This web page is intended as a appetizer for Ground Potential Theory (GPT), intended to inspire the inquisitive reader to investigate further. The standard model of particle physics treats the electron mass as a constant; however, an as yet unproven theory predicts a small but measurable upwards drift of the electron mass. Below is a brief summary describing why and how one would expect the electron mass to change over time.
Every day chemical and nuclear reactions on Earth convert potential energy into kinetic energy or heat. The sum of all such reactions causes energy in the form of heat to flow into space while maintaining charge constant. The resulting change in energy per charge (E/q) means that ground potential is falling in absolute terms.
In the GPT framework the mass of isolated protons which have never undergone a chemical or nuclear reaction is treated as constant. With constant mass of 938… MeV, the isolated proton has a constant potential of about 930 MV. GPT goes further to claim that no particle has a higher energy-to-charge ratio than a proton and therefore establishes potential as absolute in the same way that \(c\) represents the absolute speed.
Earth is composed of heavy elements (mainly iron) – its mass per nucleon is lower than that of an isolated proton, because most of the elements had to go through numerous nuclear fusion reactions in order to form the elements of Earth. Each of these reactions converted potential energy into gamma rays and heat, leaving the nucleus with less mass. Earth’s surface potential is therefore the average mass per nucleon of all its isotopes.
In standard general relativity, differences in potential show up as tiny shifts in photon energies (often discussed under the heading of “gravitational redshift”). In the present GPT picture the emphasis is slightly different: the focus is on how the changing average potential of matter in and around Earth can be used as a clock for the electron mass, rather than on the detailed GR description of the metric.
The changing surface potential can therefore be measured against the absolute potential of a proton according to the following equation:
\[ a = \frac{(c-b)}{2} \sqrt{1-\frac{b^2}{c^2}}\]
Where \(a\) is the electron potential, \(c\) is the proton potential, and \(b\) is ground potential (observer’s potential).
While still unproven, recent advances in measurement accuracy have brought experimental proof within close reach.
The demonstration clock above showing the predicted mass change is based on Ground Potential Theory (GPT) . It takes the difference in potential between absolute potential and current ground potential and divides it by the current best estimate of the Universe’s age.
! The units eV are understood as the average energy per charge \(e\); by convention we can divide by \(e\) and simply express ground potential in units of volts.
* Values for constants obtained from: NIST.
Scientists are developing better and better ways to measure the electron mass with ever increasing accuracy, and their results are published by NIST every 4–5 years. The electron mass change predicted by Ground Potential Theory (GPT) is sufficient to confirm or deny the theory within a timeframe of around 5–10 years.
GPT predicts a drift rate of order \(5.9\times 10^{-5}\,\text{eV/yr}\) in the electron mass energy, large enough that it should become testable in the next CODATA evaluation. At face value this contrasts with mainstream bounds from quasar spectroscopy, where long-baseline measurements of atomic spectra typically limit variations of dimensionless constants such as the fine-structure constant \(\alpha\) to \(|\dot{\alpha}/\alpha| \lesssim 10^{-17}\,\text{yr}^{-1}\) over cosmological lookback times.
Within the GPT framework, however, such distant observations are interpreted differently: photons are taken to propagate unchanged along equipotential surfaces, with no energy loss in flight. Successful agreement between laboratory and quasar spectra then implies that source and observer share the same potential at the instant of observation, so that all such views effectively collapse to an absolute “now”. On this reading, quasar data speak more to cosmic simultaneity than to the past invariance of local ground potential. The natural arena for measurable drift is instead terrestrial: slow changes in Earth’s potential relative to the proton reference. Future precision experiments — for example, networks of atomic clocks operated at different altitudes over many years — could, in principle, discriminate between the GPT picture and the standard interpretation.
One might speculate that the birth of our Universe began with the fusion of two protons...
One might speculate that the birth of our Universe began with the fusion of two protons into deuterium – a kind of “tiny bang”. In such a picture this first fusion step would have produced a potential drop of about 465 keV in the nucleus, followed by the formation of Helium-3, Helium-4 and so on up the periodic table. As heavier elements were assembled, the rate at which potential fell would gradually have slowed. Within this framework one can imagine that ground potential today sits near the level associated with Fe-56, which is also empirically one of the most stable nuclei.
