Law of Inertia

Law of Inertia
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[/caption]In the world of physics, there are few people who have been more influential than Sir Isaac Newton. In addition to his contributions to astronomy, mathematics, and empirical philosophy, he is also the man who pioneered classical physics with his laws of motion. Of these, the first, otherwise known as the Law of Inertia, is the most famous and arguably the most important. In the language of science, this law states that: Every body remains in a state of constant velocity unless acted upon by an external unbalanced force. This means that in the absence of a non-zero net force, the center of mass of a body either remains at rest, or moves at a constant velocity. Put simply, it states that a body will remain at rest or in motion unless acted upon by an external and unbalanced force.

Prior to Aristotle’s theories on inertia, the most generally accepted theory of motion was based on Aristotelian philosophy. This ancient theory stated that, in the absence of an external motivating power, all objects on Earth would come to rest and that moving objects only continue to move so long as long there is a power inducing them to do so. In a void, no motion would be possible since Aristotle’s theory claimed that the motion of objects was dependent on the surrounding medium, that it was responsible for moving the object forward in some way. By the Renaissance, however, this theory was coming to be rejected as scientists began to postulate that both air resistance and the weight of an object would play a role in arresting the motion of that object.

Further advances in astronomy were another nail in this coffin. The Aristotelian division of motion into “mundane” and “celestial” became increasingly problematic in the face of Copernicus’ model in the 16th century, who argued that the earth (and everything on it) was in fact never “at rest”, but was actually in constant motion around the sun.Galileo, in his further development of the Copernican model, recognized these problems and would later go on to conclude that based on this initial premise of inertia, it is impossible to tell the difference between a moving object and a stationary one without some outside point of comparison.

Thus, though Newton was not the first to express the concept of inertia, he would later refine and codify them as the first law of motion in his seminal work PhilosophiaeNaturalis Principia Mathematica (Mathematical Principals of Natural Philosophy) in 1687, in which he stated that: unless acted upon by a net unbalanced force, an object will maintain a constant velocity. Interestingly enough, the term “interia” was not used in the study. It was in fact JohanneKepler who first used it in his Epitome AstronomiaeCopernicanae (Epitome of Copernican Astronomy) published from 1618–1621. Nevertheless, the term would later come to be used and Newton recognized as being the man most directly responsible for its articulation as a theory.

We have written many articles about the law of inertia for Universe Today. Here’s an article about Newton’s Laws of Motion, and here’s an article about Newton’s first law.

If you’d like more info on the law of inertia, check out these articles from How Stuff Works and NASA.

We’ve also recorded an entire episode of Astronomy Cast all about Gravity. Listen here, Episode 102: Gravity.


Emissivity of Materials

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[/caption]In the last few centuries, in which time we have had several scientific revolutions, our understanding of heat, energy and the exchange thereof has grown exponentially. In particular has been the increasing ability to gauge the amounts of energy involved in particular processes and in turn create theoretical frameworks, units, and even tools with which to measure them. One such concept is the measurement known as Emissivity. Essentially, this is the relative ability of a material’s surface (usually written ? or e) to emit energy as radiation. It is expressed as the ratio of the emissivity of the material in question to the radiation emitted by a blackbody (an idealized physical body that absorbs all incident electromagnetic radiation) at the same temperature. This means that while a true black body would have an emissivity value of 1 (? = 1), any other object, known as a “grey body”, would have an emissivity value of less than 1 (? < 1). In general, the duller and blacker a material is, the closer its emissivity is to 1. The more reflective a material is, the lower its emissivity. Emissivity also depends on such factors as temperature, emission angle, and wavelength of the radiation. At the opposite end of the spectrum is the material’s absorptivity (or absorptance), which is the measure of radiation absorbed by a material at a particular wavelength. When dealing with non-black surfaces, the relative emissivity follows Kirchhoff's law of thermal radiation which states that emissivity is equal to absorptivity. Essentially an object that does not absorb all incident light will also emit less radiation than an ideal black body. An important function for emissivity has to do with the Earth’s atmosphere. Like all other “grey bodies”, the Earth’s atmosphere is able to absorb and emit radiation. The overall emissivity of Earth's atmosphere varies according to cloud cover and the concentration of gases that absorb and emit energy in the thermal infrared (i.e. heat energy). In this way, and by using the same criteria by which they are able to calculate the emissivity of “grey bodies”, scientists are able to calculate the amount of thermal radiation emitted by the atmosphere, thereby gaining a better understanding of the Greenhouse Effect. Every known material has an emissivity coefficient. Those that have a higher coefficient tend to be polished metals, such as aluminum and anodized metals. However, certain materials that are not metals and are non-reflective, such as red bricks, asbestos, concrete and pressed carbon, have equally high coefficients. In addition, naturally occurring materials such as ice, marble, and lime also have high emissivity coefficients. We have written many articles about emissivity of materials for Universe Today. Here's an article about heat rejection systems, and here's an article about absorptivity. If you'd like more info on emissivity, check out these articles from Engineering Toolbox and Science World.

