Our understanding of the Big Bang begins with the Planck Epoch, when the universe was 1 Planck time old, 1 Planck length in diameter, and had a Planck temperature of 1. At that moment, quantum theory as presently understood becomes applicable. Understanding the universe when it was less than 1 Planck time old requires a theory of quantum gravity that would incorporate quantum effects into general relativity. Such a theory does not yet exist.

In particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of five universal physical constants, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units.

Originally proposed in 1899 by German physicist Max Planck, these units are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are only one system of several systems of natural units, but Planck units are not based on properties of any prototype object or particle (that would be arbitrarily chosen), but rather on only the properties of free space.

Planck units have significance for theoretical physics since they simplify several recurring algebraic expressions of physical law by removing dimensions. They are relevant in research on unified theories such as quantum gravity. The Planck scale expresses the region in which the predictions of the Standard Model of quantum field theory and of general relativity are no longer reconcilable, and quantum effects of gravity are expected to dominate. This region may be characterized by energies around 1.22×1019 GeV (the Planck energy), time intervals around 5.39×10−44 s (the Planck time) and lengths around 1.62×10−35 m (the Planck length).

The five universal constants that Planck units, by definition, normalize to 1 are:

the speed of light in a vacuum, c,

the gravitational constant, G,

the reduced Planck constant, ħ,

the Coulomb constant, 1/4πε0

the Boltzmann constant, kB

Each of these constants can be associated with a fundamental physical theory or concept: c with special relativity, G with general relativity, ħ with quantum mechanics, ε0 with electromagnetism, and kB with the notion of temperature (statistical mechanics and thermodynamics).

Planck units are derived by “normalizing” the numerical values of certain fundamental constants to 1. These normalization’s are neither the only ones possible nor necessarily the best. Moreover, the choice of what factors to normalize, among the factors appearing in the fundamental equations of physics, is not evident, and the values of the Planck units are sensitive to this choice.

Planck units are free of anthropocentric arbitrariness. Some physicists argue that communication with extraterrestrial intelligence would have to employ such a system of units in order to be understood. Unlike the meter and second, which exist as base units in the SI system for historical reasons, the Planck length and Planck time are conceptually linked at a fundamental physical level.

Natural units help physicists to re-frame questions. Frank Wilczek puts it succinctly:

We see that the question [posed] is not, “Why is gravity so feeble?” but rather, “Why is the proton’s mass so small?” For in natural (Planck) units, the strength of gravity simply is what it is, a primary quantity, while the proton’s mass is the tiny number [1/(13 Quintilian)].

While it is true that the electrostatic repulsive force between two protons (alone in free space) greatly exceeds the gravitational attractive force between the same two protons, this is not about the relative strengths of the two fundamental forces. From the point of view of Planck units, this is comparing apples to oranges, because mass and electric charge are in-commensurable quantities. Rather, the disparity of magnitude of force is a manifestation of the fact that the charge on the protons is approximately the unit charge but the mass of the protons is far less than the unit mass.

In any system of measurement, units for many physical quantities can be derived from base units. Their use is mostly confined to theoretical physics because most of them are too large or too small for empirical or practical use and there are large uncertainties in their values.

Any system of measurement may be assigned a mutually independent set of base quantities and associated base units, from which all other quantities and units may be derived. In the International System of Units, for example, the SI base quantities include length with the associated unit of the meter. In the system of Planck units, a similar set of base quantities may be selected, and the Planck base unit of length is then known simply as the Planck length, the base unit of time is the Planck time, and so on. These units are derived from the five dimensional universal physical constants in such a manner that these constants are eliminated from fundamental selected equations of physical law when physical quantities are expressed in terms of Planck units.

This is why Planck units or any other use of natural units should be employed with care. Referring to G = c = 1, Paul S. Wesson wrote that, “Mathematically it is an acceptable trick which saves labor. Physically it represents a loss of information and can lead to confusion.”

The Planck units are based on the quantum of action, now usually known as Planck’s constant. Planck called the constant b in his paper, though h is now common. Planck underlined the universality of the new unit system, writing:

…ihre Bedeutung für alle Zeiten und für alle, auch außerirdische und außermenschliche Kulturen notwendig behalten und welche daher als »natürliche Maßeinheiten« bezeichnet werden können…

…These necessarily retain their meaning for all times and for all civilizations, even extraterrestrial and non-human ones, and can therefore be designated as “natural units”…

credit: Wikipedia; edited by Pierre J. Hébert

2017/7/15