Quantum mechanics

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I think I can safely say that nobody understands quantum mechanics.
Richard Feynman, The Character of Physical Law (1965)

Quantum mechanics (QM) is a branch of physics developed to deal with the behavior of atoms, molecules, and sub-atomic particles. Most of the foundations of QM were laid down during the first three decades of the 20th century. Since then, it has been used extensively in the study of chemistry and materials, including biological research, and in cosmology, astrophysics and astronomy.

Because quantum mechanics behaves in ways contrary to our understanding of macroscopic mechanics and to all previously accepted laws of physics, it has a reputation as weird and incomprehensible. Even/especially early quantum physicists had trouble accepting what they were finding. Max Planck, the who first discovered quantization, remained reluctant, while an oft-repeated quote is Albert Einstein sceptically referring to entanglement as "spooky action at a distance".[1] The weirdness and hints of controversy make it a popular subject of pop-science media and attracts an outsize share of woo. In particular, overwhelmingly Old QM and philosophical interpretations are presented to the interested lay person, who would be forgiven for having the impression that that's what physics is about, while current research is focussed on very different aspects.

What Quantum Mechanics explains[edit]

One of the earliest ideas sparking the development of Quantum Mechanics is due to Max Planck in 1900. He proposed that the energy of a light wave is the integer multiple of a constant (, pronounced "h-bar") times the light's frequency, and that it can only increase or decrease by this amount, i.e. that the energy spectrum of light is discrete — this is also where Quantum Mechanics gets the name from, "quantum" meaning "coming in discrete packets". The proposal was made to help explain the spectrum of blackbody radiation which Classical Mechanics failed to explain.[2]

Quantum Mechanics, along with Quantum Field Theory (which is a modern upgrade to the older Quantum Mechanics), also explains or predicts a host of other phenomena, like superconductivity (used in MRI machines and some high-speed trains), Hawking radiation (theoretically emitted by black holes), how magnets work, the biochemical properties of proteins, why metals conduct and plastic doesn't, and more. It also explains many everyday things like why glass is both reflective and transparent; light has a probability of going through the glass and a probability of being reflected back. The mathematics and physical assumptions of Quantum Field Theory are combined with experimental evidence that created a framework for describing how all known fundamental particles work and how they interact with each other. This framework is called the Standard Model and its validity is tested by particle accelerators such as the LHC in Geneva, Switzerland.

In short, Quantum Mechanics is essentially a more accurate version of Classical Mechanics that can actually meaningfully predict phenomena happening at small scales. At large scales, however, Classical Mechanics is a great approximation for the plethora of small underlying quantum effects.

It still has some limitations though. While physicists have an understanding of how three of the four fundamental forces, i.e. electromagnetism, and the weak and strong interactions, work at small scales, nobody yet understands how gravity acts at very small scales.[3] Furthermore, dark matter, dark energy and neutrino physics remain poorly understood, as are the origin and fate of the Universe.

Core principles[edit]

There are a few basic core principles for understanding quantum mechanics and the supposedly spooky oddness that goes on at the level of atoms. It is very important to remember one key thing: quantum mechanics is not classical mechanics. Quantum theory is mostly a mathematical description of how the world works at the atomic level based on very good evidence. Taking any of the interpretations too literally would be a mistake.

Quantization of energy[edit]

Prior to quantum theory, energy was thought of as necessarily analogue; taking any value indiscriminately and acting as a smooth transition. In the macroscopic world, this observation remains fairly true. Like a hosepipe that can deliver whatever amount of water you like by turning the tap in small amounts.

For bound systems at the quantum level, such as electrons bound to atoms, energy can take on certain discrete values. This is analogous to a car that can only travel at 10, 20, 30 or 40 (and so on) miles per hour, rather than a smooth and seamless increase of speed. If you don't give it enough energy to make the transition between 20 mph and 30 mph, it'll stay at 20 mph. This forms the basis of spectroscopy — and without this quantisation of energy, such analytical tools would be impossible.

To muddy the waters even further, particles need not be in a single energy state at all, but might be in what is called a "superposition of states". Using the previous car as an example, this is analogous to that car travelling at 20, 30, and 50 mph all at once. A particle in this state cannot even really be said to have an energy, although it can be said to have an average energy depending on how much of it is in each state.

