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Experiments have not found a permanent electric dipole moment for the electron. In the shorthand used by physicists, that makes the electron spherical to the precision of current measurements—not a photographed geometric sphere, but a particle whose spin-aligned charge asymmetry is consistent with zero.

The strongest numerical limit in the measurements discussed here is |dₑ| < 4.1 × 10⁻³⁰ e·cm at 90% confidence, reported in 2023 with trapped molecular ions. That null result is important because a nonzero electron electric dipole moment would violate parity and time-reversal symmetries and would signal a source of CP violation beyond the simplest Standard Model picture.

What “spherical electron” means in physics

An electron is an elementary particle, not a tiny solid ball with a surface that an instrument can photograph. Its apparent “shape” is inferred from how its electric charge is distributed relative to its angular momentum, or spin. The relevant quantity is the permanent electron electric dipole moment, written dₑ.

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A dipole consists of equal and opposite charges separated by a distance. If an electron had a permanent electric dipole aligned with its spin, reversing the spin relative to an electric field would change the particle’s energy. That orientation-dependent energy would be evidence that the electron has a minute preferred direction—an asymmetry described conversationally as a departure from perfect roundness.

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Experiments therefore do not test a literal radius or outline. They measure whether the electron’s spin precesses, or whether the energy of a spin state changes, when electric fields and molecular orientations are reversed. A result statistically compatible with zero sets an upper limit on how large dₑ could be.

The 2011 YbF experiment summarized its result by saying that it “indicates that the electron is spherical at this improved level of precision.” The qualification matters: “spherical” means no detectable dipole within the experiment’s uncertainty, not proof of an exact mathematical sphere at every possible scale.

Why an electric dipole would reveal asymmetry

The interaction between an electric dipole and an applied electric field can be represented schematically as:

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ΔE = −dₑ · E

Here, the energy shift depends on the relative direction of the dipole and field. For an electron whose dipole is tied to its spin, the sign of the shift changes when the spin direction is reversed relative to the field. The expected effect is extraordinarily small, so the experiment must compare two otherwise identical configurations and search for a reproducible difference.

A permanent electron EDM has unusual symmetry consequences. Under a parity transformation, ordinary spatial directions are inverted; under time reversal, angular momenta and motions reverse. A spin-aligned permanent EDM violates both parity (P) and time-reversal (T) symmetry. Assuming the CPT theorem, a T-violating EDM also implies CP violation. That connection makes EDM measurements a precision test for new sources of CP violation, one of the places where theories beyond the Standard Model might appear.

A null result does not show that all new physics is absent. It rules out, or tightly restricts, models that predict an electron EDM larger than the measured limit. Models can survive if their predicted EDM is below the experimental sensitivity or if different contributions cancel.

How the experiments look for the signal

Prepare a controlled spin state

Researchers first create atoms or molecules in well-defined quantum states. The electron spin is prepared so that its precession can be read out optically or through another state-sensitive measurement. The apparatus then lets the state evolve for a controlled time in an electric field.

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Reverse the field and molecular orientation

The key comparison is a reversal. If an EDM is present, changing the direction of the effective electric field relative to the spin should change the phase or energy. Reversing magnetic fields, molecular polarization, and spin state in carefully chosen combinations helps distinguish a true EDM signal from effects caused by magnetic-field drifts, stray fields, imperfect alignment, or detector changes.

Measure a phase or precession difference

After the interrogation period, the experiment reads the spin state, often through laser-induced fluorescence. The measured quantity is a small phase, frequency, or population difference between the reversed configurations. Repeating the cycle many times reduces statistical uncertainty; independent reversal patterns and calibration data are used to identify systematic errors.

Why molecules make the tiny effect measurable

Molecular systems provide two major advantages. Heavy polar molecules can generate a very large effective internal electric field at the electron, amplifying the energy shift associated with a given EDM. They also offer closely spaced quantum levels and controllable orientation states that make reversals and interference measurements practical.

The ACME experiments use thorium monoxide (ThO) in a cryogenic molecular beam. A Johns Hopkins University description of the platform gives an effective ThO internal field of approximately 75 GV/cm. This is an internal effective field used to amplify the EDM interaction, not a claim that a laboratory has produced a uniform external field of that magnitude.

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The 2023 molecular-ion experiment used trapped ions instead of a beam. Trapping lets the molecules remain under observation much longer; the report describes coherent evolution for up to three seconds. Longer coherent evolution can increase sensitivity because a small EDM-induced phase has more time to accumulate, although maintaining coherence and suppressing systematic shifts becomes correspondingly demanding.

What the major measurements found

The following results are separate experiments performed with different molecules, apparatuses, dates, and statistical and systematic controls. Their limits should not be treated as interchangeable readings from one continuously upgraded instrument.

