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This Monday, July 4, 2022, is remarkable for a number of reasons. It happens to be aphelion: the day where the Earth is at its most distant from the Sun as it revolves through the Solar System in its elliptical orbit. Its the 246th anniversary of when the United States officially declared independence from, and war on, Britain. And it marks the annual date where the wealthiest nation in the world sets off more explosivesin the form of fireworksthan any other.

Whether youre an amateur hobbyist, a professional installer, or simply a spectator, fireworks showsare driven by the same laws of physicsthat govern all of nature. Individual fireworks all contain the same four component stages: launch, fuse, burst charges, and stars. Without quantum physics, not a single one of them would be possible. Heres the science behind how every component of these spectacular shows works.

The anatomy of a firework consists of a large variety of elements and stages. However, the same four basic elements are the same across all types and styles of fireworks: the lift charge, the main fuse, a burst charge, and stars. Variations in the diameter of the launch tube, the length of the time-delay fuse, and the height of the fireworks are all necessary to ignite the stars with the proper conditions during the break.

The start of any firework is the launch aspect: the initial explosion that causes the lift. Ever sincefireworks were first inventedmore than a millennium ago, the same three simple ingredients have been at the heart of them: sulfur, charcoal, and a source of potassium nitrate. Sulfur is a yellow solid that occurs naturally in volcanically active locations, while potassium nitrate is abundant in natural sources like bird droppings or bat guano.

Charcoal, on the other hand, isnt the briquettes we commonly use for grilling, but the carbon residue left over from charring (or pyrolyzing) organic matter, such as wood. Once all the water has been removed from the charcoal, all three ingredients can be mixed together with a mortar and pestle. The fine, black powder that emerges is gunpowder, already oxygen-rich from the potassium nitrate.

The three main ingredients in black powder (gunpowder) are charcoal (activated carbon, at left), sulfur (bottom right) and potassium nitrate (top right). The nitrate portion of the potassium nitrate contains its own oxygen, which means that fireworks can be successfully launched and ignited even in the absence of external oxygen; they would work just as well on the Moon as they do on Earth.

With all those ingredients mixed together, theres a lot of stored energy in the molecular bonds holding the different components together. But theres a more stable configuration that these atoms and molecules could be rearranged into. The raw ingredientspotassium nitrate, carbon, and sulfurwill combust (in the presence of high-enough temperatures) to form solids such as potassium carbonate, potassium sulfate, and potassium sulfide, along gases such as carbon dioxide, nitrogen, and carbon monoxide.

All it takes to reach these high temperatures is a small heat source, like a match. The reaction is a quick-burning deflagration, rather than an explosion, which is incredibly useful in a propulsion device. The rearrangement of these atoms (and the fact that the fuel contains its own oxygen) allows the nuclei and electrons to rearrange their configuration, releasing energy and sustaining the reaction. Without the quantum physics of these rearranged bonds, there would be no way to release this stored energy.

The Macys Fourth of July fireworks celebration that takes place annually in New York City displays some of the largest and highest fireworks you can find in the United States of America and the world. This iconic celebration, along with all the associated lights and colors, is only possible because of the inescapable rules of quantum mechanics.

When that first energy release occurs, conventionally known as the lift charge, it has two important effects.

The upward acceleration needs to give your firework the right upward velocity to get it to a safe height for explosion, and the fuse needs to be timed appropriately to detonate at the peak launch height. A small fireworks show might have shells as small as 2 inches (5 cm) in diameter, which require a height of 200 feet (60 m), while the largest shows (like the one by the Statue of Liberty in New York) have shells as large as 3 feet (90 cm) in diameter, requiring altitudes exceeding 1000 feet (300 m).

Different diameter shells can produce different sized bursts, which require being launched to progressively higher altitudes for safety and visibility reasons. In general, larger fireworks must be launched to higher altitudes, and therefore require larger lift charges and longer fuse times to get there. The largest fireworks shells exceed even the most grandiose of the illustrations in this diagram.

The fuse, on the other hand, is the second stage and will be lit by the ignition stage of the launch.Most fusesrely on a similar black powder reaction to the one used in a lift charge, except the burning black powder core is surrounded by wrapped textile coated with either wax or lacquer. The inner core functions via the same quantum rearrangement of atoms and electron bonds as any black powder reaction, but the remaining fuse components serve a different purpose: to delay ignition.

