One definition of “quantum” is: a tiny packet of energy at the atomic level. A quantum is the smallest possible unit of energy that can occur in nature. It is a term that applies to the atomic and subatomic world. The plural is “quanta.”

The term “quantum” is used in three different ways in quantum physics: 1) as noted, the smallest possible unit of energy that a particular force, such as light, carries, 2) a fundamental particle that carries a single unit of energy, and 3) a unit of anything else that is the smallest naturally-occurring unit—for example, a quantum of angular momentum or, even, a quantum of spacetime (think of a “pixel” of spacetime).

**1. A quantum as a unit of energy.** The first use of the term “quantum” was as a description of the smallest possible amount of the energy delivered by light. In 1900, Max Planck, a German physicist, discovered that light delivers its energy in tiny packets. He called such a packet of energy, a “quantum.”

To get an idea of the size of a quantum of light energy: in bright light, the human eye absorbs about 250,000,000 quanta of light each second.^{1}This number is from a post by HH on the website: https://medium.com/on-a-whim/estimating-the-number-of-photons-that-hit-the-eye-c0208e7e0b64, posted Aug. 20, 2016. As you can see (no pun intended), quanta are ridiculously tiny.

Quanta are “naturally occurring” in the sense that energy is measured out and delivered in these little packets by Mother Nature, herself. Just as a grain of sand is a “naturally occurring” unit of rock, a quantum is a naturally occurring unit of energy.

But, it’s important to mention one of the key differences between grains of sand and quanta. Whereas each grain of sand varies in size, each quantum is always the same amount of energy—at least, for every particle of the same type. For example, a quantum of energy delivered by a particular red photon is exactly the same in amount as a quantum of energy delivered by every other red photon of the identical shade.^{2}Photons of the identical shade also have identical wave frequencies. Max Planck discovered the relationship between frequency and energy in 1900. The equation that he developed is: **E = hv**,

** Quanta are discrete entities.** The description “packet of energy” is appropriate for quanta because they are discrete, that is, discontinuous. They aren’t like a lump of silver; they’re like a silver dollar. Whereas you can measure out fractions of a lump, like .5, or .25, or .247632… and so on, it will do you no good to tear a silver dollar in half, offer it to a cashier, and expect to buy anything. A lump of silver is thought of as being continuous in amount—you can cut it into smaller pieces with ever finer measurements. In contrast, coins are discrete; cutting them into smaller pieces doesn’t fit our system of coins. Similarly, Mother Nature offers quanta of energy but never pieces of them.

While nature doesn’t work with fractions of a quantum, it does work with multiples of quanta. That’s, again, similar to silver dollars—if you’re lucky, you’ll have lots of them. Back to the atomic world, a subatomic particle might emit 1 quantum of the energy of light or 2 or 3 quanta. It would do this by spitting out 1 photon or 2 or 3. Quanta are always counted with whole numbers: 1, 2, 3, 4, etc.

** Four forces of nature carry quanta of energy. ^{3}These four forces are electromagnetic radiation (including visible light), the Strong Force, the Weak Force, and gravity. However, the idea that gravity occurs in particles (gravitons), each of which delivers **The energy of all four forces of nature are carried in the form of quanta. So, for example, one can speak of quanta of the Strong Force, the force that holds atomic nuclei together. However, much less is known about quanta of the other forces than is known about quanta of light.

**2. A quantum as a subatomic particle. **In 1905, based on Planck’s work, Albert Einstein, published equations explaining light in terms of its smallest particles, that is, photons.^{4}When “quantum” refers to a photon rather than to just the energy it carries, one may be emphasizing the visualization of a photon as a vibration or wave in a While one can say that a photon delivers a quantum of light, one can also call the photon, itself, the “quantum of light” or a “quantum.”

And one can call any fundamental particle a “quantum” in the sense that it carries a quantum of energy. Here’s an example of a sentence in which “quantum” means a subatomic particle, as opposed to a tiny packet of energy: Electrons and photons are two types of quanta.

**3. Other entities thought of as quanta.** In the atomic world, if a property has a minimum size, the property can be measured in quanta. For example, nature measures out the electrical charge of a particle in quanta. An electron has one unit of negative charge, one negative quantum of charge. Three quarks, taken together, have one unit of positive charge, one positive quantum of charge.