This superposition of states is fundamental to quantum mechanics, and in particular, to the idea of "wavefunction collapse" in the Copenhagen interpretation,[4] which states that an observation of energy forces a particle that was in a superposition state into one of the states it is composed of with various probabilities depending on the specifics of the superpostion. So a measurement of the quantum car in a superposition of 20, 30, and 50 mph will show the speed as 20, 30, or 50 mph, and after the measurement the car will be in the single energy state corresponding to whichever speed you measured.

The Photoelectric Effect[edit]

In the late-19th century, James Clerk Maxwell formulated a theory of electromagnetism that described a wide range of electrical phenomena, and in particular described light as an electromagnetic wave. Despite the success of this theory, the early-20th century found it unable to describe certain aspects of the photoelectric effect.

When exposed to light, certain materials release electrons. Studying this effect, researchers found that for a fixed frequency of light, the rate of electron emission is directly proportional to the intensity of the indecent incident light, but if the frequency of the light was below a certain threshold, no electrons would be emitted no matter how intense the light was. It was no longer a matter of how much power was being imparted to the photoelectric material — a very high-power, but low frequency source was incapable of liberating electrons, while a source with significantly lower power output at a higher frequency would liberate electrons.

This effect was explained, by Albert Einstein in 1905, by describing the light as a stream of particles, called "photons". Each photon has a small amount of energy which is proportional to its frequency. More intense light has more photons, but each photon has the same energy. The electrons in the photoelectric material only interact with one photon at a time, so if a single photon doesn't have enough energy to liberate an electron, no electron will be liberated no matter how many photons per second are interacting with the material.

Needless to say, this description of light as a series of particles, albeit ones with a "frequency" associated with them, conflicted with Maxwell's description.

Particle-wave duality[edit]

Classical mechanics treats particles and waves as different things. A particle is a point, a speck with mass and an exact location. A wave is a little more abstract but it has wavelength — it's spread out, with frequency and speed. In quantum mechanics there is no distinction. Particles can be waves and waves can be particles — although really they're something else entirely with some, but not all, of the properties of both. We've evolved in a macroscopic world where we can see a distinction, but this is the quantum world, kid.

The evidence for this comes from two experiments. Classically, light was treated as a wave — there was no quanta or a concept of individual particles, just waves of energy. This explained Isaac Newton's optics pretty well. However, work done on something called the photoelectric effect, which Albert Einstein won the Nobel Prize for, smashed this interpretation. Einstein noted that the details photoelectric effect — where a metal gave off electrons when exposed to light of discrete kinetic energy — could only be explained if light was a particle. If light consisted as particles then it would explain why the effect was instant (waves would take time to absorb as light waves are hundreds of times larger than atoms), that energy given off was proportional to the frequency and there was a cut-off point where the effect didn't happen below a certain frequency. Each photon carried a discrete amount of energy, proportional to its frequency, and delivered it to the metal. Needless to say, starting to describe light as a particle seriously caused issues with optics and the concept of frequency; waves can have a frequency, but particles cannot.

Simulation of a particle wave function: double slit experiment

After this, however, came the double-slit experiment. This experiment fired electrons through two slits. Under classical mechanics, the electron was a particle. The last thing you would expect from a particle being fired through two slits would be an interference pattern, but this is what was observed. The electrons were exhibiting interference, a property of waves. The extra "spooky" part was that when the electrons were reduced to the point where only one would flow through the slits at a time the pattern was still seen; not only did the wave of the electron interfere with other electrons, it interfered with itself.

From these observations, particle-wave duality was born. At the quantum level, there is no clear distinction between waves and particles. Various interpretations have been put forward to explain this in a way that "makes sense" — however, they sometimes suffer from the fact they are trying to interpret quantum mechanics as classical mechanics.


Star Trek fan: "How do the Heisenberg compensators work?"
Gene Roddenberry: "They work just fine, thank you."

With the wave-like nature of quantum mechanics established, problems began to arise in figuring out the location of particles. Waves do not have a specific location; they're spread out over an area and aren't described the same way as particles. Thus the "uncertainty principle" was established; in short it means you cannot know the location and momentum of a particle to the same degree of accuracy. This isn't a limit in scientific instruments but a fundamental aspect of physics. Even a god can't know the location and velocity of particles at the same time. It is a physical impossibility.

