According to quantum mechanics, there is a definite limit to the accuracy of any measurement. This limit is not dependent on the accuracy of a measuring instrument, but is a property of nature. This is the result of two factors:
- The wave-particle duality
- The unavoidable interaction between the system under observation and the observing instrument
Uncertainty due to the unavoidable interaction between the system under observation and the observing instrument
Consider using light to locate an object in a dark room. If the object is normal day objects(e.g. mobile phone), there will be no change to its position. However, if light is used to locate a sub-atomic particle, the photon will strike the sub-atomic particle. Hence, much of the photon momentum will be transferred to the sub-atomic particle, hence changing the motion and position of the sub-atomic particle in an unpredictable way.
The mere act of measuring the position of an object at one time makes our knowledge of its future position inaccurate.
Uncertainty due to wave-party duality
Consider using photons to measure simultaneously the position,x, and velocity(or momentum,p) of an electron. Since the position of the electron, is accurate up to the wavelength of the radiation(light) used. To measure the location of the electron as accurately as possible, we must use a short wavelength radiation. However, short wavelength = high frequency, and according to E=hf, corresponds to high energy. The more energy the photons have, the more momentum they are likely to impart to the electron when they strike it. This results in an increase in the uncertainty in measurement of the electron’s momentum.
However, if a longer wavelength radiation (and thus lower frequency and energy) is used in the detection of the electron, it would imply lower resolution and hence greater uncertainty in determining an object’s position.
The mere act of observing produces a significant uncertainty in either the position or the momentum of the electron.
Heisenberg’s uncertainty principle:
$$\Delta x \, \Delta p \ge \frac{\hbar}{2} \, \text{ , where } \, \hbar = \frac{h}{2 \pi}$$
