# The Subtlety of Quantum Mechanics

## The Soul of Quantum Mechanics

Heisenberg’s Uncertainty Principle is the savior of quantum world. If it weren’t in quantum mechanics then, quantum mechanics would have fallen down before it even started. According to Heisenberg, it states, *“If you make the measurement with an uncertainty in momentum, you can’t, at the same time, know its x-position more accurately than Δx=ℏ∕Δp”*. It has no evidence in the real world but it’s, more or less, like a soul of the quantum world. In spite of the fact that Quantum Mechanics and Theory of Relativity are the foundations of modern science, these two theories are the two extremes of Physics. They both don’t satisfy the same observation at the same time. For instance: look at this figure given below

## Quantum Entanglement

Quantum Entanglement is one of the skeptical theories of Quantum Mechanics. It states that “If two particles are entangled, or in unison, then no matter how far they are in universe, you can predict the behavior of one particle by observing the other". Dr. Michio Kaku, in his book *‘Physics of the Impossible’*, talked about Quantum Entanglement. “Let’s say that a friend always wears one red and one green sock, in random order. Let’s say you examine one leg, and that leg has a red sock on it. then you know, faster than the speed of light, that the other sock is green”, he explained. Albert Einstein said, this effect, "spooky-action-at-a-distance", and did not agree with Quantum Mechanics because the information travels faster than the speed of light which opposes the second law of Theory of Relativity - Nothing can travel faster than the speed of light in vacuum. So, was Einstein wrong? Does information travel faster than the speed of light? From the above example, you might be thinking the answer to both the questions is Yes but Michio Kaku said that this information is useless since the information was random. ‘Information actually traveled faster than light, but this information is useless. No signal containing non-random information can be sent via this method’, he added. Found that strange? Me too. Tighten your seat belt and grab a packet of chips because it’s gonna be stranger.

## Double-Slit Experiment

The concept of photons, used by Max Planck to show the thermal equilibrium between the matter and the electro-magnetic radiation and later used by Einstein to describe the Photoelectric Effect, gives rise to the theory of duality of the particle. The term ‘duality’ refers to the state of a particle where the particle shows dual nature: particle nature and wave nature. This effect is shown by every particle and observable only on a microscopic level or quantum level, but not on a macroscopic level. Richard Feynman showed this quantum behavior in an experiment with the more familiar behavior of particles like bullets and waves. After getting familiar with the difference in result between the bullet experiment and wave experiment, he took electrons to show that electron behaves both as a wave and a particle at the same time. In 1999, a team of Austrian Physicists performed the same experiment using Buckyballs (molecules made of sixty carbon atoms). In the book *‘Grand Design’*, Stephen Hawking talked about this experiment by taking an analogous thought experiment which was akin to that of Feynman’s Bullet Experiment. Stephen Hawking, in his thought experiment, considered soccer balls as electrons to show the quantum behavior of electrons.

The double-slit experiment contains all the mysteries of quantum mechanics

— Richard FeynmanHere is the experiment: An electron gun fires electrons randomly over a large angular distance. In front of the gun, there’s a wall with two holes or slits in it (small enough to pass only the electron). Behind this wall, there’s another wall, called screen, with a buzzer. Whenever an electron strikes the screen, the buzzer produces a sound. Now, when one of the slits is open, the electron goes through only one slit and hit the screen. When a plot is drawn between the probability of hitting the screen when either slit 1 or slit 2 is open versus the distance along the screen, it looks like the plot in Fig. 1 (blue line shows that slit 1 is open and red line shows that slit 2 is open) shown above.

When both slits are open, 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 when we get higher number of electrons (or higher probability than previous case) but at other regions, we get lower number of electrons. At some regions, the probability of electrons striking the screen came out to be zero. This is quite intimidating. In the Fig. 2 shown above, the points where the plot touches the horizontal axis are the points of zero probability.

## 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 when both slits were open. That means that 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.

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 the Mars and comes back on Earth to strike the screen. Looks like the sci-fi movie but it isn’t. According to him, when both slits are open, the electron goes through slit 1 and interfere with the path in which it goes through slit 2 which causes the interference. I have a different perspective to comprehend this phenomenon (this doesn’t happen in reality, it’s just for understanding): 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: electron may be behind the slit or it may be crossing the slit with 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.

## Need of Uncertainty Principle

You might be thinking that we should make an apparatus which 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 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 it changes the outcome and we get a different plot (Fig. 3) which shows no interference pattern. It seems like observing the electron changes its behavior. The photons which are emitted from the light source hit the electron and get scattered. This photon gives an impulse to the electron and changes its path such that the electron didn’t strike the region where it supposed to when there was no light source and therefore, 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. Momentum of the photon(p) is inversely proportional to its wavelength(λ): p = h / λ (h = Planck’s constant). When the wavelength is made 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 a 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, Δp (or increase Δλ) then, Δx increases, and vice-versa. So, it’s hard to build such an apparatus which can locate the electron without disturbing the result. It was Heisenberg who suggested there should be some limitation to make the laws consistent. Since quantum mechanics is such a successful theory in explaining many phenomena like Gravitational Waves, 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. 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

## Questions & Answers

**© 2018 Dishant Varshney**

## Comments

You are obviously a phycisist of first rate. I, being a mere historian, have been interested in the concept of quantum mechanics and have heard the term frequently in scientific circles. I am ashamed to say that your knowledge and explanation of the subject still goes over my head. For one whose specialty is in the humanities, you will need to simplify your explanations a notch or two for us laymen.

Also what would a more complete understanding of Quantum Mechanics have on technology? In other words, because of the invention of the vacuum tube, the era electronics was born. What marvelous devices or enhanced technological understanding can improve life for us all in the near future?