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A perfect continiuum for the wave function

In my past blog "Heat transfer faster than light", I have introduced the situation in which if we set up a rectangular initial temperature distribution in a one dimensional thermal conductor that is insulated from the external world, the temperature distribution function will spread instantaneously to far region faster than light speed.

Recently, I have noticed that the propagation faster than light speed is possible, and is happening everyday in microscopic world.  When an observation on an electron is made, then its wave function collapses to the Dirac's delta function.  After then the wave function will soon spread out and change from infinite spike Dirac's delta function to finite mild Gaussian function instantly, i.e., in no time.  This means that the front of the base of the Gaussian curve proceeded outwardly with infinite speed!  Can you imagine this phenomenon, or can you accept this fact?

Therefore I thoght that the mere pure vacuum space might be a perfect continuum at least for a quantum mechanical wave fucntion.

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