In 1894, electricity companies commissioned Planck to discover how to generate the greatest luminosity from light bulbs with the minimum energy. To get to a solution, Planck turned his attention to the black-body radiation problem.
In 1900, Planck had a theoretical answer. With great distaste, he had borrowed ideas from statistical mechanics that had been introduced earlier by Austrian physicist Ludwig Boltzmann.
Planck had a strong aversion to treating thermodynamics’ laws as statistical rather than absolute gospel. Being compelled to apply statistics to get an agreeable solution he considered “an act of despair.”
Planck achieved concordance with experimental results via a simple formula: E = hv, where E is the energy of a wave, v is the frequency of the radiation, and h is a very small number that came to be known as Planck’s constant (aka Planck’s action quantum).
To his consternation, what Planck found was that energy absorption and radiation was not continuous. Energetic work instead happens in discrete amounts: quanta of energy, with the Planck constant (h) as the quantum. What was supposedly entirely wavelike manifested in particulate form.
(The elementary quantum of action, known as Planck’s constant, is 6.626 × 10–34 joule/second in meter/kilogram/second units, with just a bit of uncertainty.)
“It seemed so incompatible with the traditional view of the universe provided by physics.” ~ Max Planck
At first, Planck considered quantization only “a purely formal assumption” which he “did not think much about.” But then he tried to stuff the quantum genie back into the bottle and found that he could not.
“My unavailing attempts to somehow reintegrate the action quantum into classical theory extended over several years and caused me much trouble.” ~ Max Planck
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Statistical classical mechanics requires the existence of the Planck constant, but does not define its value. Planck ushered the recognition that physical action cannot take an arbitrary value. In other words, there is a fundamental order to Nature, which begins with the infinitesimal.
Phenomena must be a multiple of the Planck constant. Planck’s quantum of action essentially states that only certain energy levels may manifest, while values in between are forbidden to do so. Physics cannot explain why.
(Planck’s constant represents the limit of empirical existence. The least possible distance is Planck length. Minimal matter has Planck mass. The shortest duration is measured in Planck time.)
Existence consists of interacting fields which necessarily manifest in particulate form. Even thermal energy (heat) quantizes. We’ll see that this duality is both illusory and necessary for existence.
The dynamics of quantum systems are encoded in the amplitude and phase of wave packets. ~ French quantum physicist V. Gruson et al
The science of the quantum world is alternately called quantum mechanics (accenting the statistical nature of the study), quantum field theory (QFT) (emphasizing that quanta are merely manifest fields), or simply quantum theory (which points out that all the packets under discussion are entirely theoretical, and not to be confused with reality).
Packets of Light
Einstein instantly appreciated Plank’s discovery of quantization. He later called it “the basis of all 20th century research in physics.”
“Without this discovery, it would not have been possible to establish a workable theory of molecules and atoms and the energy processes that govern their transformations. Moreover, it has shattered the whole framework of classical mechanics and electrodynamics and set science a fresh task: that of finding a new conceptual basis for all of physics.” ~ Albert Einstein
In 1905, addressing classical physics’ inability to explain the photoelectric effect, Einstein argued that radiant energy consisted of quanta.
“The energy of a light ray is not continuously distributed over an increasing space but consists of a finite number of energy quanta which are localized at points in space, which move without dividing, and which can only be produced and absorbed as whole units.” ~ Albert Einstein*^
(The photoelectric effect is the glow of objects when absorbing radiation. Electrically charged particles, either electrons or ions, are emitted when a body takes on energy.)
(American chemist Gilbert N. Lewis termed these packets of light photons in 1926.)
Echoing Plank’s equation, Einstein’s formula for photonic energy was: E = hf, where E is the energy of light at frequency f, tempered by Planck’s action quantum (h).
Einstein generalized the quantum hypothesis in 1907 by using it to interpret the temperature-dependence of the specific heats of solids. As a follow-on, Einstein treated thermodynamic fluctuations in two 1909 papers. Though he did not use the word duality or make any assertion of principle, Einstein introduced wave/particle duality into physics. This was one of several instances where Einstein failed to appreciate the implications of his assertions.
