Planck Units

Having discovered the fundamental constant h, which relates energy to frequency, Max Planck realized that he had all the constants required to calculate fundamental units of length, mass, time, charge and temperature.

Simple calculations

The calculations were simple to the point of being trivial. All Planck needed to do was to play around with fundamental constants until they combined in such a way that the calculated values come out with a single dimension. The combination that yielded a number denoted in meters became the Planck length. The combination that resulted in a number denoted in seconds became the Planck time. Planck mass is similarly denoted in gram, charge in Coulomb and temperature in Kelvin. Together, they are known as Planck units.

Clear thinking

The thinking was clear. If fundamental constants are truly fundamental, then any unit derived from these constants must also be fundamental. These units must tell us something fundamental about the universe and its components. For example, there should be something in the universe that has the radius, diameter or circumference of a Planck length. Similarly, there should be things in the universe that correspond to Planck’s calculated units of mass, time, charge and temperature.

In this respect, it’s interesting to note how the Planck length and time fit with the ideas of distance and time laid out in my proposed physics. Planck length is calculated from Planck’s constant h, the light speed c and the gravitational constant G. This yields a very small number.

In my book, the smallest possible ruler we can use to measure distance is the electron, a very small particle, and therefore also a very small number.

Planck time is in turn the Planck length divided by the speed of light. This is identical in form to my proposed definition of time, where the smallest possible time unit is the time that it takes a photon to cross an electron.

Once again we see that my theory ends up with similar results to what has been arrived at by conventional physics. But the difference in approach has led to some significant differences.

Differences in results

Max Planck arrived at his units through a purely mathematical approach. He uses no mechanical model to explain any of it. That’s the precise opposite approach to mine.

I start with a mechanical model and arrive at certain conclusions. One being that no length smaller than the circumference of an electron can ever be measured with certainly. Another one being that no timespan shorter than the time it takes a photon to cross an electron can ever be detected.

As it turns out, both Planck length and Planck time are shorter than my units, which begs the question, what exactly do Planck length and Planck time represent, if not the limits to precision in measuring length and time?

Likely source of error

It appears that Max Planck made some incorrect assumption somewhere, and that this led to quantities that don’t seem to have any fundamental meaning. For instance, he uses the gravitational constant G in all of his computations, but we have good reasons to believe that G isn’t in fact a constant.

However, this doesn’t take away the genius of Planck’s thinking. It point to something fundamental, and the fact that both Planck’s length and time are short relative to what we would expect is a big hint. There appears to be something not quite right about one of our fundamental constants, and G is our prime suspect.