2015 : The Planck(-Bronstein) mass [concept] has more than 100 {only} 80 years

History of science can teach us something

Here is a long excerpt from a text by the researcher in philosophy and history of science Gennady Gorelik (available online) which illustrate the statement in the title:

Planck introduced his cGh values in 1899, without any connection to quantum gravity. Quantum limits to the applicability of general relativity (and, implicitly, their Planck scale) were first discovered in 1935 by the Soviet theorist Matvey P. Bronstein (1906-1938). It was not until the 1950s that the explicitly quantum-gravitational significance of the Planck values was pointed out almost simultaneously by several physicists.[...] In the fifth installment of his continuing study of irreversible radiation processes (Planck 1899), Max Planck introduced two new universal physical constants, a and b, and calculated their values from experimental data. The following year, he redesignated the constant b by the famous letter h(and in place of a, he introduced k = b/a, the Boltzmann constant).  

In 1899, the constant b (that is, h) did not yet have any quantum theoretical significance, having been introduced merely in order to derive Wien's formula for the energy distribution in the black-body spectrum. However, Planck had previously described this constant as universal. During the six years of his efforts to solve the problem of the equilibrium between matter and radiation, he clearly understood the fundamental, universal character of the sought-for spectral distribution. 

It was perhaps this universal character of the new constant that stimulated Planck, in that same paper of 1899, to consider a question that was not directly connected with the paper's main theme. The last section of the paper is entitled "Natural Units of Measure" ["Natürliche Maasseinheiten"]. Planck noted that in all ordinary systems of units, the choice of the basic units is made not from a general point of view "necessary for all places and times," but is determined solely by "the special needs of our terrestrial culture" (Planck 1899, p. 479). Then, basing himself upon the new constant h and also upon c and G, Planck suggested the establishment of

"units of length, mass, time, and temperature that would, independently of special bodies and substances, necessarily retain their significance for all times and all cultures, even extraterrestrial and extrahuman ones, and which may therefore be designated as natural units of measure." (Planck 1899, pp. 479-480)

[...]The quantum-gravitational meaning of the Planck values could be revealed only after a relativistic theory of gravitation had been developed. As soon as that was done, Einstein pointed out the necessity of unifying the new theory of gravitation with quantum theory. In 1916, having obtained the formula for the intensity of gravitational waves, he remarked:

"Because of the intra-atomic movement of electrons, the atom must radiate not only electromagnetic but also gravitational energy, if only in minute amounts. Since, in reality, this cannot be the case in nature, then it appears that the quantum theory must modify not only Maxwell's electrodynamics but also the new theory of gravitation." (Einstein 1916, p. 696).

For two decades after Einstein pointed out the necessity of a quantum-gravitational theory in 1916, only a few remarks about this subject appeared. There were too many other more pressing theoretical problems (including quantum mechanics, quantum electrodynamics, and nuclear theory). And, the remarks that were made were too superficial, which is to say that they assumed too strong an analogy between gravity and electromagnetism. For example, after discussing a general scheme for field quantization in their famous 1929 paper, Heisenberg and Pauli wrote:

"One should mention that a quantization of the gravitational field, which appears to be necessary for physical reasons, may be carried out without any new difficulties by means of a formalism wholly analogous to that applied here. (Heisenberg and Pauli 1929, p. 3)"

They grounded the necessity of a quantum theory of gravitation on Einstein's mentioned remark of 1916 and on Oskar Klein's remarks in an article of 1927 in which he pointed out the necessity of a unified description of gravitational and electromagnetic waves, one taking into account Planck's constant h. 

Heisenberg and Pauli obviously intended that quantization techniques be applied to the linearized equations of the (weak) gravitational field (obtained by Einstein in 1916). Being clearly approximative, this approach allows one to hope for an analogy with electromagnetism, but it also allows one to disregard some of the distinguishing properties of gravitation—its geometrical essence and its nonlinearity. Just such an approach was employed by Leon Rosenfeld, who considered a system of quantized electromagnetic and weak gravitational fields (Rosenfeld 1930), studying the mutual transformations of light and "gravitational quanta" (a term that he was the first to use). 

The first really profound investigation of the quantization of the gravitational field was undertaken by Matvey P. Bronstein. The essential results of his 1935 dissertation, entitled "The Quantization of Gravitational Waves," were contained in two papers published in 1936. The dissertation was mainly devoted to the case of the weak gravitational field, where it is possible to ignore the geometrical character of gravitation, that is, the curvature of space-time. However, Bronstein's work also contained an important analysis revealing the essential difference between quantum electrodynamics and a quantum theory of gravity not thus restricted to weak fields and "nongeometricness." This analysis demonstrated that the ordinary scheme of quantum field theory and the ordinary concepts of Riemannian geometry are not sufficient for the formulation of a consistent theory of quantum gravity. At the same time, Bronstein's analysis led to the limits of quantum-gravitational physics (and to Planck's cGh-values). [...] 

For two decades after Bronstein's work, there was calm in the field of quantum gravity. Only in the mid-1950s did the length l0 = (Gh/c3)1/2 appear almost simultaneously in a few different forms in a few papers. For example, in 1954, Landau pointed out that the length l= G1/2h/ce (= a-1/2l0, very near to the Planck length) is "the limit of the region outside of which quantum electrodynamics cannot be considered as a self-consistent theory because of the necessity of taking into account gravitational interactions" (Gm^2/r ~ e2/r, when m ~ p/c ~ h/lc) (Abrikosov, Landau, Khalatnikov 1954).[...] 

The term "Planck values," which is now generally accepted, was introduced later (Misner and Wheeler 1957). According to Wheeler, he did not know in 1955 about Planck's "natural units" (private communication).

A history of the Planck values provides interesting material for reflections on timely and premature discoveries in the history of science. Today, the Planck values are more a part of physics itself than of its history. They are mentioned in connection with the cosmology of the early universe as well as in connection with particle physics. In considering certain problems associated with a unified theory (including the question of the stability of the proton), theorists discovered a characteristic mass ~ 10¹⁶m_p (m_pis the proton mass). To ground such a great value, one first refers to the still greater mass 10¹⁹m_p. In the words of Steven Weinberg:

"This is known as the Planck mass, after Max Planck, who noted in 1900 that some such mass would appear naturally in any attempt to combine his quantum theory with the theory of gravitation. The Planck mass is roughly the energy at which the gravitational force between particles becomes stronger than the electroweak or the strong forces. In order to avoid an inconsistency between quantum mechanics and general relativity, some new features must enter physics at some energy at or below 10¹⁹ proton masses." (Weinberg 1981, p. 71).

The fact that Weinberg takes such liberties with history in this quotation is evidence of the need to describe the real historical circumstances in which the Planck mass arose. As we saw, when Planck introduced the mass (ch/G)^1/2 (~10¹⁹m_p) in 1899, he did not intend to combine the theory of gravitation with quantum theory; he did not even suppose that his new constant would result in a new physical theory. The first "attempt to combine the quantum theory with the theory of gravitation," which demonstrated that "in order to avoid an inconsistency between quantum mechanics and general relativity, some new features must enter physics," was made by Bronstein in 1935. That the Planck mass may be regarded as a quantum-gravitational scale was pointed out explicitly by Klein and Wheeler twenty years later. At the same time, Landau also noted that the Planck energy (mass) corresponds to an equality of gravitational and electromagnetic interactions.

First Steps of Quantum Gravity and the Planck Values,

by Gennady Gorelik (1992)

Studies in the history of general relativity. [Einstein Studies. Vol.3].

To know more about Matvei Bronstein,  (an Ettore Majorana who came in from the cold, so to speak)