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The textile material is typically made of multiple woven and coated strings. The coatings make the device water resistant, so they can work regardless of weather. The woven strings control the rate of burning, dependent on what theyre made out of, the number and diameter of each woven string, and the diameter of the powder core. Slow-burning fuses might take 30 seconds to burn a single foot, while fast-burning fuses can burn hundreds of feet in a single second.

The three main configurations of fireworks, with lift charges, fuses, burst charges and stars all visible. In all cases, a lift charge launches the firework upward from within a tube, igniting the fuse, which then burns until it ignites the burst charge, which heats and distributes the stars over a large volume of space.

The third stage, then, is the burst charge stage, which controls the size and spatial distribution of the stars inside. In general the higher you launch your fireworks and the larger-diameter your shells are, the larger your burst charge will need to be to propel the insides of the shell outward. In general, the interior of the firework will have a fuse connected to the burst charge, which is surrounded by the color-producing stars.

Theburst chargecan be as simple as another collection of black powder, such as gunpowder. But it could be far more complex, such as the much louder and more impressiveflash powder, or a multi-stage explosive that sends stars in multiple directions. By utilizing different chemical compounds that offer different quantum rearrangements of their bonds, you can tune your energy release, the size of the burst, and the distribution and ignition times of the stars.

Differently shaped patterns and flight paths are highly dependent on the configuration and compositions of the stars inside the fireworks themselves. This final stage is what produces the light and color of fireworks, and is where the most important quantum physics comes into play.

But the most interesting part is that final stage: where the stars ignite. The burst is what takes the interior temperatures to sufficient levelsto create the light and colorthat we associate with these spectacular shows. The coarse explanation is that you can take different chemical compounds, place them inside the stars, and when they reach a sufficient temperature, they emit light of different colors.

This explanation, though, glosses over the most important component: the mechanism of how these colors are emitted. When you apply enough energy to an atom or molecule, you can excite or even ionize the electrons that conventionally keep it electrically neutral. When those excited electrons then naturally cascade downward in the atom, molecule or ion, they emit photons, producing emission lines of a characteristic frequency. If they fall in the visible portion of the spectrum, the human eye is even capable of seeing them.

Whether in an atom, molecule, or ion, the transitions of electrons from a higher energy level to a lower energy level will result in the emission of radiation at a very particular wavelength. This produces the phenomenon we see as emission lines, and is responsible for the variety of colors we see in a fireworks display.

What determines which emission lines an element or compound possesses? Its simply the quantum mechanics of the spacing between the different energy levels inherent to the substance itself. For example, heated sodium emits a characteristic yellow glow, as it has two very narrow emission lines at 588 and 589 nanometers. Youre likely familiar with these if you live in a city, as most of those yellow-colored street lamps you see are powered by elemental sodium.

As applied to fireworks, there are a great variety of elements and compounds that can be utilized to emit a wide variety of colors. Different compounds of Barium, Sodium, Copper and Strontium can produce colors covering a huge range of the visible spectrum, and the different compounds inserted in the fireworks stars are responsible for everything we see. In fact,the full spectrum of colors can be achievedwith just a handful of conventional compounds.

The interior of this curve shows the relationship between color, wavelength, and temperature in chromaticity space. Along the edges, where the colors are most saturated, a variety of elements, ions, and compounds can be shown, with their various emission lines marked out. Note that many elements/compounds have multiple emission lines associated with them, and all of these are used in various fireworks. Because of how easy it is to create barium oxide in a combustion reaction, certain firework colors, such as forest green and ocean green, remain elusive.

Whats perhaps the most impressive about all of this is that the color we see with the human eye is not necessarily the same as the color emitted by the fireworks themselves. For example, if you were to analyze the light emitted by a violet laser, youd find that the photons emerging from it were of a specific wavelength that corresponded to the violet part of the spectrum.

The quantum transitions that power a laser always result in photons of exactly the same wavelength, and our eyes see them precisely as they are, with the multiple types of cones we possess responding to that signal in such a way that our brain responds to construct a signal thats commensurate with the light possessing a violet color.

A set of Q-line laser pointers showcase the diverse colors and compact size that now are commonplace for lasers. By pumping electrons into an excited state and stimulating them with a photon of the desired wavelength, you can cause the emission of another photon of exactly the same energy and wavelength. This action is how the light for a laser is first created: by the stimulated emission of radiation.

