Quantum Theory of Time (Clock)

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Quantum Time Clock Theory describes a clock whose minute hand can only point to whole-minute tick marks and not in between. As such it jumps from one tick to the next.

The fundamental principle of quantum time clock is that if you are scheduled to work at 9am and you punch in one second later (at 9:00:01), you are late.

This means the clock hand jumps from 9:00am to 9:01am at 9:00:01 (or any time after 9:00:00.000...). From this one fact we deduce the rest.

Contents

Clock Correction

Clock Correction is the fundamental operation of sticking the minute hand to a tick. Clock correction, by definition, produces the correct time. It is not an "adjustment."

The fundamental principle says that if you are one second late when punching in, you are one minute late. What about punching out? If you are one second early, you are one minute early. Therefore, clock correction depends on whether you are punching in or punching out. One is the negative of the other.

  • Because the clock correction operation depends on the motion of the employee relative to the employer/observer (either arriving or leaving), we could call this a relativistic quantum time (clock) theory.

To be clear on what the fundamental principle implies, if you punch in or out exactly "on time," you are, by definition, on time. One might think that when the clock just turns to the scheduled punch-in time that you become late at that moment (that is, "on time" means "up to but not including"). This is not the case. Instead, "on time" includes the scheduled start time for exactly one increment of the calculation ("measurement") resolution. The reason is as follows. Say you are able to measure time down to one second and you are scheduled to work for one hour from 1pm to 2pm. It is easy to see that you can punch out at exactly 2:00:00pm to be considered "on time" (and not one second before). Because you were scheduled to work for one hour, we presume by definition that subtracting your punch in time from the punch out time will yield exactly one hour, or in this case 3,600 seconds. This is true only if you punched in at exactly 1:00:00pm. QED.

Therefore, when punching in, the clock sticks to the next minute, as shown:

  Raw -> Fixed    Status
-------  -------  --------
8:58:01  8:59:00  Early
8:58:59  8:59:00  Early
8:59:00  8:59:00  Early (for one second)
8:59:01  9:00:00  On Time
8:59:59  9:00:00  On Time
-------
9:00:00  9:00:00  On Time (for one second)
9:00:01  9:01:00  Late
9:00:59  9:01:00  Late
9:01:00  9:01:00  Late

When punching out, the clock sticks the previous minute. This occurs naturally when converting seconds to minutes in the normal manner of lopping off the seconds:

  Raw -> Fixed    Status
-------  -------  --------
4:59:00  4:59:00  Early
4:59:01  4:59:00  Early
4:59:59  4:59:00  Early
-------
5:00:00  5:00:00  On Time
5:00:01  5:00:00  On Time
5:00:59  5:00:00  On Time
5:01:00  5:01:00  Late
5:01:01  5:01:00  Late
5:01:59  5:01:00  Late

It is important to see that in both cases uncorrected time with zero seconds (at the top of a minute) is the same as the corrected time. 2:00:00pm as read on the clock registers as 2:00pm whether punching in or punching out, and is always considered "on time."

  • If you are still having trouble visualizing how this works, or why, imagine you are paying an employee $100 per second (that is, $360,000 per hour), and visualize a $100 bill flying out of your hand as each second ticks away on the clock. Now imagine said employee scheduled to work at 9am standing in front of the time clock reading 9:00am, ticking away, not doing any work. If the clock were not corrected, up to 59 $100 bills could fly away before the employee punches in. The first $100 bill flies at the stroke of 9:00:01. The 59th flies at the stroke of 9:00:59. The employee pushes the button after that but before 9:01:00, registers a 9am punch-in, and collects the $5,900 up to that point.
  • When the employee punches in at exactly 9am (that is, between 9:00:00 and 9:00:01), you are paying $100 for that one second at the stroke of 9:00:01. When punching out at exactly 5pm (between 5:00:00 and 5:00:01), you are not paying for the button push, since the last $100 went out just before at 5:00:00. It's symmetrical in that way — you have to pay for either the first second or the last one, but not both. By saying that punching out precisely at the scheduled time is on time, we are breaking the symmetry (like choosing a left or right-hand water glass at a round table) and thus making the punch-in time work the way it does.
  • The keen observer will notice that the same symmetry described above at the one-second level also applies at the one-minute level, and may then wonder why we are bothering with this theory at all, because punching in and punching out will balance out one another and employees will be paid correctly if we just truncate the seconds on both ends as we do for punching out. The answer: scheduling — and the precise definitions of early, late, grace, and bump with respect to a schedule. Without a schedule, we don't need this theory. Therefore, without a schedule interface or implied schedule, RPOWER just truncates times.

Scheduling

A schedule fixes the punch in and punch out "target" times on a given date for an employee. In the discussion to follow, these target times act as "sticky points" or "attraction points" for the minute hand, as if magnets were placed on the clock.

Clock Rounding Basics

Clock rounding is defined as banker's rounding for time. Banker's rounding makes 1.4999... = 1 and 1.500... = 2. We can do the same using seconds (or fractions of seconds). If rounding to 15 minutes, for example, 8:47:29 is 8:45 and 8:47:30 is 9:00. 9:07:29 is 9:00 and 9:07:30 is 9:15.