“The theory of relativity has changed our view of the nature of light insofar as it does not conceive of light as a sequence of states of a hypothetical medium, but rather as something having an independent existence just like matter.” ~ Albert Einstein in 1909
In the 5th century BCE Empedocles conceptualized Nature as comprising atomic elements. A century later Aristotle elaborated that these elements comprised a physical substrate which emerged from ethereal “forms” – an idea originally espoused by Plato, Aristotle’s teacher. Forms comprised the essences which begat Nature: the exhibition of existence. Forms took form as elements.
Atoms were considered the most minuscule particle of matter until 1897, when English physicist J.J. Thomson found something smaller, which he called corpuscles. What Thomson discovered was the subatomic particle now called the electron.
Experimenting with cathode ray emissions, Thomson concluded that atoms were divisible into constituent corpuscles. From this he concocted a plum-pudding model for atoms. To explain the overall neutral charge of an atom, as contrasted to the corpuscle (electron) negative charge, Thomson proposed that corpuscles floated in a sea of positive charges, with electrons embedded like plums in a pudding; though Thomson’s model posited rapidly moving corpuscles instead of plopped plums.
One of Thomson’s pupils, English physicist and chemist Ernest Rutherford, disproved Thomas’ atomic plum pudding in 1909. In its place, Rutherford imagined in 1911 a planetary atomic model: a cloud of negatively charged electrons swirling in orbits over a compact positively charged nucleus.
Rutherford was working with Danish physicist Niels Bohr, who conjectured in 1913 that electrons moved in specific orbits, which were regulated by Planck’s quantum of action. By 1921, Rutherford and Bohr had come up with an atomic model comprising protons, neutrons, and electrons. This model was validated in the 1950s, when atomic nuclei were manually disassembled by newly developed subatomic particle accelerators and detectors.
In 1924, French physicist Louis de Broglie turned Einstein’s quantified light inside-out, by wondering whether electrons and other elementary particles exhibit wavelike behavior. A fascinated Austrian physicist, Erwin Schrödinger, took the idea and ran with it. He unknowingly injected uncertainty into quantum mechanics with his 1926 publication, which described an electron as an ongoing wave function, rather than a particle at any point in time. This became known as Schrödinger’s equation.
A most significant consequence of describing electrons as waveforms, as Schrödinger had done, was to make it mathematically impossible to state both the position and momentum of an electron at any point in time. Werner Heisenberg’s 1926 observation of this became known as the uncertainty principle: a measurement may be made to get a sense of either a quantum’s position or momentum, but not both at the same time.
In 1927, English physicist George Thomson, son of J.J., passed a beam of electrons through a thin metal film and observed interference patterns (electron diffraction), proving that subatomic quanta were simultaneously particles and waves.
Quantum particles cannot be described as a point-like object with a well-defined velocity, because quanta inherently behave as a wave; and for a wave, momentum and position cannot both be defined accurately for any instant. This is true both in Nature and mathematically.
What to make of this inherent uncertainty? Physicists heatedly disagreed about what it meant.
Considering wave/particle duality a reality, Schrödinger at first took uncertainty literally. He later recanted, declaring himself utterly confused.
“I do not like it, and I am sorry I ever had anything to do with it.” ~ Erwin Schrödinger
Thinking that God “does not play dice,” Einstein fell back on faith to deride the uncertainty of the quantum particle/wave duality which he himself discovered.
“Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing.” ~ Albert Einstein
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“All particles must be transported by a wave into which it is incorporated.” ~ Louis de Broglie in 1927
Louis de Broglie, who brought the matter up in the first place, came up with the pilot wave theory, which rendered local events determinate by virtue of a coherent force that provides every wave with its own guidance. The price was acknowledging that the entire universe was entangled: affording nonlocal interactions between particles. Though pilot wave theory is largely ignored, de Broglie was essentially correct.
