~ quantization of certain physical properties
~ entanglement
~ principle of uncertainty
~ wave–particle duality"

~ light (and all other stuff) is pixelated; made up of "quanta", photons (in the case of light), and their energy is (integer/whole number) multiples of a constant value, Planck's constant.

It starts with Max Planck and a consideration of
"black body radiation".

Matter, when it has any thermal energy above "absolute zero" (0 degrees Kelvin), emits electromagnetic radiation. (The famous "cosmic background microwave radiation" corresponds to a temperature of 2.7K) A dark body starts to glow with visible light (dully red) at around 800K. At 1000K it glows red. At 6000K it glows white.
          "Classical physics" cannot explain "black body radiation" as it is observed. It predicts that there should be enormous quantities of ultraviolet light in the spectrum: but this is not what happens.
          So, in 1900, Max Planck tried to fudge the math. He found that if he modeled his equation as if light could only be emitted with energetic values that are multiples of a particular finite constant (numerical value), h (Planck's constant), then the math agreed with observed phenomena.
          (Joule seconds)
          According to wiki: Planck's postulate says that electromagnetic energy can only be emitted in discrete "bundles" or "energy elements": "in other words, the energy could only be a multiple of an elementary unit , where h is Planck's constant ... and is the frequency of the radiation."

Randall* explains that this means that at high frequencies the energies needed to generate the quantum particle just aren't there so that only lower frequencies are seen (apparently).
     

Einstein and the "photoelectric effect"

If you shine light at a surface it can, in certain circumstances/conditions cause electrons ("photoelectrons") to be emitted from that surface.
          At the beginning of the twentieth century science "knew" that light was electromagnetic phenomenon made up of waves of particular frequencies. According to wiki, "According to classical electromagnetic theory, this effect can be attributed to the transfer of energy from the light to an electron in the metal. From this perspective, an alteration in either the intensity or wavelength of light would induce changes in the rate of emission of electrons from the metal. Furthermore, according to this theory, a sufficiently dim light would be expected to show a time lag between the initial shining of its light and the subsequent emission of an electron. However, the experimental results did not correlate with either of the two predictions made by classical theory.
          "Instead, electrons are only dislodged by the impingement of photons when those photons reach or exceed a threshold frequency. Below that threshold, no electrons are emitted from the metal regardless of the light intensity or the length of time of exposure to the light. To make sense of the fact that light can eject electrons even if its intensity is low," but not if the frequency (and therefore energy) falls below a certain threshold value, "Albert Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets (photons), each with energy hf."

So, Einstein is saying that electromagnetic waves exist as discrete wave-packets, "light quantum", Lichtquant. Planck has said that there is a minimum energy to these "bundles" or "energy elements".: :
and (I think) this implies that:
~ there is a minimum energy value to a photon, 1h, and a corresponding minimum frequency and maximum wavelength
~ the electromagnetic spectrum is not continuous but rather rather makes little quantum leaps (where the energetic leap is increments of h joule.seconds - that's tiny! but "discrete").
(~ and later we'll come to a minimal (spatial) length, "Planck's length", and we therefore have a maximally energetic theoretical photon whose wavelength approaches Planck's length.)

Hmm. I wonder if I've got this right? (I shall check.)

"Quanta": wikisays: In 1900, the German physicist Max Planck was studying black-body radiation and suggested that the energy carried by electromagnetic waves could only be released in "packets" of energy. In his 1901 article in Annalen der Physik he called these packets "energy elements". The word quanta (singular quantum) was used before 1900 to mean particles or amounts of different quantities, including electricity.
     Later, in 1905, Albert Einstein went further by suggesting that electromagnetic waves could only exist as discrete wave-packets. He called such a wave-packet the "light quantum" (German: das Lichtquant).
     (In another entry wikisays ""quanta" was used in a 1902 article on the photoelectric effect by Philipp Lenard, who credited Hermann von Helmholtz for using the word in the area of electricity.)

The seminal "article" was titled, "On a Heuristic Viewpoint Concerning the Production and Transformation of Light"
Einstein, Albert (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt". Annalen der Physik 17 (6): 132–148.

"Photon": wikisays: the name photon derives from the Greek word for light. Arthur Compton used photon in 1928, referring to Gilbert N. Lewis usage. The same name was used earlier, by the American physicist and psychologist Leonard T. Troland, who coined the word in 1916...

