Q:

Sudden large drop in standing ("top percentage overall") without numeric change in "reputation"

My standing on the Physics Stack Exchange went from "top 16% overall" to "top 67% overall" during a period when I posted only one question or answer (a question posted Jan.5, 2020, MST), plus a few comments.  The question has received 0 votes so far, and I hadn't noticed any up-votes on the comments I've re-checked.  
I understand that the user names can be duplicated, although mine, with the French-language spelling "Edouard", doesn't currently have any duplicates in PSE.
Given my lack of any formal training in college-level physics and a knowledge of it that's been gained almost entirely through a combination of direct observations with my reading of popularizations by well-known physicists (plus a few biographical and philosophical texts reviewing their activities, and some online visits to other physics-oriented websites), I'm imagining my "top 67%" standing, among other users of PSE, to be much the more realistic among the two possibilities I've seen mentioned, but, as the most classic of "idiots savants", I'm curious as to whether the disparity (which has caused me no inconvenience or serious embarrassment) occurred accidentally or experimentally.  
I have not changed my biographical information, which mentions one or two of my naive observations.  Of course, I'll be disregarding my position in the top-to-bottom range, unless an error is disclosed to me.

A:

Are you sure it didn't say "top 16% this year" or "top 16% this quarter"?
I'm quite sure that looking at my profile, I had a similar change, and I believe it's because it was showing me my yearly or quarterly user percent before the new year, and now it is showing the all time percentage ranking.  I'm pretty sure it's the same for you.  
Although people moving up could account for some shifting of the number, given the size of the userbase in physics SE, there would need to have been a lot of activity on users around your reputation for it to change from you being in the top 16% going down to the top 67%.  Like I think that would take at least tens of thousands of users passing your reputation in that time, which seems unlikely to me.
I think the simple explanation is that it changed from a yearly or quarterly ranking, to an all time ranking.

A:

It's funny that your reputation has only increased in 2019, but you believe you have fallen in the sitewide rankings. (You're currently #5200-ish out of 8200-ish users with 200+ reputation points.)  
The blurb that shows on your profile page changes to show you something flattering.  For instance, if you asked a high-visibility question and got 200 points all at once, it might say "top 1% this week" for a while, before reverting eventually to "top 50% this year." I remember being confused by this as a new user.
As another answerer says, if this is a real change it seems more like many other users overtaking you than a change in your rep.  However, the network recently made a change which suddenly increased the reputation scores of nearly every user on the network. So if it's been a couple months, you might have been passed in the rankings by lots of people who were retroactively rewarded for past questions.

A:

The correct tool to explore this is the Reputation Leagues page for this site, which (importantly) allow you to examine the results for the current time period as well as for the previous periods (i.e. last year, last quarter, etc.).
Up to December 31 2019, as pointed out by JMac, you were likely seeing your rank coming from the entire year of 2019,

i.e. a reputation change over the year of +215, making you #1030 of 6,279 with positive rep changes over the year, which puts you in the top 16.4% for the year 2019...
...or, with a slightly lower likelihood, you were seeing your results for the fourth quarter of 2019,

in which you had a reputation change of +104, giving you the rank #665 out of 3,760 users with positive rep changes on that period, i.e. on the top 17.7% for Q4 2019.
When 2019 ended, those statistics stopped getting shown, and the system resets to whatever it thinks will be more flattering, i.e. your highest rank for the current week / month / quarter / year / all time. Here the results are easy to see: while you have one question from 2020, you have (as of this writing) not earned any rep this year. Thus, the system will default to your all-time standing.
(You can easily find evidence of this behaviour by the system by going through the top users by time period on the Reputation Leagues. Thus, if you go to week, the top user right now is this one, and their profile shows "top 0.21% this week". Similarly, the month league is currently topped by this user, whose profile attempts to flatter by showing "top 0.10% this month". There's similar stuff for this year, though note that, since this quarter is currently synonymous with this month, currently nobody gets shown a "top X% this quarter" banner -- those will start appearing on 1 February.)
So, with that in mind:

My standing on the Physics Stack Exchange went from "top 16% overall" to "top 67% overall"

It's extremely unlikely that the system reported you as "top 16% overall" at any time, but it's perfectly reasonable that it showed you "top 16% this year" previously, and, upon noticing the drop to top 67%, your brain filled in the blank on the time period with the available evidence (i.e. top X% all time). Given the evidence above that the time period displayed most prominently on the profiles changes depending on what the rankings are: how sure are you that it really was "top 16% overall"?

