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Quantum physics dictates that there are probabilities that determine the outcome of an event, ie: the probability of a quark passing through a wall is X, due to the size of the quark in comparison to the wall), but couldn't macroscale events be predicted this same way, assuming all variables were accounted for (lets hypothetically say we have a computer powerful enough to take into account all factors).

My understanding is that as the scale of an object increases, the probability of it doing anything other than what classical physics dictates is almost 0%, but could conceivably do something not predicted (Example: a human being cannot pass through a wall, but given an infinite timescale, eventually s/he would because of probability not being 0). Is this accurate? If so, then shouldn't we, (except as a tool for conceptualization, like how we round 9.8 m/s^2 or pi to 3.14), use only quantum mechanics to explain events in any scale (for more accuracy)?

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Have a look at my answer and comment to… – anna v Aug 13 '12 at 17:37
up vote 2 down vote accepted

Quantum physics applies to all events in the Universe, whether they're microscopic or not. However, for macroscopic events, classical physics (approximately) holds, too. In other words, one may show that whenever the relevant products of powers of quantities that describe a system are much greater than $\hbar$, Planck's constant, we may use approximate laws to describe the behavior of the system, namely the laws that are formally the $\hbar\to 0$ limit of the laws of quantum physics: the corresponding classical theory.

The emergence of classical physics as a limit of a quantum mechanical theory has many conceptual and mathematical aspects, see e.g.

Concerning your particular question on tunneling, macroscopic objects may tunnel through the wall; it's just very unlikely. Consider a pair of macroscopic objects, a wall and a ball. Each of them has $10^{25}$ particles. If the microscopic probability of an atom's penetration through another atom is $q$, then the penetration of the two macroscopic objects through each other is pretty much the "penetration of each atom of a ball through each atom of a wall" and the probability is therefore $${\Large P\sim q^{10^{25}\times 10^{25}} = q^{10^{50}} \sim \exp(-10^{50})} $$ if $q\sim \exp(-1)$ is a reasonable suppression for the microscopic process. Let me emphasize that the probability $P$ above has the form $0.000\cdots 0001$ and the number of zeroes after the decimal point in this sequence of digits isn't just fifty. Instead, the number of zeroes in the tiny number is $10^{50}$ i.e. 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. It is a ludicrously tiny number which is why the tunneling of macroscopic bodies may be neglected and considered impossible. The largest object for which such a tunneling could be meaningfully considered would be a biological molecule such as a protein.

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Lubos, would that probability be the same if the macroscopic state be in a coherent state, say, a bose condensate? – lurscher Aug 13 '12 at 18:52
So basically you are saying that until computational power is powerful enough, approximations with the classical theory are good enough. Thank you for your concise reply. – Matthew Spencer Aug 13 '12 at 18:52
Dear @lurscher, your point is surely right. There could be special arrangements of a macroscopic state that could change the counting, perhaps seriously so. A Bose-Einstein condensate could, under some circumstances, behave as a single particle or a small bound state, for example. One should probably talk about more specific setups in that case. More generally, it's definitely the case that even macroscopic collections of matter may display quantum phenomena - although superconductivity etc. should really be said to be "classical phenomena mathematically analogous to some quantum ones". – Luboš Motl Aug 13 '12 at 21:23
That means that even since some time after the Big Bang (not one second after) till now, no quantum macroscopic event has occurred in the Universe? – jinawee Mar 25 '14 at 22:56

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