B. Roy Frieden

Frieden has used Fisher information and the EPI principle to derive most existing fundamental laws of physics, and some new and existing laws of biology, cancer growth, chemistry, and economics. Frieden argues that Fisher information, especially its loss I − J during observation, and EPI make up a general method for deriving scientific laws.

There is a view that puts into doubt the physical and mathematical correctness of Frieden's ideas, this coming from from Raymond F. Streater's Lost Causes in Theoretical Physics: Physics from Fisher Information, and Cosma Shalizi's review of Physics from Fisher Information.

Since criticism has been intorduced here, it is only right that some of their conceptual perforations should be considered.

Streater's claims:

Streater has a short section in his text referring to lost causes in theoretical physics, essentially making three claims against EPI.

Claim 1: Streater claims that: Frieden generally identifies I with the kinetic energy, and J with the potential energy. Rebuff: It is Streater who claims I is equals the kinetic energy in this criticsm: a wrong and baseless claim, except in quantum mechanics. To explain further, EPI is formulated through aims and operations that center on demonstrating, algebraically and philosophically, that the central, elementary laws of physics arise out of Fisher Information. These are expressed by values of information functions I and J generally, with I generally not being the kinetic energy and J not being the potential energy. It is quite clearly shown that I and J are informations that, only outwardly, look like the familiar energies of mechanics; and that these associations were made merely to motivate a person with a standard physics background to think in a different direction on this fundamental level. Our thesis is that the laws of physics arise out of information. The derivations of each chapter demonstrate this. The right physics results out of I and J in each case, something that Streater has not denied.

Claim 2: Streater claims that “Frieden claims to have derived quantum mechanics from information theory, forgetting that he started with Schrodinger's equation.” Rebuff: Frieden’s approach does not start with the Schrodinger equation. It starts with general forms I and J as above. Schroedinger himself was ever-mystified as to where the Fisher Information (called ‘kinetic energy’ in standard introductory physics) came from in his now-standard Lagrangian-based approach. Schrodinger never resolved this issue; but had he been a biologist he might have heard of R.A. Fisher’s foundation work using his ‘Fisher Information.’ Fisher’s biological work, in the UK, was, in fact, going on during the same years (circa 1922-25) that early quantum mechanics was being developed just across the channel in Denmark, Germany and France. Too bad Schrodinger was not aware of this.

Claim 3: Streater claims that “Frieden claims that the position of a particle does not send it into an eigenstate of energy. As it is, his result is hardly new, being the basis of the Rayleigh-Ritz method of finding the eigenvalues, known since the nineteenth century.” Rebuff: Frieden did not originate the statement “measuring the position of a particle does not send it into an eigenstate of energy.” It originated in the work of the esteemed John A. Wheeler. He believed in, and championed, a participatory universe, whereby each physical effect follows from the way a user carries through on it with a particular choice of observing apparatus. Indeed, even when the apparatus is changed during the experiment (a so-called “delayed choice” experiment) the output changes accordingly.

Shalizi's Claims

Shalizi has a more extended claims against EPI, though curiously he notes at the end of his commentary that it may not have peer support. It might be seen why this could be the case when considering some of his claims.

Claim 1: Shalizi claims that Frieden does not really maximize Fisher Information; he simply requires that its variation be stationary. Worse yet, says Shalizi, he is admirably candid about the fact that simply doing this doesn't give us any very interesting equation of motion. To get that, he subtracts from the Fisher information a new quantity of his own devising, the "bound information," and requires that the difference between these two, which he calls the "physical information," have stationary variation. Rebuff: Fisher Information really is maximized, but out of the variation of quantity I - J, not just of I, and the assumption of such stationary variation is standard in physics, as Shalizi undoubtedly knows. This is particularly apparent in quantum mechanics, where the Fisher Information I = J, the full amount needed to launch quantum mechanics via the ‘participatory universe’ thesis of John A. Wheeler.

Claim 2: Shalizi is unable to see any reason why the physical information should be maximized. Rebuff: Unlike a Lagrangian, Fisher Information is generally not invariant under change of coordinates, e.g. from Cartesian to spherical, so Shalizi would have liked some reassurance on this point, which is not forthcoming. As the book makes clear, there are no “correct” physical variables, until you first define what you mean by “information.” It’s not C.E. Shannon’s form, but rather the continuous generalization due to Fisher.

Claim 3: Shalizi claims that Frieden evidently believes that Nature thinks in Cartesian coordinates. He tries to justify his "extremal physical information principle" (pp. 79--82) by saying that physicists are in a non-cooperative game with Nature, trying to seize as much data as we can from Her, and the upshot of this is that physical information should have stationary variation. I couldn't say why he thinks this should convince anyone not raised on the lumpenfeminist idea that modern science is a way of raping and torturing Nature. Rebuff: The inference is wrong. Observers do not want to seize a maximum amount of data but, rather, a maximum amount of information in the data taken. It’s not quantity - it’s quality that matters. As a matter of fact, Nature itself operates by this principle: “natural selection” (Darwin) is selection for maximum information I.

Claim 4: Shalizi claims that adding bound information (or rather, subtracting it off) reduces the scheme to vacuity. Frieden pulls these terms from out of, to put it politely, the air, and they seem to have no independent significance whatsoever. They are simply whatever he needs to get the equation he wants at the end of the variational problem, subject only to the (really rather mild) constraint that they have the right symmetry properties. Frieden's scheme is at best mathematically equivalent to orthodoxy; it adds nothing empirical; places fundamental and useful concepts in doubt; does nothing to unify physics either internally or with statistics; and it is associated with some really bad metaphysics, though that last perhaps reflects more on Frieden than on the scheme itself. I see absolutely no reason to prefer this scheme to conventional mechanics, rather the reverse. This is at best an extended mathematical curiosity. Rebuff: The reason is, as shown throughout the book - from one physical scenario to another - Nature simply acts that way (also, see Wheeler’s previously noted hypothesis). For example, in biology: Darwinian “natural selection”, i.e., “survival of the fittest,” can be derived on the basis of the principle of Fisher Information J – I = minimum. See Frank, J. Evolutionary Biology, “Natural selection maximizes Fisher Information”, Jan. 2009, https://doi.org/10.1111/j.1420-9101.2008.01647.x As to Shalizi’s other remarks, “placing fundamental and useful concepts in doubt” is the purpose of any worthwhile new theory; e.g., Galileo’s assertion of having observed a non-centrist universe. Was he wrong: in fact, and in trying to make it known? Shalizi just doesn’t ‘like’ the idea behind the book; but evidently, this is not out of having read and well-understood it. Finally, contrary to what he claims, information does rule.

That information rules is supported by Meijerin (http://www.sintropia.it/journal/english/2013-eng-3-01.pdf), who argues that Frieden's Fisher Information framework has a fundamental property of intrinsic information, and this produces matter. Intrinsic information is defined to be the most complete way of describing a contextual object. This is consistent with Barbieri (https://www.researchgate.net/publication/257780021_The_Paradigms_of_Biology ) who explains that there are three paradigms that reflect on reality, the chemical/physical paradigm, the information paradigm, and the meaning paradigm, and where information can be an intermediary between the other two.