Some physics theories, including String Theory, describe spacetime, itself, as being made up of quanta. A pixel in a video game is a good analogy. In these theories, each quantum of spacetime can be thought of as a pixel.

More About the Quantum

**The quantum as a central idea of quantum physics. **When Max Planck developed the notion of a quantum, he gave birth to entire new field of physics, quantum physics. The laws of this field depart from those of the Newtonian world of tables and chairs in many ways, and these differences start with how energy is conceptualized and measured. In the world of tables and chairs, we do not measure energy in individual, discrete packets; we conceptualize and measure it in continuous amounts.

For example, the energy in a chocolate bar might be 311 calories if we eat the whole thing. But, let’s say that halfway through the bar we suddenly remember our diet and throw the other half out the window. While munching, maybe we took in 159 calories of energy. If we had a scientific instrument and could measure more precisely, we might be dismayed to learn that it was actually 159.2 calories. With an even more precise measurement, turns out it was 159.23 calories. Theoretically, with sufficiently precise instruments, we could get more and more precise by adding more and more decimals.

The energy measured by calories is conceptualized as “continuous,” that is, infinitely divisible into smaller and smaller amounts. If calories were, instead, conceptualized as quanta, the energy in the bar would be made of little packets, each packet delivering a calorie of energy. You couldn’t bite the packet in half and adhere to your diet by eating only half a calorie. Mother Nature would give you one packet delivering one calorie or just don’t eat.

Of course, at bottom, the chocolate bar is made of those little packets of energy, quanta. But quanta are too tiny to be a practical measure of energy in our everyday world. For all practical purposes, we can measure energy in calories and consider them continuous.

Not all atomic-level measurements are made with quanta. Not all properties at the atomic level occur in the form of quanta. For example, the mass of a fundamental particle, such as an electron, is continuous rather than “quantized.”

All types of electromagnetic energy occur in the form of photons, each bearing a quantum of energy. Photons are the particles of any type of electromagnetic radiation, not just visible light. Each of these photons delivers a quantum of energy.

Physicists use the term “light” differently from laypeople. Physicists may use “light” to mean visible light, as laypeople do, but often they mean any form of electromagnetic radiation, visible light being just one form. When physicists say that photons are the force-carriers of light, they are referring to all forms of electromagnetic energy: X-rays, microwaves, radio waves, and the other types of electromagnetic radiation. One can speak, for example, of an X-ray photon and the quantum of energy that it carries.

**Photons of different frequencies deliver different amounts of energy. **The amount of energy that a quantum delivers depends on the frequency of the photon. Each type of electromagnetic light has its own frequency. For example, X-rays have higher frequency photons than the photons of visible light. The higher the frequency, the higher the energy of the photon. For details of this relationship, see Footnote 2.

As X-rays carry much more energy than visible light, they deliver much more punch. This is what makes X-rays dangerous to the cells of our body. The energy of X-rays can break apart molecules within cells and cause chaos.

In contrast, we can sit under our bed light and read for hours with no damage to our cells. Streams of “gazillions” of photons are hitting us during that time. But, each photon is low-frequency compared with an X-ray photon, and individually, it doesn’t have the energy to break apart a molecule. To have any effect on our cells, a number of photons as a group would have to hit the same exact spot in the cell and, in this way, deliver a bigger impact. This is an unlikely event. You’re safe when you read at night.

**The quantum as understood in the wave conceptualization of Quantum Field Theory. **Quantum Field Theory is the version of quantum mechanics current as of this writing (2017). In this theory, quanta can be thought of as units of energy gained by or lost from a field that extends throughout the universe.

Some physicists prefer to conceptualize Quantum Field Theory in terms of particles and some in terms of waves. While it’s most common for physicists to call photons, for example, “particles,” they could just as easily be called “waves.” This becomes clear if one remembers that photons have both frequency and wavelength, properties that in the macroscopic world belong only to waves.

The preference for the term “particles” is often based on the greater ease of visualizing particles. However, many physicists feel that the wave conceptualization better captures the nature of reality^{5}See, for example, Frank Wilczek (Nobel Laureate in physics), *The Lightness of Being*; Basic Books, 2008, New York, Chapter 8..

