The Spacetime Metric
Section 4Inertia, gravity and the vacuum

Weigh the vacuum

National lab for the full experiment; university for the useful contribution. · 2 min read

What it proposes

Quantum theory fills empty space with energy. General relativity says energy has weight. Put a Casimir cavity on a balance and ask whether the shortfall of vacuum energy inside it is pushed upward, the same bookkeeping as a body displacing water. If it is, the join between the site's chapter on the vacuum and its chapter on gravity stops being an argument and becomes a laboratory reading.

Who it is forPrecision-mechanics engineers · Low-noise metrology engineers · Cryogenic materials people · Seismologists

Why the library suggests it

Walk the accounting once before reading the experiment.

Before you move anything — what do you expect?

Optional, and there is no score. The instrument below works exactly the same whether you answer or not.

Two plates close to within a hundred nanometres of each other. What do you expect happens to the vacuum energy in the gap?

Below the ambient level, not below nothing

Four steps, and the phrase comes out right at the end of them. Start with the surrounding vacuum. Close two plates, and the longest modes no longer fit in the gap. What is left inside is the same field minus a thin sliver — still an overwhelmingly positive quantity. Only when you move the zero of the scale up to the ambient level does the reading go negative, and that is all the word negative ever meant here.

Walk the four steps

Step 1 / 4 — The ambient vacuum

The plate separation
An accounting bar for the energy in a Casimir gap, against the ambient vacuum levelA single vertical bar measured against a level line marked as the ambient vacuum. In the first step the bar reaches the line. Closing the plates removes a thin sliver from the top, drawn magnified so it is visible at all, and the bar still stands almost the full height. The final step moves the zero of the scale up to the ambient line, and the same bar now reads as a small quantity below it. The absolute level inside the gap is positive at every separation.

The sliver is drawn magnified by 2,000 times, so that it is visible at all.

Watch the last step carefully: the zero of the scale slides up to the ambient line, and nothing else moves. The bar is the same height it was, the overwhelming majority of the field is still inside the gap, and only the place we measure from has changed.The vertical axis is a proportion of the ambient vacuum level, not an absolute energy density. The excluded fraction is a bounded teaching model, pinned so that a hundred-nanometre gap gives the order of magnitude quoted in the chapter — a small fraction of one per cent excluded, and the overwhelming remainder still inside.Nothing here moves on its own. The diagram advances only when you press a step control.

This is the surrounding vacuum, and it is the unit of the whole drawing. Everything below is measured against this line.

Energy inside the gap, against an absolute zero
99.990%
The same energy, measured from the ambient level
-0.010%
Fraction of the field still inside the gap
99.990%
The excluded sliver: the long modes that no longer fit
0.010%

The bar never reaches zero. At every separation in this drawing the absolute energy inside the gap is positive, and the negative reading appears only after the zero of the scale has been moved.

Scope: an accounting diagram for the label, not a calculation of the Casimir force. It fixes the wording the chapter depends on and asserts no absolute energy density.

The source sheet: Davis and Puthoff, experimental concepts for generating negative energy in the laboratory

What the balance is being asked to weigh is a thin sliver of long waves the closed gap can no longer hold — not an emptied volume.

Enrico Calloni and seventeen colleagues, Carlo Rovelli among them, propose cycling high-temperature superconducting plates through their transition so the cavity's reflectivity — and therefore its vacuum energy — switches on and off, and watching a balance for a force of about ten to the minus sixteen newtons (The Archimedes experiment, 2015). The prototype is built: a half-metre aluminium arm read by a Michelson interferometer, running closed-loop in the seismically quiet Sos Enattos mine in Sardinia, reaching a torque noise of about seven times ten to the minus thirteen newton-metres per root hertz — its own suspension's thermal limit, which is exactly the level the final cryogenic balance was designed around (Thermal noise-limited beam balance as prototype of the Archimedes vacuum weight experiment, 2024). The theoretical stake is set out by Ulf Leonhardt, who argues that doing the same renormalisation cosmology skips — the one laboratory Casimir physics does routinely — leaves a cosmological constant of the right size, and that an expanding universe plays the part a moving mirror plays in the dynamical Casimir effect (Casimir cosmology, 2022).

The experiment or build

The full balance is a large collaboration in a deep mine. But the enabling problems are separable and every one of them is a thesis: the superconducting sample stack, the transition-cycling drive, the thermal-noise budget of the suspension, the seismic isolation. The settling measurement is the force in newtons on the balance as the sample is cycled through its superconducting transition, against a non-superconducting dummy of identical mass and geometry cycled through the same temperature range. That control is the whole experiment: the dummy separates a change in vacuum energy from a change in temperature.

Research context

The record describes a funded collaboration, a prototype that has reached its designed noise floor, and a named next machine.

Take it up

The measurement that settles it
The settling measurement is the force in newtons on the balance as the sample is cycled through its superconducting transition, against a non-superconducting dummy of identical mass and geometry cycled through the same temperature range.
What it costs to start
National lab for the full experiment; university for the useful contribution.
The engineer it grows
It is also the most direct answer this field can give to the question a sceptical reader is entitled to ask: does any of this weigh anything.

What it rests on

Where it sits in the curriculum

Casimir Physics and Vacuum-Force Engineering · The Zero-Point Field, Inertia, and Gravity · What Is the Vacuum? From Empty Space to a Structured Medium · The Vacuum at Cosmic Scale