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One of the first results of Einstein s speed-of-light axiom is the fact that there can be no such thing as an absolute time standard It is impossible to synchronize the clocks of two obervers so that they will see both clocks as being in exact agreement unless both observers occupy the exact same point in space In recent decades we have built atomic clocks, and we claim that they are accurate to within billionths of a second (where a billionth is 0000000001 or 10 9) However, this has meaning only when we are right next to such a clock If we move a little distance away, then the light (or any other signal that we know of) takes some time to get to us, and this throws the clock s reading off The speed of EM-field propagation, the fastest speed known, is approximately 300 million meters per second (300 108 m/s), or 186,000 miles per second (186 105 mi/s) A beam of light therefore travels about 300 m (984 ft) in 0000001 s (one microsecond or 1 s) If you move a little more than the length of a football field away from a superaccurate billionth-of-a-second atomic clock, the clock will appear to be in error by a microsecond, or 1,000 billionths of a second If you go to the other side of the world, where the radio signal from that clock must travel 20,000 km (12,500 mi) to reach you, the time reading will be off by 0067 s, or 67 thousandths of a second If you go to the Moon, which is about 400,000 km (250,000 mi) distant, the clock will be off by approximately 133 s If scientists ever discover an energy field that can travel through space instantaneously regardless of the distance, then the conundrum of absolute time will be resolved In practical scenarios, however, the speed of light is the fastest possible speed (Some recent experiments suggest that certain effects can propagate faster than the speed of light over short distances, but no one has demonstrated this on a large scale yet, much less used such.

0 0 0 1 0 0

Part III:

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effects to transmit any information such as data from an atomic clock) We can say that the speed of light is the speed of time Distance and time are inextricably related

To create an aggregate of each month to populate these YTD columns, you first need to use data items that retrieve all the members leading up to This Year Selected Period This example shows a Query Explorer screen that contains the data items needed to retrieve this information The data items are This Year Periods To Date, Last Year Periods To Date, and 2 Years Ago Periods To Date

0 0 1 0 0 0

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Double-click any of these data items to open the Data Item Expression screen If you double-click This Year Periods To Date, the expression displays in the Expression Definition pane, as shown next:

(727)

Imagine that there are eight clocks in space arranged at the vertices of a gigantic cube Each edge of the cube measures 1 light-minute, or approximately 18 million km (11 million mi) long, as shown in Fig 16-1 We are given a challenge: Synchronize the clocks so that they agree within the limit of visibility, say, to within 1 second of each other Do you suppose that this will be easy Because the clocks are so far apart, the only way we can ascertain what they say is to equip them with radio transmitters that send time signals

This expression uses the data item This Year Selected Period to retrieve all the members from the beginning of the year through the period selected in the prompt in This Year Selected Period Last Year Periods to Date and 2 Years Ago Periods To Date use Last Year Selected Period and 2 Years Ago Selected Period, respectively, as follows: Last Year Periods to Date: periodsToDate([PowerCube][Years][Years][Years],[Last Year Selected Period]) 2 Years Ago Periods to Date: periodsToDate([PowerCube][Years][Years][Years],[2 Years Ago Selected Period]) These expressions return the entire set of members from the period to date, which is not necessary if you want to view the sum of the revenues up to a particular month in a given year The aggregate expressions used in the YTD columns solve this problem by rolling these values for each year into a single value

In this model, 3 is a ctitious driving noise For the acceleration state, the above model has assumed that a = 3 For simplicity of the description, this discussion will assume that 3 is a 2 Gaussian white noise process with PSD of 3 Many other possible acceleration models could be hypothesized In fact, this is one of the drawbacks of this approach The model is attempting to force a time invariant Markov model on the acceleration signal when in fact the acceleration process is not even a stationary random signal Typically, the parameter 3 of the acceleration model will be selected so that the [P]33 element is large, to cause the Kalman lter to use the acceleration measurement to correct the acceleration state Note that the selection of the acceleration model is a hypothesis It does not have the same rigorous support as does the modeling of the stationary sensor error processes that were discussed in Section 492 and used in the approach of Section 71 As a result, the acceleration model may require signi cant tuning to achieve satisfactory performance

12:

Figure 16-1 A hypothetical set of eight clocks, arranged at the vertices of a cube that measures one light-minute on each edge How will we synchronize these clocks

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