Digital with analog override/rev II

(Credit: OrangeDog and Szdori/Wikimedia Commons)

Thanks to Max Planck and Niels Bohr, we know energy's digital because whenever energy, in the form of the photon, is absorbed by an electron orbiting an atom's nucleus, the electron in question will jump to a more distant orbit in discrete fashion as seen by the graphic above. Conversely, when an electron emits a photon (aka light) due to a loss of energy, it drops in similar fashion to a lower orbit as needs warrant. This same either/or concept of digital also applies to electrons (aka fermion/lepton) as they must exist in different quantum states in order to share orbits with other electrons as expressed by the Pauli Exclusion Principle, the indispensable reason as to how existence functions at grand scale. 

As you can see, the 1s and 2s subshells for beryllium atoms can hold only two electrons and when filled, the electrons must have opposite spins. Otherwise they will have the same four quantum numbers, in violation of the Pauli Exclusion Principle.

But Bohr’s model was just that: a model that successfully described what was seen. What it didn’t do was explain why this set of rules would exist at all, or provide a set of axioms that allowed such rules to be derived.

That’s where the Pauli Exclusion Principle comes in. Simply by demanding that no two identical fermions in the same quantum system occupy the same quantum state, this complex structure emerges: for the behavior of electrons within atoms, as well as for all other composite systems containing multiple identical fermions.

If it weren’t for the Pauli Exclusion Principle, the matter we have in our Universe would behave in an extraordinarily different fashion. The electrons, you see, are examples of fermions. Every electron is fundamentally identical to every other electron in the Universe, with the same charge, mass, lepton number, lepton family number, and intrinsic angular momentum (or spin).

If there were no Pauli Exclusion Principle, there would be no limit to the number of electrons that could fill the ground (lowest-energy) state of an atom. Over time, and at cool enough temperatures, that’s the state that every single electron in the Universe would eventually sink to. The lowest energy orbital — the 1s orbital in each atom — would be the only orbital to contain electrons, and it would contain all of the electrons inherent to every atom.

In essence, existence as we know it would not exist ...

Pauli in 1945

Although, at a fundamental level, the Universe is made up of point-like quantum particles, they assemble together to create objects of finite sizes and masses, occupying specific amounts of volume. This artist’s illustration shows several electrons orbiting an atomic nucleus, where the electron is a fundamental particle but the nucleus can be broken up into still smaller, more fundamental constituents.

The rise of quantum ...

The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition, now known as the Planck postulate, that electromagnetic energy could be emitted only in quantized form, in other words, the energy could only be a multiple of an elementary unit:

E=h\v  

where h is Planck's constant, also known as Planck's action quantum (introduced already in 1899), and ν is the frequency of the radiation. Note that the elementary units of energy discussed here are represented by hν and not simply by ν. Physicists now call these quanta photons, and a photon of frequency ν will have its own specific and unique energy. The total energy at that frequency is then equal to hν multiplied by the number of photons at that frequency.

German physicist Max Planck (c. 1930)

Digital also applies to ...

The uncertainty principle states that we cannot know both the position and speed of a particle, such as a photon or electron, with perfect accuracy; the more we nail down the particle's position, the less we know about its speed and vice versa.

In other words, if we could shrink a tortoise down to the size of an electron, we would only be able to precisely calculate its speed or its location, not both at the same time.

At its base level, reality is digital as per the subatomic zoo seen below.

Fermions form one of the two fundamental classes of subatomic particles, the other being bosons. All subatomic particles must be one or the other. A composite particle (hadron) is a fermion).

Bosons are particles that carry energy and forces throughout the universe. Think Photons :) 

An elementary particle (electron) is both a lepton & fermion.

Hadrons consist of quarks. Think protons and neutrons :)