The main theories of physics can be distinguished by which combination of the speed of light c, the quantum of action ℏ and the gravitational constant G they contain.
The version shown here puts a limit of a physical observable at each corner, except for the first corner. That limit value defines the respective theory.
Learning physics starts at the bottom left, where no limits are assumed, and proceeds towards the top right, where all observables are limited.
Several of the limits found in the cube are not well known, despite being decades old. About the maximum force c4/4G, see the page dedicated to the topic. The papers mentioned there also cover the limit 1/4G that defines classical gravitation and the limit c4/4Gℏ that defines relativistic quantum gravity, the complete description of motion.
History: The physics cube is often called Bronshtein cube (that is how he wrote his name himself) or also Bronstein cube. The syllable `shtein' or `stein' rhymes with `shrine', as can be seen from the original Russian. The cube dates from the 1930s.
The Bronshtein cube with limits shows that physics laws are simple.
Consequences and predictions
Describing nature with limits implies that there are no infinite quantities in nature, neither infinitely large nor infinitely small.
The force limit implies the prediction that there is no physics beyond general relativity. There are no higher-order terms in the Lagrangian. Maximum force also suggests that the hoop conjecture is valid; both concepts are closely tied to horizons.
The speed limit implies the prediction that there is no physics beyond special relativity.
The action limit implies the prediction that there is no physics beyond quantum theory.
Together, all the limits also imply, as explained on a separate page, that all of physics can be summarized in 9 lines.
Note: the limits are not unique. Other choices are also possible, using other powers of c, 4G and ℏ. There is a maximum power, a maximum mass flow rate, a minimum length, a minimum area, a minimum volume, a maximum acceleration, a maximum mass density, etc.
The cube is three-dimensional. (If the Boltzmann constant k is taken as separate line, one can try to define a four-dimensional hypercube.) Understanding the origin of the number of dimensions of the physics cube is not straightforward.
The cube also structures the adventure presented in the volumes of the free Motion Mountain Physics Textbook.
The limits further imply that the Planck scale is the central scale in nature.
The limits also imply that there are no trans-Planckian effects in nature. In particular, the limits imply:
- There is no continuous space-time,
- There is no doubly special relativity,
- There are no higher dimensions,
- There are no lower dimensions,
- There is no space-time foam,
- There is no discrete space-time,
- There is no non-commutative space-time,
- There is no space-time lattice,
- There is no time-independent discrete space-time structure,
- The equations of nature follow from inequalities involving limits.
In short, the Bronshtein cube imposes strict requirements on the complete description of motion.
Almost no conjecture on the complete description of motion found in the research literature satisfies these requirements.
Another version of the Bronshtein cube
The history of the cube is confused. It depends on the point of view, in particular on whether is it taken as a cube of theories, as a cube of fundamental constants, or a cube of something else.
This often-cited reference is about c, G and h, but does not define the cube: G. Gamov, D. Ivanenko and L. Landau, Zh. Russ. Fiz. Khim. Obstva. Chast Fiz. 60, 13 (1928), (in Russian). Reprinted in G. Gamow, D. Ivanenko & L. Landau, World constants and limiting transition, Physics of Atomic Nuclei volume 65, pages 1373–1375 (2002). https://doi.org/10.1134/1.1495650
This often-cited reference is hard to find: M. Bronshtein, K voprosu o vozmozhnoy teorii mira kak tselogo [On a possible theory of the world as a whole], in Osnovnye problemy kosmicheskoy fiziki [Basic problems of cosmic physics], Kiev, ONTI (1934), pp. 186-218 (in Russian).
This often-cited reference has nothing on the cube itself: M. Bronshtein, Physikalische Zeitschrift der Sowjetunion, 9, 140 (1936). https://doi.org/10.1007/s10714-011-1285-4
A third version of the Bronshtein cube
It has more details and mentions the adventures encountered in the different theories: