Similarly, the Star Wars "laser" does not at all behave like a laser. It is currently thought to be a massless beam weapon composed of extremely high energy luxons, the lightspeed particles binding together all tardyonic matter -- reactions between the individual particles produce the visible "bolt". If you wanted to know how you can get enough energy to blow up a third-world country out of a potato, now you know. (<-- deliberate SLIGHT exaggeration)
Wait, that doesn't make sense. Reading the Star Wars Visual Dictionary, I came to find that the lasers are rather super-heated bolts of plasma, thus the need for both a gas and energy cartridge in the weaponry. Now, this seems to be followed through in the movies, in counter of them being light-speed particles. Watch the tracking of the weapons: you always have to lead targets, and even in the movies the lasers don't appear to travel anywhere near light speed. Thus I'd think they are rather the plasma the Visual Dictionary says.
Anyway, getting back to CT... I find both the explanation by CTCronoboy and GrayLensman quite interesting, and both makes sense. Of course, I'd still go with the more mystical approach, stemming from theories similar to say, those of the Hellenic Natural Philosophers, and the elemental make-up of the universe (as some of them spoke of it), but if one needs to put it into scientific terms, based on the physics and reality of our world, I think both of these are quite valid, though I'd lean more to GL's side, which takes into account the five basic forces of the universe, rather than the forms that energy takes.
As GrayLensman, I'd think Lightning must go along with electro-magnatism. Moreover, the VoltBite shows that there is potential-energy in Crono's attacks: a volt is potential difference, after all. As for the healing, the electromagetism can act similar to a those heart boosters or whatever they're called, that they use when someone has a heart attack. Life, essentially then, can refire the synaptic pathways after a short instance of braindeath. I cannot remember rightly... does Crono have any other healing besides Life? If not, then this explanation fully explains it. We also have to remember that, in addition to Lightning, electromagnetism is also responsible for light, thus x-rays and gamma-rays, which may well be what Luminaire is: a burst of EM radiation across a wide spectrum, which peaks at such a point that light appears white, not unlike a nuclear blast.
I'd agree also that Shadow seems to be more of a gravitational force (though, as these are inherently magical forces, I find certain aspects difficult to reconcile with our own world laws.) The effects of despair, Dark Mist and Dark Matter and the like... well, Dark Mist may disrupt space-time in the minds of the opponents, causing them to hallucinate, lose concentration, and thus despair, in addition to injury. A very grievous attack, I'm certain. Dark Matter... well, I'm not sure how gravitational forces can cause such a thing - I cannot quite remember what it is? Is it when the electron spin about the atom is inverse of what it usually is, or is that anti-matter? Or is Dark Matter antimatter? If that is the case, it would indeed be potent! I'm not sure how Janus could reverse an electron's spin, but, oh, well...
Water is, quite plainly, simple water in the game, and healing is a thing often attributed to it; I think it technically only stems from one of the four elements one of the Natural Philosophers outlined, and really cannot be fully reconciled into any force. But for the sake of argument here, I'll take the suspension of disbelief and look at the theories... however, as I'm uncertain exactly how quantum mechanics affects thermodynamics (I can see there may well be a connection, but I'm not versed well in that field at all), I cannot make much of a comment. CTCronoboy's comment is also well thought through, so I'll leave this one be. The problem with it being entropy, however, is that it is very difficult to condense enough water out of the air to accomplish this.
Ice, it appears, drains the energy out of something. If Marle is powerful enough to drain all energy from a material so that it attains absolute zero it would, to my knowledge, suffer atomic decay, falling apart because it has no energy.
Finally, fire... I think that fire needs a reaction to occur, and cannot simply be kinetic energy. As for GL, I'm once again not well enough versed in the grand theories to be able to argue for or against this... wait... weak nuclear is inter-molecular bonds, correct? If so, it would govern oxidization and fire reactions. That makes sense. Apologies for a mind slow to pick up on this.
So, I suppose that I'd have to agree with GL, at least if a scientific explanation is sought (I prefer a mystical one, which I elaborated on to great length at the CTNP, but as I said, this is for sake of science and argument.) Althought, in saying that, he is also saying that there really is no distinction between the various magics: electro-magnetism is already tied into the weak nuclear, so already Lightning and Fire are connected, and are aspects of the same force. In time, we may well have the GUT, which will give us a connection between all forces. Thus, all four are essentially aspects of a single force and, in the Crono world, a single magic force. Woe betide he who challenges one who would be innate to that, eh?
The only grave difficulty with these theories is that whatever energy one gets out of it all, one has to put in. Some things, such as creating a sizable gravitational field or affecting strong/weak nuclear forces, would required immense energies that cannot come from nowhere. Either these people in their mind hold immense energy, or else it must come from somewhere else, effectively draining the area of its native energy. Furthermore, how would they control such forces with only their mind? It is inherently magic, and thus I think is difficult to reconcile on only scientific grounds by nature.
(My apologies if I wrote that in a very disorganized manner. I'm very tired, and my mind is not functioning well, it appears. Hopefully my comments were not fully useless, although I know I pretty much just reiterated what was already said.)