Universe Full of Probabilities

Our universe is full of probabilities. We cannot be certain of most things in our world. We can only guess whether it will rain or not tomorrow. If you are living in Cherrapunji, then the probability that it will rain tomorrow will be high, let’s say 0.9. However still there is chance of it to not rain tomorrow (0.1). In other words, we can say that we are uncertain if an event will occur or not. The same uncertainty governs the modern physics.

                       

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A very famous physicist, Werner Heisenberg, came up with a principle which declared the existence of uncertainty and probabilities in physics. This principle is known as The Principle of Uncertainty. The theory implies that:

                 “It is impossible to determine the position and the momentum of a body simultaneously with any arbitrary precision. This has nothing to do with the limitations of the instrument.”

The above statement can be expressed mathematically as:

                                                        ΔxΔp≥ħ/2

                Δx= uncertainty in position

                Δp= uncertainty in momentum

                ħ= reduced Planck’s constant= 1.054 x 10^-34 J.s

This shows us that Δx and Δp are inversely related. If uncertainty in momentum increases, uncertainty in position decreases and vice versa. If we can accurately determine the position of a body i.e. Δx= 0 then, we will have no idea about the momentum i.e. Δp= ∞. The vice versa is also true.

Let us now discuss graph and what we can conclude from them:

Case (i)

Fig.1.

 

Here uncertainty in position is very less. We can easily say there is high possibility of finding the particle in the peak. However, what about momentum? The graph below shows us that we have no idea about momentum. The uncertainty in momentum is very high. Heisenberg Principle of Uncertainty in proved true.

Fig.2

If Δx↓ then Δp↑

Case (ii)

Fig.3

 

Here we don’t have a clear idea about the position of the body. Probability of finding the particle at a given position is the same at all points. The momentum of the same particle is shown in graph below and we see the uncertainty in momentum is very less i.e. we can make good predictions about the momentum of the particle.

Fig.4

If Δx↑ then Δp↓