Facts
These are the facts the paper rests on. Each is an observation with its number and source, and the last two are calculations whose inputs are all such facts. Nothing on this page depends on the theory.
Bell correlation
- Observed
- Bell correlation between two distant readings follows the cosine of the angle difference. S was measured as 2.697 ± 0.015 (Aspect 1982), 2.73 ± 0.02 (Weihs 1998), 2.42 ± 0.20 (Hensen 2015, loopholes closed), 2.37 ± 0.09 (Yin 2017, 1,203 km).
- Sources
- Aspect 1982, Weihs 1998, Hensen 2015, Yin 2017
One end alone
- Observed
- One end alone reads +1 half the time whatever the other end is set to (every Bell test above, and the no-signalling theorem of Eberhard 1978 and Ghirardi–Rimini–Weber 1980).
- Sources
- Eberhard 1978, Ghirardi, Rimini, Weber 1980
One click at a time
- Observed
- Single particles build interference fringes one click at a time, and the click count follows the wave's intensity. Seen with electrons (Tonomura 1989, Bach 2013). C60 molecules (Arndt 1999) gave a diffraction pattern counted molecule by molecule with a scanning detector.
- Sources
- Tonomura 1989, Bach 2013, Arndt 1999
One photon, one click
- Observed
- One photon at a beam splitter does not click both detectors, α = 0.18 ± 0.06 (Grangier, Roger, Aspect 1986).
- Sources
- Grangier, Roger, Aspect 1986
720°
- Observed
- Two-valued particles return after 720°, neutrons at 716.8 ± 3.8° (Rauch 1978).
- Sources
- Rauch 1978
No fourth direction seen
- Observed
- No fourth direction of space down to 52 µm (Lee 2020). Gravitational waves spread as in D = 4.02 +0.07 −0.10 (Pardo 2018).
- Sources
- Lee 2020, Pardo 2018
Dark places
- Observed
- At a dark fringe, closing one of the two openings brings clicks there. With both open the place stays dark (Bach et al. 2013, single slit masked against both open, and Young-type experiments generally). In a Mach–Zehnder interferometer the dark port lights up when one arm is blocked (Kwiat et al., PRL 74, 4763, 1995, interaction-free measurement).
- Sources
- Bach et al. 2013, Kwiat et al. 1995
Zeros are below resolution
- Observed
- In waves of two or more dimensions, intensity goes to zero, within instrument resolution, at points or lines where the phase is not defined (Nye and Berry, Proc. R. Soc. A 336, 165, 1974, and optical vortices measured since). An instrument reads a minimum below its noise, never an exact zero.
- Sources
- Nye and Berry 1974
No medium
- Observed
- No light-carrying medium shows up. The Michelson–Morley 1887 shift was below about 0.02 of the expected 0.4 fringe, and light speed is isotropic to Δc/c below about 10⁻¹⁷ (Herrmann et al. 2009).
- Sources
- Michelson–Morley 1887, Herrmann et al. 2009
Moving water
- Observed
- Light in moving water is carried by the fraction 1 − 1/n² of the water's speed (Fizeau 1851, Michelson–Morley 1886). It follows from relativistic speed addition with no medium (Laue 1907).
- Sources
- Fizeau 1851, Michelson–Morley 1886, Laue 1907
The Bell numbers from the cosine and the clicks
- Calculated on facts
- From the one click at a time (clicks follow intensity) and the Bell correlation (the measured cosine), the Bell numbers follow with no further line. S at the CHSH angles is 2√2 times the visibility, and the visibilities read from the measured S (S / 2√2) are 0.954 (Aspect), 0.965 (Weihs), 0.856 (Hensen), 0.838 (Yin).
- Sources
- from bell correlation and one click at a time
Where a wave can be zero
- Calculated on facts
- A complex wave is zero only where two conditions hold at once (real part 0 and imaginary part 0). In a plane those places are isolated points, and in space they are lines. They are generic and stable (Nye and Berry 1974). Points and lines have no area or volume, so the chance that a click lands exactly on one is zero. A zero can exist in the description and still never be read.
- Sources
- Nye and Berry 1974