.

Abstract. This paper is a continuation of a previous paper of the
author[1] which explains how a chemical analysis of the composition
of plain water (presence of different isotopes of O and H would not
affect the experiment), the ratio by weight of ^{16}O and ^{1}H, could
decide if the mass-energy equivalence of E=mc^{2} is verified or refuted; a
refutation would mean a full revival of the classical law of conservation
of mass without any need of mass-energy equivalence consideration.
The proposed experiment is by electrolysis of water as an aqueous
solution of potassium sulfate. Oxygen produced at the anode is trapped
while the hydrogen produced at the cathode are allowed to escape
freely. With three weighing with an analytical balance in vacuum, the
ratio of O/H could be determined with a high degree of accuracy. The
mass-energy equivalence principle accepted in present day physics may
be said to be the foundational assumption in present day physics. If it
fails, then current high energy physics would collapse. This includes the
Standard Model of particle physics widely promulgated by CERN and
much of all modern physics. The irony is that mass-energy equivalence
and the equation E=mc^{2} have never been experimentally verified. This
has been explained in detail in the author’s other paper [2].

Date: 14 Nov 2021.

Key words and phrases. Einstein, special relativity, mass energy equivalence, e=mc2, conservation of mass, Lorentz force law.

This paper is a continuation of a previous paper of the author[1] which explains
how a chemical analysis of the composition of plain water (presence of different
isotopes of O and H would not affect the experiment), the ratio by weight of
^{16}O and ^{1}H, could decide if the mass-energy equivalence of E=mc^{2} is verified or
refuted; a refutation would mean a full revival of the classical law of
conservation of mass without any need of mass-energy equivalence
consideration. The mass-energy equivalence principle accepted in present day
physics may be said to be the foundational assumption in present day physics.
If it fails, then almost all of current high energy physics would collapse. This
includes the Standard Model of particle physics widely promulgated by
CERN and much of all modern physics. The irony is that mass-energy
equivalence and the equation E=mc^{2} have never been experimentally
verified. This has been explained in detail in the author’s other paper
[2].

Currently, the mass of nuclides is determined using the Penning trap, supposedly the most precise weighing technique ever invented to measure atomic mass. The author has explained in his other paper [3] that the Penning trap is a weighing method that has not been calibrated. Whatever precision achievable with the Penning trap is irrelevant unless it has been calibrated, and calibrated with the traditional scale balance. It is an irony in mass metrology that, despite the very advanced technological achievement of our present age, there is still no substitute for this traditional scale balance as the one and only method of calibration for all other method of weighing techniques - the traditional balance scale is the standard reference for weighing mass. It is a natural constraint that physical nature has dictated concerning mass measurement. The high reputation of the Penning trap does not exempt it from the scrutiny of the humble scale balance handed down us since the time of Archimedes of ancient Greece.

In the early days when the atomic weights of elements were examined, it was
noticed that the atomic weights of elements tend towards a whole number
relative to the atom of hydrogen. This whole number rule is known as "Proust’s
hypothesis". In the early 1920s, mass spectrometry became popular and finally
accepted; atomic mass was then determined through measurement using
mass spectrometry. The atomic mass of elements as determined by mass
spectrometry was found to contradict Proust’s hypothesis; the hypothesis was
quickly dismissed. In its place, mass energy equivalence based on E=mc^{2}
became the rule. The difference in atomic mass from its whole number mass
number became accepted as a "mass defect", a defect that was introduced as
the basis of the high binding energy of the nucleus of atoms. But mass
spectrometry is all wrong simply because it assumes the Lorentz magnetic force
law: F = q(v X B) to be valid as an exact matematical relation; it is not. In fact, even the
Lorentz magnetic force law has never been experimentally verified. The so
called mass defect of nuclides is a systemic error contribution from mass
spectrometry itself. Mass spectrometry - together with the Penning trap - is
not an accurate method to measure mass of nuclides. It gives only an
approximate mass of the nuclides! The true mass of any nuclide could only be
weighed by the traditional scale balance, the same scale balance used by
Archimedes.