But if you look at that same color that appears as violet not from a monochromatic source like a laser, but from your phone or computer screen, youll find that there are no intrinsically violet photons striking your eyes at all! Instead,as Chad Orzel has noted in the past,

Our eyes construct what we perceive as color from the response of three types of cells in our retina, each sensitive to light of a particular range of colors. One is most sensitive to blue-ish light (short wavelength), one is most sensitive to red light (long wavelength), and the third to a sort of yellow-green. Based on how strongly each of these cells responds to incoming light, our brains construct our perception ofcolor.

In other words, the key to producing the fireworks display you want isnt necessarily to create light of a specific color that corresponds to a specific wavelength, but rather to create light that excites the right molecules in our body to cause our brain to perceive a particular color.

A violet laser emits photons of a very particular, narrow wavelength, as every photon carries the same amount of energy. This curve, shown in blue, emits violet photons only. The green curve shows how a computer screen approximates the same exact violet color by using a mix of different wavelengths of light. Both appear to be the same color to human eyes, but only one truly produces photons of the same color that our eyes perceive.

Fireworks might appear to be relatively simple explosive devices. Pack a charge into the bottom of a tube to lift the fireworks to the desired height, ignite a fuse of the proper length to reach the burst charge at the peak of its trajectory, explode the burst charge to distribute the stars at a high temperature, and then watch and listen to the show as the sound, light, and color washes over you.

Yet if we look a little deeper, we can understand how quantum physics underlies every single one of these reactions. Add a little bit extrasuch as propulsion or fuel inside each starand your colored lights can spin, rise, or thrust in a random direction. Make sure you enjoy your fourth of July safely, but also armed with the knowledge that empowers you to understand how the most spectacular human-made light show of the year truly works!

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Fireworks are only possible because of quantum physics - Big Think

An artists impression of a black hole and its accretion disk. Illustration: XMM-Newton, ESA, NASA

Twenty-five years ago, in 1997, an Argentine physicist named Juan Martin Maldacena published what would become the most highly cited physics paper in history (more than 20,000 to date). In the paper, Maldacena described a bridge between two theories that describe how our world works, but separately, without meeting each other. These are the field theories that describe the behaviour of energy fields (like the electromagnetic fields) and subatomic particles, and the theory of general relativity, which deals with gravity and the universe at the largest scales.

Field theories have many types and properties. One of them is a conformal field theory: a field theory that doesnt change when it undergoes a conformal transformation i.e. one which preserves angles but not lengths pertaining to the field. As such, conformal field theories are said to be mathematically well-behaved.

In relativity, space and time are unified into the spacetime continuum. This continuum can exist in many possible spaces. Some of these spaces have the same curvature everywhere, and come in three forms (roughly, universes of certain shapes): de Sitter space, Minkowski space and anti-de Sitter space. de Sitter space has positive curvature everywhere like a sphere (but is empty of any matter). Minkowski space has zero curvature everywhere i.e. a flat surface. Anti-de Sitter space has negative curvature everywhere like a hyperbola.

Because these shapes are related to the way our universe looks and works, cosmologists have their own way to understand them. If the spacetime continuum exists in de Sitter space, the universe is said to have a positive cosmological constant. Similarly, Minkowski space implies a zero cosmological constant and anti-de Sitter space a negative cosmological constant. Studies by various space telescopes have found that our universe has a positive cosmological constant, meaning it is approximately a de Sitter space (but not exactly since our universe does have matter).

In 1997, Maldacena found evidence to suggest that a description of quantum gravity in anti-de Sitter space in N dimensions is the same as a conformal field theory in N 1 dimensions. This AdS/CFT correspondence was an unexpected but monumental discovery that connected two kinds of theories that had thus far refused to cooperate.

The Wire Science had a chance to interview Maldacena about his past and current work in 2018, in which he provided more insights on AdS/CFT as well.

In his paper, Maldacena showed that in a very specific case, quantum gravity in anti-de Sitter space in five dimensions was the same as a specific conformal field theory in four dimensions. He conjectured that this equivalence would hold not just for the limiting case but the full theories. So the correspondence is also called the AdS/CFT conjecture. Physicists have not proven this to be the case so far but there is circumstantial evidence from many results that indicate that the conjecture is true.

Nonetheless, the finding was hailed as a major mathematical victory for string theory as well. This theory is a leading contender for one that can unify quantum mechanics and general relativity. However, we have found no experimental evidence of string theorys many claims.

