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## Main Question or Discussion Point

I've always been curious about the boundary between the quantum and classical regimes, and I've often wondered if the weather is not just a chaotic system, but if it had a degree of true randomness, if it is significantly influenced by quantum events. So I tried to calculate the approximate magnitude of quantum effects in the atmosphere.

Earth's atmosphere contains about 5*10^15 tons of gas. 3/4 of the mas is concentrated within 11km of earth's surface, and the atmosphere gets thinner as one travels further from the surface of the earth. If the earth's radius is 6389.1 km, then this means that the volume of containing 3/4 of the atmosphere's total mass is 5.63*10^18 m^3 If the atmosphere is about 80% N

I'm not quite sure how to interpret this. On the one hand, I'm positive detonating a gigaton explosive would have an effect on the weather. However, what little I know of thermo and QM suggests to me that this energy uncertainty would be infinitesimal and evenly spread out among each particle, and entropy would prevent a cataclysmic event from happening randomly and all at once.

So would a .01 degree difference in temperature (on any distance scale) have a noticeable effect on the weather (and on what time scale)? I've heard of the butterfly effect, but I'd like to know if the clouds I'm looking at right now would be a different shape if the quantum jostling of their constituents had played out differently.

Earth's atmosphere contains about 5*10^15 tons of gas. 3/4 of the mas is concentrated within 11km of earth's surface, and the atmosphere gets thinner as one travels further from the surface of the earth. If the earth's radius is 6389.1 km, then this means that the volume of containing 3/4 of the atmosphere's total mass is 5.63*10^18 m^3 If the atmosphere is about 80% N

_{2}and 20% O_{2}, then the average weight of a molecule of gas is 4.78*10^-26 kg. Dividing the total mass by the molecular mass, their are 7.84*10^43 molecules in 3/4 of the atmosphere, and the average spacing between each one is 4.16*10^-9 m in each dimension. So the uncertainty in momentum in each dimension is 1.27*10^-26 kg*m/s (so I believe the total uncertainty per particle is sqrt{([tex]\Delta[/tex]p_{x})^{2}+([tex]\Delta[/tex]p_{y})^{2}+([tex]\Delta[/tex]p_{z})^{2}} = 2.20*10^-26 kg*m/s). If the average temperature of the atmosphere is 15 degrees C, this corresponds to an uncertainty in the temperature of each particle on the order of .01 K. This nets to an uncertainty in energy on the order of 10^19 Joules, or several gigatons of TNT.I'm not quite sure how to interpret this. On the one hand, I'm positive detonating a gigaton explosive would have an effect on the weather. However, what little I know of thermo and QM suggests to me that this energy uncertainty would be infinitesimal and evenly spread out among each particle, and entropy would prevent a cataclysmic event from happening randomly and all at once.

So would a .01 degree difference in temperature (on any distance scale) have a noticeable effect on the weather (and on what time scale)? I've heard of the butterfly effect, but I'd like to know if the clouds I'm looking at right now would be a different shape if the quantum jostling of their constituents had played out differently.