Niels Bohr interpreted the uncertainty principle holistically: the universe is basically an unanalyzable whole, in which the idea of separation of particle and environment is an abstraction, except as an approximation.
“In the long run, only the entire universe can be regarded as self-determinate, while any part may be independent in general only for some limited period of time. The very mode of interaction between constituent parts depends on the whole, in a way that cannot be specified without first specifying the state of the whole.” ~ American physicist David Bohm & British quantum physicist Basil Hiley
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Whether uncertainty is actuality remains controversial. But uncertainty certainly looks like the real thing.
“The statistical view is not compatible with the predictions of quantum theory.” ~ English particle physicists Terry Rudolph, Matthew Pusey, & Jonathan Barrett
Quantum theory is founded upon the premise that so-called particles are fields with anomalies. Fields are, by definition, a synchrony of waves. Denying the reality of the wave function, and its inherent uncertainty, eviscerates quantum mechanics by denying the existence of the foundation upon which the theory is built.
“The linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave.” ~ German physicist Wolfgang Schleich
The entanglement of wave/particle duality and inherent uncertainty at the originating level of Nature suggests a deeper reality.
“The particles and fields are very, very crude statistical descriptions. Those particles and those fields are not true representatives of what’s really going on.” ~ Dutch theoretical physicist Gerard ‘t Hooft, who believes the universe is a deterministic but immaterial information system.
Since antiquity, the properties of light have fascinated physicists. In 1658, French mathematician Pierre de Fermat proposed that light always travels most efficiently: from one point to another in the least time, even when refracted: traveling through different media with distinct velocities, such as moving through air and then into water. This inscrutable optimality of light is a well-established fact.
In the figure, a ray of light going from a to b would travel the least distance via the hypothetical straight line. Instead, light actually traverses a longer distance that takes less time, as light moves slower through water than air – the straight-line path would incur a longer, sluggish passage in water.
Fermat’s principle was broadened to encompass all propagating energy waves by Dutch physicist Christiaan Huygens in 1678. In 1827, Irish physicist William Hamilton took wave transmission optimality as a universal for all dynamics in any physical system.
Via mathematics, Hamilton’s principle is encompassed in all of physics. Such matchless motion necessitates omniscience: always knowing all the information in the universe.
This profundity is no casual conclusion. For any energy wave to behave as it does, all information about actuality must be instantaneously incorporated.
Optimal propagation clearly indicates a unified, coherent intelligence from the Planck level on up, and strongly suggests teleology: that the game afoot which we call Nature has intention.
The Standard Model
“Whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed.” ~ Pakistani physicist Abdus Salam
Early particle accelerators and their detectors explored the subatomic world. What they found was a multitudinous zoo. Nature’s fondness for diversity became abundantly apparent at the quantum level.
Energetic collisions of protons and neutrons in atomic nuclei produced smaller, more “elemental” particles: hadrons. Particle accelerators proliferated hadrons into such a prodigious variety that it prompted Austrian physicist Wolfgang Pauli to remark: “had I foreseen this, I would have gone into botany.”
Hadrons were found to be comprised of even tinier constituents, called quarks, of which there are different flavors, determined by their spin and symmetry.
Going bottoms-up: quarks combine to form families of hadrons, which join together in threesomes to form protons and neutrons (2 types of baryons), which are enslaved by the nuclear force to create atomic nuclei, which combine with electrons, bound together by the electromagnetic force, to create atoms. Via a diverse variety of attractions, atoms congregate into molecules, which make up everyday matter. But bear in mind that matter is ultimately nothing more than intense interactions of localized coherent energy fields, posing as something solid.
Physicists understand matter and energy in terms of kinematics and the interactions of elementary particles. Kinematics, which is a classical-mechanics construct, characterizes the motions of bodies, without considering the forces that cause movement. This conceptual bifurcation – between matter and the forces that move matter – would live on in quantum physics’ Standard Model.
