The Talmud and Geonim seem to speak about ta'am and it's ability to transfer as being a very physical process. The literature reads as if one would be able to taste the transfer of flavor from one vessel to another. The Rambam flat out says that if one isn't sure if taste transferred, one should taste the mixture and see if taste transferred.
Mishneh Torah: Ma'achalot Assurot - Chapter 15:2
What is implied? When the fat of the kidneys3 falls into beans and becomes dissolved, the beans should be tasted. If the taste of fat cannot be detected, they are permitted. If [not only] the taste, [but also] the substance of the fat is present, they are forbidden according to Scriptural Law. If the flavor could be detected, but there is no substance, they are forbidden by Rabbinic Law.
ב כיצד חלב הכליות שנפל לתוך הגריסין ונמוח הכל טועמין את הגריסין אם לא נמצא בהן טעם חלב הרי אלו מותרין ואם נמצא בהם טעם חלב והיה בהן ממשו הרי אלו אסורין מן התורה נמצא בהן טעמו ולא היה בהן ממשו הרי אלו אסורין מדברי סופרים:
However, many modern discussions do not seem to speak about ta'am in this way, rather they speak about it in more of a metaphysical sense. Their words don't seem to be discussing a real physical entity, rather it sounds more like speaking about the transfer of purity or impurity, which can only be measured in the metaphysical/spiritual realm. An example of this would be speaking about flavor transfer without asking the question whether the material absorbed flavor to begin with, or checking to see if any flavor actually transferred.
So which is it? Is ta'am a physical entity that can be measured by our tongues, or it it a metaphysical entity that we can't quantify or interact with in a physical way?