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Below is a paragraph from chapter 11 of David Deutsch's book The Beginning of Infinity (emphasis mine). The context he is referring to is the quantum "multiverse" - his conjecture about how the quantum world operates.

The region in which the universes are different will then grow. For instance, when the couple decide to marry, they send messages to their home planets announcing this. When the messages arrive, the two instances of each of those planets become different. Previously only the two instances of the starship were different, bur soon, even before anyone broadcasts it intentionally, some of the information will have leaked out. For instance, people in the starship are moving differently in the two universes as a result of the marriage decision, so light bounces off them differently and some of it leaves the starship through portholes, making the two universes slightly different wherever it goes. The same is true of heat radiation (infra-red light), which leaves the starship through every point on the hull. Thus, starting with the voltage happening in only one universe, a wave of differentiation between the universes spreads in all directions through space. Since information travelling in either universe cannot exceed the speed of light, nor can the wave of differentiation. And since, at its leading edge, it mostly travels at or near that speed, differences in the head start that some directions have over others will become an ever smaller proportion of the total distance travelled, and so the further the wave travels the more nearly spherical it becomes. So I shall call it a sphere of differentiation.

The "voltage" bit is about a hypothetical transporter used to communicate between the two universes, which suffers a malfunction and sends a voltage surge in one of the universes.

Now, I understand the concept. The two universes just keep diverging, with the light and the radiation leaving the starship being the catalysts.

But how can you get a sphere from a collection of waves? What does David mean by "at its leading edge"?

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Spherical waves are a pretty routine construct in many areas of physics. Here is a visualization that can give you an intuitive understanding:

Spherical Wave 1

Spherical Wave 2

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  • $\begingroup$ Looks awesome. Just so I get this right: it is also implied that the starship will keep emitting radiation and light continuously, isn't it? Like the sphere would be hollow otherwise. $\endgroup$ Dec 12 '20 at 18:11
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    $\begingroup$ @PaulRazvanBerg I would expect the starship to only emit reflected light continuously (any other emission would depleted the energy of whatever is driving it). If the emission is not continuous but only one instantaneous event, then yes the sphere would be "hollow". Whether continuous or hollow, we can think of the radiation emitted (in all directions) at the very first instant to be the "leading edge" of the radiation, or in more common physics terms, the wavefront. It is the outer boundary of the physical effects of the event and/or information of the signal. $\endgroup$ Dec 12 '20 at 19:20

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