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 approach

By playing around with fundamental constants until they combined in such a way that the calculated values come out with a single dimension, he got a list of constants, one for each dimension.

The combination that yielded a number denoted in meters became Planck’s fundamental unit of length. The combination that resulted in a number denoted in seconds became his unit of time. His mass is similarly denoted in gram, charge in Coulomb and temperature in Kelvin.

Together, these are known as Planck units.

Clear thinking

Planck’s 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 Planck’s length. Similarly, there should be things in the universe that correspond to his units for time, mass, charge and temperature.

In this respect, it’s interesting to note how his length and time fit with the ideas of distance and time laid out in my book.

Planck length is calculated from the constant h, the speed of light 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. Our fundamental unit of length is 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 definition of time, where the fundamental unit is the time 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 of my approach.

I start with a mechanical model and arrive at certain conclusions. For one, no length smaller than the circumference of an electron can ever be measured with certainly. From this it follows that no event shorter than the time it takes a photon to cross an electron can ever be detected.

As it turns out, Planck’s length and time are both shorter than my units. But what exactly do these two units 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, which led to quantities that don’t have any fundamental meaning.

Our prime suspect in this case is the gravitational constant G which we have good reasons to believe isn’t in fact a constant.

It appears that conventional understanding of gravity is flawed. As a consequence, all of Planck’s units are wrong, because all of them are derived in part from G.

Conclusion

However, this doesn’t take away the genius of Planck’s thinking. His calculations point to something fundamental.

The fact that both his length and time are short relative to what we would expect hints at a bigger problem in modern physics. Namely a flawed understanding of gravity.