We’ve also recorded an entire episode of Astronomy Cast all about Electromagnetism. Listen here, Episode 103: Electromagnetism.



[/caption]Ever since Einstein unveiled his theory of relativity, the speed of light has been considered to be the physical constant of the universe, interrelating space and time. In short, it was the speed at which light and all other forms of electromagnetic radiation were believed to travel at all times in empty space, regardless of the motion of the source or the inertial frame of reference of the observer. But suppose for a second that there was a particle that defied this law, that could exist within the framework of a relativistic universe, but at the same time defy the foundations on which its built? Sounds impossible, but the existence of such a particle may very well be necessary from a quantum standpoint, resolving key issues that arise in that chaotic theory. It is known as the Tachyon Particle, a hypothetical subatomic particle that can move faster than light and poses a number intriguing problems and possibilities to the field of physics.

In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. Their existence was first attributed to German physicist Arnold Sommerfeld; even though it was Gerald Feinberg who first coined the term in the 1960s, and several other scientists helped to advance the theoretical framework within which tachyons were believed to exist. They were originally proposed within the framework of quantum field theory as a way of explaining the instability of the system, but have nevertheless posed problems for the theory of special relativity.

For example, if tachyons were conventional, localizable particles that could be used to send signals faster than light, this would lead to violations of causality in special relativity. But in the framework of quantum field theory, tachyons are understood as signifying an instability of the system and treated using a theory known as tachyon condensation, a process that attempts to resolve their existence by explaining them in terms of better understood phenomena, rather than as real faster-than-light particles. Tachyonic fields have appeared theoretically in a variety of contexts, such as the bosonic string theory. In general, string theory states that what we see as “particles” —electrons, photons, gravitons and so forth—are actually different vibrational states of the same underlying string. In this framework, a tachyon would appear as either indication of instability in the D-brane system or within spacetime itself.

Despite the theoretical arguments against the existence of tachyon particles, experimental searches have been conducted to test the assumption against their existence; however, no experimental evidence for the existence of tachyon particles has been found.

We have written many articles about tachyon for Universe Today. Here’s an article about elementary particles, and here’s an article about Einstein’s Theory of Relativity.

If you’d like more info on tachyon, check out these articles from Science World. Also, you may want to browse through a forum discussion about tachyons.

We’ve also recorded an entire episode of Astronomy Cast all about the Theory of Special Relativity. Listen here, Episode 9: Einstein’s Theory of Special Relativity.



All About Electromagnetic Radiation
The Sun emits electromagnetic radiation

Anyone who took elementary science in grade school recalls the lesson about the three states of matter, right? That was the one where we were told that matter comes in three basic forms: liquid, solid and gas. This works for the periodic table of elements and can be extended to include just about any compound. Except perhaps for whipped cream (that damnable compound continues to defy attempts as classification!) But what if there were a fourth state for matter? It occurs when a state of matter similar to gas contains a large portion of ionized particles and generates its own magnetic field. It’s called Plasma, and it just happens to be the most common type of matter, comprising more than ninety-nine percent of matter in the visible universe and which permeates the solar system, interstellar and intergalactic environments.

