While twenty first century Quantum mechanics is highly abstract and counter-intuitive it’s not that difficult to glean a fundamental understanding of this branch of modern physics by following its history.

If we alter our usual ways of thinking that is because our adaptive thinking is not modeled on such small scale quantum dimensions- they’re outside of our ‘sensory band’ of every day perceptions and non-intuitive.

Basically, quantum mechanics describes a sub-atomic, nano-microscopic level of reality that dips into atomic nuclei that are a hundred thousand times smaller than an atom itself and this tiny abstract realm is still not fully understood by scientists today…

“… beyond the fact that it is a mathematically coherent theory, the only reason we believe in quantum mechanics is because it yields predictions that have been verified to astounding accuracy” (Brian Greene, 1999)

While the intuitive, every day physics of Isaac Newton’s laws of motion and gravity (1) give us a solid ‘hands-on’ theory of reality, that concrete picture of the world began to scientifically unravel in the mid-nineteenth century as technological advancements provided scientists with ever increasing depths and accuracies of experimental detection: the complex objects and motions of the world around us lose their solid material and predictive qualities the deeper we peer into them and our sciences were becoming increasingly abstract as a result.

James Clerk Maxwell’s 1861-62 electromagnetic theory of relativity established the idea of ‘fields’ of radiation – an infinite spectrum [of frequencies] of energy-carrying ‘waves’ that are (with the exception of visible light waves) perceptually undetectable disturbances traveling at the fixed and never changing speed of light: 299,792,458 meters per second.

But to prove valid [any] theory must become pragmatically predictable and useful but Newtonian based 19th century physics was not up-to-par with Maxwell’s theoretical leap; modern quantum theory decrees a direct proportionality between wave-frequency and energy yet turn of the century physicists lacked this formula when they attempted to calculate the energy of the electromagnetic waves radiating inside an oven [of a chosen temperature]; all they got was nonsensical results- infinite and useless results (Greene, p. 88).

Physicist Max Planck solved the quandary in 1900 - by guessing - that “… atoms could exchange energy with electromagnetic fields- that is, emit and absorb electromagnetic radiation, such as light- only in discrete units, or quanta.”… (Frank Wiczek, 2009)

Planck’s fortuitous ‘guess’ ushered in ‘quanta’ (and launched quantum theory) with his creation of the abstract ‘Plank constant’ as the needed algebraic proportion between the frequency of a wave and the ‘minimum’ amount of energy such quanta can ‘carry’:

“… if the minimum energy a particular wave can carry exceeds the energy it is supposed to contribute, it can’t contribute and instead lies dormant” (Greene, p. 92)

This made radiation predictable but bear in mind that the ‘Planck constant’ is an abstract billionth of a billionth of a billionth of a unit (1.05x10-27) (Greene, p. 93) and this is about as abstractly counter intuitive as you can get; but the Planck constant worked in explaining experimental results (Wiczek, p. 80); with Planck’s contribution at the turn of the 20th century science now possessed three universal constants…

1. The constant speed of light (Ole Romer, 1676);

2. Newton’s gravitational constant (1687) and now -

3. Planck’s constant (1900).

These three constants together form the ‘stuff’ of physical laws that are a basis of the quantum uniformity of our understanding.

(Wiczek, pp.156, 235)

Quantum science was rapidly advancing and Albert Einstein became involved with Planck’s idea of lumpy ‘units of radiating energy’ because it had fuller potentials than Planck himself even realized: it ‘meshed’ with the 1887 findings of German physicist Heinrich Hertz, who found that when light (electromagnetic radiation) is directed at a metallic object, it strikes and bounces 'loose' electrons out of the metal surface - the ‘photoelectric effect’. (Wilczek, p. 95)

“Einstein suggested incorporating Planck’s lumpy picture of wave energy into a new description of light. A light beam, according to Einstein, should actually be thought of as a ‘stream of tiny packet’- tiny particles of light- which were ultimately christened ‘photons’ by the chemist Gilbert Lewis.” (Brian Greene, 1999 p. 96)

It was this work on the photo electric effect that won Einstein the 1921 Nobel Prize, contributed to his Theory of Special Relativity and more; in the words of physicist Frank Wilczek, Einstein had disproved 19th century physics and cut the ‘Gordian Knot’ (p. 81); 20th century quantum physics would now arise but not in a nice tidy way because of a paradox known as ‘wave-particle duality’ (dubbed ‘wavicles’ to get the idea across).

What had originally disfavored Newton’s idea of light as streams of particles was the interpretation of physicist Thomas Young’s early 1800’s double-slit experiment which showed light must be a wave; when a beam of light is directed through two slits in a barrier, interference patterns are splayed across a target barrier on the other side and this clearly demonstrates wave -interference - light is a wave.

But photons being understood as ‘waves’ are a contradiction of Einstein’s ‘particle’ photons striking and bouncing ‘loose’ electrons out of metal surfaces in the photoelectric effect - light must also be a particle - so what’s going on here?

What’s going on is succinctly described with the words of physicist Brian Greene (p. 103):

“In 1923, the young French nobleman Prince Louis de Broglie added a new element to the quantum fray, one that would shortly help to usher in the mathematical framework of modern quantum mechanics and that earned him the 1929 Nobel Prize in physics. Inspired by a chain of reasoning rooted in Einstein’s special relativity, de Broglie suggested that the wave-particle duality applied not only to light but to matter as well. He reasoned, roughly speaking, that Einstein’s E=mc2 relates mass to energy, that Planck and Einstein had related energy to the frequency of waves, and therefore, by combining the two, mass should have a wave-like incarnation as well.”(2)

Thus arose the theory of ‘wave-particle duality’ but de Broglie’s formula showed that the wave-length for matter-waves is proportional to Planck’s constant - a billionth of a billionth of a billionth of a unit of everyday measure - so we can’t actually ‘see’ uniformly what’s actually going on down there.

