Not a billion billion times. You need ≈2^100 presses to get any signal, and ≈O(2^200) presses to figure out which way the signal goes. 2^200≈10^60. Planck time’s about 10^-45 seconds. If you try to press the button more than 10^45 times per second the radiation the electrons in the button will emit will be so high frequency an small wavelength that it will collapse into a black hole.
Not a billion billion times. You need ≈2^100 presses to get any signal, and ≈O(2^200) presses to figure out which way the signal goes. 2^200≈10^60. Planck time’s about 10^-45 seconds. If you try to press the button more than 10^45 times per second the radiation the electrons in the button will emit will be so high frequency an small wavelength that it will collapse into a black hole.