Concept Clarification 3: 'Instantaneous'

I wanted to do something short and fun, and this lets me bring up one of my favorite units of measure... So here we go:

In previous posts, and in many posts that will follow, I'll say things like 'if we assume we did this instantaneously' or 'If we can do this very rapidly' or 'the change happens nearly instantaneously'. On the outside, this seems pretty simple: I'm talking about something happening in a short period of time.

But how short is short? Like so many things I've mentioned: it depends on who you ask.
One inescapable truth is that there are specific timescales for different events, and depending on your point of view only some of them may be relevant.


For example: to a geologist studying the motion of the earth's crust, an event happening over the order of decades is pretty much instantaneous. For an engineer looking at quasistatic loadings, things that on the millisecond level can be considered instantaneous.What matters is the timescale of the relevant processes (sort of like the reference for 'why' something happens).

I previously mentioned I did work in simulations of radiation damage and its effect on material failure: a problem with several different relevant timescales:

Timescales for applications in nuclear waste management.

Centuries are relatively easy for people to grasp: they are a long time for most applications, so really only become an instant on geological or astronomical timescales. Sporting events can be decided by milliseconds.

But way down at the bottom of the above diagram sits the attosecond: \(10^{-18}\) seconds. As I note in the diagram, this is the timescale at which the first interactions of high energy particles and atoms occur during radiation damage processes.

But how small of a time increment is it? Saying \(10^{-18}\) seconds isn't really meaningful in an intuitive way, other than 'it's really small'. It is so short a period of time that light only travels the length of 3 hydrogen atoms. 3 hydrogen atoms (6 Bohr radii for those in the know, or a bit over 3 Å)... that's it. Down here at this timescale, electrons don't even change energy states instantaneously. There is a budding field of physics called attophysics that is attempting to resolve certain events to this timescale to reveal more details of how certain atomic and molecular events occur.

And that's why it's my favorite unit of measure.

Have a Merry Christmas!