The basic premise behind plasma is that heating a gas dissociates its molecular bonds, rendering it into its constituent atoms. Further heating leads to ionization (a loss of electrons), which turns it into a plasma. This plasma is therefore defined by the existence of charged particles, both positive ions and negative electrons.The presence of a large number of charged particles makes the plasma electrically conductive so that it responds strongly to electromagnetic fields. Plasma, therefore, has properties quite unlike those of solids, liquids, or gases and is considered a distinct state of matter. Like a gas, plasma does not have a definite shape or a definite volume unless enclosed in a container. But unlike gas, under the influence of a magnetic field, it may form structures such as filaments, beams and double layers. It is precisely for this reason that plasma is used in the construction of electronics, such as plasma TVs and neon signs.

The existence of plasma was first discovered by Sir William Crookes in 1879 using an assembly that is today known as a “Crookes tube”, an experimental electrical discharge tube in which air is ionized by the application of a high voltage through a voltage coil. At the time, he labeled it “radiant matter” because of its luminous quality. Sir J.J. Thomson, a British physicist, identified the nature of the matter in 1897, thanks to his discovery of electrons and numerous experiments using cathode ray tubes. However, it was not until 1928 that the term “plasma” was coined by Irving Langmuir, an American chemist and physicist, who was apparently reminded of blood plasma.

As already mentioned, plasmas are by far the most common phase of matter in the universe. All the stars are made of plasma, and even the space between the stars is filled with a plasma, albeit a very sparse one.

We have written many articles about plasma for Universe Today. Here’s an article about the plasma engine, and here’s an article about the states of matter.

If you’d like more info on plasma, check out these articles from Chem4Kids and NASA Science.

We’ve also recorded an episode of Astronomy Cast all about the Sun. Listen here, Episode 30: The Sun, Spots and All.



[/caption]Magnetism is a fundamental force of the universe, essential to its function and existence in the same way that gravity and weak and strong nuclear forces are. But interestingly enough, there are several different kinds of magnetism. For example, there is ferromagnetism, a property which applies to super magnets, where magnetic properties exist regardless of whether or not there is a magnetic field acting on the material itself. There is also Diamagnetism, which refers to materials that are not affected by a magnetic field, and Paramagnetism, a form of magnetism that occurs only in the presence of an externally applied magnetic field.

Materials that are called ‘paramagnets’ are most often those that exhibit, at least over an appreciable temperature range, magnetic susceptibilities that adhere to the Curie or Curie–Weiss laws. According to these laws, which apply at low-levels of magnetization, the susceptibility of paramagnetic materials is inversely proportional to their temperature. Mathematically, this can be expressed as: M = C(B/T), where M is the resulting magnetization, B is the magnetic field, T is absolute temperature, measured in kelvins, C is a material-specific Curie constant.

Paramagnets were named and extensively researched by British scientist Michael Faraday – the man who gave us Faraday’s Constant, Faraday’s Law, the Faraday Effect, etc. – beginning in 1845. He, and many scientists since, found that certain material exhibited what was commonly referred to as “negative magnetism”. Most elements and some compounds are paramagnetic, with strong paramagnetism being exhibited by compounds containing iron, palladium, platinum, and certain rare-earth elements. In such compounds atoms of these elements have some inner electron shells that are incomplete, causing their unpaired electrons to spin like tops and orbit like satellites. This makes the atoms act like a permanent magnet, tending to align with and hence strengthen an applied magnetic field. However, once the magnetic field is removed, the atoms fall out of alignment and the material return to its original state. Strong paramagnetism also decreases with rising temperature because of the de-alignment produced by the greater random motion of the atomic magnets.

Weak paramagnetism, independent of temperature, is found in many metallic elements in the solid state, such as sodium and the other alkali metals. Other examples include Iron oxide, Uranium, Platinum, Tungsten, Cesium, Aluminum, Lithium, Magnesium, Sodium, and Oxygen gas. Even iron, a highly magnetic material, can become a paramagnet once it is heated above its relatively high Curie-point.

We have written many articles about magnetism for Universe Today. Here’s an article about magnetic field, and here’s an article about what magnets are made of.

If you’d like more info on paramagnetism, check out these articles from Hyperphysics and Physlink.

