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Due to the Heisenberg Uncertainty Principle, one cannot know the complete state of a system, or particle. And so, unable to know fully certainly the state of a system, it is impossible to perfectly predict something. If one could know the full initial states, could you predict everything? If so, then since at the start of the cosmos, everything was shrunk into one spot (my cosmology isn't very good), then is that not knowing the position and velocity of everything with full accuracy?

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  • $\begingroup$ Are you also able to predict particle decay? $\endgroup$ Sep 5, 2022 at 0:43
  • $\begingroup$ @Jonathan but was there anything present at that "one spot" ?? $\endgroup$
    – Ankit
    Sep 5, 2022 at 4:44
  • $\begingroup$ Why can't you know fully and certainly the state of a quantum system? $\endgroup$
    – WillO
    Sep 5, 2022 at 5:17
  • $\begingroup$ Pre-quantum mechanics (and pre-cosmology), this idea was known as Laplace's Demon. $\endgroup$ Sep 5, 2022 at 12:03

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Due to the Heisenberg Uncertainty Principle, one cannot know the complete state of a system, or particle.

That's not quite right. You can know the complete state. That is, it's possible to prepare a system in what's known as a pure state in quantum mechanics. But the complete description of the state can't simultaneously include incompatible observables. For example, you can prepare a system in a state of definite position, but then it won't be a state of definite momentum -- and vice versa.

And so, unable to know fully certainly the state of a system, it is impossible to perfectly predict something.

So, for the same reason, this is also not true. You can put a system in a definite state, and you can then predict perfectly what state it will be in at some later time. (That's what the Schrodinger equation does.) But the system won't, for example, be a state of both definite momentum and definite position.

If so, then since at the start of the cosmos, everything was shrunk into one spot (my cosmology isn't very good), then is that not knowing the position and velocity of everything with full accuracy?

No, the big bang didn't occur at a point.

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If you knew perfectly knew the initial state of everything, could you predict everything?

If you study physics, you will learn that it is a discipline which observes and measures quantities in nature and uses various mathematical models, since the time of Newton, to fit measurements and data and , important , predict new , in order for the model to be validated. This over the two centuries has led progressively to the following physics theories, which in their specific region of validity are predictive and valid, and which in overlapping regions of variables is consistent.

  1. Classical mechanics

  2. Thermodynamics

These, for variable phase space where the Planck constant h is compatible with zero for the measurements fitted, can mathematically predict "everything" . BUT, nature had surprises for small dimensions and as studied proceeded

  1. Quantum mechanics had to be invented ( there is a list in this answer of mine for the need of quantum mechanics). Quantum mechanics can only predict accurately probability distributions, not single event values.

Underlying these theories are Galilean relativity for classical mechanics, special relativity for large velocities, and general relativity for large energies and masses.

if so, then since at the start of the cosmos, everything was shrunk into one spot (my cosmology isn't very good), then is that not knowing the position and velocity of everything with full accuracy?

Classical cosmological models using general relativity , and in general classical models, become singularities if one goes to "one spot", point, simply because of the 1/r form of the forces of nature, r cannot be zero, so there cannot be full accuracy. Present cosmological models break down for very early times where there would be a singularity classically, and quantum mechanical models are used with their probabilistic nature allowing for a large phase space for the beginning , see the mainstream big bang model.

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  • $\begingroup$ "physics is models to fit measurements and data". I observe that you write this line in every answer of yours ;) $\endgroup$
    – Ryder Rude
    Sep 5, 2022 at 6:46
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    $\begingroup$ @RyderRude I want to ground people to the view that it is not the mathematics that creates the data, but the data needs to mathematics to be usefully modeled and have predictive models. Most people answering questions here are mathematically oriented. Of course if a mathematical theory of everything in physics is found, then my reminders will be outdated. $\endgroup$
    – anna v
    Sep 5, 2022 at 7:28
  • $\begingroup$ Agreed. Reality is too bizarre for any of these toy models to fit it perfectly. $\endgroup$
    – Ryder Rude
    Sep 5, 2022 at 7:51

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