Ok, this is my train of thought:
1. We observe the universe to have constant energy and thus energy is conserved.
2. Emmy Noether proved that if the Lagrangian admits some quantity as being constant, then there is a corresponding conservation law. The inverse holds true too, to my understanding.
3. Conservation of energy (and more generally the four-momentum and stress-energy tensor), which we observe on the universe, means the laws of physics can't vary in time.
4. For there to be non-determinism (free will or events that have no cause) in the brain, the laws of physics would have to be changing locally inside the brain over time
. If there isn't that, then there is no free will.
Which point am I being mistaken on? And I honestly thought I addressed your original comments zhermnes, but here I will go at it point by point.
Yes, this is equivalent to my statement that our collective brain state is made of the entire energy state inside the brain. By Noether's first theorem this should imply the laws of physics are invariant inside our brains, and thus every neuron firing has a causal chain backwards to whenever the laws of physics were first invariant in time. Leaving no room for free will.
It is my understanding that if free will existed, then determinism must be false. An indicator that determinism is false would be the laws of physics varying in time. In fact, Noether proved the two are equivalent. So, instead of speaking of determinism, we can just talk about the laws of physics being time invariant. If they are invariant then free will is an illusion and the rearrangement of energy inside our heads is just creating the illusion of free will.
I am trying to not suppose it. I am arguing that it can be derived from our observations that the laws of physics are invariant over time. I understand that modern ideas in string theory involving the multiverse might have different laws of physics for different branes. We are also unsure if the laws of physics are even consistent in our universe at other locations that we can't observe. But thus far, locally, and for all observations, the laws of physics have been invariant in time.
Thanks for taking the time to read my ideas and I hope this clarifies. If not, then maybe I'm just too out of it... I hope not! :)