We’ve also recorded an entire episode of Astronomy Cast all about Magnetism. Listen here, Episode 42: Magnetism Everywhere.


What Is A Singularity?

Artist's conception of the event horizon of a black hole. Credit: Victor de Schwanberg/Science Photo Library
Artist's conception of the event horizon of a black hole. Credit: Victor de Schwanberg/Science Photo Library

Ever since scientists first discovered the existence of black holes in our universe, we have all wondered: what could possibly exist beyond the veil of that terrible void? In addition, ever since the theory of General Relativity was first proposed, scientists have been forced to wonder, what could have existed before the birth of the Universe – i.e. before the Big Bang?

Interestingly enough, these two questions have come to be resolved (after a fashion) with the theoretical existence of something known as a Gravitational Singularity – a point in space-time where the laws of physics as we know them break down. And while there remain challenges and unresolved issues about this theory, many scientists believe that beneath veil of an event horizon, and at the beginning of the Universe, this was what existed.


In scientific terms, a gravitational singularity (or space-time singularity) is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system. In other words, it is a point in which all physical laws are indistinguishable from one another, where space and time are no longer interrelated realities, but merge indistinguishably and cease to have any independent meaning.

Credit: ESA/Hubble, ESO, M. Kornmesser
This artist’s impression depicts a rapidly spinning supermassive black hole surrounded by an accretion disc. Credit: ESA/Hubble, ESO, M. Kornmesse

Origin of Theory:

Singularities were first predicated as a result of Einstein’s Theory of General Relativity, which resulted in the theoretical existence of black holes. In essence, the theory predicted that any star reaching beyond a certain point in its mass (aka. the Schwarzschild Radius) would exert a gravitational force so intense that it would collapse.

At this point, nothing would be capable of escaping its surface, including light. This is due to the fact the gravitational force would exceed the speed of light in vacuum – 299,792,458 meters per second (1,079,252,848.8 km/h; 670,616,629 mph).

This phenomena is known as the Chandrasekhar Limit, named after the Indian astrophysicist Subrahmanyan Chandrasekhar, who proposed it in 1930. At present, the accepted value of this limit is believed to be 1.39 Solar Masses (i.e. 1.39 times the mass of our Sun), which works out to a whopping 2.765 x 1030 kg (or 2,765 trillion trillion metric tons).

Another aspect of modern General Relativity is that at the time of the Big Bang (i.e. the initial state of the Universe) was a singularity. Roger Penrose and Stephen Hawking both developed theories that attempted to answer how gravitation could produce singularities, which eventually merged together to be known as the Penrose–Hawking Singularity Theorems.

Illustration of the Big Bang Theory
The Big Bang Theory: A history of the Universe starting from a singularity and expanding ever since. Credit:

According to the Penrose Singularity Theorem, which he proposed in 1965, a time-like singularity will occur within a black hole whenever matter reaches certain energy conditions. At this point, the curvature of space-time within the black hole becomes infinite, thus turning it into a trapped surface where time ceases to function.

The Hawking Singularity Theorem added to this by stating that a space-like singularity can occur when matter is forcibly compressed to a point, causing the rules that govern matter to break down. Hawking traced this back in time to the Big Bang, which he claimed was a point of infinite density. However, Hawking later revised this to claim that general relativity breaks down at times prior to the Big Bang, and hence no singularity could be predicted by it.

Some more recent proposals also suggest that the Universe did not begin as a singularity. These includes theories like Loop Quantum Gravity, which attempts to unify the laws of quantum physics with gravity. This theory states that, due to quantum gravity effects, there is a minimum distance beyond which gravity no longer continues to increase, or that interpenetrating particle waves mask gravitational effects that would be felt at a distance.

Types of Singularities:

The two most important types of space-time singularities are known as Curvature Singularities and Conical Singularities. Singularities can also be divided according to whether they are covered by an event horizon or not. In the case of the former, you have the Curvature and Conical; whereas in the latter, you have what are known as Naked Singularities.

A Curvature Singularity is best exemplified by a black hole. At the center of a black hole, space-time becomes a one-dimensional point which contains a huge mass. As a result, gravity become infinite and space-time curves infinitely, and the laws of physics as we know them cease to function.

