# Equivalence of inertial & gravitational mass-I need a sanity check.

1. Feb 6, 2009

### GregAshmore

Equivalence of inertial & gravitational mass--I need a sanity check.

Einstein, in his 1916 book Relativity, illustrates the equivalence of gravitational and inertial mass using the example of a braking train.

The example begins with the train at rest (of course) and the scenery moving to the rear at a constant speed. The passenger feels no force.

As the brakes are applied, the passenger says, "I feel a force. I am at rest in a gravitational field. The velocity of my surroundings is reducing at a constant rate as a result of the application of that field."

Well and good.

Now consider the case of the derailed train suspended over the side of a bridge. The passenger feels a force; both he and the surroundings are at rest. The passenger says, "I and my surroundings are at rest in a gravitational field."

The train comes loose and falls. The passenger feels no force; the surroundings accelerate upward. What does the passenger say?

Seems he would have to say, "I and my surroundings are no longer in a gravitational field. I am at rest, with no applied force. My surroundings must be under a force equal to their weight, for they are accelerating at a constant rate."

Is there a better relativistic answer?

2. Feb 6, 2009

### turbo

Re: Equivalence of inertial & gravitational mass--I need a sanity check.

I hate to complicate your conundrum (not really!) but you might want to follow the progress of the succession of projects at CERN to produce, contain and test neutral anti-hydrogen. One of their goals is to see if the gravitational infall rate of neutral antihydrogen is different than that of hydrogen. The inertial masses must be equivalent, but are the gravitational masses equivalent? Seems like a geeky question, but a negative answer here could bear on cosmology, astrophysics, and gravity theory at a minimum.

3. Feb 6, 2009

### Mentz114

Re: Equivalence of inertial & gravitational mass--I need a sanity check.

It all sounds a bit hazardous.

There are two statements that sum it up

1. In a small enough region of space, acceleration is indistinguishable from gravity
2. inertial mass ( resistance to motion) is the same as gravitational mass ( or 'gravitational charge', that which creates and responds to gravity).

Without (2) you can't get free-fall.

Now, I think (1) and (2) are the same thing.

Last edited: Feb 6, 2009
4. Feb 8, 2009

### Al68

Re: Equivalence of inertial & gravitational mass--I need a sanity check.

Well, he wouldn't have to say he is not in a gravitational field. Just that he is at rest in an inertial frame, ie freefall, with no applied force. And his surroundings are accelerating at 1G. And since weight is force due to gravitational acceleration, anyone accelerating at 1G will feel that force, just like I feel it now.

But even Newton realized that the "force" of gravity behaved suspiciously like the fictional forces encountered when using an accelerating frame of reference. Especially the fact that the "force" of gravity, like a fictional force, was proportional to an objects inertial mass. He just had no explanation for it except to call it a "spooky action at a distance."

Al