Chapter XX: The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity

What is the ideal condition for applying Galilean mechanics in space?

A region far from stars or masses, where objects remain at rest or in uniform motion—defining a Galilean reference body.

What scenario does Einstein use to model an accelerated reference frame?

A man inside a chest (room-like box) in space, pulled by a rope with constant force, causing uniform acceleration.

How does the man inside the accelerating chest perceive his environment?

As if he is standing in a gravitational field—he feels a downward force and objects fall to the floor.

What observation leads the man in the chest to conclude he's in a gravitational field?

All released objects accelerate downward at the same rate, regardless of their composition or mass.

What discovery reinforces the man’s interpretation of a gravitational field?

He sees the rope and hook pulling the chest, suggesting it is suspended in a uniform gravitational field.

Does Einstein believe the man’s interpretation is valid?

Yes—it does not violate reason or known mechanical laws, supporting an extension of relativity to accelerated frames.

What principle allows the man to interpret acceleration as gravity?

The equality of inertial and gravitational mass, which ensures all bodies fall identically in a gravitational field.

How do different observers explain the tension in a rope suspending a mass inside the chest?

• Man in chest: Tension opposes gravitational pull on the body.

• Free observer in space: Tension causes inertial acceleration of the body.

What does this dual explanation of tension illustrate?

That gravitational mass = inertial mass, providing a physical interpretation for this law via the principle of equivalence.

What key insight does the chest thought experiment provide for general relativity?

That accelerated reference frames can be interpreted as experiencing gravitational fields—leading to the general postulate of relativity.

Can gravitational fields always be “transformed away” by switching reference frames?

No—only for special cases.

For example, the Earth’s gravitational field cannot be fully eliminated by changing reference frames.

Why doesn’t the observer in the train (from Chapter XVIII) disprove the general principle of relativity?

Because he can interpret the braking force as a time-varying gravitational field, not necessarily a real acceleration.