I would like to symbolize a series of point feature classes to show a graduated level of transparency based on time - like breadcrumbs. Is this possible?
Not really within a single layer. You could create a group layer with multiple copies of your point layer that each had a definition query covering each of your date ranges and manually set each layer to a different transparency. The advantages of this set up are that you can change the layer order to stack more transparent points on top of less transparent points and all transparency levels will display overlapped.
In a single layer with multiple categories that have tranparency, only the top feature shows and all features below it are not drawn, even though the transparency makes you expect that lower features would show with blended colors. Multiple Categories also does not really work for date ranges since you would have to include every possible date in a range that may not currently exist in your data if it ever could possibly exist.
As a work around, if this is for visualization purposes, you can convert your points to circle polygons. ArcMap provides the ability to apply levels of transparency for polygons, based on a field value (symbology-advanced-transparency). Within Pro it seems you don't need this kind of a work around any more - haven't tried it: Vary transparency by attribute—ArcGIS Pro | ArcGIS Desktop
If you work with ArcGIS Online you can also set the transparency based on an attribute:
I was unaware of the symbology option, but it does not work with date fields, only numeric fields. If a numeric field is calculated to be equal to portions of the date that define the ranges, like yyyy or yyyymm these values could be used. VB and python have methods for extracting date portions. Attribute Assistant could maintain the numeric field as dates are entered during an edit session. So what date portions define the ranges you need?
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