This effect arises from the fact that there is a series of states of a particle that have a definite momentum, and a series of states that have a definite position, but those two series of states are not the same. A state with a definite momentum is a superposition of states with definite position, and vice versa. The uncertainty principle shows that a particle can be in a state that is a superposition of a small range of momenta and a superposition of a small range of positions simultaneously, but the smallness of one of those ranges cannot be made smaller without making the other range larger.


Some of the phenomena of quantum mechanics, such as entanglement were described by Albert Einstein as "spooky" because, at the sub-atomic level, physics as we think we know it breaks down and becomes almost incomprehensible.

Quantum field theory[edit]

The early equations of quantum mechanics were not compatible with relativity, a problem because in accelerators electrons and other particles come close to the speed of light. From an attempt at inventing relativistic versions of the equations, physicists eventually settled on the complicated mathematical formalism that is quantum field theory. In physics, a field holds the value of a number, vector, or similar object for each point of space(-time), think temperature (a number) or wind (a vector) on a weather map. Field theories give laws for how these fields evolve; quantum field theory is a specific version of field theory encoding the above counterintuitive behavior of quantum physics.

Quantum electrodynamics[edit]

Quantum electrodynamics, abbreviated QED, is a relativistic quantum field theory that arises when we apply the principles of quantum mechanics to electromagnetism and electrodynamics. QED covers every possible interaction between an electron (or a positron) and a photon.

A hand-wavy way to picture how QED works is to imagine electromagnetic fields reduced to a grid, and then the forces on electrically charged particles are described in terms of the exchange of photons between the particles (the photon is the carrier of the electromagnetic force). While the mathematics of QED, like all quantum field theories, are pretty esoteric, interactions involving QED can be conveniently and relatively painlessly understood through the use of Feynman diagramsWikipedia, which look like the sort of things you scribble while talking on the phone.

In 1968, with electroweak unification of electromagnetism and the weak nuclear force, QED was subsumed into Quantum Electroweak Dynamics.

Quantum chromodynamics[edit]

Animation of the mechanism of the nuclear force, showing the exchange of gluons between quarks and color changes and the exchange of pions between a proton and a neutron.

Quantum chromodynamics, abbreviated 'QCD', is a relativistic quantum field theory that describes the strong nuclear force.

Fundamentally, baryonic matter is made of quarks that bind together to form more familiar particles, such as protons and neutrons. Quarks, like protons, have an electric charge, but enjoy the additional privilege of a color charge. One can think of the color charge as analogous to electric charge, but instead of two possible charges (positive and negative) it has three: red, green, and blue. The color charge of a quark determines how the strong nuclear force acts on it.

The force carriers of the strong force are massless particles called gluons, which are analogous to photons in QED. However, while photons have no electric charge, gluons do have a color charge; thus, gluons can interact with other gluons.

The mathematical description of all of these interactions fall under the QCD umbrella.

The Haters[edit]

Jack Chick apparently rejects the idea of QCD, or at least the idea that gluons exist.[5] Read his fascinating take, then decide for yourself. 'Course, a reading of that gem calls into question his understanding of the term, since saying things like "the binding force of an atom is gluons!" is akin to saying "the force that holds my magnet to the fridge is photons!" It's semi-clear what he's trying to say, but his wording is not exactly precise. Oh, and then there's the fact he's ignoring that we know why the atomic nucleus stays together: the strong force is many times more powerful than the electromagnetic force over distances comparable to the size of nuclei.

