General Relativity Needs the Equality of Inertial and Gravitational Mass

by Albert Einstein Icon

4 minutes • 732 words

Table of contents

Gravitational Mass vs Inertial Mass

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.
In the middle of the lid of the chest, a hook is fixed externally. It has a rope attached.

This rope is pulled .

This box then moves upwards through a constant force.

The man will feel the acceleration of the box 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.

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

WTF

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!

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

We totally understand what Einstein is trying to do here: In Cartesian Physics, both gravity and electromagnetism (and therefore gravitational lensing, planetary orbits, gravitational waves, time dilation) are caused by Spacetime. Einstein tries to achieve this Spacetime effect by imposing the equality of inertial mass (electromagnetic potential) and gravitational mass (Newtonian mass). But in doing so, he puts electromagnetism as the supreme principle just as Newton put matter as supreme.

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! They need the aether!

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.