It is, however, difficult to estimate the age of the Universe from the present rate of change alone, especially given our relatively brief 21-year history of high-precision electron-mass measurements. As a crude order-of-magnitude illustration, one might take the present difference between the proton potential and ground potential (about 8 MeV) and divide it by the secular rate of change used in this clock (of order \(6\times10^{-4}\,\text{V per year}\)), which gives an age of roughly \(1.3\times10^{10}\) years, i.e. about 13.6 billion years. In this speculative scenario, ground potential today would be falling at a rate somewhere in the range \(5\times10^{-4}\) to \(5\times10^{-3}\) volts per annum.
Future CODATA evaluations from NIST may tighten the experimental bounds on any long-term drift of the electron mass (if it exists at all), so it will be interesting to see how these high-precision measurements evolve over the coming decades.
GPT theory has been developed by:
Steven Sesselmann © 2021
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Contact details via my RG profile
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| Dataset | Year | \(m_e c^2\) (MeV) | Uncertainty (MeV) | \(m_e c^2\) (eV) |
|---|---|---|---|---|
| CODATA 1998 | 1998 | 0.51099890200 | ±0.00000002100 | 510,998.90200 |
| CODATA 2002 | 2002 | 0.51099891800 | ±0.00000004400 | 510,998.91800 |
| CODATA 2006 | 2006 | 0.51099891000 | ±0.00000001300 | 510,998.91000 |
| CODATA 2010 | 2010 | 0.51099892800 | ±0.00000001100 | 510,998.92800 |
| CODATA 2014 | 2014 | 0.51099894610 | ±0.00000000310 | 510,998.94610 |
| CODATA 2018 | 2018 | 0.51099895000 | ±0.00000000015 | 510,998.95000 |
| CODATA 2022 | 2022 | 0.51099895069 | ±0.00000000016 | 510,998.95069 |
* CODATA values taken from NIST recommended data for fundamental constants.
Clock calibration note: the live display and the grey GPT line in the plot are computed from the same ingredients. We take the present-day gap between proton and ground potential, \(\Delta V_g \approx 7.894839\times10^{6}\ \text{V}\), and an assumed age of the Universe of about \(1.3\times10^{10}\) years. This fixes a very small secular fall of ground potential, \(\mathrm{d}V_g/\mathrm{d}t \approx -6.1\times10^{-4}\ \text{V/yr}\). The GPT relation \(a(b) = \frac{(c-b)}{2}\sqrt{1-\frac{b^2}{c^2}}\) then converts this into an electron drift \(\mathrm{d}V_e/\mathrm{d}t \approx 5.9\times10^{-5}\ \text{eV/yr}\) via the local slope \(\partial a/\partial b \approx -0.097\). Both the scrolling numbers at the top of the page and the straight GPT prediction line are anchored to the latest CODATA value (2018/2022) and use these same slopes, so the narrative of the plot and the clock is consistent.
In this demonstration the straight line drawn through the most recent CODATA value is not an empirical fit but a theoretical prediction from Ground Potential Theory. Starting from the relation
\[ a(b) = \frac{(c-b)}{2}\sqrt{1-\frac{b^2}{c^2}} \]
with \(c = V_p\) the proton potential and \(b = V_g\) the ground potential, we can evaluate the local response of the electron mass energy \(a = V_e\) to a small change in ground potential. Around today’s values this gives an approximately constant slope
\[ \frac{\partial a}{\partial b} \approx -0.097\ \frac{\text{eV}_e}{\text{eV}_g}, \]
which means that every 1 V drop in ground potential raises the electron mass energy by about 0.097 eV. If we assume that ground potential is falling at roughly \(\Delta V_g \approx -0.0005\ \text{V per year}\), the predicted drift in the electron mass is
\[ \Delta V_e \approx -0.097\,\Delta V_g \approx 4.9\times 10^{-5}\ \text{eV per year}. \]
On the plot this appears as a very gentle straight “GPT prediction” line, starting at the latest CODATA value and extending forwards and backwards in time, with the flashing dot marking the next CODATA epoch. In this framework \(\partial a/\partial b\) is fixed by the geometry of the potential, so any difference between the measured long-term drift of \(m_e c^2\) and this predicted slope does not invalidate the formula but instead implies that our assumed age of the Universe needs to be reconsidered.