The Standard Model[edit]

See the main article on this topic: Standard Model

Since modern quantum mechanics was completed, in around 1927, physicists have sought to construct quantum theories that would describe the fundamental forces of nature — namely gravity, electromagnetism, and the strong and weak nuclear forces — taking into account special relativity. In the 1930s, Enrico Fermi was able to characterize the weak nuclear force, which is responsible for radioactive decay. In the 1940s, Richard Feynman, Julian Schwinger and Sin-Itiro Tomogana developed the quantum-mechanical generalization of Maxwell's equations, quantum electrodynamics. Soon, physicists were able to show that in high energy interactions, electromagnetic and weak interactions are one and the same thing, hence the electroweak force. Building upon these encouraging successes, physicists set their sight on the strong nuclear force. By the 1970s, quantum chromodynamics — note that it has nothing to do with color in the ordinary sense — emerged as the best description of strong interactions available. It then became clear that the behavior of elementary particles can be described with a very high degree of accuracy if one possesses quantum theories of electromagnetism and the nuclear forces. Gravity has invariably been neglected because (1) it is a truly feeble force and (2) no one has ever been able to forge a usable quantum theory of gravity. The quantum theories of non-gravitational interactions is now known as the Standard Model and is considered to be the most accurate physical theory ever created. In July 4th, 2012, the Standard Model made it to the popular press when the Large Hadron Collider at CERN, Geneva, Switzerland, made statistically significant observations and measurements of the Higgs boson, the excitation of the field that interacts with other particles and gives them mass.

Together with general relativity, our modern theory of gravity, the Standard Model describes in exquisite detail everything physicists think they know for certain about the Universe. But of course, like all theories of science to-date, there are things not dreamed of in this theory. Besides being unable to successfully incorporate gravity, it has very little to say about neutrino physics, and indeed, nothing to say about dark matter and dark energy, which empirical evidence suggests to comprise the overwhelming majority of our Universe.


If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be Shut up and calculate!
—David Mermin (probably[6]), Professor of Physics Emeritus at Cornell University

Interpretations of quantum mechanics attempt to explain what the mathematical formalism says about the world and the objects within it. Largely the realm of history, philosophy, and pop-science, most working physicist don't spend too much thought on this.

Copenhagen interpretation[edit]

The Copenhagen interpretation is a loose term describing a collection of related views that formed in Copenhagen from discussions among the early pioneers of quantum mechanics. However there is a common core to the interpretation described here.

In this view quantum mechanics simply describes the probabilities of a quantum system inducing certain effects on macroscopic bodies. For example an electron causing an mark to develop on a detection plate. The world on this scale is considered by nature indescribable in physical terms aside from the single classical concept involved in a given experiment. The experiment can be seen as giving license to extend that classical concept to the subatomic scale. Thus in experiments such as those involving the photodetector one is allowed use the classical concepts of a particle with a position to explain the marks on the photodetector. Outside of this experimental context however references to the position of a photon, or even the photon itself, are meaningless.

By by the late 1930s Bohr in particular went further saying that "photon" was ultimately just a type of mark on a macroscopic device and its "position" was nothing more than the location of the mark on the device, one could never ascribe properties to the subatomic realm itself.[7] Quantum Mechanics does not describe subatomic systems as they truly are independent of a macroscopic agent's intervention. Although the experiment may grant license to use a classical concept one cannot know which value this concept will take, i.e. where the mark will develop on the photographic screen. This is the probabilistic element of quantum theory. This later development became the mainstream view.[8]

"Collapse" of the wavefunction is nothing more than an agent updating their knowledge in light of learning the outcome, not a physical process.[9]

Many Interacting Worlds[edit]

Despite the similarity in name with Many Worlds Interpretation, they are extremely different. According to MIW, the wavefunction is not a physically real thing (unlike MWI). The parallel worlds do not branch due to quantum events in MIW but exist from the beginning. According to this new theory, quantum mechanics exists due to the interaction of the many worlds. (In MWI, however, the multiverse branch in quantum events and thus the multiverse is a result of quantum mechanics.) This theory also postulates the interaction between these worlds, which might produce predictions.


These views attempt to explain quantum theory as the result of influences from the future affecting the present. The probabilistic aspect of the theory enters from the lack of knowledge the observer at present has about the future from which these influences emanate.[10]

Conscious observation[edit]

See the main article on this topic: Observer effect

"Observation," in the sense of the Copenhagen interpretation is a short-hand for any situation where a quantum system causes an irreversible effect to occur in a macroscopic body. There are some, however, that seem to take it as requiring conscious observation, i.e., observation by a human mind. This is highlighted in the intentional absurdity of Schrödinger's cat experiment, where the cat and the detector itself act as "observers". There are further questions for those who take the conscious observer literally, serious scientists at least tend not to subscribe to the conscious observer idea, but there are/were a few exceptions like Wigner.[11]

  1. Why should a conscious observer be significant?
  2. How can consciousness have effects that unconscious physical processes lack?

