Is it possible to suggest a physical experiment in which measurement errors are dramatically increasing? (due to the accumulation of errors) Is it possible to suggest a physical experiment in which measurement errors are dramatically increasing? (due to the accumulation of errors)
Maybe some magnetic field can be used here? Or any other idea?
 A: A very simple example might be as follows...


*

*Measure the period of a single swing of a pendulum.

*Predict the position of the pendulum an hour from now.
A: There is a opportunity for cumulative errors to slip in whenever one uses one set of measurements as a proxy for a fundamentally different parameter. This is particularly so if the measured values are some kind of derivative (e.g., time or position derivatives) of the desired parameter.
An example is "dead reckoning." Suppose you have an estimate of where a ship at sea is at some point in time. With no sightings of land after this point in time, the ship's navigator occasionally throws a log overboard from the ship so as to estimate the ship's velocity relative to the log that is dead in the water. (People argue that this is the wrong etymology. Whatever.) Regardless of the etymology of the term, the uncertainties, biases, and intermittent nature of the velocity measurements inevitably add up. The error in the ship's position is at best a random walk.
Random walks appear whenever one integrates an unbiased white noise process. Worse kinds of errors appear when the measurements to be integrated have a bias or a scale factor error.  Yet worse kinds of errors appear when the integration has to be done twice. This happens, for example, when accelerometer readings are used to estimate position. Yet worse again kinds of errors appear when the measurement is incomplete. Spacecraft accelerometers, for example, do not and cannot measure the acceleration due to gravity. These issues, along with errors that result from numerically integrating angular velocity measurements to yield orientation, make spacecraft navigation rather difficult.
A: Here is a simple experiment which will demonstrate this effect.
You can buy a device called a pedometer, which measures how far you have walked on a hike by detecting each time you take a step. The pedometer has a calibration procedure in which you tell it how many inches there are in one of your steps, and it then adds that number of inches to the distance total each time you take a step. 
If you enter 33 inches for your stride length but it is really 30 inches, then it registers a two inch error for every step you take and those errors accumulate- so if you walked 3 miles in reality, the pedometer would tell you 3.3 miles instead.