Given the idea of a photon as a wave, an obvious question is, “In what medium are photons creating waves?” Physicists often say “none.” That’s because people expect a medium to be made out of matter, like the air that sound waves travel through. But photons travel to Earth from the sun more than 93,000,000 miles through the vacuum of space, so, clearly, their medium is not made of matter.

According to Quantum Field Theory, photons and other subatomic entities are waving through fields. What’s a field? Good question. And in many physics books, it will get you a short, vague answer. Fields are not made of matter. They are among the most fundamental aspects of reality^{5}See, for example, Frank Wilczek (Nobel Laureate in physics), *The Lightness of Being*; Basic Books, 2008, New York, Chapter 8.. When you get down to a fundamental like a field, there’s nothing more fundamental that physicists can say that it’s made of.

Fields can be described mathematically. But in terms of a physical description, it’s best to say, fields are what is waving if one thinks of a photon as a wave. This, admittedly, is a circular definition of “field”: a photon is a wave that travels through a field, and a field is what is waving. However, fields can be described mathematically, and, as physicists work primarily with equations rather than with the ultimate nature of reality^{5}See, for example, Frank Wilczek (Nobel Laureate in physics), *The Lightness of Being*; Basic Books, 2008, New York, Chapter 8., many don’t trouble themselves with the question of what fields really are. See “quantum field,” for more discussion of this issue.

In some interpretations of quantum physics, such as the Transactional Interpretation,^{6}Ruth Kastner; *Understanding Our Unseen Reality, Solving Quantum Riddles*; Imperial College Press, 2015, London; p. 85. fields occupy a sublevel of reality^{5}See, for example, Frank Wilczek (Nobel Laureate in physics), *The Lightness of Being*; Basic Books, 2008, New York, Chapter 8.. They are not physical things in our spacetime, the physical universe, and don’t follow the physics rules that govern our spacetime—thus, “quantum weirdness.” However, fields create real effects in spacetime. By some definitions of “real,” a field qualifies as real because it figures in explanations that successfully account for phenomena in the physical universe.

It’s important to note that fields extend throughout the universe. When a photon travels as a wave through its field, the vibration affects the entire field, and the field extends throughout the universe. Here’s how Ruth Kastner, one of the developers of the Transactional Interpretation,^{6}Ruth Kastner; *Understanding Our Unseen Reality, Solving Quantum Riddles*; Imperial College Press, 2015, London; p. 85. describes waves traveling through a field: “Recall that a quantum field is an entity capable of being excited into higher vibrational states, like a drum head. A louder sound of the drum head is analogous to having more quanta present in the excited quantum field.^{7}*Ibid*, p. 78. ”

**Quanta are lost and gained by the entire field. **Now, back on Earth, here’s an example which explains how quanta come into the picture of fields extending throughout the universe. Let’s say a photon of sunlight hits the eye of a frog. A frog’s eye is so sharp that it can perceive and respond to a single photon. When the photon hits the frog’s eye, an electron within it absorbs the photon, and the photon disappears. Now, there’s one less photon in the universe. Upon disappearance, a quantum of energy leaves the photon’s field. The entire field has lost a quantum of energy. The effect that this little frog has created is felt, to some negligible extent, throughout the universe.

But energy is conserved. Here’s how that works. The electron, even though it’s matter, can be conceptualized as a wave in Quantum Field Theory (actually, also in the older versions of quantum mechanics). The electron absorbs the photon, and in this way, gains the quantum of energy that the photon was carrying. The electron is excited by absorbing the photon and vibrates a little more actively, adding the quantum of energy to its field. This effect is felt throughout the electron’s field, and thus, throughout the universe.

Thus, when photons and electrons are conceptualized as waves, quanta of energy are conceptualized as moving from one field to another, creating effects, however negligible, throughout the universe.

**History of the concept of “quantum.”** The concept of a quantum of light was first developed and named by the German physicist, Max Planck, in 1900. The term “quantum” had been used by scientists to mean various things prior to that. “Quantum” comes from the Latin word *quantus* meaning “how much.” The English word “quantity” is also related to this Latin word.

