How would the 'levels that are of health concern' be determined in the first place if instruments/methods required to reliably measure such levels don't exist? If you can't measure it, how do you know it's there? Would its presence be inferred somehow? I'm not trying to argue, just to understand.
Because levels of concern are typically derived from animal tests that produce No Observed Adverse Effect Levels (NOAELs) and Lowest Observed Adverse Effect Levels (LOAELs). These are typically determined in either mass/animal body weight or normalized for dosing schedules, which puts these study values in units of mg of contaminant per kg of animal body weight per day.
From there, one can use typical exposure factors, such as mean adult body weight and mean consumption rate to convert the dose associated with adverse health effects in a toxicological study to a level of concern for humans for water consumption, or food ingestion, or air inhalation, etc. This process involves the use of Safety Factors; these can often reduce the levels used in a toxicological study to up to three orders of magnitude difference in the data found in the tox study to the level that may be protective of human health.
So, even if an analytical method exists for quantifying chemicals in mammalian tissues, there's no certainty that a method of equal sensitivity exists for beef consumption or consumption of whatever else we might be interested in. Couple this with the safety factors that are use to derive a "safe" level, and the disconnect may be on the order of 1,000-fold.
Many contaminants can be quantified at levels of concern, but some cannot. It's a large area of research, to be sure.
You are proposing that this "noise" exists, but it is relatively easy to visually examine every molecule in a sample of water, and identify every element in it through a variety of tests. In other words, "what noise?"
I am not proposing anything. Analytical instrumentation has a finite level of sensitivity. Noise is the baseline signal of any sort of detector. Now, if you want to suggest that we spend hundreds of trillions of dollars to analyze every cow or every reservoir in the U.S. for every possible contaminant, I suppose it could be done. But at some point, each analytical process will have some limitation based on the signal to noise ratio of the blank signal to that signal produced by a contaminant moving through the detector.
You cannot measure zero, and to suggest that "it is relatively easy to visually examine every molecule in a sample of water" is patently absurd. And after all that, the Reporting Level/Detection Limit argument still stands.
You cannot measure zero, so there is still some possibility that something exists that cannot be measured because it cannot be detected or reliably reported above the natural noise of the instrumentation. This is a fundamental tenet in analytical chemistry or any analytical process.
Can you cite me a literature reference where "it is relatively easy to visually examine every molecule in a sample of water" is stated?