Searching for New Physics with Precision Clocks

I recently found this very accessible paper about the recently launched QSNET, a network of high precision atomic and molecular clocks in England. The paper, Measuring the stability of fundamental constants with a network of clocks, is featured in the EPJ Quantum Technology Journal, a SpringerOpen journal, and is Creative Commons. The link to the fundamental constants arises due to the spectroscopy upon which these clocks are based. But they don’t mention magnetic monopoles and I believe they should. Or maybe not . . .

How is it possible to justify a lengthy review of the physics of the magnetic monopole when nobody has ever seen one? In spite of the unfortunate lack of favorable experimental evidence, there are sound theoretical reasons for believing that the magnetic monopole must exist. The case for its existence is surely as strong as the case for any other undiscovered particle.

John Preskill, Magnetic Monopoles, a review as of 1984

Spectroscopy actually provided the earliest glimpse into the quantum realm and provided a precise tool for determining the chemical composition of materials — even stars and galaxies far, far away. Thomas Melville observed the first spectral line in 1752, while basically burning salt. But spectroscopy actually became an experimental science in the early 1800’s, after Joseph von Fraunhofer developed diffraction gratings which allowed him to accurately measure wavelengths. He then fruitfully applied this to the solar spectrum. This, similar to early cosmology, led to the collection of a significant data set with no theory to explain it. In 1885 Johann Balmer discovered his relation between the frequencies, hence wavelengths, of the known spectral lines of hydrogen:

ν/c = 1/λ = R_H(1/2^2 − 1/m^2);

where m ∈ Z^+, m > 2. This constant, R_H ≈ 1.096776 × 10^7 m^−1, is called the Rydberg constant, after Johannes Rydberg, and the above relation between this and spectral line frequency describes the “Balmer series” in the hydrogen spectrum. Balmer’s formula was subsequently generalized to:

1/λ = R_H(1/n^2 − 1/m^2);

where n, m ∈ Z^+, n < m, by Friedrich Paschen in 1908 and more and more series continued to be discovered.

This term, 1/λ, came to be known as the wave number, k, and during that same year, 1908, Walther Ritz discovered the “Ritz combination principle” where, for instance, the difference between the first two wave numbers in the Balmer series is equal to the first wave number in the Paschen series. This is simply a manifestation of energy conservation. All of these regularities together with Ernest Rutherford’s empirically grounded (scattering experiments) model of the atom and Max Planck’s relation, E = hν, led Neils Bohr to his model of the hydrogen atom. And what Bohr was really recognized for was his derivation of the Rydberg constant using his so-called Correspondence Principle:

R_H = (μe^4)/(8{ϵ_0}^2h^3c);

where μ is the electron/proton mass ratio. This has since been generalized to the modern constant, R_∞ ≈ 1.097373×107m^−1 where:

R_∞ = (1/(4πϵ_0))^2(me^4)/(4πℏ^3c).

During all of this activity, scientists also discovered the fine structure constant:

α = 1/(4πϵ_0)e^2/(ℏc).

Many spectral lines, upon finer analysis, are found to be two or more finely separated lines and the spacing of these “fine-structure” lines relative to the readily apparent lines, the “coarse-structure” lines, is proportional to α². This fine structure constant also shows up, theoretically, in the velocity of electrons confined to circular orbits, v/c = α/n, where n is the principal quantum number labeling the energy value of the stationary state. It also shows up in the mass equation for magnetic monopoles in many theories. In modern parlance, it is regarded as the gauge field coupling constant for electromagnetism, which means it dictates the strength of interaction between the electromagnetic field and charged particles. If you introduce this fine structure constant into the Rydberg constant you have:

R_∞ = c/(4πℏ)α^2m;

which is Equation (3) in the QSNET paper. And as they state immediately following Equation (3) (page 7):

It follows that, if these constants vary either in space or time, then so do atomic and molecular spectra. Clocks based on atoms or molecules rely on using the frequency of a spectral line to set the rate at which a clock ‘ticks’. Changes in the spectra will therefore result in changes in the clock frequencies. The narrower the spectral line, the more precisely the clock frequency can be determined and the better the resolution for detecting any changes. The most favourable species to be used for clocks are therefore those which possess transitions that are narrow in frequency (forbidden at least to first order) and not easily perturbed by changes in background electric or magnetic fields. Optical atomic clocks have already been demonstrated to achieve fractional frequency instabilities and inaccuracies at the level of 10^{18} and below [16, 17], making them among the most precise measurement instruments ever built. High-precision spectroscopy with atomic clocks has therefore provided some of the tightest constraints on variations of α and the electron-to-proton mass ratio, μ = m_e/m_p, with m_p the proton mass.

