Has time travel ever been discussed before in terms of Judaism? According to Judaism would (should) it be possible to travel through time?
Shivchei HaBesht records an episode where the Baal Shem Tov wrote a letter to his brother-in-law R' Gershon of Kitov, telling him how he had been taken to task by the Heavenly Court for excommunicating a Torah scholar without sufficient cause. R' Gershon wrote back to say that this indeed had happened, but only after the date of the Baal Shem Tov's letter - in other words, he "time-traveled" and saw the incident before it occurred.
The Tzemach Tzedek of Lubavitch points out (Derech Mitzvosecha, Mitzvas Haamanas Elokus) that the Divine flow of energy to the world - both its spatial and temporal aspects - gets divided progressively finer during its "evolution" through the spiritual "worlds" leading down to our own. There is a level, he says, at which one moment contains ten to fifteen years' worth of events in our realm; it is this level, he says, that the Baal Shem Tov reached and thereby foresaw what was to happen.
It could very easily be argued that the whole thing was a vision, but it does say that Moshe went and sat behind the 8th row and that he returned to G-d afterwards.
Somewhat unconventional, but:
While commenting on a different point in the gemara (Chulin 91b), R' Yitzchok questions how Yaakov was "vayifga bamakom"- he chanced upon the place (Beis El/Yerushalayim) if the pasuk implied that he already reached Charan- vayelech Charana. R' Yitzchok answers that the land shrunk for him. Assuming space and time are interwoven, Yaakov would have traveled ahead in time as well.
The gemara continues the above by questioning why the Torah wrote "ki va hashemesh"- Yaakov lodged because the sun had set- implying that it set prior to its normal time. If not for the gemara's answer (that Hashem wanted the tzadik to lodge by Him and so made the sun set early so that Yaakov would be unable to depart), it's possible to say that for Yaakov, the sun set early because time bent for him along with the land.
Note: I have no clue if the math works out.
Time-travel into the past, according to Stephen Hawking's latest Scientific-Theory, is inherently a paradox. Paradoxes cannot exist in nature and as such, reverse-time-travel is physically impossible.
According to the Rambam, Hashem only does possilbe-miracles, where Hashem uses His direct-control of the physical world to perform natural-wonders. The Rambam addresses the classic question 'could Hashem create a square-triangle' (can God do anything impossible)? The Rambam's revelation is that Hashem can't make a square-triangle (he can't do something physically-impossible), but that's not a limit of Hashem's power, since He made the restrictions of our physical world. He said something along the lines of 'let the goyim have impossible-miricles, we'll have possible ones' (their miracles can't happen, ours can and do).
Accordingly, the Rambam would hold that reverse-time-travel, as a paradox of nature, would not be a miracle Hashem could perform.
Hawking's theory, that traveling to the past is a paradox and impossible, is also supported by a halacha from Talmud Bruchos, that it's assur to pray to change the past.
If you hear that there is a fire in your town, you shouldn't pray that it wasn't your house, it's too late if your house is on fire, and Hashem isn't going to go back and change it. instead you can pray that it won't spread to your house if it wasn't your house, or that they will be able to put it out quickly.
Also along those lines, expecting parents shouldn't pray that their baby be a certain sex after the first 40 days of pregnancy, since after 40 days the fetus already formed its sex-organs and Hashem's not going to go back and change it. (Berachot 60A)
Another quantum-halacha is once something observed, it can't be changed. (once it's seen it can't be un-seen)
I don't know where this halacha is from, but I was taught that you shouldn't count your money because, if you know how much money you have (you've observed it) then Hashem can't slip you more without your knowing (Hashem can't change it once you've observed it).
This would mean that since the past was observed by the people living in it, Hashem cannot send you back to change it.