Abstract
The standard model of particle physics is remarkably successful because it is consistent with (almost) all experimental results. However, it fails to explain dark matter, dark energy and the imbalance between matter and antimatter in the Universe. Because discrepancies between standard-model predictions and experimental observations may provide evidence of new physics, an accurate evaluation of these predictions requires highly precise values of the fundamental physical constants. Among them, the fine-structure constant α is of particular importance because it sets the strength of the electromagnetic interaction between light and charged elementary particles, such as the electron and the muon. Here we use matter-wave interferometry to measure the recoil velocity of a rubidium atom that absorbs a photon, and determine the fine-structure constant α−1 = 137.035999206(11) with a relative accuracy of 81 parts per trillion. The accuracy of eleven digits in α leads to an electron g factor1,2—the most precise prediction of the standard model—that has a greatly reduced uncertainty. Our value of the fine-structure constant differs by more than 5 standard deviations from the best available result from caesium recoil measurements3. Our result modifies the constraints on possible candidate dark-matter particles proposed to explain the anomalous decays of excited states of 8Be nuclei4 and paves the way for testing the discrepancy observed in the magnetic moment anomaly of the muon5 in the electron sector6.
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Data availability
The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.
Code availability
The experimental data were analysed using a self-written analysis script, which is available from the corresponding author on reasonable request.
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Acknowledgements
This work was supported by the US National Institute of Standards and Technology (NIST) Precision Measurement Grant Program under award number 60NANB16D271 and by the LABEX Cluster of Excellence FIRST-TF (ANR-10-LABX-48-01), within the Programme investissements d’avenir operated by the French National Research Agency (ANR). We are particularly grateful to R. Jannin and C. Courvoisier, who participated actively to the construction of the experimental setup, which was initially funded by the ANR, INAQED Project number ANR-12-JS04-0009.
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The experiment was performed by L.M., Y.Z., P.C. and S.G.-K. The data were analysed by L.M., P.C. and S.G.-K. The main text was written by S.G.-K. and the Methods section by L.M. and P.C. All authors discussed and approved the data as well as the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Laser beam setup and detection.
a, Vacuum cell and laser beams used for the Raman transition and Bloch oscillations. b, Detection setup consisting of three horizontal retro-reflected light sheets, through which the atoms fall successively. The thick red line represents the probe beams of circular polarization, which are resonant with the atoms in the state |F = 2⟩. The black line represents the beam that repumps atoms from |F = 1⟩ to |F = 2⟩. c, Light pulse sequence implemented for the measurement protocol. Shown are the temporal variables used in Methods.
Extended Data Fig. 2 Control of the laser beam alignment and the magnetic field.
a, Distributions of the shot-to-shot variations of the auto-alignment procedure for mirrors M1 and M2 (see Extended Data Fig. 1a). b, Scatter plot of the contrast with respect to the sweep rate of the piezoelectric transducer of the mirror mounts (M2) for a 700-ms-long interferometer. c, Raw determinations of integrated h/m with and without Earth rotation compensation. Each point correspond to 400 sets of four spectra. The total interrogation time is 60 h. d, Blue: measured magnetic field, obtained by measuring the resonance of the magnetically sensitive |F = 1, mF = 1⟩ → |F = 2, mF = −1⟩ transition. Orange: interpolation used for the modelling of the systematic effect. e, Allan deviation of the frequency measurement.
Extended Data Fig. 3 Frequency control of Raman lasers.
a, Raman phase-lock system. Top left: laser arrangement used to extract a beat note between the two lasers. Bottom left: radio-frequency chain for the phase lock. Right: setup used for the measurement of the phase between the two lasers. NKT, fibre laser from NKT photonics; RIO, diode laser from RIO lasers; EDFA, erbium-doped fiber amplifier; SHG-PPLN, second-harmonic generation using a periodic crystal; AOM, acousto-optic modulator; PID, proportional-integral-derivative controller. b, Frequency of the radio-frequency generator of the PLL for each Raman direction (red and blue lines). ωC is changed with the Raman direction (right) to obtain symmetrized ramps. c, Average interferometric phase with respect to the average correction deduced from the phase of the beat note.