There is a context this work on quantum is being to developed to explain:

In the same year. 1905, that Einstein published hi work on the photoelectric effect, giving us quanta of light, photons, he also puiblished his special relativity giving us

meanwhile physicists are throwing stuff at stuff and watching how stuff comes apart.

and from this building a picture of the world...

like Rutherford throwing alpha-particles at stuff and only a small percentage is scatterd: from this it is deduce that the nucleus is only a small tiny spot in the centre of an atom

There is a context to this : it's when Rutherford took apart atoms ~ there are/were "radioactive radiation"

Niels Bohrs and the spectral lines of Hydrogen.

It was known that "the light radiated by the hydrogen atom"(1) produced a series of spectral lines...
          Classical theory predicted that an electron circling the nucleus in a hydrogen atom would spiral inward (radiating energy continuously at ever-higher frequencies) falling rapidly into the nucleus.
          Niels Bohr hypothesised (in 1913) that an electron did not lose it's energy gradually and continuously, but moved from one energy state to another in quantum leaps till it reached a ground state: and that the angular momentum (of the orbiting electron) is quantized in units of. Reasoning thus he could account for the observed frequencies in the line spectrum of hydrogen.

That's the easy part: light (and stuff) is pixelated; made up of "quanta", photons (in the case of light), and their energy reflects the frequency/wavelength multiplied by a constant term for the energy involved, Planck's constant. (does this relate to c? a sort of reciprical?)

The next bits are more complicated and come out of the discover of radioactivity at the end of the 19th century, the discovery of "cathode rays", electrons, and discoveries and theories about the composition of atoms. Or maybe not..

1924: de Broglie (pronouced "de Broy") conjectured that all matter should have wavelike attributes... matter waves... and calcuated...
      "de Broglie's relation"      

note: the bigger the mass, the smaller the wavelength! Which is one of the reasons large things don't apparently show "quantum behaviour".

Prof. Deybe asked Schrodinger to explain this and (1925) Schrodinger went on to explain how probability waves move, calculating "probability amplitudes" psi

according to wiki: following up on de Broglie's ideas, physicist Peter Debye made an off hand comment that if particles behaved as waves, they should satisfy some sort of wave equation. Inspired by Debye's remark, Schrödinger decided to find a wave equation for the electron.

and/or using the relativistic energy momentum relation

Schrödinger equation ... describes how the quantum state of a quantum system changes with time. ... The concept of a wavefunction is a fundamental postulate of quantum mechanics. ... “derivations” of the Schrödinger equation demonstrate [the] mathematical plausibility for describing wave-particle duality ... (wiki)

(2)    "One of the reasons for the almost immediate and universal acceptance of Schrodinger's equation was that after a decade or more of fumbling around in the dark, physicists were once more able to calculate using standard mathematical techniques. Instead of havimng to follow Bohr's mysterious rules, the energy levels of hydrogen appeared naturally as the allowed frequencies of a wave problem in three dimensions. Indeed, what was astonishing was the remarkable accuracy of these predictions.   (2)

Probability and Uncertainty

The discover of "radioactivity" in the late 19th century, with the observation of, and concept of, "half lives"... of unpredictability, had introduced probability as a theme... but not yet as a fundemental aspect of all and every thing.

Note, though: the Uncertainty Principle is different! It says there is a (fundemental, intrinsic) limit to what we can know : know about certain paired qualities such as location and/or momentum). (even the pixels are smudged? when you try to see them...

(oh; and it's from radioactivity (alpha, beta, and gamma radiation) that Bohr took apart and put together the atom, I think)

~The energy of a particle at a certain event is the negative of the derivative of the action along a trajectory of that particle ending at that event with respect to the time of the event.
~The linear momentum of a particle is the derivative of its action with respect to its position.
~The angular momentum of a particle is the derivative of its action with respect to its orientation (angular position).
~The electric potential (f, voltage) at an event is the negative of the derivative of the action of the electromagnetic field with respect to the density of (free) electric charge at that event.[citation needed]
~The magnetic potential (A) at an event is the derivative of the action of the electromagnetic field with respect to the density of (free) electric current at that event.[citation needed]
~The electric field (E) at an event is the derivative of the action of the electromagnetic field with respect to the electric polarization density at that event.[citation needed]
~The magnetic induction (B) at an event is the derivative of the action of the electromagnetic field with respect to the magnetization at that event.[citation needed]
~The Newtonian gravitational potential at an event is the negative of the derivative of the action of the Newtonian gravitation field with respect to the mass density at that event."

