# QND, CSCO, decoherence and Large N limits

While trying to actually understand the difference between QND and CSCO, I went and found the relevant reference doc, Quantum nondemolition measurements: The route from toys to tools. The key example in the paper discusses can best be summarized by looking at equations (7) and (29). Equation (7) defines the uncertainty of energy in the Standard Quantum Limit (SQL) as:

$$\Delta E_{SQL} = \hbar\omega\sqrt{N}$$

Equation (29) is a modification of (7) that takes into account "a priori" information about energy of a large object and is:

$$\Delta E_1 = \hbar\omega\sqrt{N} \dfrac{1}{\sqrt{\omega\tau}} \ll \Delta E_{SQL}$$

The argument being for large periods of observation the uncertainty in energy becomes much less than the uncertainty of the standard quantum limit.

Equation (30) then tells us:

$$\Delta E_{QND} = \dfrac{\hbar}{\tau} \ll \Delta E_1$$

The arguments in general rely upon repeated measurements over large periods of time, and it is the effect of long observations over large systems that reduces uncertainty in the measurement.

In the discussion it isn't clear how this in any way shows Heisenberg, Schrodinger, Bohr et al are wrong in any way, shape or form. The mantra of quantum mechanics has consistently maintained that classical mechanics emerges in the large N limit of quantum mechanics, and certainly if you increase the number of observations of a system over a large period of time there is no contradiction that you would approach classical mechanics. It seems that at some level this is just a misinterpretation of decoherence.

So what is new here and why do physicists and physics journalists have a hard time with this?

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Very good questions. Of course, there is nothing disproving foundations of quantum mechanics here. It's just some research "trying" to do such things whose results may be misinterpreted, especially with the help of stupid and superficial journalists, to indicate that something is questioned or challenged about quantum mechanics. In reality, all those papers work within the context discovered by Heisenberg et al. - they should celebrate it, not spit at it. Those things seem to be hyped every day, see motls.blogspot.com/2012/10/… concerning QND. –  Luboš Motl Oct 4 '12 at 14:14
I suspect there is an economic motive in creating headlines that contradict established physics. However, I can not fully understand the profit to the physicists, except that there appears to be no consequences. It makes me think that the physics community has become extremely hierarchical. I find this disconcerting since history has shown repeatedly that developments in physics, both technical and philosophical, are the single greatest predictor of long term human development. –  Hal Swyers Oct 4 '12 at 15:00
I totally agree. The physicists just become famous and it helps somewhere, among the laymen and the media etc. So as long as it doesn't hurt them elsewhere - in an ideal world, it surely should hurt them - it's a net benefit if they care about benefits more than about the truth. –  Luboš Motl Oct 4 '12 at 15:17