|
The Planck Scale
|
| Quantity |
Value
|
| Planck Mass |
1.2 x 1019
GeV/c2
|
| Planck Length |
1.6 x 10-33 cm
|
| Planck Time |
5.4 x 10-44 s
|
| Planck Temperature |
1.4 x 1032 K |
|
|
|
|
|
The Planck Scale
As we imagine extrapolating the history of the Universe backward in time, the big
bang theory tells us that the Universe becomes more dense and hotter, and the
relevant distance scales become shorter and shorter.
Quantum Mechanics
But we have seen in Chapter 5
that
if the distance scales become short enough (of atomic dimensions or smaller), the
theory of quantum mechanics must be used to describe physical events.
Therefore, as we extrapolate back in
time to the beginning of the Universe,
eventually we reach a
state of sufficient temperature and density that a fully quantum mechanical
theory of gravitation would be required. This is called the
Planck era, and the corresponding scales of distance, energy, and time
are called the Planck scale.
The Planck scale corresponds to incredibly small distances, or equivalently,
incredibly large energies. The lengths, energies, temperatures,
and times characteristic of the Planck scale
are displayed in the top right table (the unit GeV stands for 1 billion electron
volts of energy and c stands for the speed of light).
The Limits of Present Observational Knowledge
It is instructive to compare
the Planck scale with the scale on which we have actual data for the properties of elementary
particles in our Universe. In the largest particle accelerators, energies comparable to 100
GeV can be reached. The temperature of a gas having particles of this average energy and the
time after the big bang when the temperature of the Universe would have dropped to this value
are
Temperature = 1015 K
Time = 10-10 s after the
big bang
Therefore, all speculation about the Universe at times earlier than this is based on
particle properties that can only be inferred theoretically because we do not have direct
experimental data for higher energies.
Clearly the Planck scale lies far beyond our present or forseeable ability to probe it
directly.