Planck was trying to understand an anomalous phenomenon that scientists had recently discovered when working with heated metal. As metal is heated and gets hotter and hotter, it turns color: glowing red, then yellow, then white. The change of color is due to changing wavelengths of the light waves coming off the heated metal. A light wave looks red if it’s relatively long, but white if it’s relatively short. At the time of Planck’s work, that was well known.

However, scientists found that the intensity, that is, the brightness of the light, behaved differently from predictions of the mathematical equations that they were working with. For example, one proposed equation told them that as the wavelength became shorter, even shorter than white light and entered the ultraviolet (UV) band, the intensity should grow stronger and stronger.

Of course, it is the UV band that gives us sunburns. If extremely hot metal were to become extremely bright due to high intensity, we would get sunburns from hot metal. But this doesn’t happen, and lab experiments showed that the intensity of UV emitted by hot metal falls off and drops quite low. This anomaly, that is, divergence from the mathematical equation that was supposed to be applicable, was called the “Ultraviolet Catastrophe.”^{8}Here, I'm following a story traditional in physics books which relates Planck’s discovery to the Ultraviolet Catastrophe. It makes a good story. However, the equation that Planck actually focused on

The equations that the scientists were working with assumed that light is a wave. They thought of waves as delivering energy in continuous amounts, not discrete little packets. But the only way that Planck could create an equation that accurately described the results of experiments was by relying on the concept of little discrete packets of energy, which he called “quanta.” For more information, see Planck’s Equation.

A few years later, in 1905, Albert Einstein further developed the idea of quanta in a paper on the photoelectric effect. In the photoelectric effect, light hitting a piece of metal generates electricity. Understanding this effect depends upon the concept of the quantum and is a good way to learn more about it. See “photoelectric effect.”

1 | This number is from a post by HH on the website: https://medium.com/on-a-whim/estimating-the-number-of-photons-that-hit-the-eye-c0208e7e0b64, posted Aug. 20, 2016. |

2 | Photons of the identical shade also have identical wave frequencies. Max Planck discovered the relationship between frequency and energy in 1900. The equation that he developed is: E = hv, where E = energy; v = frequency, and h = a constant. (As a note, v is pronounced “nu” because it’s really the 13th letter of the Greek alphabet though it looks like the English letter v.) This equation is now called “Planck’s Equation” and h is called “Planck’s Constant.” Planck’s Constant (h) is ridiculously tiny: 6.63 times 10 to the power: minus 24. The unit of Planck's Constant is joules. Another way to express Planck’s Constant is: .000000000000000000000000000000000663 joules. A joule is approximately the amount of energy needed to lift a tomato to three feet off the ground. Planck’s Equation, E = hv, relies on the concept of energy as quanta. Planck was the first scientist to conceptualize energy at the microscopic level as quanta and by doing so, he launched the field of quantum physics. In 1918, he was awarded the Nobel Prize for his discovery of the quantum. |

3 | These four forces are electromagnetic radiation (including visible light), the Strong Force, the Weak Force, and gravity. However, the idea that gravity occurs in particles (gravitons), each of which delivers a quantum of gravitic energy, is speculative at this time. Scientists have not yet detected gravitons and are not certain that they exist. |

4 | When “quantum” refers to a photon rather than to just the energy it carries, one may be emphasizing the visualization of a photon as a vibration or wave in a field rather than as a particle. The wave approach is discussed in the final section of this article on “quantum.” Both visualizations (particle and wave) have value; however, it’s easier in this article to start by describing photons as if they were particles. |

5 | See, for example, Frank Wilczek (Nobel Laureate in physics), The Lightness of Being; Basic Books, 2008, New York, Chapter 8. |

6 | Ruth Kastner; Understanding Our Unseen Reality, Solving Quantum Riddles; Imperial College Press, 2015, London; p. 85. |

7 | Ibid, p. 78. |

8 | Here, I'm following a story traditional in physics books which relates Planck’s discovery to the Ultraviolet Catastrophe. It makes a good story. However, the equation that Planck actually focused on was not the Rayleigh–Jeans equation, which predicts the Ultraviolet Catastrophe. Rather, Planck was working with another equation, Wien’s Law. Planck made his discovery of quanta while intent on explaining why experimental results regarding low-frequency infrared emissions (rather than high-frequency UV) fail to conform to Wien’s Law. |