Ideal

Scientists that have made observations, or have obtained their results from a calculation or a simulation want to present these findings in a figure. If you are an old-fashioned scientist you use as format a dull plot with a labeled x-axis and a labeled y-axis and a curve mapping points on these axes. If you are a young guy or girl you spicy your paper up by presenting your data in fantastically shining 3D plot (from which it is always quite difficult to extract the quantitative information contained in the plot) . Usually the labels are scaled in such a way that they show cosmetically appealing numbers like 0, 1, 2. If the labels would contain numbers like 0.645 x 10^-3 we scale the axes and report in the caption what the scaling factor is. In such a way anybody that checks the figure gets all information and could - if needed - repeat the experiment or the calculation and check his graph against the published graph.

Practice

However the practice is quite different. In the first place for many experiments the measured quantities are hardly ever observed with an absolute scale. The requirement of the use of an absolute scale would be a tremendous burden for an experimentalist. She would have to go through painstaking calibration procedures that would not bring any new insight. The solution: use of arbitrary units. In an honest account the use of arbitrary units means: all my data-points contain one unknown scaling factor. Fine, but what if the graph contains two curves with on the y-axis the same arbitrary units. Is the arbitrary scale factor for curve 1 equal to the scale factor of curve 2? The bad practice is that workers do not present that information in their paper. But, and that is the crucial point, they do know in many cases the relation between the two scale factors. And if they do not, they were lazy. Even worse, in many cases the scale factors are adjusted such that the differences between the two curves are manipulated to support the conclusion of the paper.

Verification

With the abuse of arbitrary units it becomes quite difficult to compare two experiments or two theories. The scientists that wants to compare their findings of a repeat of the experiment can adjust all his curves with adjustable scale factors and can claim agreement, whereas there maybe is no agreement at all if all the relative arbitrary units would have been published.

Arbitrary units in theory

In addition the results of theory should never have any arbitrary units at all. If they do the theorist that obtained them is irresponsible and lazy. She knows all her factors. So publish them. Theoretical results should never be scaled to get agreement with experimental data that contain arbitrary units. It should be the other way around: a theorist should scale the experimental data she found in the literature to get optimal agreement with her theory. The next worker that derives a new theory will be able to compare his new theory in an absolute way with the results of a previous theory. If both theoreticians scale their theoretical results to the experimental data they might conclude that their two theories agree, whereas the theories might differ in an abolute way by orders of magnitude.

Conclusion

Authors should be honest in the representation of data with the help of arbitrary units. In many cases only one scale factor is enough for all the different datasets in one paper.

Referees, please spot the use of relative arbitrary units and unnecessary normalization of different curves in graphs. Reject those papers

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