Equivalence principle: Definition, History, Examples and Effective Mass

The equivalence principle is a fundamental law of physics that gives us information it is the equivalence of gravitational and inertial mass and the observation of Albert Einstein that the gravitational force experienced by a body standing on a massive body is the same as the pseudo-force experienced by an observer in a non-inertial reference frame.

• The principle states that a force experienced by an individual due to gravity by standing on a big surface area or a massive object is equivalent to the pseudo force that the observer in a non-inertial frame of reference will experience.
• Although general relativity was developed using the equivalence principle, it isn't a founding principle, but rather a consequence of its geometrical nature.

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Key Terms: Frame of reference, mass, acceleration, gravitational force, pseudo force, inertial mass, acceleration due to gravity, force, gravity

Read More: Mass energy equivalence

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What is the equivalence principle?

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The equivalence principle is a part of the Theory of Relativity which states that the inertial and gravitational forces are similar in nature and cannot be distinguished.

• It is one of the most notable and fundamental laws of physics through which the concepts of mass and inertia are established.
• Inertial mass can be defined as a measure of the acceleration of an object when the same force as in F = ma is provided.
• The gravitational mass is the strength of gravitational force experienced by the body when the mass is present in the gravitational force, g. 
• The principle proves that when the initial mass increases, the acceleration also decreases.

From the equivalence principle, it can be said that the gravitational mass and the inertial mass are the same. Terrace inertial mass and gravitational force are directly proportional to each other and hence the proportionality is independent of the type of matter present. 

• The equivalence principle is a fundamental law of physics that essentially states that gravitational and inertial forces are often not distinguishable. 
• The gravitational field can be expressed with the help of a metric tensor by taking the help of the equivalence principle.
• Taking the general theory of relativity into consideration, it is said that the gravitational force, when experienced locally, is the same as the pseudo force experienced in a non-inertial and accelerated frame of reference.

Check Important Difference Between Gravitation and Gravity

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History of equivalence principle

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It had come to the realization of Dr. Albert Einstein that the theory of relativity and Newton’s theory of gravity had some complexities between them. Albert Einstein set a benchmark of his own with his theory of relativity by enabling new laws for physics.

• The gravitational force theory developed by Newton, though very advanced, did not contribute fully to the development of Physics.
• The theory of relativity enfolded space and time and excluded gravity. After years of research, Albery Einstein incorporated the ideas of gravity with his own ideas of space and time.
• Thus, emerged the new idea called the theory of relativity which proved to be beneficial for further research.
• Therefore, it can be concluded that Einstein’s research benefited and eventually formed the equivalence principle.

A general theory of relativity reference was formed from the idea that even within a gravitational field, there is always a frame of reference where gravity is almost zero or absent.

• Therefore, it can also be said that laws free from the gravity of special relativity govern the laws of physics if the observations are concentrated in a controlled space and time.
• It can be said that it is the first step toward the theory of relativity.
• It is derived from what was formulated as the equivalence principle which in turn is inspired by the consequence of a freefall.

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Effective mass

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Before understanding what an effective mass is, let us first understand what mass means. 

• Mass is the property of an object which determines a measure of resistance to acceleration in the presence of an external force.
• The general theory of relativity includes the theory of effective mass which talks about gravitational and inertial mass.
• The gravitational force or attractive force between two masses can be given by the equation F= GMm/r². In this equation, G is the universal gravitational constant, M is the mass of one body, m is the mass of the second body and r is the distance between the two bodies. 
• Inertia is the resistance provided by the body against the change in its current state of motion. The force, in this case, is given by the equation F= m x a where m is the inertial mass of the object and a is the acceleration of the object. 
• The principle of equivalence is given by the equation F= GMm/r² = m X a and by rearranging, we get an equation of a = (gravitational mass/inertial mass) X G(M/r²)

Newton’s second law mainly proves that a body starts accelerating when a force is applied to the body. Effective force generally gives us information about the gravitational mass and the internal mass of the bodies.

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Examples of equivalence principle

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The equivalence principle can be established through a number of examples. It can often be problematic to differentiate between inertial mass and gravitational mass since more often than not, they indicate the same things.

• A scenario can be considered where an elevator is being accelerated in one direction.
• If an individual inside the elevator drops an object inside it, it reaches the base of the elevator.
• But if subjected to a gravitational field, the same as that of Earth, the situation might differ.
• If the cabin or elevator is accelerating at the rate of 9.8 meters per square second, the object falling hereby would experience the exact same acceleration on Earth.
• As an observer, the acceleration will not be noticeable.
• From the individual’s point of view, the two reference situations are identical.
• The observer will not be able to tell whether the object is falling under the gravity of a massive object like Earth or if the cabin floor is accelerating them. 

Thus Einstein formulated the law which clearly states that no experiment can be performed which could distinguish between a uniform gravitational field and an equivalent uniform acceleration.

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Things to remember

• The equivalent principle is a fundamental law of physics that establishes the relationship between gravitational and inertial force.
• The equivalence principle states that a force experienced by an individual due to gravity by standing on a big surface area is equivalent to the pseudo force the observer in a non-inertial frame of reference will experience.
• The gravitational force, when experienced locally, is the same as the pseudo force experienced in a non-inertial and accelerated frame of reference.
• From the equivalence principle, it can be said that the gravitational mass and the inertial mass are the same.
• Even within a gravitational field, there is always a frame of reference where the gravity is almost zero or absent.
• Mass is the property of an object which determines a measure of resistance to acceleration in the presence of an external force.

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