In the double slit experiment, if one beamed electrons through the slits at a screen, shining light at the slits and recording which slit the electrons came through, and, before looking at that data, look to see if the result shows two discrete bands or an interference pattern… then…

If the result is an interference pattern, you might infer that "observing" with a mechanism will not collapse the probability waves… and that it takes a conscious knowing (not just a potentially conscious observation) to collapse the waves.

If the results show two discrete bands (showing that the wave probabilities did indeed collapse), and one then erased the data… that would indicate that conscious observation/knowing is not intrinsic to the phenomenon of probability wave collapse… and might suggest that the wave/particles are waves until something specific happens, but discrete particles once something discrete has happened.

Has this been done?

(then after Heisenberg's uncertainty principle, Born matrixed where stuff might be; probably / possibly
possibly! it could possibly be there

(before it happens, it could be anything possible

but once it happens

it's that thing thing that happened (so it retrospect it was collapsed possibilities... which is the stuff of what takes place

I do have a poem that relates to "quantum" that I'd like to finish here with... and it goes like this...

in the weave of the world
this does not explain "knowing"
but

does "knowing" exist
in the "possible" watching
willing
in the weave of the world
as it unfolds

so that we exist in the
"watching it happen"
a "quantum" phase (forgive me)
we watch it happen
watch with will
observing acting
and without us barren moonscape

in us cultures civilizations academies
wars rumours of wars
and by jolly it is indeed "quantum"
(the "how it comes
came out of nothing")
in pixels of energy

oh our visual fields
aren't really just pixels
they are patterned and smudged iterations
of a something that is happening somewhere
sliding down time

hmm

so "knowing" exist possibly
in the waves
in the fields of probability

watching
willing
in the weave of the world

Note" the uncertainty principle is different! It says there is a limit (fundamental and intrinsic) to what we can know.

complementary variable the paired qualities are
? The energy of a particle at a certain event is the negative of the derivative of the action along a trajectory of that particle ending at that event with respect to the time of the event.
? The linear momentum of a particle is the derivative of its action with respect to its position.
? The angular momentum of a particle is the derivative of its action with respect to its orientation (angular position).
? The electric potential (f, voltage) at an event is the negative of the derivative of the action of the electromagnetic field with respect to the density of (free) electric charge at that event.
? The magnetic potential (A) at an event is the derivative of the action of the electromagnetic field with respect to the density of (free) electric current at that event.[
? The electric field (E) at an event is the derivative of the action of the electromagnetic field with respect to the electric polarization density at that event? The magnetic induction (B) at an event is the derivative of the action of the electromagnetic field with respect to the magnetization at that event.[
? The Newtonian gravitational potential at an event is the negative of the derivative of the action of the Newtonian gravitation field with respect to the mass density at that event.

A Thought Experiment: Probability Wave Collapse

In the double slit experiment, if one beamed electrons through the slits at a screen, shining light at the slits and recording which slit the electrons came through, and, before looking at that data, look to see if the result shows two discrete bands or an interference pattern… then…

If the result is an interference pattern, you might infer that "observing" the with a mechanism will not collapse the probability waves… and that it takes a conscious knowing (not just a potentially conscious observation) to collapse the waves.

If the results show two discrete bands (showing that the wave probabilities did indeed collapse), and one then erased the data… that would indicate that conscious observation/knowing is not intrinsic to the phenomenon of probability wave collapse… and might suggest that the wave/particles are waves until something specific happens, but discrete particles once something discrete has happened.

Has this been done?

One of the things I have learned studying up on "quantum" physics (reading non-fiction is a struggle for me) is that you can't really separate the strictly quantum aspects of contemporary physics from a larger understanding of 20th century and contemporary (2016) concepts of physics. Quantum comes out of the discoveries about electrons and atoms and radioactivity: photons, quarks and stuff.

They smashed stuff apart to see what is was made of

Things that are conserved (in interactions) momentum linear and angular, charge, and flavbours

Things that are conserved ares somehow linked to "symmetries", and symmetries are linked to invariance

fermion boson

(odd # ?) (even # ?)

leptons hadrons (nucleons) photons
(not reacting to gluons
strong force) baryons (3q) mesons (2q) w+ w- z
Higgs

He
(hadron with even #s)

until it happens it is a probability of what might happen
when it happens (the occurrence) it's an event somewhere and when-ish
and the problem of the observer, Russell says, was solved by bishop Barkley… spirit/awareness hears the tree fall
[probability is inherent in it, though wave-functions are collapsing all the time (where ever anything is happening)