My ultimate dream: systematical descriptions of the STATES of systems.
Scientists have always been interested in finding LAWS of physics (especially the currently most fundamental LAW), and we try to examine the LAWS as carefully as possible. However, I feel not much people try to study the STATE of the system as carefully. The system is described by the LAW and the STATE after all.
Well, STATES can be complicated and not as elegant as the LAW, but I do think there should be a systematic way to describe STATES. For instance, in statistical mechanics uniform ignorance of time gives the microcanonical-like ensembles (if the system is Ergodic, then it's truly microcanonical). This is pretty elegant!
It seems to me, we can always assume Ergodic assumptions of some kind to some internal degrees of freedom. As we obtain more information about the system, the ensemble of STATES can be updated accordingly. If we can find such a systematic way of updating, we can essentially describe the system of the system in a careful way. Of course, it might involve complicated mathematics that might be too difficult to analyze, but I think it's at least worth a shot. I think I will spend my life shooting it.
Penn State University (Condensed Matter), College Township, PA, USA
Member for 3 years, 10 months
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Last seen Aug 8 at 18:42