Science: Weighing empty space

Scientific American writes about a fascinating developing experiment called Archimedes to measure the weight of empty space. This is a really cool experiment. Knowing empty space weight will help explain why the universe is expanding as it is and what its ultimate fate is likely to be. SciAm writes: 

A vacuum is not completely empty. .... nature can “borrow” energy for extremely short amounts of time. These changes in energy, known as vacuum fluctuations, often take the form of virtual particles, which can appear out of nowhere and disappear again immediately.

Researchers can calculate the energy of the vacuum in two ways. From a cosmological perspective, they can use Albert Einstein's equations of general relativity to calculate how much energy is needed to explain the fact that the universe is expanding at an accelerated rate. They can also work from the bottom up, using quantum field theory to predict the value based on the masses of all the “virtual particles” that can briefly arise and then disappear in “empty” space (more on this later). These two methods produce numbers that differ by more than 120 orders of magnitude (1 followed by 120 zeros). It's an embarrassingly absurd discrepancy that has important implications for our understanding of the expansion of the universe—and even its ultimate fate. To figure out where the error lies, scientists are hauling a two-meter-tall cylindrical vacuum chamber and other equipment down into an old Sardinian mine where they will attempt to create their own vacuum and weigh the nothing inside.

Vacuum fluctuations have to respect some rules. A single electrical charge, for example, cannot suddenly appear where there was none (this would violate the law of charge conservation). This means that only electrically neutral particles such as photons can pop out of the vacuum by themselves. Electrically charged particles have to emerge paired with their antiparticle matches. .... The result is that the vacuum is continuously filled with a stream of short-lived particles buzzing around.

Even if we can't capture these virtual particles in detectors, their presence is measurable. One example is the Casimir effect, predicted by Dutch physicist Hendrik Casimir in 1948. According to his calculations, two opposing metal plates should attract each other in a vacuum, even without taking into account the slight gravitational pull they exert on each other. The reason? Virtual particles. 

.... many physicists are convinced virtual particles interact with gravity just as ordinary particles do. .... To verify that virtual particles interact with gravity like normal matter, the Archimedes team members want to use the Casimir effect to weigh virtual particles with a simple beam balance. 

The weight of virtual particles in the vacuum

causes one balance beam to tilt slightly and misalign the

light beam, giving rise to different light intensity that

reaches the light detector

 

Small, slow temperature changes will be used to induce electrical

property changes in one of the disks compared to the other disk 

The Casimir effect will arise inside the superconducting 

disk, causing its buoyancy to increase or decrease compared to the other disk 

The disks have a diameter of about 10 centimeters (3.9 in) and are several millimeters thick

SciAm describes it like this: As the conductivity changes in the first sample [disk], it acts like the classic two-plate [Casimir] setup, and the number of possible virtual particles within it varies. Thus, the buoyancy force periodically increases and decreases on the first weight. This variation should cause the balance to oscillate at regular intervals, like a seesaw with two children sitting on it.

If I understand this right, when one disk is superconducting and the other isn't, the number of virtual particles inside each disk will differ. If those virtual particles interact with gravity as predicted, that difference should be detectable as a tiny weight change in the superconducting disk. The tiny weight change will tilt the balance beam up or down. That tilt will be observed as a change in light intensity that is detected by the light detector.

This is really interesting in a couple of respects. The sensitivity of the balance beam is incredible. It was not possible to build such an instrument until after giant gravity wave detectors were built and started operating in 2015.[1] To detect what empty space weighs, Archimedes has to be about 10 times more sensitive than gravity wave detectors. Archimedes is designed to measure a force of about 10(-16) newton, which is akin to trying to weigh the DNA in a single cell.[2] Once fully assembled, the whole apparatus will be about three meters high, wide and deep and will weigh several tons. It will operate at near the temperature of liquid nitrogen (-320.4°F), which causes one of two weights hanging from the balance beam to become a superconductor when cooled down enough.

The instrument will be installed in an abandoned mine in Sardinia, a seismically stable, sparsely populated area of the Mediterranean. Geologically, Sardinia is one of the quietest places in Europe. Human-caused vibrations are low. Being underground insulates the instrument from vibrations that are more pronounced at the surface. The need for designing extremely sensitive instruments for precision measurements of gravitational waves was needed to pave the way for the even more sensitive instrument this experiment calls for. The area where Archimedes will be set up is 110 meters (361 ft) below ground in a chamber like this. 

Q: Is this experiment totally cool or what? 

Footnotes: 

1. Several years ago after gushing about detecting gravity waves being a whole new way to see the universe, sort of like a new wavelength of light, I recall someone commenting that it would be of little practical use. My response was wait and see. This experiment is one practical use, i.e., the design of an instrument that can measure vanishingly small weight.

2. My experience in doing biological research let to an intuitive understanding of and comfort with small sizes, weights and volumes. I learned how easily small things could be detected and sometimes have surprisingly large effects. I literally routinely measured out small weights and volumes to do my research. Adding 1 microliter of a reagent by hand to a 50 microliter (the volume of 1 drop of water) reaction volume was standard practice for me for years. There are 20 drops per milliliter and ~29 mL per fluid ounce. I bet that most of those old 50 microliter reactions I used to run all the time have shrunk to ~5 microliter and are usually prepared by machines.

The SciAm article says that the weight of the virtual particles to be weighed is tiny. That weight is about the same as the DNA weight in one cell. From the point of view of the average person that is a vanishingly small weight. But from my point of view, I'm surprised at how much weight that is. Human DNA consists of ~3 billion base pairs with each base pair consisting of about 70 atoms. Remember, the virtual particle weight equivalent of those tens of billions of atoms in DNA arise inside a solid thin disk hanging inside a vacuum. That disk is about 3.9 inches in diameter (~1.95  inch radius) and about 0.1 inch thick.

Show your work for full credit:

How much virtual particles in the universe weigh

The volume of a disk or cylinder is V=πr²h. According to the cylinder volume calculator we all know, love and use all the time: The volume of the disk in Archimedes = πr²h = π×1.95²×0.1 = 0.38025π = 1.1945906065275 inches³

The disk in Archimedes has a volume of about 1.19 cubic inches with a virtual particle weight more than as much as DNA weight a single human cell. Remember, what Archimedes is detecting is not all the virtual particles in the disk. It is only detecting the change in virtual particle weight as one disk becomes superconducting when cooled down enough. 

For context, our convenient volume of the Earth calculator says that the Earth has a volume of about 6.61²⁵ cubic inches or 66,100,000,000,000,000,000,000,000 cubic inches. Obviously, the volume of space, i.e., the universe, is a lot bigger than Earth. The universe is much bigger than ginormous. Compared to the universe, the Earth is less than a dust particle in a big room full of air.

Therefore → then an arithmetic miracle occurs → the weight of virtual particles in the universe must be millions of trillions of quadrillions of gigatons. Probably a lot more than even that.

See why this little experiment is a big deal? Little pipsqueak things can add up. A billion tons here and a gigaton there and pretty soon, one is talking about something that could be seriously influencing the entire freaking universe.