Are there examples of backward time travel in the talmud and/or midrash?

Question

The gemarah discusses a story where Moshe is taken to see the lecture hall of Rebbi Akiva and the midrash discusses God showing Adam ensuing generations and their scholars. I would like to know if there any examples of backward time travel, where someone living at a later chronological date is shown or taken to an earlier time.

Answer 1

Almost...

תענית כה א

רבי אלעזר בן פדת דחיקא ליה מילתא טובא עבד מלתא ולא הוה ליה מידי למטעם...חלש לביה ונים אזול רבנן לשיולי ביה חזיוהו דקא בכי וחייך ונפק צוציתא דנורא מאפותיה כי אתער אמרו ליה מ''ט קבכית וחייכת אמר להו דהוה יתיב עמי הקב''ה ואמרי ליה עד מתי אצטער בהאי עלמא ואמר לי אלעזר בני ניחא לך דאפכיה לעלמא מרישא אפשר דמתילדת בשעתא דמזוני אמרי לקמיה כולי האי ואפשר אמרי ליה דחיי טפי או דחיינא א''ל דחיית אמרי לקמיה א''כ לא בעינא...

Taanit 25a

R' Elazar Ben Pedat was very poor, he went through blood-letting and had nothing to eat...he felt weak and fell asleep.
The Rabbies came to ask him questions, and saw him laughing, crying and then a flare of fire came out of his forehead.
When he woke up they asked him - why did you cried and laughed?
He answered, God sat with me, and I asked him, until when I will suffer in this world?
He replied: Elazar my son, do you want me to reverse the world to it's beginning? maybe you will be born in time of prosper.
I said: just maybe?! Did I past half of my life time? He said: you did.
I said: If so, I don't want...

Answer 2

Not an example of backward time travel in the sense of someone at a later date being taken back to an earlier time, but the Sefas Emes (Purim 5637) writes that the salvation of the Jews was through Vashti's removal at Achashverosh's feast, even though the punishment of Haman was a result of the Jews eating from Achashverosh's feast. This is because God knew that the Jews would repent through love (teshuvah me-ahavah), and therefore, their sins would become merits. Thus, although it was a sin for them at the time that they partook of the feast, in retrospect it was a merit and in fact the source of their salvation.

Also not an exact match, but according to the Maharam Chalavah and a number of other sources, we recite a bracha on the miracle of leaving Egypt, even though the bracha recited on a miracle extends only two generations, because on the night of the Seder it is considered as if we ourselves left Egypt. This might also be the reason for Hallel at the Seder, which seems not to be the ordinary Hallel of Yom Tov, but Hallel on a miracle, which we can recite because "we ourselves left Egypt." Thus, the halachah that we are to see ourselves as having left Egypt has practical ramifications in other realms and may be considered a communal obligation to engage in (metaphorical) time travel.