Depending on the nature of the transition employed, different clocks are more or less sensitive to variations of specific fundamental constants. To illustrate this, let us express the frequency of clocks employing optical transitions as

ν_{opt} = A⋅F_{opt}(α)⋅cR_∞,

with A a constant depending on the specific atomic species and transition and F_{opt} (α) describing the relativistic correction to the specific transition. In contrast, microwave (MW) clocks utilise transitions between hyperfine energy levels, whose frequency can be written as

ν_{MW} = B⋅α^2F_{MW}(α)⋅μ⋅cR_∞,

where B is a constant that depends on the specific atomic species and transition and F_{MW} (α) is the relativistic correction to the specific MW transition. Finally, the frequency of molecular clocks based on vibrational transitions can be expressed as

ν_{vib} = C⋅μ^{1/2}⋅cR_∞,

with C a constant depending on the specific molecule and transition used.

The sensitivity of a certain atomic or molecular transition ν_i to variations of a fundamental constant X = {α, μ} is characterised by a sensitivity coefficient K_X which we define as

K_X = ∂ln(νi/cR∞)/∂lnX.

The larger the value of K_X, the more sensitive a specific transition is to variations of X.

Currently, it appears that QSNET simply involves three clocks, Sr (Strontium), Yb^+ (Ytterbium), and Cs (Caesium) atomic clocks, all at the National Physical Loboratory in London, with three new clocks under development: a {N_2}^+ (sodium ion) molecular ion clock at the University of Sussex, a CaF (Calcium Monoflouride) molecular optical lattice clock at Imperial College London, and a Cf (Californium) highly charged ion clock at the University of Birmingham.

These clocks are all going to be networked through existing fiber optic cable currently unused by the Telecom industry providing multiple advantages both technological and experimental. In Section 4 of their paper, pages 15–31, they discuss a respectfully broad spectrum of theory which QSNET can either outright falsify or highly constrain, all based on the search for either spatial or temporal variations in these fundamental constants. These include dark matter and dark energy models, grand unification models, models of quantum gravity, and the search for violations of the Equivalence Principle and spacetime symmetry (Lorentz invariance).

Given their range and affordability, relative to collider experiments, it seems difficult to fault these long-term “benchtop” experiments, but I wonder how successful they will be. I certainly feel that too much emphasis is placed on the high-energy domain, largely due to the theory-ladeness of experimental physics. But these experiments seem rather heavily theory-laden as well — no monopole search? To my way of thinking, the physics community should at the very least acknowledge and consider the implications of William Tiller’s body of empirical data, most gleaned from relatively inexpensive “benchtop” experiments.

Reading the QSNET paper, we find that “many theoretical frameworks that attempt to describe physics beyond the Standard Model predict or allow variations of the fundamental constants,” to include the “cosmological time evolution” of said constants. Naively, one would think that changing the structure of the spacetime vacuum would impact these fundamental constants, especially if this includes the addition of active magnetic charge contributions to the electromagnetic field. Professor Tiller never assigned a substantial prior to the “Big Bang” idea. In his theory, by some unknown mechanism, the deltron moiety oscillates globally in density causing spacetime to oscillate entropically. So, again, naively, it would seem that Professor Tiller predicts and gives reason for the cosmological time evolution of fundamental constants.

Based on my own inquiry, there exists considerable theory on magnetic monopoles (in addition to the Preskill review, see this bibliography) unsupported empirically, of course; although magnetic charges have been simulated by a nano-needle (Nature, 2014) with its tip positioned over an aperture. So I wonder if we could use the QSNET clocks to probe the nature of magnetic monopoles in a space “conditioned” to a higher gauge symmetry state? My concern is that these atomic clocks use magnetic fields to stabilize the frequency utilized and it would seem that these fields would most certainly be impacted by the introduction of magnetic charges. What is the nature of that impact though? Based on Professor Tiller’s work replicating (with others) his original pH experiments, if you condition one QSNET lab, then you condition them all. Based on subsequent work, he conjectured that this is a “source-driven, diffusion-fed, phase transition, both spatially and temporally dependent.” So, if you read the QSNET paper, then it could be interesting. And the cost would be negligible, given that they are collecting and analyzing data regardless. The Tiller Foundation sells IHD’s on their website for $250 but Professor Tiller gives away the schematic with instructions for use in his paper, Steps for Moving Psychoenergetics Science Research Into the Hands of Interested General Public Researchers.

And then we have this, from cosmology: New findings suggest laws of nature not as constant as previously thought.

In a paper published in prestigious journal Science Advances, scientists from UNSW Sydney reported that four new measurements of light emitted from a quasar 13 billion light years away reaffirm past studies that found tiny variations in the fine structure constant.

[“W]e found a hint that that number of the fine structure constant was different in certain regions of the universe. Not just as a function of time, but actually also in direction in the universe, which is really quite odd if it’s correct … but that’s what we found.”

This article relates directly to this one:

William Tiller, David Hestenes, and Guage Theory Gravity | by Wes Hansen | Dec, 2022 | Medium