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Is there a causal link between quantum property indeterminacy (randomness) and a complex molecule's location in space in any moment at larger scales aka Brownian motion?

This question is void if my premise (the paths of particles in Brownian motion cannot be predicted) is false.

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    $\begingroup$ Ultimately, we can't plot the motion of the atoms causing the Brownian motion, although "quantum property indeterminacy" is not the same thing as randomness, it's just our inability to measure the both the position and velocity of a particle, at the same time, due to the Heisenberg Uncertainty Principle. $\endgroup$
    – user108787
    Commented Jun 11, 2016 at 18:37
  • $\begingroup$ the 'cause' of brownian motion's indeterminacy when we view the particles in a classical way, is that it will be very hard to determine or take into account all the movements of all the many particles that constantly collide the molecule. If we can take all that into account, then we can determine the path of the molecule. But in the view of quantum mechanics, there's no way to determine or measure both the exact position and momentum of any particle, which means, that the path of the molecule (and the motions of other particles) will never be exactly determined. $\endgroup$ Commented Jun 11, 2016 at 22:09
  • $\begingroup$ Related: physics.stackexchange.com/q/66738/226902 and physics.stackexchange.com/a/762425/226902 $\endgroup$
    – Quillo
    Commented May 13, 2023 at 15:00

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No, there is no simple connection.

In quantum mechanics, the position of the particle is represented by a wave function so that the particle is "everywhere" and only after measurement can we localise it. This localisation has an error which is not due to the instrument's precision but rather is intrinsic in the "shape" of the wave function and indeed can be predicted regardless of the measurement apparatus.

In the case of Brownian motion, we are talking about a big particle moving erratically. However, its position and momentum are well-defined, the reason Brownian motion is modelled as a stochastic process is that it is too hard to measure it with enough precision. But if you had a very fast microscope, you could measure its position in space and time with increasing precision.

There is only one last point: because everything is at some level described by quantum mechanics, there is a sort of "leftover" indeterminacy in everything, including Brownian motion. However, for objects of bigger scale (e.g. a colloidal particle) that can often be completely neglected. Predicting or measuring exactly what fluid molecule is pushing the particle might indeed be harder and quantum-like, but measuring the position and momentum of the Brownian particle, it being a classical particle, is just a resolution issue.

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  • $\begingroup$ In essence: just because a macroscopic process is stochastic and chaotic, it doesn't mean it's a reflection of the quantum nature of molecular or atomic things. $\endgroup$ Commented Mar 11, 2021 at 11:38

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