More on clock rounding will be discussed later. Right now we need it to establish implied schedule times based on raw (uncorrected) clock times.

Implied Schedule

Without an explicit schedule, one can be implied to exist if employees are always scheduled to punch in and out at certain times, or at least certain positions on the clock.

Applying clock rounding to the raw (uncorrected) current time results in the current implied scheduled time. It is, of course, possible to have different implied clock positions for punching in and out.

Grace

Per Wikipedia, "A grace period is a time past the deadline for an obligation during which a late penalty that would have been imposed is waived." In this limited sense, grace only applies to time after a given target time. We will amend that presently. Also, later we will find that the term "grace period" can apply more generally to the combination of "grace" and "bump," which will be described later, but for now it is important to distinguish the two.

As with clock correction, punching out can be the negative of punching in, and vice-versa. Following this line of thought, positive grace would allow an employee to punch in a little late and still be considered on time, or to punch out a little early (before the appointed time) and do the same.

Therefore, the word "grace" will always mean leniency applied to the employee's benefit, and negative grace is not possible (or rather, means something else, described in the next section).

When punching in, grace stops the clock on the target time for a full number of minutes. When punching out, it jumps the clock ahead. Here is punching in with a 2-minute grace:

  Raw -> Fixed -> Graced   Status
-------  -------  -------  ------------
8:58:01  8:59:00  8:59:00  Early
8:58:59  8:59:00  8:59:00  Early
8:59:00  8:59:00  8:59:00  Early (for one second)
8:59:01  9:00:00  9:00:00  On Time
8:59:59  9:00:00  9:00:00  On Time
-------
9:00:00  9:00:00  9:00:00  On Time
9:00:01  9:01:00 *9:00:00  On Time (+1)
9:00:59  9:01:00 *9:00:00  On Time (+1)
9:01:00  9:01:00 *9:00:00  On Time (+1)
9:01:01  9:02:00 *9:00:00  On Time (+2)
9:01:59  9:02:00 *9:00:00  On Time (+2)
9:02:00  9:02:00 *9:00:00  On Time (+2) (for one second)
9:02:01  9:03:00  9:03:00  Late
9:02:59  9:03:00  9:03:00  Late
9:03:00  9:03:00  9:03:00  Late

It is important to recall that if the employee sees the clock read 9:00am when punching in, he or she is in fact punching in at 9:01am. Therefore, allowing 9:00am to really mean 9:00am requires a 1-minute grace.

Here is punching out with a 2-minute grace:

  Raw -> Fixed -> Graced   Status
-------  -------  -------  ------------
4:57:00  4:57:00  4:57:00  Early
4:57:01  4:57:00  4:57:00  Early
4:57:59  4:57:00  4:57:00  Early
4:58:00  4:58:00 *5:00:00  On Time (-2)
4:58:01  4:58:00 *5:00:00  On Time (-2)
4:58:59  4:58:00 *5:00:00  On Time (-2)
4:59:00  4:59:00 *5:00:00  On Time (-1)
4:59:01  4:59:00 *5:00:00  On Time (-1)
4:59:59  4:59:00 *5:00:00  On Time (-1)
-------
5:00:00  5:00:00  5:00:00  On Time
5:00:01  5:00:00  5:00:00  On Time
5:00:59  5:00:00  5:00:00  On Time
5:01:00  5:01:00  5:01:00  Late
5:01:01  5:01:00  5:01:00  Late
5:01:59  5:01:00  5:01:00  Late

Note that a 1-minute grace applied to adjust punching in "on time" also means that employees can punch out with the clock reading one minute before their scheduled times.

Bump

The opposite of grace is bump. It is grace applied to the employer, not the employee. We consider it separately for employers who require employees to punch in before they start their shift and punch out only after they have worked up until their scheduled time.

Here is a 3-minute punch-in bump:

  Raw -> Fixed -> Bumped   Status
-------  -------  -------  ------------
8:55:01  8:56:00  8:56:00  Early
8:55:59  8:56:00  8:56:00  Early
8:56:00  8:56:00  8:56:00  Early (for one second)
8:56:01  8:57:00 *9:00:00  On Time (-3)
8:56:59  8:57:00 *9:00:00  On Time (-3)
8:57:00  8:57:00 *9:00:00  On Time (-3)
8:57:01  8:58:00 *9:00:00  On Time (-2)
8:57:59  8:58:00 *9:00:00  On Time (-2)
8:58:00  8:58:00 *9:00:00  On Time (-2)
8:58:01  8:59:00 *9:00:00  On Time (-1)
8:58:59  8:59:00 *9:00:00  On Time (-1)
8:59:00  8:59:00 *9:00:00  On Time (-1)
8:59:01  9:00:00  9:00:00  On Time
8:59:59  9:00:00  9:00:00  On Time
-------
9:00:00  9:00:00  9:00:00  On Time (for one second)
9:00:01  9:01:00  9:01:00  Late
9:00:59  9:01:00  9:01:00  Late
9:01:00  9:01:00  9:01:00  Late

