God’s promise to Noah means that the earth will never again be destroyed by water. However, there is coming another destruction by fire.
…and the earth was formed out of water and through water by the word of God, and that by means of these the world that then existed was deluged with water and perished. But by the same word the heavens and earth that now exist are stored up for fire, being kept until the day of judgment and destruction of the ungodly. …But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up. (2 Peter 3:5-7, 10-13)
This second destruction is the one spoken of in Revelation. Allow me to cite some references from Blueletterbible.com’s Greek and Hebrew lexicons.
The Greek word “burned up and dissolved” also translated “melted” used in 2 Peter is lyo, which means:
To loosen, undo, dissolve, anything bound, tied, or compacted together
c) to annul, subvert
d) to do away with, to deprive of authority, whether by precept or act
f) to loose what is compacted or built together, to break up, demolish, destroy
g) to dissolve something coherent into parts, to destroy
h) metaph., to overthrow, to do away with
The word parerchomai meaning “pass away” is also used.
And Katakaiō, which means “burned up and consumed by fire.”
I can’t tell how figurative or literal scripture is here. I don’t know if matter will be erased and remade, or if God will just purge all evil from the earth, as you say. However, either way, the feeling behind “lyo” “parerchomai” and “katakaio” is “totally clean slate.” In fact, lyo is where we get the word “lye” which is the active ingredient in soap – a basic cleaning agent. In Noah’s time, earth remained, and mankind remained, despite massive catastrophe; in the end times, there is no remnant.
“And He who sits on the throne said, “Behold I am making all things new.” Revelation 21:5
Whether the “new heavens and new earth” are physically the same ones is not essential, because scripture says they will be utterly, completely, and practically new.
For the creation was subjected to futility, not willingly, but because of Him who subjected it, in hope that the creation itself also will be set free from its slavery to corruption into the freedom of the glory of the children of God. Romans 8:20-21
The thing I would disagree with is that this earth reaches perfection apart from the drastic work of God recalibrating everything. To say that “creation is on an upward track” and “just give it enough time and we’ll reach utopia” is humanistic. No, creation is groaning, for only the return of Christ will bring peace to the earth. So, Joel, if we both have our hope fixed solely Him, then we believe the same thing! Just as God is the author and perfecter of our faith (Hebrews 12:2), he is both the author and perfecter of his creation. What do you think about this?
The most important part of what the new heaven and earth will be like is Revelation 21:3:
“Behold, the tabernacle of God is among men, and He will dwell among them, and they shall be His people, and God Himself with be among them.”
The real crux is that, for all intents and purposes, the earth and heavens are new, and furthermore, that they are really united together, because God and man are no longer separate, but dwell together. And what his heaven, but the very presence of God?