Two versions of Alistair Gordon Lethbridge-Stewart short out the time differential between themselves. (DW: Mawdryn Undead)
The time differential was an aspect of multiple points in a single timeline which had come into contact with one another.
When a human or object met itself from a different point on its own timeline, the Blinovitch Limitation Effect meant that physical contact between the two versions would short out the time differential between them, and could result in dangerous effects such as a large energy discharge or damage to time itself. (DW: Mawdryn Undead, Father's Day, The Big Bang)
The Fifth Doctor appeared physically older when meeting his future self. (DW: Time Crash)
While multiple incarnations of the same Time Lord encountering one another did not experience dangerous effects of shorting out the time differential between themselves (DW: The Three Doctors), the earlier incarnation or incarnations would appear of a greater physical age than they should have at that point in their timeline. This otherwise harmless effect would disappear once the incarnations parted ways and the time differential was no longer shorted out. (DW: Time Crash)
When time itself became stuck and began dying as a result of River Song altering a fixed point in time by refusing to kill the Eleventh Doctor (who was secretly aboard the Teselecta which was disguised as himself) multiple points in Earth's timeline came into contact with each other as a result. The only way to repair the damage to time was for River and the Teselecta-Doctor to physically touch; as their timelines were the polar opposite points of the distortion, their contact shorted out Earth's own time differential. This enabled them to return to the fixed point, restore the required event, and repair the damage to time. (DW: The Wedding of River Song)
Exceptions
In some cases, the ill effects of two versions of a being shorting out the time differential could be avoided or suppressed. Kazran Sardick was able to make physical contact with his younger self in front of the Doctor's TARDIS without ill effects to time. (DW: A Christmas Carol)
When the universe was collapsing as a result of the Doctor's TARDIS exploding, the effects on organic beings appeared diminished as older and younger versions of Amy Pond as well as the Eleventh Doctor were able to touch and interact without ill effects. Two versions of the Doctor's sonic screwdriver, however, still produced a spark when touched together. (DW: The Big Bang)
Behind the scenes
- Originating in Mawdryn Undead, the concept of "shorting out the time differential" was used in Time Crash by Steven Moffat to finally put an on-screen explanation to the unavoidable fact that the previous Doctors in multi-Doctor television stories are visibly older than they appeared when the actors had last played the Doctor on-screen.
- It has not been revealed how Kazran and Amy were able to touch their younger selves in A Christmas Carol and The Big Bang without experiencing ill effects.