Is the mass of two vertically stacked blocks greater than when they're placed side by side?

Question

At the end of this video on mass-energy equivalence, it's states that two blocks stacked vertically have more mass than when placed side by side because they have more gravitational potential energy.

However, I can't seem to understand this. The gravitational potential energy associated with the gravitational force b/w the blocks and the earth is a property of the blocks-earth system; the energy is associated with the system, and not with any of the individual blocks themselves. So in my opinion, while the mass of the blocks-earth system is greater in the vertically stacked configuration, the mass of the blocks system itself is unchanged as it's energy is unchanged.

Could anyone shed some light on this?

Answer 1

I want to improve the experiment. So we assume that the gravity field is uniform, and the two blocks and a battery are side-by-side on a scale.

Now when one block is lifted on top of other block using energy from the battery, we will observe that the reading of the scale decreases. The blocks weigh the same, but the battery weighs less.

Also the inertia of the stuff on the scale decreases. The blocks have the same inertia, but the battery has less inertia.

The mass-energy that left the battery obviously went to some place. It went to the lifted block, and to the earth that is now less deep in the gravity well of the block.

The reason that the lifted block weighs the same as before is that in an uniform gravity field a block weighs the same everywhere.

The reason that the lifted block has the same inertia as before is that in an uniform gravity field the upper block will be accelerated to a smaller percentage of the local speed of light when the two blocks are accelerated together. Upper block has more energy, but energy is easier to move around at higher elevation.