I cannot give any scientist of any age better advice than this: the intensity of a conviction that a hypothesis is true has no bearing over whether it is true or not.
Maxwell‘s Demon waits for no one – that‘s how I was going to start this little piece or reflection or, perhaps, analysis. It is difficult to tell what these things here are, on the blog I mean. They are so various and disjointed; all of them taken together are perhaps a bricolage of texts: if you read them in toto you might see how this cognitive conglomerate [cum ego] relates to its [my] times. Or more likely not as these are the shambolically transcribed verbal traces, bread crumbs from the brain.
[Perhaps you‘ve noticed but I‘d rather tell you to be clear and safe: I am violating my good number one rule here: avoid „I“ by all means possible. I don‘t believe in anything being self-explicatory but if anything is, then this prime rule might just be it.]
As already stated – Maxwell‘s Demon waits for no one was going to be the initial phrase to get the ball rolling. It was going to achieve two ends:
vaguely remind you of secondary or Kantonsschule and reawaken that sick feeling that you are not well-prepared enough for the physics lesson and that, if the authoritarian man [with a soft heart and a flaming beard] decides it is your time to come forth to the blackboard and explain the most recent learning contents, you will be reduced to a blubbering and above-all deathly embarassed teen….you should kinda know Maxwell‘s Demon but it just doesn‘t come to mind in any way that is remotely transmissible to the blackboard…
„…waits for no one“ would‘ve served a more straightforward purpose, also finely illustrated by many a scene in notorious Lost „Jack, we‘ve got to get back to the beach now!“ „Locke….how many minutes before I got to press that button again?!“, all to say it would‘ve created a sense of urgency. Which is not even quite the fact as Maxwell‘s Demon, at the very least, has to wait for all those molecules to pass on through.
Yet instead of using that lovely dual purpose phrase to get the show off the ground I‘ll just leap straight into the middle of things. Hoffmann‘s recent book Life‘s Ratchet tells us, the biochemically underinformed masses, how life or better, its tiny cellular engines came to be from the entropical chaos and molecular storm that reign at the nano-level; the wondrous tempest that infuses every little morcel of matter while it appears to our atomically-naive eyes as calm as cake. In the course of the first few chapters he throws up a number of different hypothesis how molecular machines [not yet cells] might‘ve been able to extract energy amidst the tornadic insanit of the molecular storm [molecules, especially water molecules, bombarding each other and everything else about a billion times a second at satellite-velocities]; hypothesis he dismisses one after another. In the course of his argument he also strikes upon that ancient bogeyman of the laws of thermodynamics: Maxwell‘s Demon. The question is basically this [and, clearly, I might be 99.9% off here]: can any sort of critter/machine extract energy/work from a uniform heat bath. The examined example are two equally warm cubical volumes of space right next to each other separated only by a wall or thin membrane or some other thermo-technically irrelevant partition. How could the West be won?
[I was all ablaze with the idea for this text a few days ago. Now I‘m writing it out so I won‘t forget, now it is a sort of archival exercise, bad archive fever… and the total lack of norepinephrine as I hammer out these phrases is just heart-breaking.]
Maxwell thought-experiments a tiny demon who has control over a tiny apperture amid the partition. Though tiny, the dang gremlin is rather powerful: it can keep track of all molecules in both volumes, sees where they are going and at what speed. Then in a flash, when a fast molecule approaches from the left volume, at just the right nano-second it slides open the aperture and lets it pass into the right volume; as if that weren‘t enough Max‘s Incubus also is keeping tabs on the slowpoke molecules on the right and when one of these approaches the opening, it also opens it just so to let only this one molecule pass into the left volume. The upshot is as clear as day [before the advent of internal combustion engines]: the right volume heats up and the left volume cools down. Unfortunately, this is illegal: it defiles the second law of thermodynamics [which we‘ll just all of us pretend we perfectly well remember]. Thus legions of physicists and non-phycists have applied themselves to show or explain or calculate why this thought experiment is flawed. Given how vivid, cute and downright common-sensical the idea of the Maxwellian Demon is, yours truely was immediately also tempted to take a stab at it.
A – Maxwell‘s Demon has needs too! It might be small and punny but the fact is, it cannot be weightless, matter-less or it wouldn‘t be able manipulate that all-important apperture. Thus, if it has any weight, and if, on top of that, it has some serious tasks to take care of [e.g. observe trillions of molecules, open/shut hatch like a madman, etc.] and if the door of the aperture also has some infinitesimal weight [for otherwise it would just be a useless orifice], then, to move these little bits of matter into action, for good or bad, we‘ll have to invest some energy. This energy will be equal to or bigger than the energy gained by the heat-differential created between the left and the right volume of the one-time uniform heat bath.
B – Let us pretend that we are ancient greeks. With distrust, squinting into the sund and hot dust, we will consider the assumptions and names: Demon, infinitesimal aperture, nigh-infinite ability to observe, night-infinite speed to slide aperture, unerring [or the wrong molecule might pass], needs no food. What are we, through sweat-dazzled eyes, sitting in the shade of a Palaestra, looking at here? An almost impossible hypothetical scenario. And what end do such unrealizable scenarios have in common? They suggest, even make plausible, situations and outcomes that only serve one end: show the thinker‘s hypothesis to be realistic, yield the desired results. In other words: if you manipulate the conditions of an experiment, even a thought experiment, long enough, lo-and-behold, you end up demonstrating precisely what you set out to. In yet other terms: if you posit an impossible creature doing impossible feats, little wonder, you end up with impossible results. Instead of Maxwell‘s Demon frantically opening and shutting the hatch, we might as well have asked Jesus to wave his hands above the volumes to create the heat differential.
C – Ultimately, there also appears to exist a proto-mathematical rational to consider. Imagine the speedy molecule having shot through the aperture – will it calmly fly off into the sunset? Will it even gently glide across to the other side of the right volume? Nay and nay. Instead it will immediately, without a nano-second‘s notice, jam headfirst into the molecular storm. The collision will, on average, accelerate the molecules in the right volume, as they get hit by a fast molecule from the left volume. Thus, on average, and beginning spatially from the very aperture where the slow molecules from the right are supposed to pass through, the velocity of the molecules on the right will rise. Thus the next molecule coming from the right will have a slightly higher average speed flying into the left. With each quick molecule from the left, the average slow molecules from the right are faster and faster. My contention is that this speeding up of molecules on the right, then passing to the left will eventually compensate for the fast molecules lost on the left. Thus no matter how fast Maxwell‘s Demon flits about, due to the almost instantaneous dispersal of kinetic energy in the molecular storm he will ot be able to create an imbalance in the heat bath. Sorry.
And so now I can file these thoughts away because, to consider it in the stark light of total subjective honesty, it will be a rare day when you feel any sort of enthusiastic sentiments [much less readerly desire] concerning the Maxwellian Demon or other physical conundrums of this ilk. But yet still this seems an important entry in the anti-entropic archive. Oh comrade, my comrade, this bloody life of the mind, what a mess it is!