"Other"
Some things are determined and some things are not. Anything that follows Newtonian rules are determined. That which follows quantum field rules is not determined.
While the Newtonian things are made up from quantum things, at that scale the statistics of large numbers (the sheer number of quantum particles involved) provide predictability. like flipping a coin 5 times may indicate chaos (total randomness). Flipping a coin 100 trillion times will come out very predictably 50/50 with an infinitesimal margin of error.
That's what the Schroding's cat mind-experiment is about. It demonstrates that small causes can have big effects, that uncaused quantum events can change macroscopic things.
Also, when T equaled zero, everything was small. If you wanted to argue that things became determinate after things got big enough, you would have to pick a time later than T=0.
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(Note: I'm assuming that "time T" in the OP is a reference to the beginning of time, to T=0.)
If you're going to flip a coin 100 trillion times--and you haven't flipped the first coin yet--the expected result will be 50/50. But if you've flipped once and gotten heads, then the expected result is one more heads than tails. If you get heads on the first five flips, then the expected result is five more heads than tails.The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during a given period, it will happen less frequently in the future (or vice versa).
-- Wikipedia
Whatever chaotic thing happens in your first five flips will influence the outcome of 100 trillion flips. There is no natural pressure for an early heads to be countered by a later tails.
I'm curious. Has anyone ever performed the Schrödinger's cat experiment for real? Has the effect actually been demonstrated?
Oh, and then I found this:
I seem to be answering my own questions:The Zeno effect is known to cause delays to any changes from the initial state.
On the other hand, the anti-Zeno effect accelerates the changes. For example, if you peek a look into the cat box frequently you may either cause delays to the fateful choice or, conversely, accelerate it. Both the Zeno effect and the anti-Zeno effect are real and known to happen to real atoms. The quantum system being measured must be strongly coupled to the surrounding environment (in this case to the apparatus, the experiment room ... etc.) in order to obtain more accurate information. But while there is no information passed to the outside world, it is considered to be a quasi-measurement, but as soon as the information about the cat's well-being is passed on to the outside world (by peeking into the box) quasi-measurement turns into measurement. Quasi-measurements, like measurements, cause the Zeno effects. Zeno effects teach us that even without peeking into the box, the death of the cat would have been delayed or accelerated anyway due to its environment.
The experiment as described is a purely theoretical one, and the machine proposed is not known to have been constructed. However, successful experiments involving similar principles, e.g. superpositions of relatively large (by the standards of quantum physics) objects have been performed. These experiments do not show that a cat-sized object can be superposed, but the known upper limit on "cat states" has been pushed upwards by them. In many cases the state is short-lived, even when cooled to near absolute zero.
I think it is more cvausal plus probabilistic that deterministic plus probabilistic.
From the last systems book I read the top level system catecory is chaotic. Ubder chaotic is deterministic and probabilistic.
At all timers the air temperature is a series of causal chains over a small volume to known basic physics. What makes weather chaotic is the number and precision of all the variables needed to quantify.
I watched a video of a chaos experiment. There are three fixed magnets on a table in a triangle. A metal suspended ball is released by a mechanism. The ball starts moving around the magnets and the trajectory mapped.
Repeat the experiment and on different trials the path the ball takes starts out the same but over time diverge. Deterministic electromagnetics but unpredictable over time.
For a deterministic system plug values into functions and the path will be the same every time. The diffence is in the variables, very small uncertanties in variables over time have a big effect.
I expect that is why scientists at NIST spend careers adding a decimal point to a constant.
Given our laws of science it would seem that at any given point in time there are a limited number of future possibilities. Rerun the BB and maybe Erath exists but no life evolved.
Entropy adding an element of randomness, perhaps.