When Energy Can Be Negative:Why,How,When,Where

In this article we are going to describe when energy can be negative and detailed facts related to it.

If an atom is considered then it can be said that the formation and breakage of an atom can define negative energy. The amount of energy that is absorbed during the breakage of an atom is the same as the amount of energy that is released during the formation of that atom. The energy supplied to break an atom is considered as negative energy.

As far as the energy becomes zero,the atom becomes free. We can take a free electron as an example of negative energy. A free electron is that electron which does not exist in any orbit of an atom. When this free electron is brought from infinity to any other point close to the nucleus,the nucleus has to do some work.

Kinetic energy of an electron can never be zero as it is a product of mass and square of velocity of the electron. The ratio of potential to kinetic energy of an electron is -2. From this it can be stated that the total energy of an electron can be zero.

This work done or potential energy is negative potential energy as we all know the concept that when work done or energy is supplied to an object the energy is termed as negative energy.

when energy can be negative
Negative energy from wikipedia

Can energy ever be negative?                            

Potential energy can have both positive as well as negative value. Whether an energy has a positive or a negative value can be identified from the definition of energy. A very common source of negative potential energy is attraction force. When an electron and a positron are taken together,there comes a change in energy. From this we can explain when energy can be negative.

The value of the total energy decreases as the electron and positron pair come closer to each other and the Coulomb potential energy becomes more negative.

The sum of kinetic energy and potential energy of a bound system has a value less than zero. But the total energy which includes the masses individually gains a positive value. An isolated system should have a positive value of its total energy. Otherwise this system can move spontaneously and there is no certainty in its position. In fact the vacuum also will not be stable.

We can use the example of energy transfer between source and sink in a thermodynamic engine or refrigerator. Here the negative work done signifies that work is being done by a system. Hence total energy of the system decreases in this case.

When energy can be negative?

Let us take a hydrostatic system. It is helpful in describing when energy can be negative. This system is contained within a closed cylinder and a frictionless movable piston is fitted at the top of the cylinder. The area of the cross section of that cylinder is A and the pressure acting on the piston is P which is exerted on it by the system. Therefore the internal force acting on the system is,

Here the external force should not be taken into consideration. It is possible to neglect the external force only when there is a negligible difference between the force PA of the system and the external force. If an infinitesimal distance of dx is moved by the piston during expansion(+dV) then an infinitesimal amount of negative work (-dW) is performed by the system. Hence,



The presence of negative sign in the above equation signifies an expansion i.e, a positive dV. A negative work done by the system is yielded from this expansion. It means that the total energy of the system decreases. Hence energy can be negative in this case.

What types of energy can be negative?

There are a number of examples that can be used to illustrate when energy can be negative. They are-

Gravitational potential energy

Gravitational potential energy is the most important example to describe when energy can be negative. Let us take two heavy bodies on the earth’s surface. Now the positive attraction force between them will lead to a positive gravitational potential energy whereas the negative attraction force will lead to the same amount of negative gravitational potential energy.

If the distance between them reaches an infinite distance,the positive attraction force and the negative gravitational attraction force tend to become zero from the positive and the negative number lines respectively. As the bodies come closer to each other they obtain an accelerated motion due to gravity.

This gives to the positive kinetic energy as well as the same amount of negative gravitational potential energy so that total energy is conserved as per the law of conservation of energy.

Energy associated with virtual particles

Virtual particles are another most notable example of when energy can be negative. Virtual particle and antiparticle pairs are used to fill the vacuum space as per the uncertainty principle. These pairs exist for a very short period of time. After that they anhilitate. These virtual particles consist of negative energy.

Casimir effect

To restrict the wavelengths of quanta that are present in between two plates,the two two plates come closer to each other. This effect tends to decrease the number of virtual particles and their density in between the plates. It causes a negative energy density. This effect based on quantum theory is a very crucial example of when energy can be negative.

Casimir effect from wikipedia

Squeezed light

Energy fluctuations are random in quantum theory as suggested by the uncertainty principle. In case of squeezed quantum states this level of uncertainty is reduced. These squeezed states can have negative energy. Sometimes a number of laser beams are arranged in such a way that energy fluctuations become suppressed by the destructive quantum interference.

When energy can be negative can be explained by this.

Squeezed states of light from wikipedia

Dirac sea

Dirac theory was given by paul dirac in 1930. According to this theory negative energy has completely filled the vacuum of space.

Dirac sea from wikipedia

Hawking radiation

The short-lived virtual particle pair when entering into the black hole its energy turns into negative energy and net energy becomes zero. This is very useful in explaining when energy can be negative.


The mechanism of a wormhole is based upon Einstein’s equations. A wormhole is used to link two locations that differ by both space and time. When a wormhole is kept open,negative energy appears in it.

Wormhole from wikipedia

Warp drive

Negative energy is also involved in a warp drive which is faster than light. When energy can be negative is explainable from the concept of warp drive.

Warp drive from wikipedia

An endothermic reaction

We always write -Q when the heat is absorbed in a chemical equation. It is all about sign convention. There exists no negative energy.

How can energy be negative?

Potential energy can always possess a negative value. To explain when energy can be negative let us take two examples of a planet that is under gravitational attraction of the sun and an electron that is bound to the atom. We know that a bound system always carries a negative energy with it.

When a planet is under the gravitational attraction of the sun it is in a bound state. So it needs positive energy to be free from this gravitational field of the sun. Similarly an electron that is bound to an atom needs energy to get out of the atom and become free. So the energy of the bound electron is also negative energy.

Total energy of a bound system is sometimes negative. We know that total energy of a bound system is the sum of potential energy and kinetic energy. Now kinetic energy is the product of mass and square of velocity of the system so it can never be negative.

But we know potential energy is negative for a bound system. So if this negative value of the potential energy is greater than the positive value of the kinetic energy then the total energy becomes negative.

Where energy can be negative?

If the theory of a wormhole is taken as an example of when energy can be negative then it can describe where energy can have a negative value. Two places that are far apart from each other geographically and their space and time also differ from each other can be linked through the help of wormholes.

These two places can also be instantaneously traveled by the help of wormholes. Whenever a wormhole is kept open it acquires negative energy.

Can conservation of energy be negative?

Conservation of energy can not have a negative value as it is totally violating the law of conservation of energy. Negative energy has no particular physical proof hence it can be said that if negative energy exists then all energies within the universe will be balanced by each other causing the total energy to vanish.

This concept entirely violates the law of conservation of energy.

Ankita Biswas

Hi...I am Ankita Biswas. I have done my B.Sc in physics Honours and my M.Sc in Electronics. Currently, I am working as a Physics teacher in a Higher Secondary School. I am very enthusiastic about the high-energy physics field. I love to write complicated physics concepts in understandable and simple words. Let's connect through LinkedIn:https://www.linkedin.com/in/ankita-biswas-b95785230

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