Thanks for opening the thread. The talk about the ZPE I thought is well connected to vacuum, but the article seems to tie many issues in QM/QFT in general. I hope I can have more questions soon.

The main goal of the article, as stated in the abstract, is something quite different:

Jaynes effectively claims that quantum physics is not about properties of Nature but about human knowledge management. I find his Bayesian, subjective probability view untenable as a basis for objective physics. The last two sections of Chapter 10 of my online book give a specific critique of his views in the context of statistical mechanics (where its strength is supposed to lie).

According to the abstract, his main critique to which he targets his exploration is

though in the main text he doesn't even state what he means by this, let alone explain the content of the paradoxes and mysteries. This already shows that something is seriously wrong with the paper - it is a sequence of loosely related philosophical musings, not a proper scientific paper. (He has no qualms to talk on p.3 about the problem of generating infinities caused by using ##\infty^2## more degrees of freedom than the infinitely many degrees of freedom actually used by Nature, though ##\infty^2## times ##\infty## is still ##\infty##, as we know since Cantor.)

But I agree with this critique, and think that one cannot reasonably uphold the view that the use of density matrices in quantum physics (for Lindblad's equation or statistical mechanics) should be interpreted as due to a lack of information about the true, pure state. They contain the complete information that can be possibly obtained about the state. Once this is acknowledged, most problems associated with wave functions go away, when combined with another remark by Jaynes, on p.11:

My thermal interpretation makes this self-evident observation the basis of a common sense interpretation of quantum mechanics, without giving up objectivity or introducing human elements into the foundations.

A problem with Jaynes' arguments is that he bases much on arguments of authority from sources now mostly 50 or more years old (hence were already 30 or more years old when he wrote the paper). That he takes Bayesian computational results on p. 8 as support for Bayesian philosophy (although algorithms are immune to philosophy since all Bayesian statistics has a frequentist interpretation) is also strange.

He repeats well-known stuff summarized in his statement on p.11:

and adds (in my opinion without further gain in insight) his own subjective philosophy.

I argue in my Insight articles (and in the discussions of them) far more strongly that vacuum fluctuations cannot be real events since they lack all dynamic characteristica that go with real events.

Thus to answer your query, you can look at the section on the zero-point energy as a superficial and mostly historical discussion of some pros and cons of the two sides of the debate, and you can take the paragraph before this section and the conclusion of the paper as indication that he takes in this debate the same side as I, though for completely different reasons.

To answer the question concerning Eq. (30). Here ##\Gamma## is the width of the Lorentzian. It's easy to show by using a contour integral in the complex energy (freuquency) plain to get the Fourier transform to the time domain. It shows that ##\Gamma=1/\tau## is the inverse lifetime of the harmonic excitation described by the Lorentzian. Obviously ##\tau## is the time over which the amplitude of the oscillation decreases by a factor of ##\mathrm{e} \simeq 2.71828##.