The Standard Model (SM) is a myth about how Nature constitutes itself from basic quantum building blocks of matter, which are constantly caressed by carriers of Nature’s fundamental forces. SM proposes a set of elementary particles which compose existence at the quantum level.
The Standard Model was formulated in the 1970s. From the early 1980s, experiments verified various facets of SM. SM cannot explain many observed quantum phenomena, nor does it include all subatomic particles discovered.
As observations have often differed from SM theory, the Standard Model has undergone repeated patchwork; so much so that SM is now a set of theorems cobbled together to render an approximate fit to what has been observed, with a lot left out.
Under the Standard Model, there are 2 elementary particle types: fermions and bosons. Whereas fermions are the particles that comprise matter, bosons are force carriers.
The SM particle zoo has 17 main characters: 12 fermions and 5 bosons, complemented by an equivalent set of anti-particles, and a hypothetical hanger-on: the graviton, which is the elusive particle representing gravity.
There is also an ancillary mob to cover various observed oddities. To conclude the parade are virtual particles, which are assumed to flit in and out of existence in Planck time to lend their support to the proceedings.
Photons are the best-known boson. They are the quanta of light, which manifests as electromagnetic waves. Despite not interacting among themselves, and remaining utterly unaffected by electrical and magnetic fields, photons mystically porter the force of electromagnetism. Except for gravity, electromagnetism is the interaction responsible for practically all phenomena encountered in everyday life.
Electrons carry the field of electricity; but they are fermions, and so it is beyond their purview to act as a fundamental force. Such a lordly task is restricted to bosons. Hence bosonic photons, despite being decidedly standoffish, magically manage to insinuate electromagnetism everywhere, even in the dark, where no such light-hearted quanta putatively lurk. Photons finagle this fantastic feat by the same means of all quantum interactions: sheer mathematics.
Magnets supposedly attract each other because they exchange virtual photons. Each photon has its own frame of reference. In their supposed interaction, virtual photons exchange momentum, thereby producing electromagnetism as a relativistic effect.
“These particles do not have a pebble-like reality, but are rather the quanta of corresponding fields, just as photons are the quanta of the electromagnetic field. They are elementary excitations of a moving substratum: minuscule moving wavelets.” ~ Italian physicist Carlo Rovelli
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3 properties are typically used to characterize quantum particles: mass, charge, and spin. These properties are not what someone with a knowledge of classical physics would intuitively expect. Let’s look at mass, which gets a lot of coverage in covering quanta.
In the everyday world, mass is considered a measure of an object at rest. Special relativity shows that rest mass and rest energy are essentially equivalent. But rest mass (invariant mass) does not apply to subatomic particles, as they are never at rest.
For a quantum, mass is a euphemism. Subatomic particle mass is a mathematical representation of its isotropy (uniformity), not a measurement of anything actual. In other words, quantum mass measures the level of oddity in the wave from which a particle appears.
A practical conception of quantum mass is the threshold energy at which a certain subatomic particle may appear; put another way, the energy required for a specific quantum species to make an appearance.
A quantum is not literally a particle, like some itty-bitty billiard ball. It is instead a little localized chunk of ripple in a field that puts on a particle costume. Comprehending quanta is more about wave interactions than about particle properties. Quantum mechanics is a story of coherent field behavior, not a fable of fantastically fleeting fragments.
“Particles are epiphenomena arising from fields. Unbounded fields, not bounded particles, are fundamental.” ~ American physicist Art Hobson
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All this is what any physicist will relate as indisputable: all matter is made of atoms formed from more elementary quanta. The actuality of quanta is that they are fundamentally coherent, localized fields of energy.
However convincing, the physicality of quanta is nothing more than an illusory appearance. Which leads us to the crucial takeaway point: that what we take for physical existence, by way of objects, is a mirage.
“Although quantum field theory tells us what we can measure, it speaks in riddles when it comes to the nature of whatever entities give rise to our observations. The theory accounts for our observations in terms of quarks, muons, photons, and sundry quantum fields, but it does not tell us what a photon or a quantum field really is.” ~ German physicist Meinard Kuhlmann