An operational definition is a procedure by which a number can be assigned to a physical quantity. Such a definition typically has a range of validity. An example is length.
To assign a number to a length, we have to:
Point 1 is usually OK. We only have to worry about it when the properties of space change (as they do in general relativity). Point 2 only works if the quantity we are trying to represent with a number from our standard is "of the same type" (whatever that means). If you think about trying to measure an area by fitting a standard length against and counting the number of times it fits in you will have a problem, since our standard length has a length but no width. You could fit an infinite number of them in an area.
Points 3 and 4 limit what we can do. If we are measuring the height of a door and the door has been cut by a power saw and not sanded, there may be grooves on the edges of the door of a few millimeters or more. We could not define "the height of the door" to better than that accuracy. Even if it were sanded very smooth, the door is made up of atoms -- as is our standard measuring stick. We could not break our standard measuring stick into pieces less than a nanometer in size in order to count how many fit against the door. Nor could we measure the distance to the moon with a measuring stick. We need to find other operational definitions to extend our measurement to these regimes.
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Last revision 2. September, 2005.