Probability waveform

According to the First Doctor, points in history became fixed once a probability waveform had collapsed. (AUDIO: Daybreak, The Vardan Invasion of Mirth) As "all the commentaries agree", it was dangerous at this point to interfere, (AUDIO: Daybreak) as one could create a catastrophic paradox. (AUDIO: The Vardan Invasion of Mirth)

Such fixed points could be brought about, for instance, by learning about the nature of one's own death. The Eleventh Doctor explained that time could not be rewritten once its precise details had been read, or observed. "Once we know what's coming, it's written in stone." (TV: The Angels Take Manhattan) Once Teddy Baxter saw a biodata projection of his future, his survival up to that point became fixed. (AUDIO: The Vardan Invasion of Mirth)

On realising Teddy's future was fixed, the First Doctor expressed surprise at Michael Hart, a Vardan, not having recognised the state of a probability waveform, as Vardans held the capacity to travel along and manipulate any spatial wavelength. When Hart attempted to kill Teddy, they became trapped in a paradox. Steven Taylor was able to bring him back while in the Mediasphere, undoing the paradox, by giving the right cues. (AUDIO: The Vardan Invasion of Mirth)

Behind the scenes

Probability waves were first proposed by Max Born, who personally maintained that he would "like to regard a probability wave, even in 3N-dimensional space, as a real thing, certainly as more than a tool for mathematical calculations", as more than simply an abstract, descriptive function which conveniently helps make consistent statistical predictions about quantum phenomena. Either way, mathematically, a probability wave is described by its wave function.

The First Doctor, here, is referring to wave function collapse, as studied in quantum mechanics, which occurs when a wave function in a superposition (that is to say, when with respect to some specific observable quantity the state does not have a determined value prior to "observation" and instead is a probabilistic combination of these values) is "observed" (measured), and thus collapses into one singular possibility. In this sense, the writers of Daybreak and The Vardan Invasion of Mirth are drawing a connection between fixed points in time — as introduced in BBC Wales Doctor Who — and analogous concepts found in modern quantum theory.

Though the term "wave function" exists in the DWU, no connection has yet been made explicit.