Is the speed of heat infinite? When solving the heat equation in a semi-infinite bar, we can see that a pulse in the finite end draws an immediate change in every point of the bar. So, at any given point of the originally constant heated bar the temperature changes. That could send information at a higher speed than light rate to a distant point of the bar.
A deeper question is: Does the mathematical concept of the Real Line can model any magnitude? I mean, if every magnitude is quantified, the Real Line is "behind" reality but never gets real (sorry for the pun).
What do we know about these subjects? Are they paradoxes?
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