Extended Data Fig. 4 Analysis of the effect of local fluctuations on laser intensity.
a, Typical intensity profile of the laser beam. b, Characterization of the short-scale noise on the beam intensity. The intensity of the laser used for Bloch oscillations is reduced, leading to losses of atoms in the experiment (bottom). This induces a systematic effect on the recoil measurement (upper). To match the experimental data with the Monte Carlo simulation results, we added a small noise (2% at a scale of 50 μm) to the pictures recorded with a camera. c, Correction from the intensity profile calculated for each configuration. Only independent uncertainties are displayed, obtained from the Monte Carlo simulation. d, Results of the Monte Carlo simulation for the estimation of the effect of the one-photon light shift for different initial velocity and Raman inversion compensation (orange points: perfect compensation; blue and green points: one-photon light shift is 20% greater for one or the other Raman direction). The simulation was performed for all interferometer configurations (top: Raman high power; bottom: Raman low power) and different (TR, NB, τB) values (from left to right).
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Morel, L., Yao, Z., Cladé, P. et al. Determination of the fine-structure constant with an accuracy of 81 parts per trillion. Nature 588, 61–65 (2020). https://doi.org/10.1038/s41586-020-2964-7
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DOI: https://doi.org/10.1038/s41586-020-2964-7
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Xinhang Shen
Dear Léo Morel, Zhibin Yao, Pierre Cladé & Saïda Guellati-Khélifa,
It seems that you still don't know that Einstein's relativity has already been disproved both experimentally and theoretically. That's why you are still claiming "The standard model of particle physics is remarkably successful" which is based on special relativity.
The most reliable and well-known experimental evidence to disprove special relativity is that time is absolute as shown by all the atomic clocks on the GPS satellites which are synchronized not only relative to the ground clocks but also to one another (see "GPS" on Wikipedia), while special relativity tells us that time is relative and thus clocks can never be synchronized relative to more than one inertial reference frames no matter how you correct them.
Now let me show you the fatal error of special relativity theoretically. Special relativity postulates that the speed of light should be the same relative to all inertial reference frames, which forces the change of the definition of space and time through Lorentz Transformation. But it never verifies that the newly defined time is still the physical time measured with physical clocks. Please be aware that our physical time i.e. clock time won’t change with the change of the definition of the space and time. Actually, the newly defined relativistic time is indeed not the time measured with physical clocks any longer. It is just a mathematical variable without physical meaning.
We know a clock records the effect of time such as the angle of the arm or the number of cycles, etc, and then uses this recorded change to indirectly calculate the elapsed time. That is, our physical time T has a relationship with the theoretical time t in mechanics:
T = tf/k
where f is the frequency of the clock and k is a calibration constant. In Newtonian Mechanics, f is a reference frame independent constant and we can set k=f to make the clock to record the frame independent Galilean absolute time:
T = tf/k = tf/f = t
which also confirms that our physical time T is absolute too.
But in special relativity, the theoretical time becomes relativistic time t which is relative to the reference frame to make the frequency f reference frame dependent. Now I would like to use the behavior of our physical time in Lorentz Transformation to demonstrate that the relativistic time t defined by Lorentz Transformation is no longer our physical time T.
If you have a clock (clock 1) with you and watch my clock (clock 2) in motion and both clocks are set to be synchronized to show the same physical time T relative to your inertial reference frame at relativistic time t, you will see your clock time:
T1 = tf1/k1 = T
and my clock time:
T2 = tf2/k2 = T
where t is the relativistic time of your reference frame, f1 and f2 are the relativistic frequencies of clock 1 and clock 2 respectively, k1 and k2 are calibration constants of the clocks.
