Updated thoughts on the debate about black holes gobbling up the earth

There was a huge debate a few years ago: 

IF one of our nuclear labs should have the ability to accidentally create a tiny black hole, would this gobble up the entire earth? More precisely, would it lead to events hidden deep in the earth, following Einstein's general relativity, where the black hole grows very slowly, and then, "on a bad hair day," relatively suddenly yanks the floor out under us? (This is pretty much standard exponential growth, where the biggest effects take place at the end.)

Many of you know about the emotions and posturing which went into both sides of the debate. It amazes me how often life-or-death debates in the US seem to be decided like fashion shows.. people compare how they look in red clothes or ideologies, versus blue clothes, and the objective reality underlying the issues often does not really come out. Fashion, vested interests and politics decide, objective reality be damned.

But on the objective reality here, there are some interesting developments...

At a fundamental level, the problem is that there are two different versions of quantum field theory, the basis of the standard model of physics which all the leading mainstream people rely on. It is commonly assumed that they are equivalent, because it is very convenient for people to do so, and because it is "almost" true. But in this case, they lead to different predictions. One says we will all die if the little black hole is created; the other says not. And most people really understand only one of the two.

Of course, I don't expect any of you to take what I say on faith. And if you study the mathematical literature, you may know about DOZENS of formal versions of quantum field theory. So... to verify the basic situation, you can look at a book by Steven Weinberg, Quantum Theory of Fields,  to the first two pages in chapter 9, which can be understood well enough without getting into all the details in the rest of the book. Weinberg's account is the number one account of what quantum field theory is, in a practical sense, since Weinberg himself developed half of the standard model of physics (the better verified half), and lived what really happened. 

The two dominant mainstream theories are: (1) canonical quantum field theory, which I call KQFT (with "K" for "Copenhagen"); (2) Feynman path integral quantum field theory, which I call FQFT. As Weinberg reports, KQFT was responsible for all the great decisive victories of quantum field theory 

in the old days; the shift to FQFT among theorists was driven by the fact that a guy named 'tHooft found it easier to prove some things he wanted to approve by starting from FQFT (and making a few other assumptions..). Many powerful theorists are very deeply and emotionally committed to FQFT, but there never was any decisive experiment... except perhaps recently. It was more a matter of fashion and ways of keeping entertained.

But are they the same anyway?

Please forgive a humorous analogy. Almost 20 years ago, I was very entertained by a hard-to-read book on nuclear physics, The Skyrme Model, by Makhankov, Rybakov and Sanyuk. For years, they, in their empirical nuclear work, had used a model of strong nuclear reactions developed by a British nuclear physicist, Tony Skyrme. They dedicate their book to this great British physicist, whose work was not fully appreciated in the West, because he kept the best stuff in a drawer licked up in the most classified lab in all of the US, as a result of which the key parts of the work were almost unknown in the West but widely disseminated in Russia. 

But on a more serious note, they said that use of the Skyrme model was limirted a whole lot in  the West, because of the near-religious dveotion to Auantum Chromodynamics (QCD). But later someone proved that QCD and Skyrme model would be equivalent, in the limit as infinity equals three. That made a big impression in the West, legitimized the area, and led to quite a bit of work here.

KQFT being "almost equivalent" to FQFT isn't a case of infinity equalling three... but it is similar.

It's my understanding that KQFT is equivalent to FQFT if Hn=H.

More precisely... in KQFT, we assume that the dynamics of everything

(the universe or "multiverse") is governed by the Hamiltonian operator H. Some respected mainstream physicists even believe hat the state of reality at any time t is a wave function psi(t), which is governed by the generalized Schrodinger equation, psi dot = i H psi. From the viewpoint of KQFT, the correct Hamiltonian H is actually Hn, something called the "normal form Hamiltonian." You can see this most clearly, if you do not already know it, by looking at F. Mandl and G. Shaw, Quantum Field Theory, Revised Edition, section 4.3 ("Second quantization"), equation 4.47. (Mandl and Shaw presents QFT from the original, KQFT, perspective.) FQED effectively assumes the same dynamics, except that H is the raw Hamiltonian, based on matrix multiplication of operators, instead of the normal product. The difference between H and Hn mainly involves terms like "the vacuum energy term," which does not affect normal calculations in quantum electrodynamics, the kind of successful calculations which put QFT on the map.

"If those terms always cancel out and have no effect, then the two theoreies are equivalent."

But not quite. H also determines the level of energy of a system. The amount of gravity (of bending space) depends on the amount of energy. So it really matters. 

Also, random noise terms which cancel out in linear interactions cam have major effects when we go to nonlinear interactions, where we rely more on speculation than on empirical evidence. (As per any form of quantum gravity today.) Hawkings' prediction that little black holes will radiate away is based on FQFT. Rajaraman predicts that solitons will have a mass greater than the corresponding classical prediction, again because of those extra noise terms. (I have run through the same calculations in KQFT, and found that, unlike FQFT, it reproduces the classical mass prediction, for bosonic fields.) And folks in the INtegrity Institute say that they can build perpetual motion machines based on Casimir forces based on the same "free vacuum energy" which they, like FQFT, believe is really there, even though there is not a shred of empirical evidence to show that they are. "Have faith, the angels of political correctness and superstrings will save the earth." Einstein's work was not quite so speculative.

But there is another way to test the difference between the theories. The stochastic terms in FQFT predict certain transitions called "instantons" beyond what KQFT would predict. That prediction has been tested recently,

in the world of hard core empirical physics:

APPLIED PHYSICS LETTERS 98, 242504 _2011_

Little–Parks oscillations at low temperatures: Gigahertz resonator method

Andrey Belkin,a_ Matthew Brenner, Thomas Aref, Jaseung Ku, and Alexey Bezryadin

Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

They did their best not to make waves... and the evidence needs much more investigation, both in theory and in experiment... but for now, the tentative conclusion is that FQFT fails while KQFT fits.

Of course, these are all just my personal impressions on a Saturday morning, not representing anyone. But is any of us really safe to just ignore the uncertainties and risks here? Is it rational to rely on faith, even if the risk should be only 10 percent?

Fortunately, I feel that the probability is less than 50% that humans have managed to create a small black hole... yet. But if we start to understand strong nuclear forces better, i HOPE we will learn to dispose of more energy...  and I hope we will try to understand what we are doing early on, and also that we will develop and use low cost access to space to allow some experiments a bit further from the planet we depend on.

(e.g. the DARPA project XS-1 may be more important than we know as yet, if they can stay the course and do it right, without giving in to lazy contractors who would prefer to use old expendable vertical technology.)