UNCERTAINTY PRINCIPLE

UNCERTAINTY PRINCIPLE

The universe imposes certain restrictions on our knowledge. One of them is in the form of uncertainty principle. This principle is one of the pillars of Quantum mechanics and is the ultimate precision limit of the universe.  It was first stated by  German physicist Werner Heisenberg in 1927 . So, it is also called Heisenberg’s uncertainty principle.

STATEMENT

The exact position (x) and momentum (p) of a particle cannot be determined simultaneously with absolute certainty. The more precisely the position is determined, the less precisely the momentum can be determined and vice versa.

rule

where ,

X is uncertainty in position
p is the uncertainty in momentum

 h is reduced plank constant

Another form of the uncertainty principle relates the uncertainty in energy and the uncertainty in time available for the measurement . So, the more precise the energy measurement, the less precise the time measured and vice versa.

EXPLANATION OF THE UNCERTAINTY PRINCIPLE

experiment

 The uncertainty principle is a direct consequence of “wave particle duality “. A particle exists as a particle and as a wave and that too at the same time. A particle has an exact position, but a wave does not. Similarly, the momentum is related to the wavelength(λ) by

p=h/λ

To see an electron, we would inevitably have to incident a photon of light towards it. If the wavelength of the light used to make the measurement is λ, then momentum of each photon will be h/λ. When one of these photons will hit the electron, the photon will be scattered, and this scattered photon will be analyzed to make measurements of position and momentum.

But when the photon strikes the electron, the original momentum of the electron will be changed. One cannot predict the exact change in momentum, but it will be of the same order as the momentum of the photon itself.

Δp = h/λ

is equation gives the uncertainty in momentum.

In order to reduce the uncertainty in momentum, one must use light of longer wavelength. But using longer wavelength will be increase the uncertainty in the position. This is because the position of electron will be order of wavelength of light. Hence uncertainty in position is

Δx=λ

Alternatively, to reduce uncertainty in position, one must use light of shorter wavelength. But using shorter wavelength will decrease the accuracy of momentum measurement. On the other hand, if one uses light of longer wavelength, the accuracy in momentum measurement increases, but the accuracy in the position measurement decreases. So, by multiplying the two equations, we get:

ΔxΔp=h

UNCERTAINTY PRINCIPLE

FUNDAMENTAL PROPERTY OF EVERY SYSTEM

Many people confuse the uncertainty principle with the “observer effect” in the classical physics. But the observer effect is the limitation of the measuring systems and human limitations. On the other hand, the uncertainty principle states a fundamental property of quantum systems and is not a statement about the observational success of current technology.  Even with most perfect instruments and methods, this uncertainty will always remain there.

Another area of concern is uncertainty principle on big objects. By big, we mean anything bigger than an atom. The principle is universal and is applied to every object, but in big objects the phenomena is too small to be detected. Nevertheless, the uncertainty principle imposes a fundamental limit to what we can know about the behavior of quantum systems and ultimately about the universe.