.

ABSTRACT. Despite E= mc^{2} being a foundational equation of
modern physics, it has not been experimentally verified. Though
four eminent physicists claimed ‘A direct test of E=mc2’ (Nature
2006) giving verification accurate to 1:10^{6}, the experiment
was not any verification of E=mc^{2}, but rather an alternative
experiment to deduce the mass of the neutron. Instead of the
usual deuteron interaction, they used the nuclear interaction
involving sulfur ^{32}S and silicon ^{28}Si. The claim of accuracy of
1:10^{6} is about the comparison of the new value with the accepted
value of the mass of the neutron. This paper shows that a
chemical analysis (with a good analytical balance) of the mass
composition of oxygen and hydrogen in plain distilled water may
show that the law of conservation of mass is universally valid
without the need for the hypothesis of mass-energy equivalence;
this would also imply an unequivocal refutation of the equation
E=mc^{2}. Such an experiment could easily be carried out by
any laboratory in today’s universities. The experiment should be
simple and straightforward, yet its outcome may have enormous
consequences for the world of physics.

Date: 17 December 2019.

Key words and phrases. mass spectrometry, Penning trap, Einstein, special relativity, atomic mass, Prout’s hypothesis, law of mass conservation, mass-energy equivalence, E=mc2.

It may be said that the equation E=mc^{2} is the most important equation in
all of physics. This equation is the basis of the principle of mass-energy
equivalence. It also leads to the energy momentum equation of relativistic
mechanics E^{2}=(pc)^{2}+(m_{
0}c^{2})^{2} which underlies the foundation of modern
high energy physics including the particle physics of the Standard
Model and all of nuclear physics. If these equations fail, then the
hypothesis of mass-energy equivalence too would be invalidated and the
whole of modern physics would collapse. Such a scenario is beyond
imagination.

The equation E=mc^{2} is well known. It seems to have been fully
accepted with no one interested ever to raise any doubts about its validity.
What is not well known is that the equation has not been experimentally
verified. The author has a paper [1] which elaborates on this issue. This is
despite a group of four eminent physicists who claimed to have
done a ‘A direct test of E=mc2’ (Nature magazine 2006) [2] which
gives it an accuracy close to 1:10^{6}. I think the experiment would
by now be an embarrassment to the physicists involved as - for
whatever reasons - they misinterpreted the very experiment which they
set up. The experiment was never anything close to any test of
E=mc^{2}. It was just another experiment to deduce the mass of the
neutron relying on the very principle of mass-energy equivalence.
There is an accepted deduced mass of the neutron based on the
binding energy involving the deuteron. What the new experiment
did was to use an alternative nuclear interaction instead of the
usual deuteron interaction. They use neutron capture by sulfur
^{32}S and silicon ^{28}Si and then deduced the neutron mass through
computations involving the binding energies. The accuracy obtained of
‘one-part-per-million’ is the accuracy of their new deduced neutron mass as
compared to that of the accepted value - nothing at all about verifying
E=mc^{2} accurate to one part per million. The current situation is that
Einstein’s special relativity and E=mc^{2} have been fully incorporated
into modern physics despite the equation being not experimentally
verified. This issue should be of the utmost of concern to the physics
community.

In the 19th century, the early chemists who studied the chemical
composition of compounds found some patterns regarding the atomic
mass of the elements. Atoms have masses that are close to whole numbers
as compared to the atomic mass of hydrogen. The English chemist William
Prout in 1815 and 1816 published papers that proposed the ‘Prout’s
hypothesis’, that elements are composed of whole numbers of atomic
hydrogen as the basic constituent. This imply that the atomic mass of
elements would be whole numbers as measured in our current unified
atomic mass units. This would be consistent with the law of mass
conservation, that mass cannot be created nor destroyed. All these
changed after Einstein introduced special relativity in 1906 which lead to
the equation E=mc^{2} and the principle of mass-energy equivalence. The
notion of mass-energy equivalence eventually gained full acceptance. This
happened after the invention of mass spectrometry which became the
principle technique to measure atomic mass replacing the traditional
chemical method using the scale balance. Today - for whatever reasons
- the chemical method to measure atomic mass has been totally
abandoned.

The author in his paper [3] has shown that mass spectrometry cannot
measure atomic mass accurately. The US NIST (National Institute Of
Standards And Technology) database of atomic masses are all measured
experimentally with the Penning trap, an instrument based on mass
spectrometry. The Penning trap is touted as a most advanced instrument
capable of the highest precision ever for measurement of atomic mass; it
claimed a precision as high as 1:10^{10}; but precision is not the same as
accuracy.