Experiment Platform Reported result What it established
Hudson and colleagues, 2011 YbF molecular beam Measured value: (−2.4 ± 5.7stat ± 1.5syst) × 10⁻²⁸ e·cm; 90% confidence bound: |dₑ| < 10.5 × 10⁻²⁸ e·cm A result consistent with zero and a substantially improved bound for that time
ACME II, 2018 ThO cryogenic molecular beam |dₑ| < 1.1 × 10⁻²⁹ e·cm A tighter limit using a polarized molecular beam and strong effective internal field
Roussy and colleagues, reported in 2023 Trapped molecular ions Measured value: (−1.3 ± 2.0stat ± 0.6syst) × 10⁻³⁰ e·cm; 90% confidence bound: |dₑ| < 4.1 × 10⁻³⁰ e·cm A null result and an improvement of about 2.4 times over the previous best bound; coherent evolution reached up to three seconds
ACME III, 2024 conference abstract Planned upgraded ThO apparatus No new EDM bound reported; the upgrades were projected collectively to improve statistical sensitivity by an order of magnitude An apparatus-development projection, not a completed measurement

The 2023 molecular-ion publication is the latest numerical bound in this timeline. The 2024 ACME III report describes planned or integrated hardware and a projected sensitivity gain, so it should not be quoted as a new electron-EDM limit.

How to read an EDM limit correctly

The central value can be nonzero without being a detection

The 2023 result has a central value of −1.3 × 10⁻³⁰ e·cm, but its statistical and systematic uncertainties are larger than that offset. Because zero lies within the allowed range, the result is consistent with no EDM. A central value by itself is not evidence of a discovery.

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A 90% confidence bound is an upper limit

The statement |dₑ| < 4.1 × 10⁻³⁰ e·cm at 90% confidence means the analysis restricts the magnitude of the EDM to values below that threshold under the experiment’s statistical model and treatment of uncertainties. It does not mean there is a 90% probability that the electron has a dipole somewhere below the number in a simple frequency sense, nor does it establish that the true value is exactly zero.

Statistical and systematic errors are different

Statistical uncertainty shrinks when more independent measurements are collected. Systematic uncertainty comes from effects such as imperfect field reversal, magnetic contamination, calibration errors, or uncontrolled changes in the apparatus. A longer run improves the result only if the dominant systematic effects are also understood and suppressed.

Why the null result matters for particle physics

The electron EDM is a compact way to test symmetries with extraordinary precision. Many extensions of the Standard Model introduce additional particles or interactions that can generate CP-violating effects. Those effects may also be connected to questions such as why the observable universe contains much more matter than antimatter. An EDM search does not answer the matter–antimatter question by itself, but it tests one of the symmetry violations that candidate explanations often require.

Every improvement in the EDM limit removes part of the parameter space available to such theories. A model that predicted an electron EDM above the 2011 YbF limit could survive only by changing its parameters or adding a cancellation. The 2018 ACME limit and the 2023 trapped-ion limit impose progressively tighter requirements. Conversely, a future nonzero signal would need to repeat under independent reversal patterns and in a different apparatus before it could be accepted as evidence for new physics.

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What makes the measurement difficult

  • The signal is tiny. The best bound is expressed at the 10⁻³⁰ e·cm scale, so ordinary laboratory imperfections can be larger than the effect being sought.
  • Magnetic fields can imitate an EDM. A small uncontrolled magnetic field or a change in magnetic field during reversal can shift spin precession in a way that resembles an electric-field-dependent phase.
  • Electric-field reversal is never perfectly ideal. Reversing voltage can alter electrode charging, leakage currents, molecule trajectories, or nearby magnetic materials.
  • Molecules must remain coherent and controlled. Collisions, stray light, electric-field gradients, and state leakage can shorten the useful interrogation time or bias the readout.
  • Detection itself can drift. Laser power, fluorescence collection, detector gain, and timing changes can create false differences unless they are monitored and randomized.

These problems explain why a credible result requires more than a single frequency difference. Experiments build in reversals, blind analyses, calibration runs, and consistency checks so that a putative EDM must track the electric-field orientation rather than an accidental feature of the apparatus.

What the next generation is changing

The ACME III upgrade described in a 2024 APS DAMOP abstract combines several changes: an electrostatic lens to improve molecular transport, a longer precession region, more efficient fluorescence collection, silicon photomultiplier (SiPM) detectors, and improved control of electric and magnetic fields. The team stated that these upgrades were intended collectively to increase statistical sensitivity by an order of magnitude and to suppress known systematic sources.

That wording describes an aim and an apparatus projection. It is not a claim that the projected improvement has already produced a ten-times-smaller EDM bound. A future result will have to demonstrate both the expected statistical gain and control of the systematic uncertainties that become important at higher sensitivity.

So, is the electron actually a perfect sphere?

Physics cannot establish an exact geometric sphere by pushing one measurement to a final decimal place. It can establish that any spin-aligned permanent electric dipole is smaller than a stated experimental limit. On that operational definition, the electron remains spherical to at least the precision reached by the 2023 trapped-molecular-ion measurement: no EDM was resolved, and values larger than 4.1 × 10⁻³⁰ e·cm were excluded at 90% confidence by that experiment.

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The phrase “still spherical despite efforts to prove otherwise” therefore describes a continuing experimental contest. Researchers keep improving fields, molecules, coherence times, optical readout, and statistical power because a tiny nonzero EDM would be a landmark sign of symmetry violation beyond the established framework. Until such a signal survives those tests, the measured electron remains round in the only sense these experiments can currently probe.

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