# What's the distance required for an omnidirectional wave of light of the highest possible amplitude to reach the lowest possibly measurable amplitude?

I'm interested in finding the distance it takes a single omnidirectional pulse of light of a given wavelength under ideal conditions to spread out from the highest possible amplitude to the lowest possibly measurable amplitude.

I intend to after after getting my answer calculate how many digits of Pi are required to use this as the diameter of a perfect circle down to Planck length and pinpoint any point in space and time or spacetime within down to the levels of Planck time and length. However first things first, I don't know how to calculate the distance required under ideal conditions and so require assistance.

Essentially my question is: How do I calculate the distance required for an omnidirectional wave of light of a given wavelength to spread out from the highest possible amplitude to the lowest possible measurable amplitude under ideal spacetime conditions. By 'ideal' I mean flat infinite space free of expansion. The reason for assuming the described ideal conditions is to simplify calculations while also allowing this to be readily adapted to different conditions.

• this and the velocity of light hyperphysics.phy-astr.gsu.edu/hbase/Forces/isq.html Jun 30, 2021 at 4:13
• What do you mean by highest possible amplitude? Jun 30, 2021 at 8:12
• Thank you Anna V 4 that really helps. Chris Long, by highest possible amplitude I mean intensity or the density of a given wave. le.ac.uk/se/centres/sci/selfstudy/lac2.htm :"The amplitude of a wave tells us about the intensity or brightness of the light relative to other light waves of the same wavelength." Jun 30, 2021 at 8:24
• The concept of the lowest possible measurable amplitude doesn't seem clear enough to allow a non-opinion-based answer. Within a wave model, it depends on the available technology. In the real world, there is an intensity level below which the wave model of light breaks. Jul 9, 2021 at 4:04
• GiorgioP, would it help if one assumes the lowest possible measurable amplitude to be equivalent to a single photon within an area equal to its wavelength plus its calculated uncertainty in position based on its given wavelength? Surely at this point the described omnidirectional pulse of light can be considered to have separated into many single photon waves with completely distinct coordinates and directions from each-other with each single photons energy equaling the frequency times Planck's constant. Does that work? Jul 9, 2021 at 9:42