The latest paper that I'm aware of on this topic deals with a very detailed calculation of calculating the tipping time of a quantum rod[1]. In this calculation, the author showed that the classical problem can be recovered when the Planck constant goes to zero, and draws the conclusion that:

.. the tipping of the quantum rod can be understood as having been triggered by the uncertainty in angular momentum engendered by localization of the initial state...

The article is a bit difficult to follow, and I didn't get any direct value of the tipping time.

The more interesting papers that I've found earlier on the same topic are much more illuminating than this one. A paper by Don Easton presents a caution for people who tries to apply QM as the basis of the tipping time[2]. His calculation of the tipping time, using QM, gives a humongous number: 0.6 million years. He examined why some posted solutions actually gave a balancing time of the order of 3 seconds, and why those treatment may be faulty.

Another paper that cautioned the use of the HUP in calculating the tipping time is a paper by Shegelski et al.[3] Here, they caution that one can't just use the HUP alone, and they also compared this to the faulty application of the WKB approximation to this problem.

Fascinating! Certainly something that I read in bed before going to sleep! :)

Zz.

[1] O. Parrikar, Eur. J. Phys. v.31, p.317 (2010). You can also get a free copy of the paper within the first 30 days of online publication at this link.

[2] D. Easton, Eur. J. Phys. v.28, p.1097 (2007).

[3] M.r.A. Shegelski et al., Am. J. Phys. v.73, p.686 (2005).

## 2 comments:

Thanks for this highly informative post! I will be citing this blog as a read for my students.

trying to present this problem.

I am totally at sea about which solution i should follow

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