what is the plank length? What do they mean when they say it’s the “shortest length”?
In: Physics
The Planck length is a unit of length in a set of natural units called Planck units. Natural units are units that are defined in such a way so that certain physical constants are 1. For instance, in Planck units the speed of light in a vacuum (~300,000 km/s), the gravitational constant (a measure for the strength of gravity, ~6*10^(-11) Nm²/kg²), the reduced Planck constant (a constant that relates the wavelength of light to its energy, ~6*10^(-34) Js), the Coulomb constant (a measure for the strength of electromagnetism, ~9*10^(9) Nm²/C²), and the Boltzmann constant (a constant that relates the average kinetic energy of the particles in a gas with the gas’ temperature, ~10^(-23) J/K) are all normalized to be 1.
By now manipulating these constants, until you get something that only has metres as its units, you get the Planck length. Similarly, you can get the Planck mass, Planck time, Planck charge and Planck temperature. In this set of units, a Planck length is about 10^(-35) m, which is tiny. In fact, even smaller than anything we’ve ever observed. Similarly, a Planck time is incredibly tiny, and conversely the Planck temperature is really massive (~10^(32) K, as a comparison, the Sun’s core is about 15*10^(6)K). The Planck charge and Planck mass aren’t really special, besides being derived from the same normalized constants.
But, at the scale of the Planck units that *do* matter (Planck length, time, temperature and energy), our known models stop making sense. That means that we can’t apply our known laws of nature, but there are a whole set of new ones. Ones we don’t know (yet). This is similar to quantum theory. When you go small enough, we can’t use regular Newtonian physics to predict stuff. We needed a new theory, which was quantum theory. And if you go big and fast enough, we can’t use Newtonian physics either, but have to resort to relativity. So in that sense, the Planck length is ‘the smallest length’, with the caveat that it’s the smallest length at which our current knowledge of physics stops working. But this doesn’t mean it’s the smallest length period. It’s just a really really tiny length, where things get even weirder than with quantum mechanics.
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