The earlier post has problems of its own: it works with an action with nonstandard units (in particular, mass is missing), its sign is backwards from the typical definition, and it doesn’t address how vector potentials should be treated. The Lagrangian doesn’t have to be positive, so interpreting it as any sort of temporal velocity will already be troublesome, but the Lagrangian is also not unique. It simply does not make sense in general to interpret a Lagrangian as a temporal velocity, so importing that notion into field theory also does not make sense.
The problem with all these entropic arrows of time is that a time reversible random walk tends to increase entropy both forward and backward in time. Without touching on time reversibility, fluctuation theorems, Liouville’s theorem in classical mechanics and unitarity in quantum mechanics, fine-grained vs coarse-grained entropy, etc, I don’t think this makes sense as an explanation of the arrow of time. As a physicist, this doesn’t come across as a coherent description.
The earlier post has problems of its own: it works with an action with nonstandard units (in particular, mass is missing), its sign is backwards from the typical definition, and it doesn’t address how vector potentials should be treated. The Lagrangian doesn’t have to be positive, so interpreting it as any sort of temporal velocity will already be troublesome, but the Lagrangian is also not unique. It simply does not make sense in general to interpret a Lagrangian as a temporal velocity, so importing that notion into field theory also does not make sense.
The problem with all these entropic arrows of time is that a time reversible random walk tends to increase entropy both forward and backward in time. Without touching on time reversibility, fluctuation theorems, Liouville’s theorem in classical mechanics and unitarity in quantum mechanics, fine-grained vs coarse-grained entropy, etc, I don’t think this makes sense as an explanation of the arrow of time. As a physicist, this doesn’t come across as a coherent description.