Question: In quantum mechanics, what is defined in terms of the energy operator as a time derivative of the wave function?

Answer: energy

<hl> In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. <hl> The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: (where is Planck's constant and the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.

In quantum mechanics, <hl> energy <hl> is defined in terms of the energy operator as a time derivative of the wave function. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: (where is Planck's constant and the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.

question: In quantum mechanics, what is defined in terms of the energy operator as a time derivative of the wave function?, context: In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: (where is Planck's constant and the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.


Question: What equates the energy operator to the full energy of a particle or a system?

Answer: The Schrödinger equation

In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. <hl> The Schrödinger equation equates the energy operator to the full energy of a particle or a system. <hl> Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: (where is Planck's constant and the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.

In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. <hl> The Schrödinger equation <hl> equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: (where is Planck's constant and the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.

question: What equates the energy operator to the full energy of a particle or a system?, context: In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: (where is Planck's constant and the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.


Question: What describes the space-and-time dependence of a slowly changing wave function of quantum systems?

Answer: The Schrödinger equation

In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. <hl> The Schrödinger equation equates the energy operator to the full energy of a particle or a system. <hl> Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: (where is Planck's constant and the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.

In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. <hl> The Schrödinger equation <hl> equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: (where is Planck's constant and the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.

question: What describes the space-and-time dependence of a slowly changing wave function of quantum systems?, context: In quantum mechanics, energy is defined in terms of the energy operator as a time derivative of the wave function. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics. The Schrödinger equation describes the space- and time-dependence of a slowly changing (non-relativistic) wave function of quantum systems. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta. In the solution of the Schrödinger equation for any oscillator (vibrator) and for electromagnetic waves in a vacuum, the resulting energy states are related to the frequency by Planck's relation: (where is Planck's constant and the frequency). In the case of an electromagnetic wave these energy states are called quanta of light or photons.


Question: What is it called when the rest mass of individual particles is destroyed but the inertia equivalent of the system of the two particles remains?

Answer: electron–positron annihilation

<hl> For example, consider electron–positron annihilation , in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. <hl> This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.

For example, consider <hl> electron–positron annihilation <hl>, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.

For example, consider <hl> electron–positron annihilation <hl> , in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass.

question: What is it called when the rest mass of individual particles is destroyed but the inertia equivalent of the system of the two particles remains?, context: For example, consider electron–positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.


Question: What is the inverse process called?

Answer: pair creation

For example, consider electron–positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. <hl> This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from energy of two (or more) annihilating photons. <hl> In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.

For example, consider electron–positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process – the inverse process is called <hl> pair creation <hl> – in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.

question: What is the inverse process called?, context: For example, consider electron–positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.


Question: What is the process in which the rest mass of particles is created from energy of two or more annihilating photons?

Answer: pair creation

For example, consider electron–positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. <hl> This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from energy of two (or more) annihilating photons. <hl> In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.

For example, consider electron–positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process – the inverse process is called <hl> pair creation <hl> – in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.

question: What is the process in which the rest mass of particles is created from energy of two or more annihilating photons?, context: For example, consider electron–positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process – the inverse process is called pair creation – in which the rest mass of particles is created from energy of two (or more) annihilating photons. In this system the matter (electrons and positrons) is destroyed and changed to non-matter energy (the photons). However, the total system mass and energy do not change during this interaction.


Question: What states that there are strict limits to how efficiently heat can be converted into a work in a cyclic process?

Answer: Carnot's theorem

<hl> There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. <hl> However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by <hl> Carnot's theorem <hl> and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

question: What states that there are strict limits to how efficiently heat can be converted into a work in a cyclic process?, context: There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.


Question: What is the direction of transformations in energy?

