Can Yom in Genesis 1 be translated "aeon" meaning "an age"? What is its semantic range?
I have read a few translations which translated days as: "From darkness to light, the sixth creation phase" and "the mixing and the breaking forth were the time sixth" in Genesis 1:31. Now, if these are credible translations of the Hebrew text, why all the controversy?
OP question #1:
Can "Yom" in Gen 1 be translated "aeon" meaning "an age".
The short answer is "not quite". יוֹם (yôm) can refer to some unspecified period of time, as in "the day of the LORD" (as e.g. in Amos 5:18), but that is usually regarded as quite a specialized meaning.
Typically, the "unspecified period" is used with the plural, "days", however: e.g. Deuteronomy 32:7: "Remember the days of old...".
Its "basic" meaning is "day (as opposed to night)", i.e., "daytime" (e.g., Numbers 9:21), but it is also used of the 24-hour period (e.g., Leviticus 22:30). It also has a range of uses much like the English "day", e.g., "...the day when you came out the land of Egypt..." as a reference to the time of the exodus (Deut 16:3 -- see all the uses of "day" in verses Deut 16:3-4!).
The yôm entry in Brown, Driver, and Briggs, A Hebrew and English Lexicon of the Old Testament (OUP, 1906), pp. 398-401 gives a good sense for the range of meaning lexicographers attach to this biblical Hebrew word.
For idiomatic uses of yôm, see S.J. De Vries, Yesterday, Today, and Tomorrow: Time and History in the Old Testament (Eerdmans, 1975), and pp. 39-53 in particular.
For yet more reference material, see the "יוֹם (yôm)" article by Magne Sæbø in G. Botterweck & H. Ringgren (eds), Theological Dictionary of the Old Testament (Eerdmans, 1990), vol. 6, pp. 7-32.
OP question #2:
Now if these are credible translations of the Hebrew text, why all the controversy?
The translations cited by OP are not credible: survey the range of translations for "public" versions of Genesis 1:31: the "creation time" and "mixing and breaking forth" wordings here and throughout Genesis 1 in the "translation" cited by OP are simply fanciful, and do not correspond to the wording of the Hebrew.
(Beyond this, the question has to do not only with Hebrew semantics but with commitments beyond the linguistic, and best discussed either at Mi Yodea or Christianity.SE.)
A little known fact that is often left out of this type of discussion is that we ourselves do not have 24-hour days. It also depends on what definition of "day" you use, you could use the "one full rotation of the Earth around its axis" (rotation period or sidereal day) or "the time it takes for the sun to go back to its position in the sky" (solar day).
For an excellent explanation of this see How long is a day?
Some relevant quotes from that site:
It actually takes the Earth slightly over 23 hours and 56 minutes to rotate once around this axis. In this time all the stars appear to revolve once around the Earth and return to their starting positions. Astronomers call this period of time a sidereal day.
and
But the Earth's axis is inclined at an angle of about 23.5° from the perpendicular to the plane of the Earth's orbit. And although the Earth's orbit is close to being circular, it is actually an ellipse, so it is shaped like a slightly squashed circle.
These two factors mean that the time taken for the Sun to return to a position due south in the sky varies slightly throughout the year. On average this period of time is 24 hours. But at some times of the year it is slightly longer and at other times of the year it is slightly shorter.
So, how long is a day? We cannot say that a day is by necessity 24 hours. And therefore we also cannot say that a yom is 24 hours either. Especially since the sun (or "greater light to rule the day") was not created until the fourth day (Genesis 1:16).
In other words, it is eisegetical to insert the meaning of "24 hours" to the word "day" (even in English), since even in our present time, it is not so. We say a day is 24 hours out of convention and pragmatism (imagine if we started using strict sidereal days or solar days, the mess that would create), not any other reason.
As other answers point out, the day "yom" is not used to refer only to a solar day or rotation period, but can refer to events such as "the Day of the Lord", "the day I took you out of Egypt", etc. Again, as noted in other answers, you can check any concordance for this, and if you can read basic Hebrew, the BDB (Brown, Driver and Briggs A Hebrew and English Lexicon of the Old Testament) for occurrences of "יוֹם" and how it is used in each given context.