The analysis of the O/H composition of oxygen to hydrogen in water can be
done through the electrolysis of an aqueous solution of potassium sulfate; the
electrolysis results only in splitting the water producing oxygen and hydrogen
without changing the amount of the salt. The atomic masses of ^{16}O
and ^{1}H as found in the 2012 NIST tables are: 15.99491461957(19) and
1.00782503223(9). If the NIST values are correct, the ratio O/H should
give a value consistent with 15.87072567961(30). With our analytical
balances that could weigh to accuracy 1:10^{5}, we should be able to have
O/H to be 15.8707(2). If the classical mass conservation law is correct,
the experiment would give O/H to be 16.0000(2) as the atomic mass
of any nuclide is just the mass number in unified atomic mass unit, a
whole number. The uncertainty of 0.0002 to the difference 0.12928 is
1:650, a huge figure that may accommodate a fairly large margin for
experimental accuracy. This proposed electrolysis of water experiment could
easily be achieved with a high degree of accuracy and the result should
clearly show if the hypothesis of mass-energy equivalence is verified or
refuted.

2.1.

2.2.

- Filling the tube with an initial amount of electrolyte - The apparatus has to be filled with an initial amount of electrolyte with the upper valve closed such that no air is trapped below the upper valve. If we then weigh the apparatus, it would give the weight of the apparatus plus the electrolyte. The apparatus has to be properly cleaned for weighing. Before weighing, a small amount of machine oil is added to the open arm of the tube. The oil layer formed will prevent water evaporation during the air extraction process and also during electrolysis (the weight of this oil layer will not enter into our calculations as we only need the differences in the three weight values). The apparatus is allowed to be dried by leaving it alone for some time before weighing.
- The electrolysis - Electrolysis would begin when a sufficient dc voltage is connected to the electrodes. For every 4.6g (12cm) of water split, 4.0g (8cm at NTP) oxygen would be produced and trapped. The electrolyte level on the cathode side would dropped by about 4cm. The rate of electrolysis of water is about 3.0 amp-hr/gram. With a current of 1A, the time taken would be 14hr. When the electrolysis is completed, the apparatus is weighed. This weight is the total weight of the oxygen, the remaining amount of electrolyte and the apparatus.
- Weighing after releasing the oxygen - After the above weighing, the oxygen gas is released allowing it to escape. If the apparatus is now weighed, it would give the weight of the remaining electrolyte and the apparatus only - without the oxygen. To prevent the evaporation of water during the evacuation of the air, a thick layer of machine oil has to be added to the anode arm of the tube through the valve. The weight of oil used has to be known accurately. To do this, a small amount of oil is put into a small glass beaker and weighed. A sufficient amount of the oil is then poured through the upper valve into the tube to form a thick covering layer. The apparatus is then weighed together with the beaker with the remaining amount of oil. This weight found less the weight of the beaker of oil would give the weight of the apparatus and the remaining amount of the electrolyte.

2.3.

- w1; weight of apparatus + initial amount of electrolyte
- w2; weight of oxygen + apparatus + remaining amount of electrolyte
- w3; weight of apparatus + remaining amount of electrolyte
- w4 = w2 − w3; weight of oxygen produced
- w5 = w1 − w3 − w4; weight of hydrogen produced

The ratio by weight of oxygen to hydrogen in water is w4/w5. As there are two
atoms of hydrogen to every atom of oxygen in water, the ratio O/H of the
atomic mass of ^{16}O to that of ^{1}H is given by 2w4/w5.

The mass-energy equivalence of E=mc^{2} would be verified if the value of O/H is
found to be 15.8707(2). Otherwise, if the value is 16.0000(2), it would mean an
unequivocal repudiation of mass-energy equivalence and E=mc^{2}. Such an
experimental outcome would mean that the classical law of conservation of
mass is upheld.