"In fact, the latest results from ATLAS, one of the two giant detectors at the LHC, show that there's no evidence for many of the particles all the way up to 700 GeV, or over 100,000 times the mass of the electron and the two lightest quarks."
Abstract
I show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. I call devices with that structure "inference devices". I present a set of existence and impossibility results concerning inference devices. These results hold independent of the precise physical laws governing our universe. In a limited sense, the impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. Alternatively, these impossibility results can be viewed as a non-quantum mechanical "uncertainty principle". Next I explore the close connections between the mathematics of inference devices and of Turing Machines. In particular, the impossibility results for inference devices are similar to the Halting theorem for TM's. Furthermore, one can define an analog of Universal TM's (UTM's) for inference devices. I call those analogs "strong inference devices". I use strong inference devices to define the "inference complexity" of an inference task, which is the analog of the Kolmogorov complexity of computing a string. However no universe can contain more than one strong inference device. So whereas the Kolmogorov complexity of a string is arbitrary up to specification of the UTM, there is no such arbitrariness in the inference complexity of an inference task. I end by discussing the philosophical implications of these results, e.g., for whether the universe "is" a computer.
Physics might be defined as the subject that tries to figure out why the world may look incomprehensibly complex at first, but on closer examination is governed by simple laws. Those laws, applied repeatedly, build up the complexity. From this definition, you'd presume that physicists have at least sorted out what they mean by "law".
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