Does Quantum Mechanics Allow Macroscopic Anomalies? I've read a few other posts, and none seem to give me an answer that satisfies my curiosity. Thus far I've only been studying time independent QM, so I'm not even sure how wave functions evolve over time for microscopic things, let alone macroscopic things. However, what mandates that events that expect to happen actually happen? Why does it make sense that when I put something in  a box, that it should remain in the box, rather than tunneling elsewhere? Or why should a pot ever come to a boil? Certainly these questions are being caused from a tragic misunderstanding of quantum theory, can someone clarify for me? At the end of the day, there is a nonzero probability that macroscopic anomalies will occur, right?
 A: As with many things in Quantum Mechanics and Statistical Mechanics, the answer is: "There is a non-zero probability that 'anomalies' will happen, but the probability of them occurring is infinitesimal".
Take, for instance, one of the examples you brought up: why, if I put something (let's say, for simplicity's sake, an electron) in a box (in the electrons, case, this "box" would be potential barriers that have higher energy than the electron has), does it have to stay in the box? Why can't it tunnel outside of the box?
The answer is, it can. But the probability of this happening is (depending on the conditions I guess) very small.
As far as macroscopic examples go, tunneling is so well understood, and predictable (statistically) that it is actually utilized in electronics now, in areas like touch screens, where differences in tunneling rates are used to ascertain the pressure of a press on a screen (from what I've read at least). 
A: First, there are effects from quantum mechanics that can be observed in macroscopic scale. I also have few words for "anomalies". Considering the following examples:


*

*Line in optical spectrum 

*Floating metal with superconductivity

*Micro-Marco entanglement of millions photon

*Schrodinger cat state with hundreds 


For (1), when you use a prism, you can see the spectrum of, say, sun light with many black line. This is the effect of quantized energy level. So, it is definitely a effect of quantum mechanics, but likely you may think that is normal.
For (2), you may be impressed by the fact that a metal can float in the air. But a balloon can also float! We also know that a big metal can "float" in air, that is what helicopter and airplane does, isn't it? Without knowing the underlying mechanism, there is nothing special about quantum mechanics. Right?
The (3) and (4) are usually considered as strong quantum effects because the non-classical correlation is not limited by speed of light. Even though they are separated far away, there is still entanglement between. However, you can't really see it by your eye. For the Schrodinger's cat, what you can really see is either a dead cat or live cat, not a half-dead-half-live cat. The difference can only be proved if you have done lots of measurements with a statistical inference.

Indeed, most quantum phenomenon looks like classical phenomenon with random errors. A main reason is that measurement for macroscopic system is usually statistical, such as average number of photon, the average position, etc. Therefore, it is often hard to differentiate true randomness from quantum mechanics and randomness from statistics. It requires accurate equipments and careful measurements. This is not something that you can see by bare eye.
In particular, most quantum interference are easily confused with classical interference in the macroscopic scale. Considering the single photon double slit experiments already. It basically mean that either you keep observation a system and it behaviours classically. Or, you let the system evolves quantum mechanically, but now you can only observe an initial position and ending position. For the later case, a single photon tells you nothing. Only when you repeat it thousand times you can see the pattern. But a light beam actually give the 
Lastly, it is pretty well understood that a non-isolated quantum system interacting with environment leads to decoherence which will make the system behaviours classically.
A: I think that the problem has been stated in a way that begs the question. Any interpretation of QM that bases itself on the notion that the basis of the phenomena is wave interference by the particle itself, has to place some part of the "particle" in regions outside the box, so to speak. However, if one looks on the field that holds the particle as being quantized, then the field may not continuously form a barrier, and the particle can exit without the need to concoct an ad-hoc "anomaly". I've been exploring this idea and put together a clip as to how this relates to the twin slit experiment.
https://vimeo.com/91475662
A: Hello Anthony,
           One mind boggling example of quantum effect in macroscopic level is hawking radiation. In this particular case the whole black hole which is one of the massive thing in the universe can disappear from universe (if you have enough patience and possess immortality) while taking quantum effects into account.Link for further reading....
               1) http://www.mpa-garching.mpg.de/lectures/ADSEM/SS03_Schmidt.pdf
               2) http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html
Another example is as previously described as electron (quantum) tunneling and its correlated effect in macroscopic world "human tunneling"... We all know peculiar effect of quantum tunneling in our daily use like cellphone but the question here can be raised that can human pass through wall??   
Tunneling is explained using the Heisenberg uncertainty principle and the wave–particle duality of matter. Now according to de brogli's equation lambda=h/p as mass of particle increases its wavelength decreases. So we can not see quantum effect like wave particle duality in classical world , because human weighs much much more than single electron. So we can not see human pass through wall as frequent as electron . But again if you wait too much (have patience and possess immortality)  then you can yourself pass through wall.
  http://www.beck-shop.de/fachbuch/leseprobe/9780521800020_Excerpt_001.pdf

In this link please refer cat and moon scenario.... In it they give reference to passing carbon buckyball(C60) in two slit with interference pattern which is best example of quantum effect at macroscopic level.