Nonetheless, thanks to the correspondence, (mathematical) physicists have found that some problems that are hard on the AdS side are much easier to crack on the CFT side, and vice versa all they had to do was cross Maldacenas bridge! This was another sign that the AdS/CFT correspondence wasnt just a mathematical trick but could be a legitimate description of reality.

So how could it be real?

The holographic principle

In 1997, Maldacena proved that a string theory in five dimensions was the same as a conformal field theory in four dimensions. However, gravity in our universe exists in four dimensions not five. So the correspondence came close to providing a unified description of gravity and quantum mechanics, but not close enough. Nonetheless, it gave rise to the possibility that an entity that exists in some number of dimensions could be described by another entity that exists in one fewer number of dimensions.

Actually, in fact, the AdS/CFT correspondence didnt give rise to this possibility but realised it mathematically. The awareness of the possibility had existed for many years until then, as the holographic principle. The Dutch physicist Gerardus t Hooft first proposed it and the American physicist Leonard Susskind in the 1990s brought it firmly into the realm of string theory. One way to state the holographic principle, in the words of physicist Matthew Headrick, is thus:

The universe around us, which we are used to thinking of as being three dimensional, is actually at a more fundamental level two-dimensional and that everything we see thats going on around us in three dimensions is actually happening in a two-dimensional space.

This two-dimensional space is the surface of the universe, located at an infinite distance from us, where information is encoded that describes everything happening within the universe. Its a mind-boggling idea. Information here refers to physical information, such as, to use one of Headricks examples, the positions and velocities of physical objects. In beholding this information from the infinitely faraway surface, we apparently behold a three-dimensional reality.

It bears repeating that this is a mind-boggling idea. We have no proof so far that the holographic principle is a real description of our universe we only know that it could describe our reality, thanks to the AdS/CFT correspondence. This said, physicists have used the holographic principle to study and understand black holes.

In 1915, Albert Einsteins general theory of relativity provided a set of complicated equations to understand how mass, the spacetime continuum and the gravitational force are related. Within a few months, physicists Karl Swarzschild and Johannes Droste, followed in subsequent years by Georges Lematre, Subrahmanyan Chandrasekhar, Robert Oppenheimer and David Finkelstein, among others, began to realise that one of the equations exact solutions (i.e. non-approximate) indicated the existence of a point mass around which space was wrapped completely, preventing even light from escaping from inside this space to outside. This was the black hole.

Because black holes were exact solutions, physicists assumed that they didnt have any entropy i.e. that its insides didnt have any disorder. If there had been such disorder, it would have appeared in Einsteins equations. It didnt, so QED. But in the early 1970s, the Israeli-American physicist Jacob Bekenstein noticed a problem: if a system with entropy, like a container of hot gas, was thrown into the black hole, and the black hole doesnt have entropy, where does the entropy go? It had to go somewhere; otherwise, the black hole would violate the second law of thermodynamics that the entropy of an isolated system, like our universe, cant decrease.

Bekenstein postulated that black holes must also have entropy, and that the amount of entropy is proportional to the black holes surface area, i.e. the area of the event horizon. Bekenstein also worked out that there is a limit to the amount of entropy a given volume of space can contain, as well as that all black holes could be described by just three observable attributes: their mass, electric charge and angular momentum. So if a black holes entropy increases because it has swallowed some hot gas, this change ought to manifest as a change in one, some or all of these three attributes.

Taken together: when some hot gas is tossed into a black hole, the gas would fall into the event horizon but the information about its entropy might appear to be encoded on the black holes surface, from the point of view of an observer located outside and away from the event horizon. Note here that the black hole, a sphere, is a three-dimensional object whereas its surface is a flat, curved sheet and therefore two-dimensional. That is, all the information required to describe a 3D black hole could in fact be encoded on its 2D surface.

Doesnt this remind you of the AdS/CFT correspondence? For example, consider a five-dimensional anti-de Sitter space inside which there is a black hole. We can use the correspondence to show that the entropy of the theory that describes the boundary of this space matches exactly with the entropy of the black hole itself. This would realise the conjecture of t Hooft and others except here, the information is encoded not on the event horizon but on the boundary of the five-dimensional space itself.

This is just one example of the wider context that the AdS/CFT correspondence inhabits. For more examples and other insights, do read Maldacenas interview with The Wire Science.

The author is grateful to Nirmalya Kajuri for discussion and feedback on this article.

Originally posted here:

AdS/CFT: 25 Years of the 'Bridge' to an Unknowable Universe - The Wire Science