Thompson's Lamp

[epolo]

@Max_S

@Half_Man_Half_Wit

It doesn’t assume time is continuous, and ‘converges to 0,5’ isn’t the mathematical answer. Each point in time at which a switch happens is after a rational time interval \frac{1}{2^n} is rational for all n ), and the rational numbers aren’t a continuum (there’s always an irrational number between any two rational numbers). That’s nitpicking of course—you presumably meant that the difference between two successive switches shrinks without lower bound. That’s true, but it’s true for time in all of our best physical theories (in fact, time is a continuum in all of our best physical theories)—the fundamental nature of the Planck time being only conjectural at this point. More to the point, the series that determines the state of the lamp after two seconds is 1 - 1 + 1 - 1 + … The limit of this isn’t 0,5—it’s divergent, so it simply has no well-defined limit.

~originally posted by Half_Man_Half_Wit

Even without the limit of the Planck time, at some point the switch - no matter how small it is - would need to be moving faster than the speed of light. Thompson’s Lamp can’t exist in the real world. Not that that removes its usefulness as a thought experiment.