You say this theory of your predicts “that localized quantum fields will maximize proper time”. It’s not clear how it’s a prediction of this theory, since the statement of the prediction is the first time you mention proper time in this article. I looked through the follow-up link to see if the prediction came from there, but the link doesn’t mention entropy (nor does this post mention action). And I don’t believe that “The physics establishment sidesteps this quandary by defining time to progress in the direction of increasing entropy” is a fair assessment of how most physicists think about time and entropy. If you want to talk about the physics establishment and entropy, it would be helpful to address the work on fluctuation theorems.
I also have problems with the description of Lagrangian mechanics in the link about proper time. The description of the δq in Noether’s theorem as being “oriented along the direction of the particle’s path” isn’t accurate; it’s oriented in whatever direction corresponds to the symmetry in question. The statement that Lagrangian density should be considered as a “temporal velocity density” doesn’t have any justification, and seems difficult to mesh with the Lorentz invariance of the Lagrangian density. The substitution made for the field theory version of the Euler-Lagrange equation in terms of the d’Alembertian of the Lagrangian density is also incorrect.
My post on Noether’s theorem is a follow-up to this post which explains why the Lagrangian should be considered “temporal velocity”. The idea of Lagrangian density as “temporal velocity density” comes from dividing both sides of the Lagrangian = “temporal velocity” equation by space.
My theory predicts that time points in the direction maximizing an entropy function. Locally, this theory predicts that the smallest things (localized quantum fields) evolve in the direction of time within their own reference frame i.e. they maximize proper time.
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.
You say this theory of your predicts “that localized quantum fields will maximize proper time”. It’s not clear how it’s a prediction of this theory, since the statement of the prediction is the first time you mention proper time in this article. I looked through the follow-up link to see if the prediction came from there, but the link doesn’t mention entropy (nor does this post mention action). And I don’t believe that “The physics establishment sidesteps this quandary by defining time to progress in the direction of increasing entropy” is a fair assessment of how most physicists think about time and entropy. If you want to talk about the physics establishment and entropy, it would be helpful to address the work on fluctuation theorems.
I also have problems with the description of Lagrangian mechanics in the link about proper time. The description of the δq in Noether’s theorem as being “oriented along the direction of the particle’s path” isn’t accurate; it’s oriented in whatever direction corresponds to the symmetry in question. The statement that Lagrangian density should be considered as a “temporal velocity density” doesn’t have any justification, and seems difficult to mesh with the Lorentz invariance of the Lagrangian density. The substitution made for the field theory version of the Euler-Lagrange equation in terms of the d’Alembertian of the Lagrangian density is also incorrect.
My post on Noether’s theorem is a follow-up to this post which explains why the Lagrangian should be considered “temporal velocity”. The idea of Lagrangian density as “temporal velocity density” comes from dividing both sides of the Lagrangian = “temporal velocity” equation by space.
My theory predicts that time points in the direction maximizing an entropy function. Locally, this theory predicts that the smallest things (localized quantum fields) evolve in the direction of time within their own reference frame i.e. they maximize proper time.
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.