The two events:
(Clock1, T1=T, x1=0, y1=0, z1=0, t1=t)
(Clock2, T2=T, x2=vt, y2=0, z2=0, t2=t)
are simultaneous measured with both relativistic time t (i.e. t1=t2=t) and clock time T (i.e. T1=T2=T) in your reference frame. When these two clocks are observed by me in the moving inertial reference frame, according to special relativity, we can use Lorentz Transformation to get the events in my frame (x', y', z', t'):
(clock1, T1', x1'=-vt1', y1'=0, z1'=0, t1'=γt)
(clock2, T2', x2'=0, y2'=0, z2'=0, t2'=t/γ)
where
T1' = t1'f1'/k1 = (γt)(f1/γ)/k1 = tf1/k1 = T1 = T
T2' = t2'f2'/k2 = (t/γ)(γf2)/k2 = tf2/k2 = T2 = T
γ = 1/sqrt(1-v^2/c^2)
We can see that no matter observed from which inertial reference frame, the events are still simultaneous measured with physical time:
T1 = T2 = T1' = T2' = T
i.e., the two clocks are always synchronized measured with physical time T, but no longer synchronized measured with relativistic time t':
t1' != t2'
which means that our physical time and the relativistic time behave differently in Lorentz Transformation and thus they are not the same thing. The change of the reference frame only makes changes of the relativistic time from t to t' and the relativistic frequency from f to f', which cancel each other in the formula:
T = tf/k
to make the physical time T unchanged i.e. our physical time is still absolute in special relativity. Thus, relativistic time is not our physical time, but a mathematical variable without physical meaning. Based on such a meaningless time, special relativity is wrong, and thus all relativity based theories including the Standard Model of Particle Physics are wrong.
What do you think? If you don't agree, please leave your refutation here and I will be glad to have a debate with you. Science is serious which should never tolerate any known mistake!
For more information, please check
https://www.researchgate.ne...
https://www.researchgate.ne...
Regards,
Xinhang Shen
Charles Binns Replied to Xinhang Shen
I have a TOE on my FB page. Please help solve the puzzle (If Possible.)https://www.facebook.com/Th...
Marcel-Marie LeBel
“our result modifies the limits on a possible substructure within the electron”. In QM, there is no provision for the existence of little balls with electric E- tinsel stuck to it. The electron 4 electrical (unit) E- lines are generated by the corresponding unit pair (2) of opposite magnetic monopoles under h/2. Above h/2 the charge is positive. Forget the little balls … It’s all waves... and the electron has an electric field lines generating substructure... Let's recap; the unit electric charge implies a unit magnetic charge. Where do you find this unit magnetic charge? At the end (source) of the electric unit charge!
In other words, it was good to find by deduction the symmetry of category between a unit electric charge and a unit magnetic charge. Now, to realize the concept of a unit magnetic charge, .i.e, to move it from a category to something real, we have to admit the causal link between the two, the production of one by the other, by induction.
Luis Reis
How many decimal places do we need to consider on calculus and work related to fine structure constant (for example on Pi)? Thank you.
TEJINDER PAL SINGH
This result above is a beautiful experimental result. It makes even more urgent the issue of origin of the limiting low energy value of the FSC. Several theorists over the years have of course pondered over this. It could well be that this question can only be answered after unifying electromagnetism with other interactions:
A first principles derivation of the low energy value of the fine structure constant from generalised trace dynamics and the algebra of the octonions (the exceptional Jordan algebra).
January 2021
Time is a classical concept, external to quantum theory. There ought to exist a reformulation of quantum theory which does not depend on classical time. Such a theory is a prequantum prespacetime theory, and has been developed as a matrix valued Lagrangian dynamics, building on Stephen Adler's trace dynamics and Alain Connes' noncommutative geometry. The definition of spin forces this theory to be formulated in eight noncommutative octonionic dimensions, where it becomes a theory of unification of the four fundamental interactions, the symmetry group being the exceptional Lie group F4. F4 is also the automorphism group of the exceptional Jordan algebra, and the fundamental constants arise from the eigenvalues of the cubic characteristic equation of this algebra. In particular, the Lagrangian of the theory, along with the eigenvalues of this algebra, leads to a derivation of the exact value of the low energy limit of the fine structure constant!
https://www.researchgate.ne...