DST doesn’t have anything to do with the oscillation of the true noon at any location by +/-15 minutes around the year (that cycle is not even summer/winter).
The chart shows at what time noon happens when you have a 24-hour clock calibrated to get it right on average. For example, a clock showing GMT assuming you’re in Greenwich.
If you add or subtract hours to your clock instead of keeping a 24 hours day length then yes, you will have jumps. But those jumps are caused by you playing with the clock, they are not real.
The fact that Daylight Savings Time exists doesn’t have anything to do that the duration of the day is sometimes a few seconds longer and sometimes a few seconds shorter than 24 hours.
If noon was always 24 hours after the previous one the line in that chart would be flat. With discontinuities if you want to include DST shifts in the chart, but I really don’t see the interest in doing so.
The rationale for applying DST has nothing to do with that variation, it would be just the same if the time from noon to noon was always 24 hours.
This feels like a classic case of talking past each other.
First, I will acknowledge you answered precisely what I asked. Thank you.
I would like to get DST back in context, since it is in that context that I asked. The assertion seemed to be that solar noon being at local noon had some advantages. I agree that is begging the question to assume it, but I am just exploring the consequences.
So, assuming I was asking for drift of solar noon to local noon, we have to account for our messing with the clock. Because we do and did. Would there be advantage to us having a mechanism that more closely aligned them? More, what would that mechanism look like? I was guessing that it would look similar to DST, just with 30 minute swings, not 60.
Let’s assume you’re at longitude 0 and noon happens for you at 12:00 (on average). If there were 24 timezones of exactly 15 degrees of longitude each there will be places at longitude +/- 7.4999 which are in your time zone where noon happens at 11:30 or 12:30 (on average) and never at 12:00. If you want to “fix” this problem you need to add timezones, not to mess wit the clock.
If you only care about your (latitude 0) time of noon which is given by that chart and you want to make it closer to 12:00 by splitting the year in “winter” and “summer” time (with only two changes in the year) you would have winter time from late-december to mid-june and summer time from mid-june to late-december and apply a time shift of about 10 or 15 minutes. This is just a guess, you may take that curve and optimize the timing and magnitude of the shift to approximate the curve with two constante segments. Or more that two, if you want.
That said, that chart is suspicious for not having jumps for DST. How does that work?