Conical singularities occur when there is a point where the limit of every general covariance quantity is finite. In this case, space-time looks like a cone around this point, where the singularity is located at the tip of the cone. An example of such a conical singularity is a cosmic string, a type of hypothetical one-dimensional point that is believed to have formed during the early Universe.

And, as mentioned, there is the Naked Singularity, a type of singularity which is not hidden behind an event horizon. These were first discovered in 1991 by Shapiro and Teukolsky using computer simulations of a rotating plane of dust that indicated that General Relativity might allow for “naked” singularities.

In this case, what actually transpires within a black hole (i.e. its singularity) would be visible. Such a singularity would theoretically be what existed prior to the Big Bang. The key word here is theoretical, as it remains a mystery what these objects would look like.

For the moment, singularities and what actually lies beneath the veil of a black hole remains a mystery. As time goes on, it is hoped that astronomers will be able to study black holes in greater detail. It is also hoped that in the coming decades, scientists will find a way to merge the principles of quantum mechanics with gravity, and that this will shed further light on how this mysterious force operates.

We have many interesting articles about gravitational singularities here at Universe Today. Here is 10 Interesting Facts About Black Holes, What Would A Black Hole Look Like?, Was the Big Bang Just a Black Hole?, Goodbye Big Bang, Hello Black Hole?, Who is Stephen Hawking?, and What’s on the Other Side of a Black Hole?

If you’d like more info on singularity, check out these articles from NASA and Physlink.

Astronomy Cast has some relevant episodes on the subject. Here’s Episode 6: More Evidence for the Big Bang, and Episode 18: Black Holes Big and Small and Episode 21: Black Hole Questions Answered.


Magnetic Levitation

[/caption]Overcoming the pull of gravity and fighting acceleration are major challenges for scientists looking to achieve flight and/or high-speed transportation. One way that they overcome this is the modern and growing technology known as Magnetic Levitation. Relying on rare earth magnets, superconductors, electromagnets and diamagnets, magnetic levitation is now used for maglev trains, magnetic bearings and for product display purposes. Today, maglev transportation is one of the fastest growing means of transportation in industrialized countries. This method has the potential to be faster, quieter and smoother than wheeled mass transit systems and the power needed for levitation is usually not a particularly large percentage of the overall consumption; most of it being used to overcome air drag. In William Gibson’s novel Spook Country, maglev technology was also featured in the form of a “maglev bed”, a bed which used magnets to stay suspended in midair.

Magnetic levitation (aka. maglev or magnetic suspension) is the method by which an object is suspended with no support other than magnetic fields. According to Earnshaw’s theorem (a theory which is usually referenced to magnetic fields), it is impossible to stably levitate against gravity relying solely on static ferromagnetism. However, maglev technology overcomes this through a number of means. These include, but are not limited to, mechanical constraint (or pseudo-levitation), diamagnetism levitation, superconductors, rotational stabilization, servomechanisms, induced currents and strong focusing.

Pseudo-levitation relies on two magnets that are mechanically arranged to repel each other strongly, or are attracted but constrained from touching by a tensile member, such as a string or cable. Another example is the Zippe-type centrifuge where a cylinder is suspended under an attractive magnet, and stabilized by a needle beading from below. Diamagnetic levitation occurs when diamagnetic material is placed in close proximity to material that produces a magnetic field, thus repelling the diamagnetic material. Superconductor-levitation is achieved much the same way, superconductors being a perfect diamagne. Due to the Meissner effect, superconductors also have the property of having completely expelled their magnetic fields, allowing for further stability.

The first commercial maglev people mover was simply called “MAGLEV” and officially opened in 1984 near Birmingham, England. It operated on an elevated 600-metre (2,000 ft) section of monorail track between Birmingham International Airport and Birmingham International railway station, running at speeds up to 42 km/h (26 mph). Perhaps the most well-known implementation of high-speed maglev technology currently in operation is the Shanghai Maglev Train, a working model of the German-built Transrapid train that transports people 30 km (19 mi) to the airport in just 7 minutes 20 seconds, achieving a top speed of 431 km/h and averaging 250 km/h.

