Uncertainty Principle

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All moving objects in our daily life have well defined paths or trajectories. The path or trajectory of an object can be determined by knowing its position and velocity at various intervals of time. However, Werner Heisenberg, in 1927, pointed out that we can never measure accurately both the position and velocity (or momentum) of a microscopic particle as small as an electron. Consequently, it is not possible to talk of the trajectory of an electron. On this basis, Heisenberg put forward a principle known as uncertainty principle. According to Heisenberg's uncertainty principle, it is not possible to measure simultaneously both the position and velocity (or momentum) of a microscopic particle with absolute accuracy or certainty.

Mathematically, uncertainty principle may be put as: "The product of uncertainty in position and momentum is always constant". It may be expressed as:

where Dx = uncertainty in position and Dp = uncertainty in momentum.

The sign ³ means that the product of Dx and Dp can be either grater than or equal to h/(4p). It can never be less than h/(4p). The sign of equality refers to minimum uncertainty and is equal to h/(4p).

The constancy of the product of uncertainties means that:

(i) If Dx is small, (the position of the particle is measured accurately), Dp would be large, which means there would be large uncertainty in its momentum.

(ii) On the other hand, if Dp is small, the momentum of the particle is measured more accurately, Dx would be large. This means there would be large uncertainty with regard to the position of the particle.

In other words, if the position of a particle is measured accurately, there will be more error in the measurement of momentum.

Conversely, if momentum is measured more accurately, the position will not be accurately known.