I'm sorry, but this is incorrect. So many get confused by the 2 capacitor problem, but you can boil it down with a simple thought experiment. The proposed theory forces a conversion factor that corrects for the author's intuition that no energy should be dissipated when charging one capacitor with another. Dr. Satz appears to confuse dissipated energy with destroyed energy and says energy must be conserved, so classical physics is wrong. But energy dissipated to some other form or location is not destroyed. It still exists, just not where you want it.
The paper acknowledges the experimental result that once the first capacitor charges the second, the total voltage on the two capacitors is less than the initial voltage on the first capacitor. Now imagine you had a third capacitor, and you used the first two capacitors to charge the third in the same way that the first capacitor charged the second. The voltage would reduce again. If you repeat the experiment over and over, the voltage will tend towards zero, giving you a hint that perhaps energy is being dissipated. Now your intuition may argue, "Yes, but the capacitance is tending towards infinity, so a tiny voltage could still represent the same amount of energy." Hold on to that thought, because we can do a better thought experiment.
For a moment, let's recognize that in any natural system there will be some resistance and some inductance between the two capacitors. We will take that resistance and inductance back out at the end of the thought experiment, but it will be helpful for now. If the resistance is low compared to the inductance, we know the voltage will oscillate back and forth between capacitor one and capacitor two when we close the switch to charge capacitor two, eventually settling out to a shared, lower voltage, because there's always resistance somewhere. But, if the resistance is high compared to the inductance, there will be no oscillation. In other words, the system is well damped. If you aren't aware of these facts you can prove it to yourself with an experiment, a simulation, or differential equations. The simplifying realization is, the same thing happens in a pendulum! When you start a pendulum on side one and let it go (i.e. close the switch), if friction is low compared to inertia it will swing to side two and oscillate back and forth between both sides for a while before enough energy is dissipated for it to slow down and settle in the middle. If friction is high compared to inertia, it will settle in the middle on the first swing (and it won't be a very useful pendulum). If there is no friction in the pendulum, if you remove any possible loss mechanism, it will never stop oscillating (Congratulations! You have invented perpetual motion). The truth is the same thing happens in the two capacitor problem. If there is no energy dissipation, the voltage will never stop oscillating. The friction in the pendulum will dissipate exactly enough energy to cover the difference in gravitational potential energy between the starting point high on side one and the lower ending point in the middle. Electrical resistance (or yes, even radiation) will dissipate exactly enough energy to cover the difference in electrical potential energy between the full voltage on capacitor one and the reduced voltage on the combined capacitors. Trying to keep the same amount of energy after the system reaches equilibrium is no different than searching for perpetual motion. If you can get there, and I once thought I did, be sure you make lots and lots of money.
Now I promised we would take out the resistance and inductance. Reduce the thought experiment of the two capacitor problem down to a single, hypothetical "electron" and only two possible physical positions. Take away resistance, radiation, or any other imaginable loss mechanisms, and take away inductance in the macro sense that we think of it. Now let our hypothetical electron try to find an equilibrium between the two positions once you open the door from position one to position two. The positions still act like capacitors and the inertia of the particle still acts like inductance and the electron will "swing" back and forth like a pendulum forever.
When the voltage comes to an equilibrium between capacitor one and capacitor two, there must have been dissipated energy, just like there is with a pendulum. If you found a way to keep all the energy where you want it, the oscillation would never stop. Classical physics explains the problem just fine.
P.S. If you know the math, you know the potential energy stored on a capacitor is merely proportional to the capacitance, but proportional to the square of the voltage. Again, this is just like the pendulum who's energy is merely proportional to the mass of the pendulum but proportional to the square of its height. This shows you that in the first thought experiment with the infinite string of capacitors charging each other, the energy left over when the voltage reaches equilibrium after each switch closes drops faster due to the loss in voltage than what the increase in capacitance can ever make up for.
