How did memory work in Old Who multi-Doctor stories?

Question

In the 50th anniversary special The Day of the Doctor (the only multi-Doctor story in New Who), the following short exchange explains that War and Ten will be unable to remember any of the events of the episode, and only Eleven, the most recent incarnation, will retain memory of them:

WAR DOCTOR: I won't remember this, will I?
11TH DOCTOR: The time streams are out of sync. You can't retain it, no.
[...]
10TH DOCTOR: I won't remember either [...]

As well as the necessity of ensuring that Nine and Ten truly believe they destroyed Gallifrey, even in the new version of time (otherwise their entire personalities would have been different), this also neatly takes care of the question of "why doesn't Eleven, the most recent incarnation, simply remember everything that happened in this episode and tell/warn the others?"

Was this same idea of "time streams out of sync" used in the multi-Doctor stories in Old Who? If not, how (if at all) was the issue of memory retention taken care of there? Back then, how did they deal with the issue of the most recent Doctor knowing exactly what was going to happen by virtue of already having the others' memories of the same events?

Answer 1

The specifics varied from story to story and were usually glossed over entirely.

This is Lampshaded in the novel Cold Fusion which lists a variety of reasons (mostly technobabble and deliberate third party interference), from a variety of stories before admitting that sometimes memories are retained:

‘Well, if he’s your future self, why don’t you remember all this from first time round?’

‘Does everything have to have a reason?’ Forrester asked.

‘Perhaps it’s magic.’

‘No, no,’ the fifth Doctor said, ‘the rules of time travel are very precise, and Mr Cwej here has a good point. Now, on both occasions that we met Omega, that was straightforward Blinovitch Conservation.’

‘That was true all three times, yes, but it doesn’t apply here,’ the other Doctor noted from underneath the console.

‘Yes, yes, I know that. Now, Zodin erased our brains with mind rubbers.’

‘I remember it well.’

‘But that hasn’t happened this time. The crashed TARDIS might have had misphased Relativity Displacers.’

‘It might,’ the seventh Doctor conceded, ‘but it didn’t.

‘Tachyon Backflush?’ the fifth Doctor suggested.

Chris sniggered. ‘Sorry – it’s just that it sounds rude.’

Forrester shook her head disbelievingly. Her Doctor stood, brushing himself off and taking his umbrella back from his past self

The fifth Doctor straightened. ‘There is another possibility.’

‘Go on.’

‘You do remember. You’ve remembered all along.’

The Doctor smiled enigmatically and tapped the side of his nose.

At the pre-arranged signal, Forrester knocked out the fifth Doctor with a swift blow to the back of the head.