The Spirit of God identifies Edom with Babylon. (See Ps. 137:7 -8.) "Remember, My LORD, The Children of Edom, in the day of Jerusalem, who said Raze it, raze it," (i.e. make bare or destroy the Temple, as Edom did under the Romans,) "even to the foundation thereof."
"O daughter of Babylon," &c. Here we see, without any possibility of mistake, that Edom is Babylon , and all sacred and profane history confirms it. Chaldea, or Babylon, was established by Assyria. ( Isaiah 23:13,) says, "Behold the land of the Chaldeans, this people was not till the Assyrian founded it for them. The capital of Chaldea was Babylon. The Assyrian empire embraced the country on both sides of the Tigris. Babel, or Babylon, was founded by Nimrod, (see Gen. 10,) about A. M. 3416. The Assyrians descended from Taurus, and Caucasus conquered and destroyed Jerusalem, together with Syria; and these, with Phoenicia, became The Roman Empire, and was called Chaldea; as it was in the time of Jesus under Tiberius Caesar. (See Luke 3:1.) From the East the Chaldeans, or Romans, peopled all the west; first Italy, Rome, France, Germany, England and America. Rome was founded by Romulus, 750 B. C. After Jesus 325, Christianity became The Established Religion, under Constantine;* hence Babylon, Rome, Edom, and Christianity are synonymous.

Reference Source: Jewish American History Foundation The Origin of Edom, Babylon, and Rome's Christianity