Answer: what kind of energy is transformed to what other kind

There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. <hl> The direction of transformations in energy ( what kind of energy is transformed to what other kind ) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. <hl> In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (<hl> what kind of energy is transformed to what other kind <hl>) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

The direction of transformations in energy ( <hl> what kind of energy is transformed to what other kind <hl> ) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations.

question: What is the direction of transformations in energy?, context: There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.


Question: What is often determined by entropy considerations?

Answer: direction of transformations in energy

There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. <hl> The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. <hl> In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The <hl> direction of transformations in energy <hl> (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.

question: What is often determined by entropy considerations?, context: There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.


Question: Why are certain larger transformations not permitted?

Answer: because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces

There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. <hl> In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces . <hl>

There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted <hl> because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces <hl>.

In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted <hl> because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces <hl> .

question: Why are certain larger transformations not permitted?, context: There are strict limits to how efficiently heat can be converted into work in a cyclic process, e.g. in a heat engine, as described by Carnot's theorem and the second law of thermodynamics. However, some energy transformations can be quite efficient. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often determined by entropy (equal energy spread among all available degrees of freedom) considerations. In practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces.


Question: Name an example of a heavy isotope?

Answer: uranium

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. <hl> Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. <hl> This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as <hl> uranium <hl> and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

question: Name an example of a heavy isotope?, context: Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.


Question: Name another example of a heavy isotope.

Answer: thorium

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. <hl> Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium ), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. <hl> This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and <hl> thorium <hl>), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and <hl> thorium <hl> ), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth.

question: Name another example of a heavy isotope., context: Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.


Question: What is a process ultimately using the gravitational potential energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth?

Answer: nucleosynthesis

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. <hl> Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis , a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. <hl> This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by <hl> nucleosynthesis <hl>, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by <hl> nucleosynthesis <hl> , a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth.

question: What is a process ultimately using the gravitational potential energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth?, context: Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.


Question: In the case of a chemical explosion, what is transformed to kinetic energy and thermal energy in a short time?

Answer: chemical potential energy

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. <hl> Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. <hl> Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, <hl> chemical potential energy <hl> is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.

question: In the case of a chemical explosion, what is transformed to kinetic energy and thermal energy in a short time?, context: Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" (transformed to more active types of energy such as kinetic or radiant energy) when a triggering mechanism is available. Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes (such as uranium and thorium), by nucleosynthesis, a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae, to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth. This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.


Question: When does energy give rise to weight?

Answer: when it is trapped in a system with zero momentum

<hl> Energy gives rise to weight when it is trapped in a system with zero momentum , where it can be weighed. <hl> It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Energy gives rise to weight <hl> when it is trapped in a system with zero momentum <hl>, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Energy gives rise to weight <hl> when it is trapped in a system with zero momentum <hl> , where it can be weighed.

question: When does energy give rise to weight?, context: Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).


Question: Mass is also equivalent to what?

Answer: certain amount of energy

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. <hl> Mass is also equivalent to a certain amount of energy , and likewise always appears associated with it, as described in mass-energy equivalence. <hl> The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a <hl> certain amount of energy <hl>, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Mass is also equivalent to a <hl> certain amount of energy <hl> , and likewise always appears associated with it, as described in mass-energy equivalence.

question: Mass is also equivalent to what?, context: Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).


Question: Who created the formula E = mc2?

Answer: Albert Einstein

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. <hl> The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. <hl> In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by <hl> Albert Einstein <hl> (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

question: Who created the formula E = mc2?, context: Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).


Question: In what year did Einstein create E = mc2?

Answer: 1905

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. <hl> The formula E = mc², derived by Albert Einstein ( 1905 ) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. <hl> In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (<hl> 1905 <hl>) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

The formula E = mc², derived by Albert Einstein ( <hl> 1905 <hl> ) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity.

question: In what year did Einstein create E = mc2?, context: Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).


Question: What quantifies the relationship between rest-mass and rest-energy within the concept of special relativity?

Answer: E = mc²

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. <hl> The formula E = mc² , derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. <hl> In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula <hl> E = mc² <hl>, derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).

