# Determinism of Macroscopic World

• I
Hi,

If the microscopic world is not deterministic, then naturally the macroscopic world should also be not deterministic because it is based on the microscopic world. The problem is that the macroscopic world is deterministic; the evidence of this is that a lot of our technology and calculations assume that the world is deterministic. For example, the start and the end of the moon eclipse tonight is predicted very accurately. Such accuracy couldn't be obtained if the planets and the sun move in a non deterministic way.

The macroscopic world is indeed non deterministic and what we calculate is nothing more than the most probable value; however, for macroscopic objects the probability of the other outcomes is negligible.

Is this conclusion true?

stevendaryl
Staff Emeritus
Yes. If you add up a large number of random variables, the sum becomes (nearly) deterministic.

A measure of how nondeterministic a process is is given by the standard deviation. The standard deviation describes the typical departure of some quantity from the most likely value. If the standard deviation is high, then the quantity seems very nondeterministic, and if the standard deviation is low, then the quantity seems approximately deterministic.

Let's consider generating a "random" number ##h## in the range 0 to 1 as follows: Flip a coin ##N## times, and let ##h## be the fraction of results that are "heads" (so it's the ratio ##\frac{H}{N}## where ##H## is the number of "heads").

The most likely value for ##h## will be ##1/2##. The standard deviation for ##h## will be ##\frac{1}{2 \sqrt{N}}##

With ##N=1##, the standard deviation is 1/2, which is the same size as ##h##. So ##h## is pretty nondeterministic, it can be 0 or 1.

With ##N=## one million, ##h = 0.5 \pm 0.0005##. So ##h## is pretty certain to be very close to 1/2.

So if you are dealing with very large numbers of similarly distributed quantities, then the averages will appear deterministic even though each of the quantities contributing to the average may be nondeterministic.

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• bhobba, bgq and Demystifier
Yes. If you add up a large number of random variables, the sum becomes (nearly) deterministic.

A measure of how nondeterministic a process is is given by the standard deviation. The standard deviation describes the typical departure of some quantity from the most likely value. If the standard deviation is high, then the quantity seems very nondeterministic, and if the standard deviation is low, then the quantity seems approximately deterministic.

Let's consider generating a "random" number ##h## in the range 0 to 1 as follows: Flip a coin ##N## times, and let ##h## be the fraction of results that are "heads" (so it's the ratio ##\frac{H}{N}## where ##H## is the number of "heads").

The most likely value for ##h## will be ##1/2##. The standard deviation for ##h## will be ##\frac{1}{2 \sqrt{N}}##

With ##N=1##, the standard deviation is 1/2, which is the same size as ##h##. So ##h## is pretty nondeterministic, it can be 0 or 1.

With ##N=## one million, ##h = 0.5 \pm 0.0005##. So ##h## is pretty certain to be very close to 1/2.

So if you are dealing with very large numbers of similarly distributed quantities, then the averages will appear deterministic even though each of the quantities contributing to the average may be nondeterministic.
Thank you very much

bhobba
Mentor
If the microscopic world is not deterministic, then naturally the macroscopic world should also be not deterministic because it is based on the microscopic world.

My view is a bit different and based on Feynman's path integral approach. At the level of the macro-world only certain paths exist - the rest cancel - giving the principle of least action (PLA).

Form the PLA and certian symmetry considerations (essay applications of Noethers Theorem) all of classical mechanics follows - and that is deterministic.

So exactly where does the quantum weirdness go? If you look closely enough, and I am not even sure with our current technology we can, we can see those paths have a bit of a 'width' so to speak. But tons of other phenomena like Brownian motion etc make detecting it very very difficult.

Thanks
Bill