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Proton Mass Calculations

The mass of a proton has only been calculated to an accuracy of around 4% - (roughly 938 MeV/c2 or 1.672 × 10-27 kg). The constituent particles - quarks and gluons - which make up the proton, have individual masses that add up to only around 1% or so of its measured mass (which can be determined accurately with specialised devices called Penning traps see: Phys. Rev. Lett.open access 119, 033001)

In order to explain the missing 99%, the constituent particles are thought to be 'vibrating' (and otherwise interacting) at near light-speed - which, because of relativistic effects, increases their apparent mass (plus the interaction-energy of the strong nuclear forces that hold the proton together).

The picture is further complicated by the fact that protons (and neutrons) have (on average) three quarks each. Because they are in constant 'motion', calculating the forces between them invokes the classic 'Three Body Problem'.

In order to simplify the calculations, researchers instead work on the basis that the quarks are in pairs - called 'diquarks'. This is a known oversimplification. Even so, the calculations are so complex that supercomputers are needed. And the accuracy of the calculations still has a 4% error margin.

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Note that a similar lack of precision affects calculations of the mass of neutrons, which also have three quarks.

Note :

Since most of the mass of (ordinary) matter comes from the protons and neutrons which it contains, it follows that somewhere around 99% of the mass of all matter is derived from relativistic (i.e. near lightspeed) effects.

Also see : Proton radius puzzleplugin-autotooltip__plain plugin-autotooltip_bigProton radius puzzle

Until 2010, measurements (backed up by theory) had put the radius of the proton at about 0.87 femtometres, but in that year, experiments at the Max Planck Institute of Quantum Optics in Germany found a 4% discrepancy.

And in 2016, new experiments - measuring the size of the deuteron (one neutron plus one proton) found an 0.8% discrepancy.
and The Proton Spin Crisisplugin-autotooltip__plain plugin-autotooltip_bigThe Proton Spin Crisis

'Spin' is an intrinsic property of many subatomic particles - it's been likened in some ways to the 'angular momentum' of a spinning ball, - but more accurately is a mathematical 'vector' or 'property'.

After the discovery that protons are composed of three
and Proton structureplugin-autotooltip__plain plugin-autotooltip_bigProton structure

The 'textbook' explanation for the structure of the proton is that it's a 'state' of two up quarks and one down quark bound by gluons, But it has been known for 40 years or so that this is an over-simplification. According to accepted quantum theory, there should also be infinite varying probabilities for the inclusion of quark–antiquark pairs.

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