Cauterised time was a reality separate from the normal space-time continuum. The Sixth Doctor explained it as normal time being a large trampoline with cauterised time being a smaller trampoline above it, with his TARDIS serving as a weight in the smaller trampoline to make both times connect.

What happened in cauterised time stayed in cauterised time; a younger version of the Doctor questioned why his older self couldn't remember their encounter. Apart from not remembering everything, the older Doctor thought memory of events in cauterised time might be affected. (AUDIO: The Wrong Doctors)

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