest the kinetic energy by accumulating it in some rotor, inside the car. You cannot do that without a spring between two moving the bodies. If you just connect two moving bodies together they boom - crush (a lot of energy will be released by friction into thermal motion) and, finally, achieve average speed. Take two massive rotors, rotating at different speeds. You cannot connect them, transferring energy from one to another without crush and friction, as you did transferring energy into the spring. Slight friction can prevent the crush but you will loose energy. One rotor will accelerate, another slow down, as they rub together. You will end up in average speed. So, you cannot transfer kinetic to kinetic without potential form in the middle even when sacrifice the energy losses and abrasive tire down of your accumulator. Do you understand why the harmonic oscillation is called harmonic now? It allows complete, gentle and lossless (100 efficient) energy transmission.

Exaclty the same phenomena appear when attempting to transfer potential energy. I cannot concieve concieve and lossles charge transfer from one strained spring to another.

Not surprisingly, the same thing happens in the electric world: you have an capasitor (aka battary, accumulator, outlet or any other voltage source) to accumulate/store the potential energy. Nothing moves in the voltage source. If you let the charges to flow by closing a loop of wire, charges start moving. Here, voltage corresponds to the force of the spring and current is the charge speed. It is a mistake to think that current develops immediately, according to I=V/R low. Actually, charges accelerate slowly as the mass is determined by inductance. The inductance is the electric mass. As mass (aka inertia) does not allow the force to accelerate the bodies instantly to infinite speeds but rather limit the acceleration with a = dv/dt = F/m (recall the Neuton's formula). Similarly, inductance L limits the growth of current I over time: dI/dt = V/L. The voltage is the electric force and inductance is the mass L that prevents instance change of current dI/dt. This law says how your system behaves in case of zero resistance.

See commutation cell to see that, similarly to mechanics, you cannot connect one voltage source to another directly, without some blow up. And, similarly to the mechanical case, when you connect two capacitors together, one charged and another empty, you either get harmonic oscillations thanks to (parasetic) inductance or, if resitance dominates over inductace, you will loose the half of energy and charge is divided -- half will be stored in the first capacitor and half is moved into another. It is surprising how many people do not understand this (very basic acutually) fact (as Lewin points out in his "complete breakdown of intuition") and I confirm that even professional Switching Power Engeneers do not get it!

It seems related with the fact that the only two things you need to completely determine the state of any physical system are the initial positions and speeds of its particles. I remember my physical lessions - they are all about that. I remember that I have seen this stated clearly somewhere in Feynman lectures and Susskind says this (first lecuture in Theoretical Minimum of Classical Physics, October 2007. In the second lecture he confirms that the major problem of physics is determening the trajectory of the system, given initial state: position and speed.) I remember Feynman sayed somewhere in lectures that there nothing more in physics than two variables (and Dirac's equation, which needed initial acceleration of electron is wrong, therefore). Might be I just misinterpreted his discussion of symmetry of the physical laws, and particularly relativity, he pointed out that all speeds are relative in the physical world, so there is no way to determine the absolute position and speed.

State is basically the same as energy because we have two types of accumulators: kinetic accumulators accumulate the moving charge, potential accumulate the strained charge. Accumulation means a sort of memorizing (a state). I was motivated to note these my old thoughts down by the first lecture of susskind saying that you need only position x and speed dx/dt to determine the whole evlolution of the system and state consists of these two variables.

I am interested to know why x and dx/dt? Why only two, position- and speed-based energies? Why cannot you transmit energy between the same type of accumulators immediately? Susskind sorta says that this is necessary for reversibility so that position stores energy (information) in speed in order information not to be lost and system stays reversible, but I could not understand that.
Oct 2016: Looking at Knuth hypergraphs whose nodes are circles alternating with boxes, I recalled that tended to draw them myself for state/transition diagrams and realized that induction nodes may be necessary to alternate with potential accumulators because one represents the speed of change of the other. Speed and level are derivatives of each other.