Demystifying Uncertainty Principle
By: Dishant Varshney
Tags: Physics, Knowledge, Science, Future, Quantum Mechanics

I used MATLAB software to plot the curves shown in figures 1, 2 and 3

When both slits are open (fig. 2), it looks like the electron can hit the screen by going either from slit 1 or slit 2. It is understood that opening the second slit increases the number of electrons, and hence the probability of electrons striking the screen, but when a plot is drawn between the probability of hitting the screen when both slits are open versus the distance along the screen then there were regions where we get higher number of electrons (or higher probability than the previous case) but at other regions, we get lower number of electrons. In some regions, the probability of electrons striking the screen came out to be zero. This is quite intimidating. In Fig. 2 shown above, the points where the plot touches the horizontal axis are the points of zero probability.

Feynman’s Water Wave Slit Experiment | Source: The Feynman Lectures on Physics Vol. 1

Feynman’s Explanation

In fact, Feynman wrote, “The double-slit experiment contains all the mysteries of quantum mechanics.” It is observed that the pattern we got when both slits are open is similar to the plot when waves (shown above) were taken instead of particles. This concludes that electrons also interfere and behave as waves as well. This arises the regions of zero probability (destructive interference) when both slits were open. That means those electrons would have hit the screen in the zero probability region if only one slit was open and don’t strike the same region when both slits are open but here, another problem arises — Electron gun was firing one electron at a time so how does an electron know how many slits were open? “It seems as if, somewhere on their journey from source to screen, the particles (electrons) acquire information about both slits”, Hawking wrote in ‘Grand Design’.

Many possible explanations were given by many physicists to explain this quantum behavior. Feynman said that the electrons take every possible path connecting those two points i.e., from source to screen, an electron can take a straight line path or a path to Mars and comes back on Earth to strike the screen. It looks like a science-fiction movie but it isn’t.

According to him, when both slits are open, the electron goes through slit 1 and interferes with the path in which it goes through slit 2 which causes interference. I have a different perspective to comprehend this phenomenon: When both the slits are open then, electron divides into two halves which go through each slit, and interfere with each other (Interfering with itself doesn’t produce any effect). When only one slit is open, it won’t split into two. Now, the same question arises: how does an electron know about the slits? The answer is simple but intriguing. It’s because of the uncertainty in the position of an electron. It can acquire information about the slits before it reaches there.

Consider that the electron is about to enter slit 1 but due to uncertainty in its position it could be anywhere near this slit’s vicinity. For example, the electron may be behind the slit or it may be crossing the slit with a certain velocity or it may be about to enter the slit. So, before the electron reaches slit 1, it can get the information about the slit and can act accordingly.

Figure 3: When electrons are observed

The Need for Uncertainty Principle

You might be thinking that we should make an apparatus that can mark the slit whenever an electron goes through that particular slit and then we can say that the electron goes through either slit 1 or slit 2. Feynman pointed out such an apparatus. We can put the lights near the slits so, when the sound from the buzzer is heard, we see a flash either near slit 1 or slit 2. But when Feynman made such an apparatus, it changes the outcome and he got a different plot (Fig. 3) which shows no interference pattern. It seemed like observing the electron changes its behavior.

Actually, the photon which is emitted from the light source hits the electron and gets scattered. This photon gives an impulse to the electron which changes its path in such a way that the electron didn’t strike the region where it supposed to when there was no light source and hence, it shows no interference pattern. Now, to decrease the impulse given to the electron by the photon, the momentum of the photon should be decreased. The momentum of the photon(p) is inversely proportional to its wavelength(λ): p ∝ 1/ λ.

When the wavelength becomes more than the separation of the slits, the impulse gets decreased, and the plot obtained looks similar to the plot (Fig. 2) when no light was used. But by decreasing the momentum or increasing the wavelength, the flash becomes a big fuzzy when the light was scattered from electron, and it’s hard to distinguish from which slit the flash is coming.

Therefore, this experiment concludes that if we try to decrease, without disturbing the outcome, p (or increase λ) then, x (position) increases, and vice-versa. It means, if we are successful in locating the position of a microscopic particle (like an electron) then we can’t tell how much fast or slow the particle is going (uncertainty in velocity or momentum Δp) or if we successfully measure its velocity then we are unable to find its position in space (uncertainty in position Δx). We can’t know both things simultaneously with great certainty. So, it’s hard to build such an apparatus that can locate the electron without disturbing the result.

Fortunately, Quantum Mechanics’ laws don’t apply for macroscopic objects (like soccerball) otherwise we’d see the soccer ball moving in the zig-zag path when we kick it. But these laws successfully explain the phenomena where other laws failed to explain like the photoelectric effect. To save the existence of Quantum Mechanics and explain this absurdity, Heisenberg suggested there should be some limitation to make the laws consistent, and gave the Uncertainty Principle. Since Quantum Mechanics is such a powerful theory used in many upcoming technologies like Quantum Computing, we need uncertainty principle to comprehend quantum behavior of atomic and sub-atomic particles.

We Are Not Sub-Atomic Particles!

Heisenberg’s Uncertainty Principle applies to every particle but it can’t be observed on a macroscopic level because λ is very large and hence, uncertainty in position is very small. In the TV scripted series, Genius, Albert Einstein, and Niels Bohr were talking to each other about the proof of Quantum Mechanics while walking. There was a moment when they were crossing the road and Einstein intentionally threw himself toward a car but Bohr pulled him back before the car hit him. When Bohr asked him to be more careful from the next time, Albert smiled hysterically and said, “Why should I? Why should either of us? According to you if that automobile was a particle but we didn’t see it, it wouldn’t have been there at all. We would be perfectly safe”. To his defense, Bohr replied, “That principle is applied only to sub-atomic particles and automobiles are not sub-atomic particles”. In conclusion, Heisenberg’s Uncertainty Principle might save the perilous existence of Quantum Mechanics in the future but it won’t save you from the car so, be careful!

The Uncertainty Principle | Genius