There is a parallel here with the claims of psychokinesis:

  1. Psychokinesis assumes that conscious beings cause physical changes by willing them to happen.
  2. The Copenhagen interpretation assumes that conscious beings cause physical changes by observing them to happen.

The idea that consciousness is somehow special appeals to some religions and also to the purveyors of some types of quantum woo. By contrast p-zombies materialists dislike the idea that there is anything more to consciousness than physical processes within the brain and 19th century block-heads materialists are uncomfortable with the Copenhagen interpretation.

This group of interpretations is known as subjective collapse interpretations, since they hold that the wave function and its collapse are real phenomena, and that collapse is triggered by the conscious non-material mind (as in dualism). The most notable subjective collapse interpretation is the von Neumann-Wigner interpretation.

Well-known physicist and atheist author/apologist Victor Stenger argued against the Copenhagen interpretation in his book The Unconscious Quantum.

Many worlds[edit]

The primary claim of the many worlds interpretation is that the quantum state of a system describes the nature of the system independent of observation, i.e. what the microscopic system is actually like. This is in contrast to the Copenhagen interpretation which states that the quantum state is simply a summary of an observer's knowledge of the system.

During a measurement the quantum state of an observer and their lab will develop terms corresponding to the observer seeing each possible outcome. In the Copenhagen interpretation this is simply seen as a list of various possible outcomes, similar to how in classical probability if one rolled a dice and additionally modeled the person looking at the dice we would have terms corresponding to "Observer saw a roll of 1" and "Observer saw a roll of 2" etc. In the Many Worlds Interpretation however, since the quantum state is regarded as physically real, then each term in this series, being part of the quantum state, are physically real and thus we have multiple worlds. In this sense the Multiple Worlds of the interpretation are an implication of the main claim, namely that the quantum state is a literal description of the system.

This Interpretation is still a minority one within physics itself for two reasons.

First, many people, including some physicists, find the ideas about splitting or multiple realities absurd.

Second, trying to derive most of the actual empirical content of quantum theory, such as the Born Rule probability distribution of experimental outcomes, from the assumption that the quantum state literally describes the system, has never been achieved in a non-circular way, to everyone's satisfaction. In contrast there are several derivations of quantum theory from first principles where the quantum state is seen as a summary of knowledge.[12][13][14]


  • Pilot wave interpretation[15]
  • Consistent histories[16]
  • Quantum Darwinism[17]
  • Penrose Gravity interpretation[18]

Problems with interpretations[edit]

While interesting, the interpretations are the bane of a philosophy of science known as instrumentalism, which states that theories be judged entirely on predictive qualities, not their ability to make sense to our particular brains. Basically, cut it with the visualisations — they're not making any predictive difference — and just do the numbers.

Quantum woo[edit]

See the main article on this topic: Quantum woo

Quantum physics is a difficult subject and people without science degrees are rarely expected to understand it — even those with the degrees are usually expected to have a working knowledge and not a full appreciation of every aspect of it. Its difficulty is further increased by the fact that, in many cases, there really are almost[19] no decent lay explanations of how it works, so more accurate and nuanced explanations are lacking in popular science. Given the level of both complexity and counter-intuitive nature of quantum theory (and perhaps because of the quantum-based technobabble frequently employed in science fiction like Star Trek) woo-meisters can always call their wares "quantum" something or other and people are likely to expect it. Then ordinary people sometimes react with, "Well it doesn’t make sense to me but I suppose the scientists understand it." There is some psychological evidence to suggest people are more likely to believe explanations that are wrong if they are dressed up with science-like terms — indeed, advertisers have exploited this for many years, notably cosmetics commercials that border on self-parody. This all combines to make quantum woo a very attractive pseudoscience for people to engage in.

Quantum consciousness[edit]

See the main article on this topic: Quantum consciousness

Scientists have some partial understanding of quantum physics but frequently disagree with each other while ordinary people are regularly mystified. Similarly the reason for consciousness is, given current scientific knowledge, impossible to understand. (Of course various religions and woo advocates convince their dupes acolytes that they know the answer to consciousness.) Its reasoning is as follows:

  • Quantum mechanics is weird, spooky and I can’t understand it.
  • Consciousness is weird, spooky and I can’t understand what causes it.
  • Therefore perhaps the two are connected.

