Given different T_zero configs of matter and energies T_current would be different. and there are many pathways that could lead to same physical configuration (position + energies etc) with different (Universe minus cake) configurations.
Also we are assuming there is no non-deterministic processed happening at all.
After all, Feynman showed this is in principle possible, even with local nondeterminism.
(this being a text medium with a high probability of another commenter misunderstanding my intent, I must end this with a note that I am, of course, BSing :)
Why? We learn about the past by looking at the present all the time. We also learn about the future by looking at the present.
> Also we are assuming there is no non-deterministic processed happening at all.
Depends on the kind of non-determinism. If there's randomness, you 'just' deal with probability distributions instead. Since you have measurement error anyway, you need to do that anyway.
There are other forms of non-determinism, of course.
We infer about the past, based a bit on some material evidence we can subjectively partially get some acquaintance with. Through thick cultural biases. And the actual material suggestions should not come to far from our already integrated internal narrative, without what we will ignore it or actively fight it.
Future is pure fantasm, only bound by our imagination and what we take for unchallengeable fundamentals of what the world allows according to our inner model of it.
At least, that's one possible interpretation of the thoughts when an attention focus on present.
Having observed the sun go up and down reliably over my lifetime so far, I infer that it will keep doing so far quite a while, and that it has done so before I was born, too. Not much culture about it.
Every scientific measurement has elements of this.
And to be honest, we only learn about the present through a thick layer of interpretation and inference, too. The past and future aren't that special in that regard.
It becomes even more fun, when you add the finite propagation time of signals into the mix: here on earth we can never learn about the moon in the present, only how it was about 1s ago.
The original comment's was in a differnt spirit or at least how I interpreted it. It was more implying by looking at a very small slice of reality you should in theory be able to re-construct the whole universe because every particle and space quantum is being influenced (to tiniest degrees) by every other particle in the universe, which will not work if you dont know all the rules, no determinism and T_zero.
I don't know why you want to know T_zero. I assume T means time here, not temperature or so?
If you have eg randomness as your non-determinism, you can still build probability distributions of the rest of the universe and the rest of time. (And honestly, even if you have determinism in the laws, you always have measurement errors. Even in classical mechanics.)
[1]: Arguments are ongoing about whether the universe has "real" numbers (in the mathematical sense) or not. However it is undeniable the Planck constants still provide a practical barrier to any hypothetical real valued numbers in the universe that make them in practice inaccessible.