Section 20

General Relativity Needs the Equality of Inertial and Gravitational Mass

March 24, 2022

Superphysics Note: Einstein invents General Relativity by creating the idea of inertial mass which is really Newton’s third law. This is why he has to say that everything is moving – because his inertial gravity is not really gravity, but just action and reaction.

Assume that, in outerspace, there is a huge glass box that serves as our reference-body. That box has a man inside it. He floats because there is no gravity. To the middle of the lid of the chest is fixed externally a hook with rope attached. This rope is pulled . Then assume that this box moves upwards through a constant force. The man will feel the acceleration of the chest by the reaction of the floor. He must take up this pressure through his legs if he does not wish to be laid out on the floor. He is then standing inside the box.


If he releases a stone in his hand, it will also go to the floor of the box with an accelerated relative motion. He will feel that he and the box are in a gravitational field which is constant with regard to time.

Even though the box is being accelerated with respect to outer space, the box is at rest* relative to itself. This is grounds for extending the principle of relativity to General Relativity (GR) to include bodies of reference which are accelerated with respect to each other.

Einstein Con-man


*Superphysics note: WTF!!! Gravity is not equivalent to the Second or Third Law of Newton! When our car moves forward and we are pushed back by inertia, we never say that there was gravity behind the car! This is really why Einstein equated the gravitational mass with inertial mass in the previous section. The unity of gravitational and inertial mass does not support General Relativity. Instead, it is General Relativity that needs that unity!

Gravitational Mass vs Inertial Mass

GR is based on the law of the equality of inertial and gravitational mass.

This law is the fundamental property of the gravitational field that gives all bodies the same acceleration*.

*Superphysics Note: G to Newton was based on gravitational mass. But G to Einstein is based on both inertia and gravitational mass which he imposes as a new law of gravity, instead of as another theory.

If this natural law did not exist, the man in the moving box=

  • would not be able to feel the gravity in the box
  • would not see his box to be at rest

Because of this law, if the man hangs a rock from the box’s ceiling through a rope, he will see that=

  • the rope neutralizes the box’s gravity through tension
  • the mass of the rock determines the tension.

However, an observer outside will see that the hanging rope joins the box’s motion which it transmits to the rock. The rope’s tension is just large enough to make the rock accelerate downards. The rock’s inertial mass determines the rope’s tension.

Thus, GR requires the law of the equality of inertial and gravitational mass*. A gravitational field exists for the man in the box, despite the fact that there was no such gravity in the spacetime before the box moved.

*Superphysics note: Yes, GR needs inertial and gravitational mass to be the same. But those masses do not need GR!

We might think that:

  • the gravitational field is always only an apparent field
  • we can change our viewpoint so that that gravitational field will not be a gravitational field anymore.
But in reality, this is only true for special gravitational fields. For example, it is impossible to choose a viewpoint where the earth’s gravitational field totally vanishes. This solves our argument against GR at the end of Section 18.

Einstein Con-man

The observer in the train jerks forwards as a result of the train braking. This shows to him the non-uniformity of motion of the train. But he is compelled by nobody to refer this jerk to a “real” acceleration of the train. This is because his viewpoint in the train is at rest*.

The brakes created a gravitational field which was directed forwards and is variable with respect to time. Because of this [fake] gravitational field, the embankment’s backward movement slowed down.

*Superphysics note: Einstein sources gravity from the the weird idea that non-moving large masses are actually moving and that massless bodies are not moving.