Illustrated Physics
physics, drawn
Concept

Fine tuning — where it appears

A situation in which a measured quantity requires large contributions to cancel to many decimal places with no mechanism enforcing the cancellation. The Higgs mass needs thirty-two places against a Planck cutoff and the vacuum energy needs a hundred and twenty, and both are taken as evidence of something missing rather than as contradictions.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The one prediction the Planck scale makes. The energy density the vacuum should have, from summing the zero-point energy of a field's modes up to a cutoff, against where that cutoff is put — thirty decades of cutoff energy and a hundred and thirty of density, both logarithmic. The horizontal line is what is measured: 5.34e-10 joules per cubic metre, the dark energy that accounts for sixty-nine per cent of the universe. Cutting the sum off at the Planck energy — which is where dimensional analysis says every description available runs out — overshoots it by 10^121. That is the largest disagreement between an estimate and a measurement anywhere in physics, and the slope of the line is why it cannot be argued away: the density goes as the fourth power of the cutoff, so cutting off at the electroweak scale still overshoots by 10^54 and cutting off at one electronvolt — below which no physics is in doubt at all — still overshoots by 10^8. The cutoff that would give the right answer is 8.0e-3 electronvolts, which is a wavelength of about a tenth of a millimetre and corresponds to no known physics whatever.

The estimate that misses by a hundred and twenty

Every argument about the Planck scale is an argument about consistency rather than about data, with one exception. The zero-point energy of the quantum fields gravitates, dimensional analysis at the Planck cutoff says how much, and what is measured is 10¹²¹ times smaller. It is the largest disagreement between an estimate and a measurement anywhere in physics, and lowering the cutoff does not rescue it.

astrophysics · Planck scale How large the hidden dimensions would have to be. The size extra dimensions would need, for gravity's true scale to be at a TeV rather than at 10¹⁹ GeV, against how many of them there are — a logarithmic axis of metres, for three choices of the true scale. The relation is the one that makes the arrangement work: the Planck mass observed in four dimensions is M_*^(2+n)Rⁿ, so gravity is weak because its field spreads into a volume nothing else can enter. Solved for R at a true scale of a TeV: 1 dimension needs 2.9e+13 m, 2 dimensions needs 2.4e-3 m, 3 dimensions needs 1.0e-8 m, 4 dimensions needs 2.2e-11 m, 5 dimensions needs 5.4e-13 m, 6 dimensions needs 4.5e-14 m. The two horizontal lines are where experiment has been. One extra dimension would have to be of order a hundred astronomical units, which would have wrecked the orbits of the planets and is excluded absolutely. Two would have to be of order a millimetre — which is what made the arrangement famous, because a millimetre is a distance a laboratory can test, and torsion balances have since verified the inverse-square law down to fifty-two micrometres and excluded it. Three or more sit below a nanometre, where no gravitational measurement reaches, and are untouched.

The scale that may not be where it looks

Every Planck number assumes gravity is four-dimensional all the way down. If it is not — if the field spreads into dimensions compact enough to have escaped notice — the true scale where gravity becomes strong could be at a TeV, and the whole remoteness of the Planck scale would be an artefact of where the field lines go. It is the one part of the subject an experiment can address, and the experiments have addressed it.

astrophysics · Planck scale

Named alongside it

The objects these essays reach for when they reach for this one.

Dimensional analysisEnergyPlanck scaleQuantum gravityBlack holeBlackbodyCosmological constantExtra dimensionsGravitationMeasurementScatteringThe second law

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