Cosmox Blogs

Aug 06, 2022

Uncertainty principle

In our day to day lives we unnotice so many things happening around us at the quantum level, every object corresponding to its dual nature acting as both a particle and a wave forces the classical physics to step down and all predefined laws become meaningless in the realm of quantum mechanics.

The uncertainty principle is a great example representing the mysterious nature of the universe at the quantum level, the concept was first introduced by the German physicist Werner Heisenberg (one of the founders of quantum mechanics) in 1927, this theory stated that you cannot measure the exact velocity and the exact position of a particle simultaneously and therefore it is meaning less to calculate the exact velocity and exact position of a particle simultaneously.

To understand further things we need to first understand what it means to behave like both a particle and a wave, now particles exist in a single place at any instant in time. We can represent this by a graph  

V represents the velocity of the particle which is zero at t(s) any instant in time.

Waves on the other hand are vibrations spread out in space just like ripples in water. The most essential part of a wave is its wavelength which is the length between two adjacent peaks, but a wave can never be assigned a specific position, it has a really good probability of being in lots of different positions.

Wavelength

The wavelength is really essential in quantum mechanics because an object’s momentum (p = mv) is related to its wavelength the more momentum an object possesses the shorter will be its wavelength a fast moving object corresponds to a shorter wavelength, a heavy object also has lots of momentum even if it doesn’t move very fast this is the reason we don’t notice the wave nature of everyday objects, if you toss a ball in the air it’s wavelength will be a billionth of trillionth of a trillionth of a meter which is really small to be detected. But we can detect the wavelength of tiny things like atom, electron because they have big enough wavelength which can be detected. Now we can know the momentum or velocity of a by its wavelength but not its positon while we can know a particle’s position but not its velocity since it has no wavelength. If we want to get a particle’s both its positon and its velocity we need to mix the two things, we need to combine the wavelengths of different waves which will have different velocities. When we combine two waves there are some places where the peaks line up making a bigger wave and in other places the peaks fill in the other peaks, now if we keep adding up the waves we can get a wave packet. 

Wavepacket

Now as a result we get a clear wavelength in one small region and that’s a quantum object with a dual nature which is also called as wave – particle duality. Now the uncertainties about both the velocity and position of a quantum object are connected, if you want to reduce the uncertainty about the position by making a smaller wave packet you need to add more waves which will give you a bigger uncertainty about the velocity and if you want to reduce the uncertainty about the velocity by decreasing the waves making the wave packet bigger you get a bigger uncertainty about the position. 

Conclusion

So this was the Heisenberg uncertainty principle which is one of the most fundamental concepts of quantum mechanics. So far we still have not known the dual nature of these mysterious wiggling particles but as we further do new discoveries in the field of quantum physics we will enter the realms of shattering truths about the nature of our universe and who knows what may come next but we will surely be waiting for it even it has a dark truth about our existence or maybe something else.