Experimental evidence for vacuum fluctuations (zero-point fluctuations in quantum fields) come from the observations of the Lamb shift in the energy levels of the Hydrogen atom, observations of the Casimir effect and the g-2 experiments with electrons and muons.
Lamb shift
The tiny difference between the 2S(1/2) and 2P(1/2) energy levels of the Hydrogen atom was measured by Willis E. Lamb in 1947 [1][2][3]. He was awarded the Nobel Prize in Physics in 1955 for this remarkable achievement.
The Lamb shift could not be explained by the Dirac equation. Later, the Lamb shift was successfully explained (with the right sign and magnitude) by the Quantum Field Theory which takes into account the interaction between vacuum fluctuations and the hydrogen electron in different orbitals.
Casimir effect
Fluctuations of the zero-point energy of a quantized field in the intervening space between the objects give rise to observable forces between those objects.
The Casimir force is the mutual attraction of two closely spaced (few nanometers apart), parallel, and uncharged conducting plates due to quantum fluctuations in the space between the plates. The Casimir force persists even at absolute zero temperature.
This effect was predicted in 1948 by Dutch physicist Hendrick Casimir. The first direct measurement of the Casimir force was achieved by Steven K. Lamoreaux in 1997.
I recommend Kimball A. Milton’s paper [4] for a scientific review. You can also consult [5] and [6].
g-2 experiments
There is a constant known as “g” which relates a charged particle’s intrinsic spin to its magnetic moment. In Dirac theory the “g” for spin=1/2 charged particles is exactly 2.
The measured value of “g” for the electron, however, is slightly larger than 2. The difference is due to electron’s interaction with vacuum fluctuations.
QED (Quantum Electrodynamics) which takes the vacuum fluctuations into account predicts the deviation from 2 accurately. QED calculated value of g-2 agrees with the measurements with a precision better than 1 part in billion.
Muon’s “g” value has been measured by the E821 experiment at the Brookhaven National Laboratory. Muon “g” is slightly larger than 2 as well. Again, the difference is due to muon’s interaction with vacuum fluctuations.
Muon is approximately 207 times heavier than electron. Because of its larger mass interactions of muon with vacuum fluctuations are more complicated. Calculations are harder. The latest calculated value was posted recently.
Fermilab’s muon g-2 experiment (E989) is currently running. E989 is expected to achieve a precision of 140 parts in billion (4 times better than E821 precision). Particle physicists are anxiously waiting for the E989 results. A statistically significant discrepancy between the measured and calculated value of muon g-2 may give us hints about new physics. This is a separate discussion. Let’s not conflate this with the existence of zero-point fluctuations in quantum fields.
It is hard to deny the existence of vacuum fluctuations of the quantum fields. We cannot explain the Lamb shift, Casimir effect, and the measured values of “g” without vacuum fluctuations.
References
[4] [hep-th/9901011] The Casimir Effect: Physical Manifestations of Zero Point Energy (arxiv.org)
Suresh Emre
Renaissance Universal 