We have written many articles about magnetic levitation for Universe Today. Here’s an article about the uses of electromagnets, and here’s an article about how magnets work.

If you’d like more info on the magnetic levitation, check out these articles from How Stuff Works and Hyperphysics.

We’ve also recorded an entire episode of Astronomy Cast all about Magnetism. Listen here, Episode 42: Magnetism Everywhere.


Helmholtz Coil

[/caption]A magnetic field is a pretty awesome thing. As a fundamental force of the universe, they are something without which, planetary orbits, moving electrical charges, or even elementary particles could not exist. It is therefore intrinsic to scientific research that we be able to generate magnetic fields ourselves for the purpose of studying electromagnetism and its fundamental characteristics. One way to do this is with a device known as the Helmholtz Coil, an instrument that is named in honor of German physicist Hermann von Helmholtz (1821-1894), a scientist and philosopher who made fundamental contributions to the fields of physiology, optics, mathematics, and meteorology in addition to electrodynamics.

A Helmholtz coil is a device for producing a region of nearly uniform magnetic field. It consists of two identical circular magnetic coils that are placed symmetrically, one on each side of the experimental area along a common axis, and separated by a distance (h) equal to the radius (R) of the coil. Each coil carries an equal electrical current flowing in the same direction. A number of variations exist, including use of rectangular coils, and numbers of coils other than two. However, a two-coil Helmholtz pair is the standard model, with coils that are circular and in shape and flat on the sides. In such a device, electric current is passed through the coil for the purpose of creating a very uniform magnetic field.

Helmholtz coils are used for a variety of purposes. In one instance, they were used in an argon tube experiment to measure the charge to mass ratio (e:m)of electrons. In addition, they are often used to measure the strength and fields of permanent magnets. In order to do this, the coil pair is connected to a fluxmeter, a device which contains measuring coils and electronics that evaluate the change of voltage in the measuring coils to calculate the overall magnetic flux.In some applications, a Helmholtz coil is used to cancel out Earth’s magnetic field, producing a region with a magnetic field intensity much closer to zero. This can be used to see how electrical charges and magnetic fields operate when not acted on by the gravitational pull of the Earth or other celestial bodies.

In a Helmholtz girl, the magnetic flux density of a field generated (represented by B) can be expressed mathematically by the equation:

Where R is the radius of the coils, n is the number of turns in each coil, I is the current flowing through the coils, and ?0 is the permeability of free space (1.26 x 10-6 T • m/A).

We have written many articles about the Helmholtz Coil for Universe Today. Here’s an article about the right hand rule magnetic field, and here’s an article about magnetic field.

If you’d like more info on the Helmholtz Coil, check out an article from Hyperphysics. Also, here’s another article about the Helmholtz Coil.

We’ve also recorded an entire episode of Astronomy Cast all about Magnetism. Listen here, Episode 42: Magnetism Everywhere.


Dipole Moment

[/caption]It has long been known that all molecules possess two equal and opposite charges which are separated by a certain distance. This separation of positive and negative charges is what is referred to as an electric dipole, meaning that it essentially has two poles. In the case of such polar molecules, the center of negative charge does not coincide with the center of positive charge. The extent of polarity in such covalent molecules can be described by the term Dipole Moment, which is essentially the measure of polarity in a polar covalent bond.

The simplest example of a dipole is a water molecule. A molecule of water is polar because of the unequal sharing of its electrons in a “bent” structure. The water molecule forms an angle, with hydrogen atoms at the tips and oxygen at the vertex. Since oxygen has a higher electronegativity than hydrogen, the side of the molecule with the oxygen atom has a partial negative charge while the hydrogen, in the center, has a partial positive charge. Because of this, the direction of the dipole moment points towards the oxygen.

In the language of physics, the electric dipole moment is a measure of the separation of positive and negative electrical charges in a system of charges, that is, a measure of the charge system’s overall polarity – i.e. the separation of the molecules electric charge, which leads to a dipole. Mathematically, and in the simple case of two point charges, one with charge +q and one with charge ?q, the electric dipole moment p can be expressed as:p=qd, where d is the displacement vector pointing from the negative charge to the positive charge. Thus, the electric dipole moment vector p points from the negative charge to the positive charge.

