Anthony Aguirre's ideas about entropy and time symmetry are interesting about the the nature of time, entropy, and the structure of the universe. His views create debates and foundational questions in thermodynamics and cosmology due to the analysis of this initial state at low entropy implying these time symmetric cosmologies.
If we take the entropy , time and this arrow of time, so this entropy measures the disorder and the links between the micro and macro states, we know that in thermodynamics this entropy increase in isolated state and implies this arrow of time and the evolution of events from lower to higher states, in all the cases when we consider the classical thermodynamics, so this idea of Anthony Aguirre considering the initial state highly ordered at this lower state become intriguing philosophically speaking , but taking the staistics it is unsual . It is like a mirror of a kind of opposite BB and so a time reversal.
I ask me how to consider the statistics and probabilities in this reasoning knowing our limitations physical and philosophical for this time reversal and entropy decrease. Our statistical mechanics for this entropy and the Boltzman entropy equation permit to understand the macro systems and entropy increasing with the lower and higher states, that said it is indeed different in cosmologyy probably , we can see this in the Bekenstein Hawking entropy near BHs or the hubble entropy , so in these cases indeed the entropy are considered differntly than for the local classical thermodynamics.
It is this that I like in the idea of Aguirre for the time reversal at a minimum entropy surface and initial conditions at this BB, that said this BB even if we have datas relevanmt with the CMB and others is a philosophial assumption, we could have like in my model a central sphere , a super matter energy made of photons, DM and DE at this initial state, The mathematics it is that said relevant to extrapolate possibilities at lower entropy states , it is there that it is relevant the idea of Aguirre for the time and bacward or forward evolution, that is why that implies this bridge between the physicalit at this initial state and many possibilities even with the multiverse or even with an infinite eternal consciousness in 0D even behind this initial state.
This eternal inflaion and time symmetric cosmology intrigue me philosophically I must say, How must we consider the problem and the analysis of the space and the different states and rates , In my model I consider an universal sphere in evolution, so the spherisation but if we have multiverse or multispheres, and even different physical conditions, all this become complex and intriguing but alread our actual universe it is not easy to encircle it and mainly its philosophical origin, But indeed this time symmetric cosmology providing a framework for the eternal inflation with 2 directions of time is interesting,the einstein field equations for this inflating spacetime with boundary conditions with this entropy becomes challenging, from lower o higher states. In all the saces it is well to try to understand how this universe has begun and the fact to extrapolate the entropy states philosophically.
After all several equations in physics are time reversal like the maxwell or schrodinger ones, , so why not for the cosmology . There are also interesting extrapolations to do with the quantum cosmology and wavefunctions of the universe , a little bit like in the model of Hartle and Hawking if my memory is correct, but how to consider the philosophical origin of this universe , that is the question, materialism, pantheism., mathematical.....we don t know. We have the same problem for this consciousness also, it becomes a philosophical problem.
I ask me how to consider the statistical mechanics and this arrow of time in this logic and the thermodynamcis and second law , if the time symmetruc model implies a decreasing entropy towrd the initial state , that contredict the priciple of this second law and it is maybe there the relevance . An other problem is the observations , we have not actually time reversal phenomena. This quantum gravitation and initial conditions seem a key and we can speculate actually ,it could be well if the penrose diagrams can utilise the maths about the causal structure oif this spacetime, and if the time symmetric cosmology can nbe correlated with entropy states and correlated with the inflation. It is mainly avout the boundary conditions after all and the Einstein field equations and entropy states but we must find exact concrete solutions in maths.