The formula <hl> E = mc² <hl> , derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity.

question: What quantifies the relationship between rest-mass and rest-energy within the concept of special relativity?, context: Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc², derived by Albert Einstein (1905) quantifies the relationship between rest-mass and rest-energy within the concept of special relativity. In different theoretical frameworks, similar formulas were derived by J. J. Thomson (1881), Henri Poincaré (1900), Friedrich Hasenöhrl (1904) and others (see Mass-energy equivalence#History for further information).


Question: Matter may be converted to what?

Answer: energy

<hl> Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. <hl> However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.

Matter may be converted to <hl> energy <hl> (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.

question: Matter may be converted to what?, context: Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.


Question: Energy may be converted to what?

Answer: Matter

<hl> Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. <hl> However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.

<hl> Matter <hl> may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.

question: Energy may be converted to what?, context: Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.


Question: Why is a loss of energy difficult to measure by weight?

Answer: mass equivalent of a unit of energy is minuscule

Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. <hl> Conversely, the mass equivalent of a unit of energy is minuscule , which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. <hl> Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.

Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the <hl> mass equivalent of a unit of energy is minuscule <hl>, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.

Conversely, the <hl> mass equivalent of a unit of energy is minuscule <hl> , which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large.

question: Why is a loss of energy difficult to measure by weight?, context: Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.


Question: Where are examples of energy transformation into matter found?

Answer: high-energy nuclear physics

Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. <hl> Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics . <hl>

Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in <hl> high-energy nuclear physics <hl>.

Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in <hl> high-energy nuclear physics <hl> .

question: Where are examples of energy transformation into matter found?, context: Matter may be converted to energy (and vice versa), but mass cannot ever be destroyed; rather, mass/energy equivalence remains a constant for both the matter and the energy, during any process when they are converted into each other. However, since is extremely large relative to ordinary human scales, the conversion of ordinary amount of matter (for example, 1 kg) to other forms of energy (such as heat, light, and other radiation) can liberate tremendous amounts of energy (~ joules = 21 megatons of TNT), as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why a loss of energy (loss of mass) from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (i.e., kinetic energy into particles with rest mass) are found in high-energy nuclear physics.


Question: Thermodynamics divides energy information into what two kinds?

Answer: reversible processes and irreversible processes

<hl> Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes . <hl> An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).

Thermodynamics divides energy transformation into two kinds: <hl> reversible processes and irreversible processes <hl>. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).

Thermodynamics divides energy transformation into two kinds: <hl> reversible processes and irreversible processes <hl> .

question: Thermodynamics divides energy information into what two kinds?, context: Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).


Question: What divides energy transformation into two kinds reversible processes and irreversible processes?

Answer: Thermodynamics

<hl> Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes. <hl> An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).

<hl> Thermodynamics <hl> divides energy transformation into two kinds: reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).

question: What divides energy transformation into two kinds reversible processes and irreversible processes?, context: Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).


Question: A reversible process is one in which this does not happen.

Answer: dissipation

Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. <hl> A reversible process is one in which this sort of dissipation does not happen. <hl> For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).

Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of <hl> dissipation <hl> does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).

question: A reversible process is one in which this does not happen., context: Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, quantum states of lower energy, present as possible excitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomisation in a crystal).


Question: As the universe evolves in time, more and more of its energy becomes trapped in what?

Answer: irreversible states

<hl> As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). <hl> This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.

As the universe evolves in time, more and more of its energy becomes trapped in <hl> irreversible states <hl> (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.

question: As the universe evolves in time, more and more of its energy becomes trapped in what?, context: As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.


Question: What is it referred to when more and more of energy becomes trapped in irreversible states?

Answer: inevitable thermodynamic heat death of the universe

As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). <hl> This has been referred to as the inevitable thermodynamic heat death of the universe . <hl> In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.

As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the <hl> inevitable thermodynamic heat death of the universe <hl>. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.