Another way to look at it is to represent the Dipole Moment by the Greek letter m, m = ed, where e is the electrical charge and d is the distance of separation. It is expressed in the units of Debye and written as D (where 1 Debye = 1 x 10-18e.s.u cm). A dipole moment is a vector quantity and is therefore represented by a small arrow with a tail at the positive center and head pointing towards a negative center. In the case of a Water molecule, the Dipole moment is 1.85 D, whereas a molecule of hydrochloric acid is 1.03 D and can be represented as:

We have written many articles about dipole moment for Universe Today. Here’s an article about what water is made of, and here’s an article about molecules.

If you’d like more info on dipole moment, check out these articles from Hyperphysics and Science Daily.

We’ve also recorded an entire episode of Astronomy Cast all about Molecules in Space. Listen here, Episode 116: Molecules in Space.


What is Fermi Energy?

When it comes to physics, the concept of energy is a tricky thing, subject to many different meanings and dependent on many possible contexts. For example, when speaking of atoms and particles, energy comes in several forms, such as electrical energy, heat energy, and light energy.

But when one gets into the field of quantum mechanics, a far more complex and treacherous realm, things get even trickier. In this realm, scientists rely on concepts such as Fermi Energy, a concept that usually refers to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature.


Fermions take their name from famed 20th century Italian physicist Enrico Fermi. These are subatomic particles that are usually associated with matter, whereas subatomic particles like bosons are force carriers (associated with gravity, nuclear forces, electromagnetism, etc.) These particles (which can take the form of electrons, protons and neutrons) obey the Pauli Exclusion Principle, which states that no two fermions can occupy the same (one-particle) quantum state.

Neils Bohr's model a nitrogen atom. Credit:
Neils Bohr’s model a nitrogen atom. Credit:

In a system containing many fermions (like electrons in a metal), each fermion will have a different set of quantum numbers. Fermi energy, as a concept, is important in determining the electrical and thermal properties of solids. The value of the Fermi level at absolute zero (-273.15 °C) is called the Fermi energy and is a constant for each solid. The Fermi level changes as the solid is warmed and as electrons are added to or withdrawn from the solid.

Calculating Fermi Energy:

To determine the lowest energy a system of fermions can have (aka. it’s lowest possible Fermi energy), we first group the states into sets with equal energy, and order these sets by increasing energy. Starting with an empty system, we then add particles one at a time, consecutively filling up the unoccupied quantum states with the lowest energy.

When all the particles have been put in, the Fermi energy is the energy of the highest occupied state. What this means is that even if we have extracted all possible energy from a metal by cooling it to near absolute zero temperature (0 kelvin), the electrons in the metal are still moving around. The fastest ones are moving at a velocity corresponding to a kinetic energy equal to the Fermi energy.

Bosons, fermions and other particles after a collsion. Credit: CERN
Image showing bosons, fermions and other particles created by a high-energy collision. Credit: CERN


The Fermi energy is one of the important concepts of condensed matter physics. It is used, for example, to describe metals, insulators, and semiconductors. It is a very important quantity in the physics of superconductors, in the physics of quantum liquids like low temperature helium (both normal and superfluid 3He), and it is quite important to nuclear physics and to understand the stability of white dwarf stars against gravitational collapse.

Confusingly, the term “Fermi energy” is often used to describe a different but closely-related concept, the Fermi level (also called chemical potential). The Fermi energy and chemical potential are the same at absolute zero, but differ at other temperatures.

We have written many interesting articles about quantum physics here at Universe Today. Here’s What is the Bohr Atomic Model?, Quantum Entanglement Explained, What is the Electron Cloud Model, What is the Double Slit Experiment?, What is Loop Quantum Gravity? and Unifying the Quantum Principle – Flowing Along in Four Dimensions.

If you’d like more info on Fermi Energy, check out these articles from Hyperphysics and Science World.

We’ve also recorded an entire episode of Astronomy Cast all about Quantum Mechanics. Listen here, Episode 138: Quantum Mechanics.