A Definition and Controversy of Energy

Energy Summary

• The article addresses the fundamental question, “What is energy?” and explores why discussions about energy can be challenging.
• It introduces the Newtonian mechanics definition of energy, which defines energy as the capacity of a system to do work and work as a force applied over a distance.
• The concept of kinetic energy, derived from the laws of Newtonian mechanics, is explained as the energy associated with the motion of an object.
• The work-energy theorem is mentioned, which states that the net work done on a rigid object is equal to the change in its kinetic energy.
• The article acknowledges that energy has different definitions in thermodynamics, Lagrangian mechanics, and quantum mechanics, all of which can be related to each other.
• It highlights how conversations about energy often go wrong, including when questioners seek a more complex or hidden explanation beyond the defined quantity of energy.
• The misconception of energy as a tangible “stuff” with independent existence is discussed, emphasizing that energy is merely a defined quantity used to describe a system, similar to other physics-defined quantities like mass and charge.
• The importance of using consistent definitions to avoid confusion in physics discussions is emphasized, even though different contexts may have subtly different meanings for the same term.
• The article concludes by emphasizing that energy’s usefulness lies in its conservation and its relationships with other essential physical quantities.

What is energy?

Energy is a fundamental concept that refers to the capacity of a system to do work. It is a scalar quantity, meaning it has magnitude but no specific direction. Energy is a crucial concept in understanding the behavior of the physical world, and it comes in various forms, each with its unique properties.

1. Kinetic Energy (KE): This is the energy of an object in motion. The kinetic energy of an object depends on both its mass and its velocity. The formula for kinetic energy is KE = (1/2) * m * v^2, where “m” is the mass of the object, and “v” is its velocity.
2. Potential Energy (PE): This is the energy that is associated with the position or configuration of an object. Gravitational potential energy, for example, depends on an object’s height above the ground. The formula for gravitational potential energy is PE = m * g * h, where “m” is the mass, “g” is the acceleration due to gravity, and “h” is the height.
3. Mechanical Energy: This is the sum of kinetic and potential energy in a mechanical system. According to the law of conservation of mechanical energy, in the absence of non-conservative forces (like friction), the total mechanical energy of a system remains constant.
4. Thermal Energy: This is the internal energy of a system due to the random motion of its particles. It’s often associated with temperature and is a fundamental concept in thermodynamics.
5. Chemical Energy: Chemical reactions involve the rearrangement of atoms and molecules, and this process is associated with energy changes. The energy stored in the chemical bonds of molecules is referred to as chemical energy.
6. Electromagnetic Energy: This includes energy associated with electromagnetic waves, such as light, radio waves, and X-rays. It can also be in the form of electrical or magnetic energy.
7. Nuclear Energy: This is the energy associated with changes in the structure of atomic nuclei. Nuclear reactions release a significant amount of energy.

Energy in Newtonian mechanics

The first definition of energy that is usually encountered is “energy is the capacity of a system to do work”.  Work is then defined as a force applied over a distance.  When an object with some speed collides with another object it can exert a force on that other object and move it some distance.  So a moving object has “the capacity to do work” which is energy, specifically called kinetic energy.

From the laws of Newtonian mechanics and these definitions, it is possible to derive the work-energy theorem.  This theorem says that for a rigid object, the net work done is equal to the change in kinetic energy.  Similarly, it is possible to derive other forms of energy, such as gravitational potential energy or elastic potential energy, and to show how those forms of energy can be converted to other forms or transferred from one system to another through work.

Energy in other contexts

Other definitions of energy are used in thermodynamics, Lagrangian mechanics, and quantum mechanics.  Some proofs demonstrate how energy in one context is related to energy in other contexts.  Those other definitions are also often brought up in a discussion about What Energy is, and many people have a preferred definition.  For simplicity, we will stick with the usual first textbook definition, in no way implying that it is preferable to any other definition.  The discussion below applies to all the other definitions as well.

How the conversation goes wrong

The first way that conversations about energy go wrong is that, when someone provides a definition, the questioner essentially says “No, it cannot be that easy, what is energy”.

It is that easy.  Energy is a defined quantity, and the definition tells you what it is.  It doesn’t matter if you ask “What is energy” or “What is energy truly actually” The answer is the same: the definition.  For any word, X, the answer to “what is X” is the definition of X, and this includes energy.  Energy is simply a defined quantity, defined as above.  The reason that we are interested in energy is not that the definition is tricky or involves any hidden magic, but that it is useful.  It is useful because it is conserved and it is related to other useful quantities.

The second way that conversations about energy go wrong is when questioners have the impression that energy is some type of “stuff” that has its independent existence and they seek to find out what material the “stuff” of energy is made of.  In some ways, this impression is well-founded.  After all, energy is conserved and it can be moved from one system to another, just like you would expect from your everyday experience with “stuff.

Energy is not a thing with an independent existence.  It is just a defined quantity used to describe a system.  This is similar to mass, charge, momentum, and any other similar defined quantity that we use in physics.  Just like you cannot have “pure mass” independent of a system that “has” the mass, the same thing holds with energy.  Sometimes questioners mistakenly think of light (photons) as being “pure energy”, but the light has momentum and other properties also.

The third way that conversations about energy go wrong is when a poster knows and understands the definition of energy (either the “capacity to do work” definition or one of the others not covered here), but refuses to accept it for some reason.

There is not much to say about this one.  We use definitions so that we can understand each other.  If someone refuses to use the same definition as other people, then confusion results.  In physics (as in the rest of life), often the same word is used with subtly different meanings in different contexts.  It is important to be familiar with the various definitions when you are dealing with the different contexts mentioned above.  It certainly is not a problem to have a favorite definition and to explain why it is your favorite, but recognize that the other definitions have their place also.