Relativity - when size does does matter

Alright, I promised Science and now it is here. I took my time thinking about how to write this one. In my research I work with mass spectrometers. They are designed to detect substances based upon their mass (actually mass to charge ratio, as substances enter the mass spectrometer as ions thus allowing their motion and detection in the electromagnetic field).

So what is it I am going to write about? Well, I am going to write about how the most basic concept every scientist needs to understand - units of concentration. But before I begin, I am going to spend a little bit of time on an introductory lesson - if you are already familiar, then skip down to the rant.

When dealing with a mass spectrometer there are some fundamental concepts that you must understand, the first we all should have heard of and possibly learned in high school - Einstein's theory of special relativity. As defined by Wikipedia (and it's really a decent explanation), this is it:

Special Relativity:

Special relativity is a theory of the structure of spacetime. It was introduced in Albert Einstein's 1905 paper "On the Electrodynamics of Moving Bodies". Special relativity is based on two postulates which are contradictory in classical mechanics:

1. The laws of physics are the same for all observers in uniform motion relative to one another (Galileo's principle of relativity),
2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

The resultant theory has many surprising consequences. Some of these are:

* Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock.
* Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
* Relativity of simultaneity: two events that appear simultaneous to an observer A will not be simultaneous to an observer B if B is moving with respect to A.
* Mass-energy equivalence: E = mc2, energy and mass are equivalent and transmutable.

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell's equations of electromagnetism and introduction to special relativity).

Now if you read the bottom statement, then you might be wondering about the Lorentz transformations and Maxwell's equations. I am not going to go into them, but suffice it to say that one equation which is extremely important to understanding mass spectrometry, is partially derived from the Lorentz Force Law. It is the following equation:

Here, m represents the mass of the ion, Q is the ionic charge, a is the acceleration, E is the electric field, v x B is the vector cross product of the velocity and the magnetic field. This equation describes the movement of an ion in a vacuum. I am not going to do math or discuss physics at length in this post, but I am going to summarize the gist of my point with reference to this equation and Einstein's special theory.

So back to my point. I get annoyed when people don't refer to proper molarity units when working with mass spectrometers. Why? It is simple, molarity takes the molar mass, or size of the molecule into account when calculating concentration. What then happens is you can discuss the number of molecules that will be hitting the detector for both small and large molecules and their size will not affect your discussion. In mass spectrometry, mass-to-charge is unit-less and the amount of ions observed, or the signal, will be determined absolutely by the number of moles present (certain limits apply but these are physical based upon technology).

Unfortunately, for the last few years I have had to work with environmental scientists who insist on discussing concentration in part-per-units which is a way to convert units like ug/g and re-word them as parts per million. Either way it is a macro unit of mass/mass or volume/volume unit and can become troublesome when dealing with more than one substance that have different molecular masses. For instance, when a molecule of 10000 g/mole is present in a concentration of 1 ppm, it's molarity is 10E-7 whereas a molecule of 100 g/mole is present in a concentration of 1 ppm, it's molarity is 10E-5. Suppose I were to take two solutions, one with 1 ppm of molecule A which is of 10000 g/mole and the other with 1 ppm of molecule B which is of 100 g/mole, and then analyze these on a mass spectrometer, I would have a much lower signal for molecule A becuase its mass is increasing it's relative molar concentration in the ppm calculation. Therefore size is important when it comes to calculation of concentration of molecules of trace analysis.

Einstein managed to demonstrate that mass and energy could be equivalent and now we can use the force created by small masses in electromagnetic fields to our advantage. In these magnetic fields, molecular mass affects velocity and we measure discreet difference in molecular mass and energy to identify small, unknown substances in mass spectrometry. I cannot see the point of using a unit that does not consider molecular mass when calibrating and creating analytical methods with a mass spectrometer. I hope that anyone who uses mass spectrometers reading this will use molarity units to improve consistency of results and interpretation across all disciplines.