Discussion
Some Planck units are suitable for measuring quantities that are familiar from daily experience. For example:
- 1 Planck mass is about 22 micrograms;
- 1 Planck momentum is about 6.5 kg m/s;
- 1 Planck energy is about 500 kWh;
- 1 Planck charge is slightly more than 11 elementary charges;
- 1 Planck impedance is very nearly 30 ohms.
However, most Planck units are many orders of magnitude too large or too small to be of any practical use, so that Planck units as a system are really only relevant to theoretical physics. In fact, 1 Planck unit is often the largest or smallest value of a physical quantity that makes sense according to our current understanding. For example:
- A speed of 1 Planck length per Planck time is the speed of light in a vacuum, the maximum possible speed in special relativity;
- Our understanding of the Big Bang begins with the Planck Epoch, when the universe was 1 Planck time old and 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;
- At a Planck temperature of 1, all symmetries broken since the early Big Bang would be restored, and the four fundamental forces of contemporary physical theory would become one force.
Relative to the Planck Epoch, the universe today looks extreme when expressed in Planck units, as in this set of approximations (see, for example, and).
| Property of present-day Universe |
Approximate number of Planck units |
Equivalents |
|---|---|---|
| Age | 8.0 × 1060 tP | 4.3 × 1017 s, or 13.7 × 109 years |
| Diameter | 5.4 × 1061 lP | 8.7 × 1026 m or 9.2 × 1010 light-years |
| Mass | approx. 1060 mP | 3 × 1052 kg or 1.5 × 1022 solar masses (only counting stars) 1080 protons (sometimes known as the Eddington number) |
| Temperature | 1.9 × 10−32 TP | 2.725 K temperature of the cosmic microwave background radiation |
| Cosmological constant | 5.6 × 10−122 tP−2 | 1.9 × 10−35 s−2 |
| Hubble constant | 1.23 × 10−61 tP−1 | 70.4 (km/s)/Mpc |
The recurrence of the large number 1060 in the above table is a coincidence that intrigues some theorists. It is an example of the kind of large numbers coincidence that led theorists such as Eddington and Dirac to develop alternative physical theories. Theories derived from such coincidences are often dismissed by mainstream physicists as "numerology."
Read more about this topic: Planck Units
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