The Penning trap is designed based on the Lorentz magnetic force law
and it assumes that the law is an exact mathematical relation which it is
not. The Lorentz magnetic force law is only an approximate law. What
mass measurements which the Penning trap gives are not true atomic
mass, but approximate predictions of atomic mass based on the
Lorentz magnetic force. The measurements made would differ by a
slight amount from the mass number of an atom - a whole number.
This slight difference in mass came to accepted to be correct and
was referred to as ‘mass defects’ of atoms. It is these mass defects
which is the cause of violation of mass conservation in nuclear
interactions - mass could be ‘lost’ in nuclear interactions. The huge
amount of energy released in nuclear fission was then ascribed
to the conversion of the ‘mass loss’ to energy using the equation
E=mc^{2}. With mass-energy equivalence being fully accepted, the law of
conservation of mass was deemed to have been refuted. In its place, the
conservation law has been extended to a law of mass-energy conservation.
The author has a paper [4] which argues that mass conservation
without mass-energy equivalence is the correct universal conservation
law.

It is difficult to directly verify the validity of E=mc^{2}, but we know that
mass-energy equivalence as implied by the equation means a refutation of
the law of mass conservation. Mass conservation and mass-energy
equivalence are mutually contradictory - only one of them could be valid,
not both. This fact could be used in experiments designed to investigate
the validity of E=mc^{2}.

2.1. Mass Ratio Of Oxygen/Hydrogen In Water.

Water has the formula H_{2}O. If water is formed from the isotopes ^{16}O and
^{1}H, the mass ratio of O/H in this water could be found by chemical
analysis of its mass composition. The atomic masses of ^{16}O and ^{1}H
as found in the 2012 NIST tables are: 15.99491461957(19) and
1.00782503223(9) (the figures in the brackets represent the error in
the last digits). If the atomic masses as given in the NIST tables
are correct (measured using the Penning trap), then a chemical
analysis of the mass ratio of O/H should give a value consistent with:
15.99491461957/1.00782503223 or 15.87072567961(30). The analytical
balances of today are capable of measuring mass with an accuracy of
1:10^{5} for some mass range. If the NIST masses are correct, then the
experiment should give a figure of about: 15.87072(15) for accuracy of
1:10^{5}. If the law of mass conservation is the correct universal conservation
law, then the atomic mass of any nuclide is simply its mass number in
unified atomic unit - a whole number (there is not even a need to do any
measurement for atomic mass). In this case, the analysis of the mass
composition of the water as above should give a figure of about:
16.00000(16).

So the experimental result of the experiment as above would give either
one of the two values: 15.87072(15) or 16.00000(16). Without fail, a
good analytical balance could easily distinguish between the two values
which have a relatively huge difference of 0.12928. If the experimental
result gives the ratio of O/H to be 16.00000(16), it would be an
unequivocal verification that the law of mass conservation is correct.
As mass conservation and mass-energy equivalence are mutually
contradictory, it would mean an unequivocal refutation of mass-energy
equivalence and the equation E=mc^{2}. On the other hand, if the resulting
figure were to be 15.87072(15), it would be a clear refutation of the
law of mass conservation. In this case, the experiment would be a
validation of the NIST values of atomic masses for precision of
1:10^{5}. This experimental result would still not be an experimental
verification of the equation E=mc^{2}. The equation would still remain
unverified.

Although the above experiment is for chemical analysis of water formed
from pure isotopes of ^{16}O and ^{1}H, using plain distilled water would not
make any difference to the experiment. Oxygen in nature has three stable
isotopes: ^{16}O 99.76%, ^{17}O 0.04% and ^{18}O 0.2%. For hydrogen, it has two
stable isotopes: ^{1}H 99.98% and deuterium ^{2}H 0.02%. We may assume that
ordinary water has the pure isotope ^{16}O and hydrogen having the natural
composition of ^{1}H 99.98% and deuterium 0.02%. The O/H ratio for this
would be 16/(1*0.9998+2*0.0002) or 15.99680. The difference
between 16.00000 and 15.99680 is insignificant for the purpose of our
experiment.

Physics experiments of today often require funding going into the millions of dollars and even billions for some major experiments. The chemical analysis of distilled water to determine the oxygen and hydrogen composition by mass using an analytical balance should be a fairly straightforward experiment. Most laboratories in today’s universities would not have difficulty to perform such a simple experiment - a simplest of experiment by today’s standards, yet one which may have an outcome with enormous consequences in the world of physics.

[1] Chan Rasjid Kah Chew. Mass Energy Equivalence Not Experimentally Verified. http://vixra.org/abs/1810.0003.

[2] Simon Rainville, Maynard Dewey, H.G. Borner, M. Jentschel. World Year of Physics: A direct test of E=mc2. Nature 2006. DOI: 10.1038/4381096a

[3] Chan Rasjid Kah Chew. Is Mass Spectrometry Accurate? http://vixra.org/abs/1809.0491.

[4] Chan Rasjid Kah Chew. Coulomb Electric Gravity And A Simple Unified Theory (SUT). http://vixra.org/abs/1808.0211.

Email address: chanrasjid@gmail.com

URL: http://www.emc2fails.com

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