How did Einstein discover that light is sensitive to gravity?

The Elevator Thought Experiment

History

The Genesis: The Equivalence Principle

In 1907, Einstein had his famous “happiest thought”: the Equivalence Principle.

  • He realized that, locally, the effects of acceleration (such as being in a running rocket) are indistinguishable from the effects of gravity (such as standing on Earth).
  • The Elevator Analogy: Imagine a beam of light crossing a box (or an elevator) that is accelerating upwards. To an observer inside, the light would appear to bend downwards as it travels across.
  • Since acceleration is equivalent to gravity, Einstein deduced that gravity must also cause light to bend.

The Revolutionary Hypothesis

This idea led him to formulate the Theory of General Relativity between 1907 and 1915.

  • Unlike Newton’s gravity, which is a force, Einstein postulated that gravity is a curvature of spacetime caused by the presence of mass and energy.
  • Since light (even without rest mass) must always follow the shortest path, if spacetime itself is curved, then light must follow that curvature.
  • Conclusion: Gravity does not “pull” on light; light simply follows the warped geometry of space around a massive object.

The Experimental Confirmation (1919)

Einstein had predicted that the light from a distant star, passing close to the Sun, should be deflected by a precise angle.

  • In 1919, British astronomer Arthur Eddington organized an expedition to West Africa to observe a total solar eclipse.
  • The eclipse made it possible to see stars near the Sun. Eddington’s team measured the apparent position of these stars.
  • Result: The stars’ positions were shifted exactly as predicted by Einstein’s theory (an angle twice as large as classical physics predicted).
  • This spectacular confirmation made Einstein famous worldwide and proved that gravity indeed affects light by curving spacetime.

Physics Behind the Elevator Analogy

Recap on Newton’s Second Law

Also known as Newton’s Second Law, this theorem is a fundamental principle of classical mechanics that relates the force applied to a body to the acceleration it undergoes.

In a Galilean reference frame, the vector sum of the external forces \(\vec{F}_{\text{ext}}\) applied to a point mass body of mass \(m\) is equal to the product of its mass \(m\) and its acceleration vector \(\vec{a}\).

Mathematical Formulation

The Fundamental Theorem of Dynamics is expressed by the following vector relation:

\[\sum \vec{F}_{\text{ext}} = m \cdot \vec{a}\]

Where:

  • \(\sum \vec{F}_{\text{ext}}\) is the vector sum of the external forces applied to the body (in Newtons, \(\text{N}\)).
  • \(m\) is the mass of the body (in kilograms, \(\text{kg}\)).
  • \(\vec{a}\) is the acceleration vector of the body’s center of mass (in meters per second squared, \(\text{m/s}^2\)).

FTD Equation with Gravity Only

This is the classic situation of free fall (without air resistance). If the only external force applied to a body of mass \(m\) is gravity (the weight \(\vec{W}\)), the equation of the Fundamental Theorem of Dynamics (FTD, or Newton’s Second Law) becomes:

  1. General Vector Form

The equation always starts with the sum of external forces \(\sum \vec{F}_{\text{ext}}\): \[\sum \vec{F}_{\text{ext}} = m \cdot \vec{a}\]

Since only the Weight force \(\vec{W}\) is acting, the equation becomes: \[\vec{W} = m \cdot \vec{a}\]

  1. Substituting for Weight

We use the vector expression for Weight: \(\vec{W} = m \cdot \vec{g}\). \[m \cdot \vec{g} = m \cdot \vec{a}\]

  1. Simplification (Constant Acceleration)

By canceling out the mass \(m\) (which is non-zero), we get the fundamental result for free fall:

\[\vec{a} = \vec{g}\]This means the body’s acceleration \(\vec{a}\) is equal to the acceleration due to gravity \(\vec{g}\), regardless of its mass.

Thought Experiment

This experiment is based on the Equivalence Principle, which states that it is impossible to locally distinguish between the effects of gravitation (being stationary on a planet’s surface) and those of acceleration (being in a uniformly accelerating rocket far from any gravity).

Scenario 1: The Accelerating Cabin

  • Imagine an elevator cabin very far from any source of gravity, but being pulled upward by a rope, giving it an acceleration of \(9.81 \text{ m/s}^2\) (Earth’s acceleration).
  • A beam of light enters through a small hole in a side wall and heads toward the opposite wall.
  • During the time it takes for the light to cross the cabin, the cabin accelerates and moves upward.
  • To an observer inside the cabin, the light beam appears to follow a curved path downward, because the point of impact on the opposite wall is lower than if it had remained opposite the entrance hole.

Scenario 2: The Cabin in a Gravitational Field

  • Now imagine the same cabin, stationary but resting on Earth (subject to gravity).
  • Under the Equivalence Principle, the observer inside cannot distinguish this from the previous scenario. The laws of physics must be the same.
  • Conclusion: If the light beam is bent by acceleration in the first case, it must therefore be bent by gravitation in the second case!

Major Implication

This experiment led Einstein to conclude that gravity is not a Newtonian “force” that attracts objects (including light), but rather a deformation of spacetime caused by the presence of mass and energy.

Light, even though it is massless, simply follows the “straightest” possible path (a geodesic) within this curved spacetime.