Planck’s constant is the smallest possible unit of energy. Energy, like space and time, is a key concept of physics that was initially thought to be continuous. It was defined in the nineteenth century as the ability to move matter around, which was called work, so burning coal in a steam engine produced work by converting coal energy to the kinetic energy of the moving train. The idea that energy allows work that transfers energy explained how engines operate, but there was a problem.
The problem was that light waves didn’t follow the rules. The furnaces of the time gave off light at many frequencies, so as they got hotter, all the frequencies should increase, but they didn’t. Hot furnaces didn’t give off lethal doses of x-rays that killed their workers, so physics called that fact the ultraviolet catastrophe because for them, that their laws didn’t apply was a disaster.
The law in question was that the energy of a physical wave increased as its frequency squared, so twice the frequency gave four times the energy. Heating a furnace should then increase all its light frequencies equally, including the dangerous ones. Why it didn’t was a puzzle, until Planck proposed that atoms emit light energy in multiples of a basic amount, later called Planck’s constant, by the equation:
Light Energy = Plank’s constant x Frequency
That light energy varied directly with frequency predicted the observed result, but no-one knew why. In theory, waves are continuous, so adding energy to high frequency light should just increase it, but heating a furnace didn’t increase all frequencies equally. Einstein then showed that light comes in little packets, called photons, based on the photo-electric effect. Heating a furnace then didn’t produce as many high frequency photons because they need more energy to happen, so the ultraviolet catastrophe was avoided.
It followed that energy isn’t continuous but comes in basic units represented by Planck’s constant, the smallest unit of energy. Why light comes in indivisible units called photons remained a mystery but a processing approach attributes it to there being a core process that can’t be divided further. Planck’s constant then represents this process, which is the basic operation of quantum network. Light comes in little packets because each photon is one Planck process and photons are indivisible because the process behind them is indivisible. Equally, Planck’s constant is the smallest energy transfer because it represents the smallest network transfer operation.
Energy in processing terms is then the processing transfer rate at a point. If every photon is the same process distributed, shorter wavelength photons transfer more processing at each point and so have more energy. In contrast, a long wavelength photon transfers less processing at each point, so it has less energy. It follows that the energy of a photon depends directly on its wavelength, and hence its frequency, just as Planck described. By this logic, the equation Planck assumed can be derived from processing principles (Note 1).
To recap, one photon is one Planck process divided over its network wave length, which can’t increase or decrease by less than a point. Adding a point distributes the process more, so the transfer rate we call energy is less, and reducing a point makes the transfer rate we call energy increase.
But if every photon is the same process divided more or less, why does high frequency light have more energy? If every photon makes the same dot on a screen, shouldn’t every photon have the same energy? It does, but high frequency light delivers more photons per second, and so more energy. Increasing a photon’s frequency doesn’t increase its total energy, just the rate at which it arrives. X-rays deliver more photons per second than radio-waves, not more energy per photon. The energy of light varies linearly with frequency, not its square, as it would for a physical wave.
Note 1. Let one photon be a Planck process divided over the points of its wavelength, and the constant h represent that process as a quantum network transfer. Let energy E be the processing transfer rate at a point and W be the number of points in the photon wavelength. Every photon is then one Planck process divided between W points, so the processing transfer rate at a point E = h/W. If f is the number of network cycles each point takes to run a Planck process that it can complete in one cycle, then f = 1/W. The equation E = h.f then follows, where E, h, and f are defined in quantum units. Converting these units to per second terms then gives E = h.f, which is Planck’s equation. Plank’s constant then represents the transfer of one Planck process.