Beyond Moore's Law

If Moore’s law continues at its current pace, sometime between 2040 and 2050 the basic elements of a computer will be atomic sized. And even if Moore’s law slows, we eventually hope that computers will be made of components which are atomic sized. Either way, we really believe that it might be possible to get to “the end of Moore’s curve.” A question I like to ask (especially to those employed in the computer industry) is “What will happen to your job when we hit the atomic size barrier for computer components?” (or more interestingly, “will you still have a job when Moore’s law ends?” Yes, I know, software is important, architecture is important, etc. I still think the end of Moore’s law will result in major changes in the industry of computers.)
One question which comes up when we think about the end of Moore’s law is that in some sense, the end of Moore’s law that we’re talking about is the end of a particular manner of creating fast computing devices. Mostly we are thinking about the end of silicon based integrated circuits, and even more broadly we are thinking about the end of transistor based computers (i.e. we include both silicon based circuits and also molecular transistors, etc.) And the fundamental speed of these devices is rooted in physics. So what can physics tell us about what lies beyond Moore’s law?
Well first of all, the length scales involved in the traditional version of Moore’s law are atomic length scales. The barrier we are hitting is basically the barrier set by the laws of atomic physics. But we know, of course, that there are smaller length scales possible. In particular the next step down the ladder of sizes is to go to nuclear length scales. But we also need to say something about the speeds of operations. What are the limits to the speeds of gates which an atomic physics based computer can operate at? Interestingly, there is often a lot of confusion about this question. For example, suppose you are trying to drive an atomic transition (this is nothing like our transistors, but bare with me.) with your good old tabletop laser. The speed at which you can drive this transition is related to the intensity of the laser beam. So it might seem, at first guess that you can just keep cranking up the intensity of the laser beam to get faster and faster transitions. But eventually this will fail. Why? Because as you turn up the intensity of the laser beam you also increase the probability that your system will make a transtion to a state you don’t want it to be in. This may be another energy level, or it may be that you blow the atom appart, or you blow the atom out of whatever is keeping it in place, etc. Now, generally the intensity of the laser beam at which this becomes important is related to the energy spacing in the atomic system (if, say you are trying not to excite to a different level.) Note that the actually energy spacing of the levels you are driving is NOT the revelant information, but most of the time, this spacing is the same order of magnitude of the spacings to levels you are trying to avoid. So this allows us to, roughly, argue that the maximum speed we will achieve for our transition is Plancks constant divided by the energy spacing.
Now for atomic systems, the energy levels we are talking about might be, say a few electron Volts. So we might expect that our upper limit of speeds from our gate is something like 10^(15) Hz. Note that today’s computers, which don’t operate by driving atomic transitions, but in a different manner, operate with clock speeds of 10^(9) Hz (yeah, yeah, clock speed is no guarantee of instructions per second, but I’m a physicist, so order of magnitude is my middle name.) Only 6 more orders of magnitude to go!
So what does happen if we hit the end of atomic sized computing devices? As I mentioned the next step on the length scale slash energy scale are nuclear systems. Here we find energy scales which are typically millions of electron Volts. But I have absolutely no idea how to build a computer where internal nuclear states are used to compute. Which, doesn’t mean that it’s impossible, of course (which reminds me of a great quote by the late great John Bell: “what is proved by impossibility proofs is lack of imagination.”) So there’s a good problem for a nuclear physicist with a few spare moments: think up a method for computing using nuclear transitions.
One can continue up the energy scale, of course. But now it gets even more far out to imagine how to get the device to compute. Is it possible to turn the large hadron collider, currently being built at CERN, into a computer opperating at 10^(27) Hz (energies of terra electron Volts)? Now THAT would be a fast computer!