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What’s an “Infinite Second?”

I have absolutely no idea. It's the closest thing I could come with to calling a point in time that is infinitely small - a number that has no end. If you try to convert a number with no end into time you've got a point in time that is infinitely small.

Physically, such a thing probably doesn't exist. The Planck Time is about 10^-43 seconds, which has around 43 digits [when measured in seconds] but is not a non-terminating decimal. If we assume the remainder of π - 314 is in days, the closest we got to π was ≈ 137.605270158... seconds after midnight (local time.) If the expansion was in hours, it'll happen at ≈ 15.9265359... hours, or just before 4 PM local time.

3/14/2015
Once-in-a-century Pi Day.

Pi, like e – the base of natural logarithms – is a transcendental number. It’s not a rational number – it can’t be expressed as a ratio of two integers. Pi’s exact value has an infinite number of decimal places.

Twice today, the date & time was 3/14/15 9:26:53 . . . The numerical string representation of the date & time matched the first ten digits of Pi.

Let’s say we have a perfectly calibrated digital clock that displays the precise time to an arbitrary level of precision (decimal places). Also, the clock “ticks” in increments of the smallest time interval that has any meaning in the physical world (explained below).

During the one second between 9:26:53 and 9:26:54, at an infinitesimally brief point, the digital clock display will match exactly the value of Pi, to an arbitrarily long string of decimal places.

From classical & nuclear physics, the smallest possible physical elapsed time is the time it takes for the fastest thing in the universe (light) to travel the shortest possible distance in the universe (”diameter” of a neutron or proton). Distance = rate * time. Time = distance / rate. So that’s about (1.65*10^-13 cm) / (3*10^10 cm / second) = 5.5*10^-24 seconds; mighty quick. That’s 5.5 yoctoseconds. (One yoctosecond = 1/1000 of a zeptosecond.)

However, from quantum physics, the briefest physically meaningful span of time is the [too small to be named] time required for light to travel one Planck wave length; that’s 10^-44 seconds. 100 quintillion of those ticks in a yoctosecond. The Planck wave length can be thought of as the essential fabric of the space-time continuum.

Let’s define 10^-44 seconds = one FReepersecond. Our digital clock ticks in FReepersecond increments.

So between 9:26:53 and 9:26:54 – for one brief shining FReepersecond moment – our digital clock display will equal Pi to 44 decimal places. At some hypothetical fraction of a FReepersecond, the display would equal Pi to any number of decimal places.

Is clear, yes?