Central to this difficulty is the 1927 ‘Heisenberg uncertainty principle’ that hangs like a heavy ‘sensory- mist’ obscuring our knowledge of sub-atomic quanta: energy and momentum are scientifically uncertain at the microscopic scale i.e., sub-atomic nuclei are about a hundred thousand times smaller than atoms and we don’t even know the size of atoms - their clouds of surrounding electrons cannot be precisely located - in accordance with the uncertainty principle.

So what was going on this time?

This quandary simply and roughly, can be likened to a billiard-ball effect of micro-nanotechnology; when you strike a sub-atomic particle with a single photon to locate its position the energy transfer from photon to particle disturbs the particle - it accelerates it away - making a dual measurement of its velocity and position impossible; we just can’t ‘see’ (or otherwise understand) what’s going on down there with any certainty - hence the uncertainty principle tells us that quantum energy and momentum are uncertain.

Uncertain or not pragmatic applications require understanding through uniformity and predictability and in 1926 physicist Max Born and his colleagues refined Erwin Schrodinger’s idea of a ‘smeared-out’ electron into today’s uniform concept…

“… the wave nature of matter implies that matter itself must be described fundamentally in a probabilistic manner. […] Just a few months after de Broglie’s suggestion Schrodinger took the decisive step toward this end by determining an equation that governs the shape and the evolution of probability waves… wave functions.”

(Greene, pp. 105-107).

Pragmatic applicability was achieved with this theoretical uniformity - the interpretation of wave functions.

Space-time gives scientific uniformity to the macro-universe yet its defining unit - the hyper-speed of light places that uniformity far beyond our daily sensory perceptions and ‘frame-of-mind’.

Vis-à-vis, Quantum mechanics on the other hand gives scientific uniformity to the micro-universe but its defining unit - the minutely small Planck constant - also places that realm far beyond our daily sensory perceptions and ‘frame of mind’ in the opposite direction.

The world we experience and the world of science diverge dramatically and to quote physicist Brian Greene again in closing-

“By 1927… classical innocence had been lost.” (p. 107)

References:

(1) Greene, Brian (3), (1999), The Elegant Universe, W.W. Norton & Company, New York, NY, p. 88

(2) Wilczek, Frank (4), (2008), The Lightness of Being, (N.Y., New York, Perseus Books Group), p.80

Endnotes:

(1) Newton's law of universal gravitation states that every massive particle in the universe attracts every other massive particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Newton's law of universal gravitation. (2011, February 5). In Wikipedia, The Free Encyclopedia. Retrieved 16:46, February 6, 2011, from http://en.wikipedia.org/w/index.php?title=Newton%27s_law_of_universal_gravitation&oldid=412173132

Newton's laws of motion consist of three motion due to those forces. They have been expressed in several different ways over nearly three centuries, and can be summarized as follows:

First law: Every body remains in a state of rest or uniform motion (constant speed in a straight line.

Second law: A body of momentum of the body.

Third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear. This means that whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction. This law is sometimes referred to as the action-reaction law, with F called the "action" and −F the "reaction". The action and the reaction are simultaneous.

Newton's laws of motion. (2011, February 3). In Wikipedia, The Free Encyclopedia. Retrieved 16:45, February 6, 2011, from http://en.wikipedia.org/w/index.php?title=Newton%27s_laws_of_motion&oldid=411717173

(2) E=mc2 is equal to its inversion, M=e/c2; this is mass/energy equivalency.

For further reading see: Flores, Francisco, "The Equivalence of Mass and Energy", The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N.Zalta (ed.), http://plato.stanford.edu/archives/win2008/entries/equivME/

In further explanation: Albert Einstein's initial formula: M=E/C2 and its popularized inversion E=MC2 state [in order]: (rest) Mass [M] is equal to Energy [E] divided by the speed of Light (in a vacuum) [C] squared and the popular inversion is conversely Energy [E] is equal to (rest) Mass [M] multiplied [times] the speed of Light (in a vacuum) [C] squared. Entwined concepts of Mass and Energy (Matter/Light et alia) roil within scientific complexity; see the theory of "Wave-Particle duality", as an example:

"In physics and chemistry, waveparticle duality is the concept that all matter and energy exhibits both wave-like and particle-like properties. A central concept of quantum mechanics, duality addresses the inadequacy of classical concepts like "particle" and "wave" in fully describing the behaviour of small-scale objects." 'Waveparticle duality', Wikipedia, The Free Encyclopedia, 24 March 2009, 06:51 UTC, http://en.wikipedia.org/w/index.php?title=Wave%E2%80 %93particle_duality&oldid=279318291. [accessed 26 March 2009]

(3) Dr. Brian Greene is Professor of physics and mathematics; co director, Institute for Strings, Cosmology, and Astroparticle Physics, Columbia University

(4) Dr. Frank Wilczek is Herman Feshbach Professor of Physics, Massachusetts Institute of Technology and a 2004 Nobel Laureate. See: http://frankwilczek.com/