### This version of Bronshtein's physics cube shows how the main theories of physics are connected and which limits define them.

● Consequences and predictions

● Summary: What the Bronshtein cube shows and what it doesn't

● Appendix: Another version of the Bronshtein cube

● Bibliography

### The Bronshtein limit cube of physics

The main theories of physics can be distinguished by the combination
of the speed of light c, the quantum of action ℏ and
the gravitational constant G that they contain as a *limit*.
Each limit value *defines* the respective theory.
(Note that the limits are not unique; for example, both c and c^{2}
are defining limits of special relativity.)

Physics starts at the bottom, where *no* limits are assumed, and
proceeds towards the top, increasing precision at every corner.
The topmost corner, the theory of relativistic quantum gravity, limits *all*
observables. It provides the *complete* description of motion;
and the description provides *complete* precision.

Several of the limits found in the cube are not well known.
About the maximum force c^{4}/4G, see the
page and papers dedicated to the topic.
About the "limit" 4G that distinguishes unbound and bound motion,
see this preprint.

The physics cube is often called *Bronshtein cube*
(that is how he wrote his name himself) or also *Bronstein cube*.
His cube dates from 1933.

In short, the Bronshtein cube *with limits* illustrates how the
fields of physics are defined. It also 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 speed limit, its simplicity and its confirmation by experiment
imply the prediction that there is *no physics beyond special relativity.*

The action limit, its simplicity and its confirmation by experiment
imply the prediction that there is *no physics beyond quantum theory.*

The force limit, its simplicity and its confirmation by experiment
imply the prediction that there is *no physics beyond
general relativity* – thus no higher-order terms in the Lagrangian.
Maximum force also suggests that the hoop conjecture is valid; both
concepts are closely tied to horizons.

Combining the limits implies that the double Planck length is the
shortest measurable length in nature. It does *not* mean that
length values are multiples of the shortest length. Length is *not* quantized.
Any length longer than the shortest one is possible in nature.

Together, all the limits also imply, as explained on a separate page, that
*all of physics can be summarized in 9 lines.*

Again, the limits are not unique; other choices are also possible,
using other powers of c, 4G and ℏ. For example, there is a maximum power
c^{5}/4G or a maximum mass flow rate c^{3}/4G in general
relativity, and a minimum length, a minimum area, a minimum volume,
a maximum acceleration, or a maximum mass density in relativistic quantum
gravity, the uppermost theory in the Bronshtein cube.

The Bronshtein cube is three-dimensional.
(If the Boltzmann constant k is taken as
separate line, one can extend it to a four-dimensional hypercube.)
Understanding the origin of the number of dimensions of the physics cube is
not straightforward, but most probably a *red herring.*

Together, the limits imply that the Planck scale is the central scale in
nature, because they predict the *lack of any trans-Planckian effects.*
In particular, the limits imply:

- There are no points in space or time,
- Space-time is effectively continuous, but at a fundamental scale,
- There is a smallest length,
- 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,
- There is no doubly special relativity,
- The equations of nature follow from inequalities involving limits.

In short, the Bronshtein cube imposes strict requirements on the complete description of motion. However, almost no present conjecture on the complete description of motion found in the research literature satisfies these requirements.

*

### Summary: What the Bronshtein cube shows and what it doesn't

Independently of whether one explores the Bronshtein cube or the Bronshtein hypercube – which includes the Boltzmann constant k or some other equivalent thermodynamic limit – one finds two conclusions.

1. The Bronshtein cube shows that the complete description of motion is
*near.* The defining limits are known. In other words, fundamental physics
is close to its completion.

2. However, the Bronshtein cube does not explain the origin of the elementary particles and their properties and the origin of the interactions and their properties. In particular, the origin of the values for particle masses, particle mixing angles, and the coupling constants remains open.

*

### Appendix: Another version of the Bronshtein cube

The physics cube also structures the adventure presented in the
volumes of the free Motion Mountain Physics Textbook.
This version has more details and mentions
the adventures encountered in the different theories:

*

### Bibliography

A longer writeup of this page is C. Schiller, The quadruple gravitational constant, the Bronshtein cube of limits, and implications. Download the 5-page preprint here.

The history of the cube is confused. It also depends on the point of view taken, in particular on whether is it seen as a cube of theories, as a cube of fundamental constants, or, as is done here, as a cube of limits.

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 (1928) 13, (in Russian). Reprinted in G. Gamow, D. Ivanenko & L. Landau, World constants and limiting transition, Physics of Atomic Nuclei volume 65 (2002) 1373–1375. 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) 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

The papers by Okun and by Oriti are cited in the preprint.

* * *