Planck scale

The Planck scale, named after Max Planck, marks a limit to the applicability of the known laws of physics. At distances of the order of the Planck length (about 10-35 m) would have the physics with the help of a quantum theory of gravity are described, which so far exists only in its infancy. For particles with energies on the scale of the Planck mass, the Compton wavelength is comparable to the Schwarzschild radius and the Planck mass is given by (see below):

The recommended CODATA value for the Planck mass is 2.176 51 (13 ) · 10-8 kg = 2.17651 · 10-8 kg ± 0.00013 · 10-8 kg. But it comes at the Planck mass only on the magnitude.

In particle physics and cosmology is also often the "reduced Planck mass " is used, which differs only by a constant factor of the Planck mass:

Accordingly, other sizes of the Planck scale ( Planck units) can be constructed from the three fundamental constants of nature, the gravitational constant, the speed of light and Planck's quantum of action. The Planck time is obtained, for example, from the time it takes for the light to go through the Planck length (c is the upper limit speed of any signal propagation ): ~ 10 -43 s

Orders of magnitude

Planck's length by a factor of about 1020 less than the diameter of the proton and so far beyond a direct experimental access. If one were to examine such small structures with a particle accelerator, the de Broglie wavelength of the particles used should be similar to, or comparable with their energy. The means of associated mass would be 1016 times as large as the mass of the heaviest known elementary particle, the top quark. A corresponding accelerator would have at least the diameter of our solar system. The only conceivable process could have occurred in comparable energies, the universe is about one Planck time unit according to the hypothetical Big Bang. The Planck mass is even almost " human " on the size scale - a flea weighs 4000 to 5000 Planck masses.

Derivation of the Planck mass

As already indicated above, the simultaneous application of the laws of quantum mechanics and general relativity leads at sufficiently small spatial and temporal intervals to problems such as the following consideration shows: an object or particle is in a region of space with the diameter so is due to the uncertainty principle its momentum only up to exactly determined,

Applies. This means that the pulse has to assume values ​​in the range of at least. Even for a particle without invariant mass is thus an energy and therefore a minimum mass, wherein

The mass is in a region of space with a radius smaller than its Schwarzschild radius

So it becomes a black hole. This is by choosing a sufficiently small distance, because with a reduction of growing, as is also and to eventually. However, this situation defies description by the known physics. Is obtained according to the formula for the Planck length and mass of the Planck scale by setting and the last two equations, and solving for.