Another point is to say that in Genesis 1:5, God calls the light "day", not a specific quantity of time.
If we translate "yom" in Genesis 1 to "aeon" that would add unnecessary interpretation and perhaps even greater confusion, depending on how people understand the word "aeon" (an explanation of why this cannot be thousands or millions of years would require the use of doctrine, so would belong better in a different forum than this one). It would also create a greater conflict since the fact that the creation model of 6 yomim with the 7th yom for rest was what the law of the Sabbath was based upon.
"For in six days the LORD made the heavens and the earth, the sea and all that is in them, and rested on the seventh day; therefore the LORD blessed the sabbath day and made it holy." Exodus 20:11 (NASB)
So it is important to keep the translation coherent with this reasoning, hence the choice of "day" for other languages too.
To answer your final question, the controversy is actually only a century or two old, when people started believing in evolution and saying that the earth was millions of years old (and now billions). This obviously conflicted with the biblical account of how long life has been on Earth (notice I didn't say "of how old Earth is"), and the polemic evolved (pardon the pun) as people chose sides in the matter. Only then did some find it necessary to find a different meaning for the word "yom", to attempt to reconcile wanting to sit on both sides of the fence.
In Exo. 20:9-11, it is written,
9 You shall work six days and do all your work. 10 But the seventh day is the Sabbath of Yahveh your God. You shall not do any work... 11 For Yahveh made heaven and earth in six days, the sea, and all that is in them, and He rested on the seventh day. Therefore, Yahveh blessed the Sabbath day and sanctified it.
Would it make sense for the Sabbath to be every seventh day of the week if God didn't actually make the heaven and the earth in six literal days? Because if God really created the heaven and the earth in millions of years, then Exo. 20:9-11 doesn't make any sense. Instead of every seventh day, we would expect the Sabbath to occur every million of years or so, or however long it took Yahveh to actually create the heaven and the earth and then cease (rest).
Keil and Delitzsch wrote (p. 40),
...and the almighty operations of the living God in the world are based upon the fact of its creation: In Exodus 20:9-11; Exodus 31:12-17, the command to keep the Sabbath is founded upon the fact that God rested on the seventh day, when the work of creation was complete.
Furthermore (pp. 69-70),
But as the six creation-days, according to the words of the text, were earthly days of ordinary duration, we must understand the seventh in the same way; and that all the more, because in every passage, in which it is mentioned as the foundation of the theocratic Sabbath, it is regarded as an ordinary day (Exodus 20:11; Exodus 31:17).
References
Delitzsch, Franz; Keil, Carl Friedrich. Commentary on the Old Testament, Volume I. Grand Rapids: Eerdmans, 1900.
It's easy to say "A day is 24 hours" and that's all there is to it"; however, I see at least a couple textual reasons to make me doubt that what is translated as "day" here means an actual 24-hour day.
First, on Day 3, the we are told not that God spoke the vegetation into being, but that He ordered the LAND to produce all types of seed-plants and fruit-bearing trees. This implies a natural process that would take a number of months at the very least, and probably years.
Day 6 is also problematic in this regard. God created mankind on Day 6, "male and female he created them." Genesis 2 is a more expansive explanation of that event, and it stretches the imagination to the point of disbelief to think that Adam tended the garden of Eden and named all of the animals that had been created and discovered that he was lonely and was put to sleep by God so that Eve could be created all within a 24-hr. period of time. Again, this would likely have been a process of months or years.
The real question at hand, though, is whether yom can be understood to be something other than a 24-hour period of time. I would like to hear from Hebrew speakers and Hebrew scholars on the matter, but from my understanding, several Biblical texts actually do use yom to describe a longer undefined period of time.
I found this explanation of the word to be quite helpful
There is no linguistic support for יום as any period of time other than 24 hours. In all available Hebrew and cognate languages, it's just 24 hours. So if you insist that your interpretations are based on linguistic evidence, you are out of luck. If you are willing to take a more metaphorical view of the text, well, then, off you go-- but to another site.