Here is a 3-minute punch-out bump:

  Raw -> Fixed -> Bumped   Status
-------  -------  -------  ------------
4:59:00  4:59:00  4:59:00  Early
4:59:01  4:59:00  4:59:00  Early
4:59:59  4:59:00  4:59:00  Early
-------
5:00:00  5:00:00  5:00:00  On Time
5:00:01  5:00:00  5:00:00  On Time
5:00:59  5:00:00  5:00:00  On Time
5:01:00  5:01:00 *5:00:00  On Time (+1)
5:01:01  5:01:00 *5:00:00  On Time (+1)
5:01:59  5:01:00 *5:00:00  On Time (+1)
5:02:00  5:02:00 *5:00:00  On Time (+2)
5:02:01  5:02:00 *5:00:00  On Time (+2)
5:02:59  5:02:00 *5:00:00  On Time (+2)
5:03:00  5:03:00 *5:00:00  On Time (+3)
5:03:01  5:03:00 *5:00:00  On Time (+3)
5:03:59  5:03:00 *5:00:00  On Time (+3)
5:04:00  5:04:00  5:04:00  Late
5:04:01  5:04:00  5:04:00  Late
5:04:59  5:04:00  5:04:00  Late

Bump + Grace = Grace Period

Bump and grace are separate settings. Their sum erects "windows" around schedule target times during which the clock will be "adjusted" automatically without interaction, except perhaps a pop-up note indicating that a bump or grace was applied.

As mentioned previously, the term grace period will usually be used in practice to refer to the combined bump and grace window described here.

Putting together an example, say you want the system to automatically adjust the time to 9:00am when the clock reads 8:55am (and not 8:54am) up to and including 9:00am (and not 9:01am). You are doing a 4 minute bump (not 5) and a 1 minute grace. Your total grace period is 5 minutes.

This also means that punching out at 5:00pm will occur with the clock reading anywhere from 4:59pm to 5:04pm.

Early and Late Punching

What happens when an employee attempts to punch in or out outside the grace period?

It is simple to discuss punching in late and punching out early. There is no adjustment necessary. Employees are simply not paid for the time they did not work.

Punching in early or punching out late is different. For example, employees who arrive to work 10 minutes before their scheduled times may need a few minutes to prepare to go on station (put away personal effects, change into uniforms, etc.). It may be perfectly acceptable for them to punch in "a little extra early" on the system and still register their originally scheduled times.

Punching out is a little different. Employees typically punch out before they get ready to leave the establishment. That is to say, punching out is the reverse of punching in, not the opposite. Therefore, it is generally not acceptable to punch out late and still be considered on time.

When punching in, extra time needs to be allocated to still punch in "on time" without manager intervention, but with a different message from the bump, indicating that a manager can adjust a time clock entry if in fact the employee is early. This extra time window is simply called the Extra Early Bump. We define this number to be the total bump before the scheduled time, overlapping the regular bump, so that changing the regular bump minutes would not affect this setting. Punching in before the Extra Early Bump time would simply not be allowed without manager approval, and with such approval the punch-in would register the current (corrected) clock time. In order to punch in "on time," the employee would simply have to wait until the Extra Early Bump time begins.

When punching out, however, no extra time needs to be allocated. Manager approval will be required regardless. However, the manager needs to be able to choose whether to register the current (corrected) time or the originally scheduled time.

Clock Rounding

Employers sometimes like to have all of their time clock entries begin and end on certain fractions of hours to make time clock reports and their totals easier to read. State law comes into play here. Generally, we assume:

  1. Rounding has to be done without bias. In particular, it cannot specifically favor the employer.
  2. Rounding cannot be done to increments greater than 15 minutes.

Rule 1 means that rounding has to be done on the raw clock. Clock correction, though "correct," could be considered a bump in the employer's favor (because, well, it is just that — it removes an unfair advantage to the employee). However, since clock correction is primarily done for the purpose of preparing for adjustment very close to scheduled times, rounding the clock first by a larger increment will have no effect whatsoever on the final result.

Rule 2 implies that it only makes sense to round in 5, 10, or 15-minute intervals.

Clock rounding most likely makes grace and bump settngs moot. Extra-early bump may still apply.

Summary of Settings

  • Punch-In Bump (forward for early in): E.g., 3 or 4. Default is 4.
  • Punch-In Grace (back for late in): E.g., 1 or 2. Default is 1.
  • Punch-Out Grace (forward for early out): E.g., 1 or 2. Default is 0.
  • Punch-Out Bump (back for late out): E.g., 1 or 2. Default is 2.
  • Implied schedule interval: E.g., 10, 15, 20, 30, 60. Default is 0.
  • Extra-early bump (forward for early in w/o manager): E.g., 10, 15, 20. Default is 0.
  • Round clock to: Only 0, 5, 10, or 15 allowed. Default is 0.
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