In Inventing Temperature by H. Chang, the author asks a simple question: How did people made the thermometer and measured the temperature for the first time? If you are to make a thermometer, you need to know the temperature. But to know the temperature, you need a thermometer. It seems like an infinite logical loop and there seems to be no way out. I find this problem worths thinking in context of my own research work.

I am kind of facing a similar problem. Our (strictly speaking, my colleagues’, who perform actual measurements in the lab) recent data seem to indicate orbital current in a couple of solid state heterostructure devices. But to claim this, we need to have a device equivalent to “orbital-current-meter” (basically this should convert the signal into electrical current/voltage in a reliable way). But again, to make the orbital-current-meter, we need to know how to measure the orbital current.

This seems like an impossible problem if we consider only expeirments. Fortunately we can make a theory starting from first principles which proved to be sold enough over the history of physics. In our case, it is quantum mechanics of electrons and atomic nuclei. “In principle” (I don’t like this pharse!), we can rely on such first-principles-based theory and compare with experiments. So the task is to make the experimental setup as close to our assumptions made in the theory (top-down), and develop complexity of the theory to be as close to the experimental setup (bottom-up). This is not an easy job, but slowly the agreement between theory and experiment gets better and the measurement becomes more solid.

Although I have not yet read the whole chapter of Inventing Temperature, according to what I have roughly skimmed through, I see that such kind of progression over repetitive comparision between theory and experiment is the key to establishing measurement standard for a new physical quantity. I believe that over the time we will get close to unambigious quantification of the orbital current and make “orbital-current-meter” at the end.

PS.
Still, it’s not really easy to measure orbital current. Not only conceptually as I discussed above, but also technically due to lack of facilities and methods we can access. “In principle”, with very high resolution spectroscopy may be able to measure orbital angular momentum and spin angular momentum independently in each part of the sample from known selection rules. Yeah, the problem is the resolution (spatial resolution and magnitude resolution): Heterostructure devices are in nanometer thickness scale and the transient angular momentum excited by electric current or whatever is far smaller than the equilibrium moment. Electrical transport measurement is usually quite sensitive enough to detect such transient effect, but there are too many side effects that we cannot properly charaterize yet.