Quantum consciousness is just one example where the woo-meisters can make it big time.

See also[edit]

External links[edit]


  1. Mermin, N. David (April 1985). "Is the Moon There When Nobody Looks? Reality and the Quantum Theory". Physics Today 38 (4): 38–47. doiWikipedia:10.1063/1.880968. 
  2. “1 - Microscopic Theory of Radiation.” Quantum Field Theory and the Standard Model, by Matthew Dean. Schwartz, Cambridge University Press, 2013, ISBN 978-1-107-03473-0
  3. Sushkov, A. O.; Kim, W. J.; Dalvit, D. A. R.; Lamoreaux, S. K. (2011). "New Experimental Limits on Non-Newtonian Forces in the Micrometer Range". Physical Review Letters. 107 (17): 171101. arXiv:1108.2547. Bibcode:2011PhRvL.107q1101S. doi:10.1103/PhysRevLett.107.171101. PMID 22107498. It is remarkable that two of the greatest successes of 20th century physics, general relativity and the standard model, appear to be fundamentally incompatible. But see also Donoghue, John F. (2012). "The effective field theory treatment of quantum gravity". AIP Conference Proceedings. 1473 (1): 73. arXiv:1209.3511. Bibcode:2012AIPC.1483...73D. doi:10.1063/1.4756964. One can find thousands of statements in the literature to the effect that “general relativity and quantum mechanics are incompatible”. These are completely outdated and no longer relevant. Effective field theory shows that general relativity and quantum mechanics work together perfectly normally over a range of scales and curvatures, including those relevant for the world that we see around us. However, effective field theories are only valid over some range of scales. General relativity certainly does have problematic issues at extreme scales. There are important problems which the effective field theory does not solve because they are beyond its range of validity. However, this means that the issue of quantum gravity is not what we thought it to be. Rather than a fundamental incompatibility of quantum mechanics and gravity, we are in the more familiar situation of needing a more complete theory beyond the range of their combined applicability. The usual marriage of general relativity and quantum mechanics is fine at ordinary energies, but we now seek to uncover the modifications that must be present in more extreme conditions. This is the modern view of the problem of quantum gravity, and it represents progress over the outdated view of the past."
  4. Other interpretations of quantum mechanical observation that don't involve wavefunction collapse, such as the many-worlds hypothesis, are postulated, but the wavefunction collapse interpretation is one of the oldest and easiest to describe.
  5. Chick tract titled "Big Daddy?"; scroll down to the bottom panels.
  6. ["https://neuroself.files.wordpress.com/2011/12/mermin-shut-up-and-calculate.pdf" "Could Feynman Have Said This?"]. 
  7. Plotnitsky, Arkady, Niels Bohr and Complementarity (2012) Springer-Verlag New York
  8. Heisenberg, W., Physics and Philosophy
  9. Laloë, Franck, Do We Really Understand Quantum Mechanics? 2nd Edition (2019) Cambridge University Press
  10. Ruth E. Kastner, The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility, Cambridge University Press, 2012.
  11. Consciousness and Quantum Physics The author claims to have a Ph.D. and be a former professor. The text is difficult to understand but if you read carefully there is the unproved assumption that consciousness creates reality. Take that assumption away and all the nice spirituality fails.
  12. Giulio Chiribella, Adán Cabello, Matthias Kleinmann, and Markus P. Müller (2020), General Bayesian theories and the emergence of the exclusivity principle, Phys. Rev. Research, volume 2, 040021(R).
  13. Ludwig, G., An Axiomatic Basis for Quantum Mechanics and The Foundations of Quantum Mechanics. Four Volume work. 1984-1987
  14. Quantum Theory from First Principles: An Informational Approach, Giacomo D'Ariano et al
  15. https://plato.stanford.edu/entries/qm-bohm/
  16. https://plato.stanford.edu/entries/qm-consistent-histories/
  17. https://www.nature.com/articles/nphys1202
  18. https://en.m.wikipedia.org/wiki/Penrose_interpretation
  19. SMBC: "The Talk"