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 value is a limit that defines the respective theory.
Physics starts at the bottom, with Galilean physics, where no limits are assumed, and proceeds towards the top, increasing precision at every corner by adding a limit. The topmost corner, the theory of relativistic quantum gravity - the unified theory - limits all observables. It provides the complete description of motion with complete precision.
Several of the limits found in the cube are not well known. About the maximum force c4/4G, see the page and papers dedicated to the topic. About the "limit" 4G that distinguishes unbound and bound motion, and all the other limits, see the preprint C. Schiller, From the Bronshtein cube of limits to the degrees of freedom of relativistic quantum gravity, https://www.researchgate.net/publication/366570060.
The physics cube is often called the Bronshtein cube (that is how he wrote his name himself) or also the Bronstein cube. Bronshtein, a brilliant physicist, was born in 1906 in Vinnitsya in Ukraine. He developed the concept of the physics cube as a young man and published it in 1933 and in 1934. He was killed by Stalin's henchmen at the age of 31. He was rehabilitated in the 1950s.
In short, the Bronshtein cube with limits illustrates how the fields of physics are defined. It shows that physics laws are simple.
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. A maximum force also suggests that the hoop conjecture is valid; both concepts are closely tied to horizons.
Combining all limits implies that the double Planck length is the shortest measurable length in nature. The minimum length (4Gℏ/c3)1/2 is extremely small, about 3 · 10-35m, twice the Planck length, and thus is not noticeable in the effectively continuous space of everyday life.
The limits of nature at each corner of the cube are not unique; other choices are also possible, using other powers of c, 4G and ℏ. For example, there is an equivalent maximum power c5/4G, a maximum mass flow rate c3/4G, or a maximum mass per length ratio c2/4G in general relativity. All are achieved only by black holes. Likewise, in relativistic quantum gravity, the uppermost corner of the Bronshtein cube, there is an equivalent minimum time (4Gℏ/c5)1/2 ≈ 10-43s, a minimum area, a minimum volume, a maximum acceleration, and a maximum mass density.
Together, the limits in the physics cube also confirm, as explained on a separate page, that all of physics can be summarized in 9 lines.
The Bronshtein cube is three-dimensional. Explaining the origin of its number of dimensions is not straightforward. (The problem remains even if thermodynamics and the Boltzmann constant k is added.)
Together, the limits in the cube imply that the Planck scale is the central scale in nature: the limits state and predict the lack of any trans-Planckian effects. In particular, the limits imply:
- All equations of physics follow from inequalities involving limits.
- There is a minimum length.
In short, the Bronshtein limit cube simplifies physics, its understanding and its teaching.
In addition, the Bronshtein limit cube simplifies research on the unification of physics. On the one hand, space-time is effectively continuous at larger scales. On the other hand, the minimum length, which applies both to measurement results and to measurement precision, implies:
- There are no points in space or time.
- There is no time-independent discrete or regular space-time structure.
- There is no non-commutative space-time.
- There is no space-time lattice.
- There are no higher dimensions.
- There are no lower dimensions.
- There is no space-time foam.
- There is no additional underlying mathematical space-time structure.
- There is no doubly special relativity.
- There are no point particles.
- There are no singularities.
- There is no conformal gravity.
- There is no conformal field theory.
- There is no dS or AdS space.
- There is no AdS/CFT correspondence.
- There is no supersymmetry.
- There is no supergravity.
- There is no spin network.
- There are no twistors.
- There is no holographic principle.
Each of these ideas is an idealization resulting from approximations that are extrapolated into domains where they do not apply. In particular, each of these ideas neglects the minimum length and its implications. About unification, the Bronshtein limit cube thus tells clearly: nullius in verba. Don't be bound by the words of authorities.
In addition, the minimum length implies that the common constituents of space and particles are at the same time Planck-sized and extended. Only in this way can particles, black hole entropy, and space arise. Exploring this in more detail, one finds that the common constituents are long, extremely thin, fluctuating, without ends, and without bifurcations.
In short, the minimum length imposes strict requirements on relativistic quantum gravity, the unified description of motion. Almost no conjecture on the unified description of motion found in the research literature satisfies the requirements imposed by the minimum length. The minimum length and area also imply that space and particles are made of filiform, fluctuating constituents. For details and about the way to proceed further, see the research page.
Summary: What the Bronshtein limit cube shows and what it doesn't
1. The Bronshtein limit cube shows that physics is simple. Each theory, each part of physics, is defined by a limit value.
2. The Bronshtein limit cube shows that relativistic quantum
gravity, the unified description of motion, is defined by the minimum
l ≥ (4Gℏ/c3)1/2 = 3 · 10-35m,
twice the Planck length. Equivalently, any other limit that contains c, ℏ and 4G can be used. All measurable consequences follow from this and the other limits of nature.
3. The Bronshtein limit cube shows that the unified description of motion, relativistic quantum gravity, is near. In particular, relativistic quantum gravity is already known in all its experimental and theoretical consequences: relativity, gravity and quantum physics. The lack of additional effects is predicted.
4. By eliminating many alternatives, the Bronshtein limit cube with its minimum length provides strong hints about the origin of the elementary particles and their properties, as well as the origin of the interactions and their properties. The hints are explored here.
5. Because of the smallest length, there is no unifying equation of
is told in detail here. It must be mentioned that the result disagrees
with an important authority on the topic,
linked here, for copyright reasons. Calvin's statement that there is
one simple unifying equation is known to be wrong, implicitly, for
over 50 years, due to the minimum length. In reality, as the Bronshtein
cube shows, all phenomena can be summarized in three simple unifying
v ≤ c, F ≤ c4/4G, W ≥ ℏ,
together with the principle of minimum action. Or four inequalities, if one includes the limit on entropy S ≥ k ln 2. Unification is based on these inequalities.
Websites, references and history
In 2022, a new website dedicated to Bronshtein's physics cube appeared: https://cube-of-physics.org/.
The history of the cube is complex. It also depends on the point of view that is 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 reference is the origin of the cube, but 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). The text also appeared in 1933.
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 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 on the cube by Okun and by Oriti are cited in the preprints.
The shortest summary of physics is C. Schiller, From maximum force to physics in 9 lines and towards relativistic quantum gravity, published in Zeitschrift für Naturforschung A (2022) https://doi.org/10.1515/zna-2022-0243.
The most recent publication about maximum force is A. Kenath, C. Schiller and C. Sivaram, From maximum force to the field equations of general relativity - and implications, International Journal of Modern Physics D 31 (2022) 2242019, 10.1142/S0218271822420196. The paper won an honourable mention in the 2022 Competition of the Gravity Research Foundation. Download the pdf here.
The text that presents the cube of limits, and uses minimum length to deduce research results is C. Schiller, From the Bronshtein cube of limits to the degrees of freedom of relativistic quantum gravity, https://www.researchgate.net/publication/366570060 (preprint).
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:
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