## - Challenging Physics

In the early ’60s, Rolf Landauer of the IBM research laboratories was worrying about the physics of the computing process. His goal, of course, was to help IBM find paths to bigger and better computing machines. But in this process, he apparently made a mistake. In his work, he claimed that erasing computer bits was tantamount to physical dissipation. In fact, there is no such connection, as many scientists have shown since the early work.* The issue lies in the concepts of phase space. If we have a single physical particle, then classically it has a position in three dimensions and a momentum, or velocity, in three dimensions. Thus, it takes six dimensions to express its position and velocity. If we have N particles, we need 6N dimensions to express fully all of the positions and velocities. This is the phase space of the N particles. Now, the issue is that if the particles lose energy, their momenta are reduced, hence it requires less volume in the 6N dimensional space to contain the points that describe each particle’s position and momentum. We say that this compresses the phase space occupied by these particles, and this compression

represents a dissipative process. On the other hand, a computer bit has two values, 0 or 1. Hence, it has one dimension which has only 2 points in the dimension. If we have N bits, then we have N dimensions in this phase space. The issue is whether or not there is a connection between these two phase spaces-that of the physical representation of the computer bits and that of the logical representation of the bits. Landauer suggested that there was a connection, and if we erased a bit, that would entail a physical dissipative process which compressed the physical phase space. It is this suggested connection that is deemed to be wrong these days. That is, the erasure of a random logic bit does not require any corresponding reduction in the computer bit phase space, since the states still exist. It may or may not lead to a reduction in the physical phase space.