This isn't the way the world works as you think. The quantum realm explains our world at the atomic level. We know all these stories. And I know we all are fed up listening the story of quantum mechanics again and again. But the science it has that very few people are aware of, is a story that has another level of geniusness in it. So, what are we doing here? Are we trying to learn quantum mechanics' principles in a completely new way? No, these principles that we learn are just like how we experience science in real life. Science is connected to our life, our vision. But quantum as you all know, is connected to our atomic life, no vision, perhaps, an imaginary and revolutionary vision. So this is what we are going to learn. We'll create a vision. Welcome to Science Specials Week Season 2.
Exploring Ideas Of Quantum Mechanics | Principle 2: The Heisenberg Uncertainty Principle
Now, in the previous session, we learnt about the first principle - Wave Particle Duality. Next up, as you might have already seen is the Heisenberg Uncertainty Principle. And that's what our topic is for today in Quantum Mechanics.
At the foundation of quantum mechanics, lies the Heisenberg's Uncertainty Principle. In simple words, it states that you can not be sure about the position or the momentum of the quantum system. What is quantum system? Just the electrons and the particles.
Position And Momentum
We know what is position. Position is the place where someone or something is located. And then, we're stuck. What is momentum? Well, its just like the word moment. In physics, momentum means the mass of a particle multiplied with its velocity. See it is so simple to understand. Let us understand it deeply. Momentum is defined as the amount of motion occurring in something that's moving or the force that drives something forward to keep it moving. It is a vector quantity, possessing a magnitude and a direction.
Mass is represented as "m" in physics and velocity is represented as "v" in physics. So, when we multiply both of them, we get the momentum of the particle. And momentum in physics, is represented by "P".
So : P = mv. That's it! This is the formula for momentum. So basically the velocity of the mass of a particle is its momentum.
The Heisenberg Uncertainty Principle
So getting back, what is this uncertainty principle? See, this principle states that if we determine or know the position of a particle, then we do not know or we are uncertain about its momentum. And if we know its momentum, we do not know the particle's position. What's going on here?
According to the principle, if you know everything about where a particle is located, you know nothing about its momentum. Conversely, if you know everything about its momentum, then you know nothing about where the particle is located. Simply put, this means that we can not measure the position and the momentum of a particle with absolute certainty.
Cracking The Formula
Mathematically, the uncertainty principle is represented by this expression:
BOOM! What is this expression? Um, no need to get super excited. Let's crack this formula!
So what is this triangle like thing? Well this is the "Delta" with symbol "Δ" in physics. What is this delta? Well, in physics, delta means a change in something. In which thing? In the variable that you write next to delta. In this case we have written Δx multiplied with Δp.
A little twist is here. Here, specifically, delta (Δ) represents the "Uncertainty".
Okay, so what is "x" here? x is the position and Δx is the uncertainty in position. Simple. And from the previous paragraph, we know what "p" stands for (in physics). Simple! "p" in physics stands for Momentum and Δp simply means uncertainty in momentum.
And as the definition itself says that we can not measure the "position" and the "momentum" of a particle with certainty, thus it is easy to derive at the first part of the formula: which is Δx multiplied with Δp. So what happens when we multiply them, we get the uncertainty of both, the position and the momentum.
Now, let us move further: You must know what this symbol means in mathematics: ≥ Yes this symbol means greater than or equal to. So in this case, Δx multiplied with Δp is either greater than or equal to what? It's greater than or equal to h/4Ï€. Wait what? Now we knew three things. First, what is delta (Δ), second, what is "x" in this case and third, what is "p" in physics. Next we need to know what is this "h/4Ï€".
Let's understand it. "h" here means a very small but special number that deserves another full post on it. What is that "h"? It is the Planck's Constant! Yes, Max Planck, a Nobel laureate was a great scientist who discovered this number.
h = 6.62607004 × 10-34 m2 kg / s.
While writing down this number, it seems very big, but in reality, if you observe it carefully, you will notice that it is a very very small number. I will surely make another post explaining everything about the Planck's constant.
Okay so, we have the Planck's constant which is a concept that energy can be expressed in discrete units or "quantized". More about Planck's constant, later. Now we have 4π. What is π? To know more on "π", read this post:
So, basically, π or pi in mathematics is nothing but the circumference divided by its diameter. Now if you are not already familiar with these terms, then read the full post on "π", link is above. So, 4π is the factor of proportionality between the product of uncertainties (Δx multiplied with Δp) in position and momentum being thought of as standard deviations and the Planck's constant itself. So, that's the significance of 4π in the formula for uncertainty principle. And thus, we have cracked all the terms given in the formula for the uncertainty principle.
More On Heisenberg's Uncertainty Principle
So, we know the theory, we know the formula, so now let us understand the uncertainty principle more clearly. Let us understand it more practically. So, this practical thing might be familiar to you. In this experiment, a laser light torch is taken, and the we take 2 blades or something and form it like a slit, in which the laser beam goes right in between the two blades and hits across on a surface. For better results for this experiment, do this thing in a dark room. I know that seeing it happen visually is more easier to understand rather than reading them into words, so here is a pictorial representation for you to have a better understanding.
So see in the above image, you can see beam of light concentrated on a place which keeps getting thinner and thinner as you bring the two blades that blocks this light more closer and closer. See, this simply means when you bring the two blades near each other, then the area in which the laser could pass through becomes lesser and lesser. And as there is less area for light to pass through, therefore only some light photons will reach the surface and hit there to form the image. Now, what happens if you bring the two blades even closer? Logically, they must get even thinner and then get disappeared, but then, quantum comes into play, instead of getting more thinner, they get more thicker! What? How! This is where Heisenberg's Uncertainty Principle is being applied. Don't believe me? See this image now:
See! As you narrow the slit, the beam, instead of getting thinner, starts getting thicker. The image is the same as before, so you can trust what I am showing. So, while we were trying to determine the position of the beam, we lost certainty in momentum. This is what is known as the uncertainty principle.
This concept is closely related to wave particle duality about which we just learnt in our previous post.
In February 1927, A great scientist named Werner Heisenberg developed a key piece of quantum mechanics- the uncertainty principle!
Albert Einstein once said - "If you wouldn't had seen it, it wouldn't had been there" which means that if we don't see a particle, it remains in its wave form and doesn't exist which is the same thing we Learned in wave particle duality!
To read principle 1: wave particle duality, click below:
So, that's it. If you liked it, I will surely make another part on this post. But for now, this should be enough for you. I hope you enjoyed learning the foundation of quantum mechanics!
This was the fourth episode of Science Specials Week S02. For more episodes, keep reading Enlightened Wisdom: Smart SCIENCE.
Created By: Naman Dwivedi
Thanks for reading!
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