If h-bar sounds like the name of a bar to you, we already have something in common. I can easily imagine a conversation that starts over a drink and, somewhere between physics, music and a difficult question, ends up exploring the nature of reality.
The name does have a precise starting point. The symbol ℏ, pronounced “h-bar”, is the reduced Planck constant. It appears again and again in quantum physics, and here it gives us a reason to introduce ourselves.
How Planck joined the conversation
In 1900, Max Planck was studying thermal radiation. To explain its energy distribution, he introduced discrete amounts of energy proportional to frequency into his calculation. The constant of proportionality was h. This assumption opened a path towards quantum physics. [1]
In 1905, Einstein proposed the idea of light quanta, which we now call photons. [2]
For a photon, the relationship between its energy E and frequency ν is:
E = hν
The Greek letter ν represents frequency. The higher the frequency of light, the greater the energy of each of its photons. An equation with three symbols gives us a precise way to connect these two quantities. [1]
In the International System of Units, the Planck constant has the exactly defined value:
h = 6.62607015 × 10⁻³⁴ J·s [3]
A long string of zeros can make a number seem difficult to approach. Its value becomes meaningful alongside its units and the relationships in which it appears. Here we have energy multiplied by time: the dimensions of the physical quantity called action.
And the little line across the h?
The reduced Planck constant is defined as:
ℏ = h/(2π)
Its numerical value is approximately:
ℏ ≈ 1.054571818 × 10⁻³⁴ J·s [4]
The factor 2π appears when we move from frequency to angular frequency. One full turn corresponds to 2π radians, so, with ω = 2πν, the expression for a photon’s energy becomes:
E = ℏω
That small change in notation is enough to make a symbol familiar throughout quantum physics. And, apparently, to give an online bar its name.
Physics, music and a little human action
The person behind the constant also had a musical life. Planck hosted musical evenings at his home, playing with colleagues, including Einstein, and professional musicians. He also loved hiking and mountain climbing. [5]
I like to think that “action” suited him beyond the units of physics, too.
The image of these people playing music together particularly appeals to me. We usually encounter them in books, beneath portraits or beside equations. Here we can imagine them listening to one another, waiting for their turn, trying to play together.
As someone who works with physics and music, I find something familiar in that scene. In a calculation, I need to pay attention to exactly what I am saying. In composition, I need to listen to what is happening. Often, the next good question appears when I stop assuming that I have already understood.
The conversation stays open
We can calculate the energy of a photon. The very possibility of making such a calculation continues to raise a philosophical question for me: how do the mathematical relationships we formulate describe what we observe so well?
Physics asks us to test our answers. Philosophy gives us room to examine what, exactly, we are asking. Music makes me stay a little longer with something I am still trying to understand.
That is how I imagine h-bar: a place where an equation, a melody and a thought can meet at the same table. With curiosity, attention to sources and enough humour to keep the conversation going.
The Planck constant has its place in our calculations. We can change the way we look.
Sources for the English article
- NIST — Kilogram: Mass and Planck’s Constant.
- NobelPrize.org — The dual nature of light as reflected in the Nobel archives.
- NIST — SI Units: Mass.
- NIST — 2022 CODATA fundamental physical constants.
- Max-Planck-Gesellschaft — Max Planck’s private life.
Until our next conversation, let’s see what will change.
Change is the only constant.
