Does "die" in Bereishit 2:17 imply the *beginning* of a process death, or simply *death*?

Question

It is true that Adam and Eve didn’t die the exact day they ate, as some seem to think Genesis 2:17 implies. The Hebrew is die-die (muwth-muwth), which is often translated as “surely die” or literally as “dying you shall die,” which indicates the beginning of dying (i.e. an ingressive sense). At that point, Adam and Eve began to die and would return to dust. If they were meant to have died right then, the text should have used muwth only once, as is used in the Hebrew meaning “dead, died, or die” and not “beginning to die” or “surely die.”

Is such an interpretation of בְּיוֹם אֲכָלְךָ מִמֶּנּוּ מוֹת תָּמוּת valid in the context of this verse?

Answer 1

here's an interpretation from shaarei kedusha part 1 gate 1 by Rabbi Chaim Vital, which could be interpreted as a progression (first death in this world, then death in the next world)

And know that after the sin of Adam harishon, which was eating from the tree of the knowledge of good and evil, his soul and body also [along with all the worlds] became mixed, each one with good and evil. This is the zuhamas hanachash (the impurity of the snake) injected in Chava (Eve) and in Adam, and through the evil and the impurity which he injected in them, he caused them sicknesses, afflictions, and death for their soul and body. And this is what is written "on the day you will eat from it, die you will die. (Bereishis 2:17)" [the hebrew word for death is repeated to indicate] death of the soul and death of the body.

Answer 2

According to Derech HaShem, before the sin Adam was much more spiritual than after the sin. So, relatively to his previous condition, he indeed became "dead" at the same day he made the sin. In other words, "death" is not an absolute thing, but rather a relative one. If somebody is "very live" and then he becomes just "live", we can call him being dead, relatively to his previous condition.

I once heard this on a lesson on Derech HaShem.