This has been referred to as the <hl> inevitable thermodynamic heat death of the universe <hl> .

question: What is it referred to when more and more of energy becomes trapped in irreversible states?, context: As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.


Question: In this heat death of energy, what does not change?

Answer: energy of the universe

As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. <hl> In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less. <hl>

As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the <hl> energy of the universe <hl> does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.

question: In this heat death of energy, what does not change?, context: As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work through a heat engine, or be transformed to other usable forms of energy (through the use of generators attached to heat engines), grows less and less.


Question: According to what, energy can neither be created nor destroyed by itself?

Answer: conservation of energy

<hl> According to conservation of energy , energy can neither be created (produced) nor destroyed by itself. <hl> It can only be transformed. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.

According to <hl> conservation of energy <hl>, energy can neither be created (produced) nor destroyed by itself. It can only be transformed. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.

According to <hl> conservation of energy <hl> , energy can neither be created (produced) nor destroyed by itself.

question: According to what, energy can neither be created nor destroyed by itself?, context: According to conservation of energy, energy can neither be created (produced) nor destroyed by itself. It can only be transformed. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.


Question: The total inflow of energy into a system must equal what?

Answer: total outflow of energy from the system, plus the change in the energy contained within the system

According to conservation of energy, energy can neither be created (produced) nor destroyed by itself. It can only be transformed. <hl> The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system . <hl> Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.

According to conservation of energy, energy can neither be created (produced) nor destroyed by itself. It can only be transformed. The total inflow of energy into a system must equal the <hl> total outflow of energy from the system, plus the change in the energy contained within the system <hl>. Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.

The total inflow of energy into a system must equal the <hl> total outflow of energy from the system, plus the change in the energy contained within the system <hl> .

question: The total inflow of energy into a system must equal what?, context: According to conservation of energy, energy can neither be created (produced) nor destroyed by itself. It can only be transformed. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.


Question: What can neither be created nor destroyed by itself; it can only be transformed?

Answer: energy

<hl> According to conservation of energy , energy can neither be created (produced) nor destroyed by itself. <hl> It can only be transformed. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.

According to conservation of <hl> energy <hl>, energy can neither be created (produced) nor destroyed by itself. It can only be transformed. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.

According to conservation of <hl> energy <hl> , energy can neither be created (produced) nor destroyed by itself.

question: What can neither be created nor destroyed by itself; it can only be transformed?, context: According to conservation of energy, energy can neither be created (produced) nor destroyed by itself. It can only be transformed. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.


Question: What shows that the conservation of energy is a mathematical consequence of translational symmetry of time?

Answer: Noether's theorem

This law is a fundamental principle of physics. <hl> As shown rigorously by Noether's theorem , the conservation of energy is a mathematical consequence of translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. <hl> Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.

This law is a fundamental principle of physics. As shown rigorously by <hl> Noether's theorem <hl>, the conservation of energy is a mathematical consequence of translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.

As shown rigorously by <hl> Noether's theorem <hl> , the conservation of energy is a mathematical consequence of translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate.

question: What shows that the conservation of energy is a mathematical consequence of translational symmetry of time?, context: This law is a fundamental principle of physics. As shown rigorously by Noether's theorem, the conservation of energy is a mathematical consequence of translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.


Question: What is the quantity which is canonical conjugate to time?

Answer: energy

This law is a fundamental principle of physics. <hl> As shown rigorously by Noether's theorem, the conservation of energy is a mathematical consequence of translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. <hl> Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.

This law is a fundamental principle of physics. As shown rigorously by Noether's theorem, the conservation of <hl> energy <hl> is a mathematical consequence of translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.

question: What is the quantity which is canonical conjugate to time?, context: This law is a fundamental principle of physics. As shown rigorously by Noether's theorem, the conservation of energy is a mathematical consequence of translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is canonical conjugate to time. This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval. The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.