Has time travel ever been discussed before in terms of Judaism? According to Judaism would (should) it be possible to travel through time?
Rab Judah said in the name of Rab, When Moses ascended on high he found the Holy One, blessed be He, engaged in affixing coronets to the letters. Said Moses, ‘Lord of the Universe, Who stays Thy hand?’ He answered, ‘There will arise a man, at the end of many generations, Akiba b. Joseph by name, who will expound upon each tittle heaps and heaps of laws’.
‘Lord of the Universe’, said Moses; ‘permit me to see him’. He replied, ‘Turn thee round’. Moses went and sat down behind eight rows [and listened to the discourses upon the law]. Not being able to follow their arguments he was ill at ease, but when they came to a certain subject and the disciples said to the master ‘Whence do you know it?’ and the latter replied ‘It is a law given unto Moses at Sinai’ he was comforted.
Thereupon he returned to the Holy One, blessed be He, and said, ‘Lord of the Universe, Thou hast such a man and Thou givest the Torah by me!’ He replied, ‘Be silent, for such is My decree’. Then said Moses, ‘Lord of the Universe, Thou hast shown me his Torah, show me his reward’. ‘Turn thee round’, said He; and Moses turned round and saw them weighing out his flesh at the market-stalls. ‘Lord of the Universe’, cried Moses, ‘such Torah, and such a reward!’ He replied, ‘Be silent, for such is My decree’.
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.
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.
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.
When we talk about time travel, we must define what we mean.
If it mean that time is not a limitation ie. The affects of time, like old age, have no affect on the person then we have a Gemara in Taanis (23a) regarding Choni Ha’maagel, who slept for 70 years. And to him it was as if it was one day.
The Sefer Magen Avos (5:21) says that the time he was asleep, did not age him, despite that the world around him did age, as his former students and teachers had passed away.
The same Sefer mentioned above also says that when Moshe was on Har Sinai for 40 days and 40 days, without food or drink, he says because Moshe was unaffected by time, as if time has stopped for him.
I believe it was the Ibn Ezra that once said, the Past is Gone, the Future is not yet, the Present is but a mere second, so why worry? In Hebrew: העבר אין, העתיד עדיין, ההוה כהרף אין, דאגה מנין.
I think that the common concept of time travel is virtually impossible as it's non-existent. But... Hashem created time, which means he's above time, so to Him past present and future are one and the same, thereby he could have theoretically taken Moshe out of the realm of time and put him in R Akiva's Yeshiva.
The question here is though, did R Akiva see Moshe, could the people around him see him? Probably not as I believe a 20 foot tall with a shining face man would really stand out. So I agree with those that say it was a vision.
There's a story in the Babylonian Talmud, Ta'anit 23a which tells of a Jewish scholar named Honi ha-M'agel who lived during the 1st-century BC.
In the Talmud, Rabbi Yohanan relates to Honi’s life being troubled by a verse in the Psalms (126:1) regarding “A Song of Ascents.” Honi wondered if it were possible to live seventy years in a dream.
The story goes that Honi was once journeying along a road where he saw an old man planting a Carob tree. Honi was eager to know the purpose of this tree. He approached the planter with his question. “How long does it takes for this tree to bear fruit?" The man replied: "Seventy years." This was because on average, it took nearly 70 years for it to grow. Honi nodded and asked him another question. “Are you certain that you will live another seventy years?" The man replied: "I found already grown carob trees in the world; as my forefathers planted those for me so I too plant these for my children." To this, Honi shrugged and sat down to have a meal. He must have wondered whether the man was foolish enough to think his children would live to see it ripe. Looking for shade, he planted himself next to the planter and rested, apparently for 70 years. When he awoke he found himself covered in rocks. Intent on finishing his journey, he walked a distance and sat next to an old tree where a man was picking fruit. Puzzled, He asked him if he were the same man who sowed the seed. the man replied no and that it was his grandfather who was responsible for this tree so that it will bear fruit and provide for further generations. To this, Honi pondered and said: "It is clear that I have slept for seventy years."
The point of the story is that others can still reap the rewards from your mitzvot if it's merited.
Taanit 23a Hebrew/Aramaic, Mechon-Mamre, Maharsha links the discrepancy of the Talmud and Josephus's account of Antiquities of the Jews, 14.2.1 21. It doesn't assume Honi was assassinated by Hyrcanus II but rather he fell into a deep sleep or a coma-state for the duration of 70 years.
We seem to have a Jewish Rip Van Winkle. Whether this supports the theory of time travel, I don't know. I tend to agree with Josephus's account and that this was a parable for the effects on others due to our good deeds
PS This story is usually associated with the holiday of Tu'Bishvat.
I'm with ZAQ - TT does not exist and can not exist according to Judaism.
I know there are lots of stories of peeking (seeing) forward and backward in time, but this is not TT.
There are no stories or even fantasies about physically moving a physical body in either direction and interacting with the environment.
There are no parallel universes with any sort of interaction between them (there might be different Olamot, but they are unrelated one to another) because if they were relevant they were mentioned elsewhere.
See Eliezer Ben Pedat's story (Taanit 25a) as G-d said to him: "To change anything I need to destroy the whole world and even then I'm not sure about your luck".
I would say, that according to Judaism, the 4D world is one piece and just unfolds before our eyes. Just like a movie file on your disk that you watch one frame at a time, but it is all on your disk. So is the Creation in G-d's eyes.
I brought additional proof in my other answer
NB. The famous saying "הפוך בה והפוך בה דכולי בה" is a sure bias in critical thinking that allows us to find firm evidence for just about anything in the Jewish tradition. We should be more careful about it and stop lying to ourselves.