Quantum Physics for Dummies

On Quora, someone had asked me to explain Quantum Physics in simplest terms. Here is my answer

The essence of Quantum Physics (QP) can be easily understood if we compare it with Classical Physics (CP), the notion of our everyday experience.

Classical Physics essentially deals with the motion of macro objects. Following are the key aspects of CP.

1. Variables to describe motion: We need two variables to describe the motion of an object - position and momentum.

2. The equation of motion: Newton's famous F = ma describes the change in momentum with time. A classical physicist would say - give me the position and momentum of an object, I will tell you the future trajectory of the object (assuming no other force) using the F = ma equation.

In other words, "position" and "momentum" are the key variables required to describe the motion of an object completely.

3. Deterministic: If we say that an object is at a point A, it is at point A. We can measure and verify this observation.

4. Particle nature: In CP, we are used to clearly distinguish particle and wave. I am a particle, a ball is a particle. Water Ripples is a wave.

The above principles are different in QP. The following notions are necessary to appreciate the basic essence of Quantum Physics (QP) and to be able to distinguish from Classical Physics (CP), the physics of everyday objects.


1. Wave-Particle duality: In CP, we perceive objects as “particles”. In QP, they are said to have both wave and particle nature. Wave description of light explains the interference patterns, while the particle description explains the photoelectric effect.



2. Wavefunction: In CP, we need two parameters to describe the motion of an object - momentum and position. Give me these two, I can describe the particle’s motion completely. These two parameters are said to have “complete information” about the object.


The QP equivalent of momentum and position is “wave function”. The wave function is supposed to have all information needed to describe the object.


3. Schrodinger’s equation: Schrodinger's equation is the CP equivalent of F = ma. In CP, given momentum and position, you can its trajectory, using Newton’s force equation (F=ma). We discussed that “wave function” in QP is “momentum-position” equivalent of CP. Similarly, in QP, given a wavefunction, Schrodinger’s equation describes the “evolution” of “wave function”, the CP equivalent of the trajectory of the object.


4. Uncertainty: You might have heard of Heisenberg’s uncertainty principle. It says that you can’t measure the position and momentum of an object simultaneously below certain error.


This has nothing to do with the precision of your measuring instrument or dimension of the object. It’s just a mathematical consequence. You can’t measure position and momentum simultaneously. That’s it. Such measurement will always have a certain error.

This relation is not just for momentum-position pair, it also applies to other pairs like energy-time etc.

Contrast this with CP, where we could say that a particle is at point A with speed X. We can't make such statements in QP. We have to say a particle is within this position range within this speed.

5. Probability: In CP, we could say that a particle is at A deterministically. In QP, we don't say that it is at A. We say that the probability of finding that particle at point A is p (p < 1). Different points in space have different probabilities of finding the particle. Such probability can be calculated from the wave function of the particle.

If we calculate the probabilities of finding an object at each point in space, you get the probability distribution of wave function. It’s more probable to find the object at certain places than others.


6. Superposition: The most important one. In CP, a body is in state A or state B. An electron is in "up spin" state or "down spin state".


It's different in QP.  If A and B are valid states of a particle then aA + bB are valid states as well (there is a mathematical restriction on the values a and b, can take which we won't go into now).


For instance, it means that if the “up-spin” and “down-spin” of the electron are the valid states, then the electron can also be in a “combination of up and down spins” with different weights to up and down spin. This is counter-intuitive but true.


7. Observation: If an electron can be in a combination of “up and down spin” states, what happens if you observe an electron, to measure its spin? Do we get to measure the detect the intermediate spin states of the electron?


Surprisingly, you will always find either an “upstate” or a “downstate”. You won’t find the other intermediate states, which are the combination of up and down. This is called Observer Effect. 

There are many interpretations of why and how this happens. The classical Copenhagen interpretation says that before measurement, the electron was in a superposition of states but on making the observation, the wave function “collapses” into one of the classical states. This is the idea behind the famous Schrodinger’s cat.

There are other interpretations like Everett’s Many-Worlds interpretation, which I think is too much for beginners. Essentially, the point is that we know the math of how it works but we don’t know the underlying mechanism yet.


8. Quantization: In CP, we are accustomed to the idea of continuous energy. In QP, energy comes only as a multiple of a minimum possible number. This is the reason for the name “Quantum” in QP. Quantum here signifies a “chunk”. It’s given this name because the fundamental characteristics of objects always come in multiples of minimum chunks. It is not continuous. For instance, energy is always a multiple of a minimum chunk. The charge is a multiple of minimum chunk etc. The intermediate values are not possible.


All of this might sound crazy, counter-intuitive, weird and even nonsensical. But hold on, we don’t get to decide what’s non-sensical. Universe has no obligation to make sense to us. All of this is true and has been experimentally verified. So, we are the ones who are to update our notions!


Consequences:

To appreciate the consequences of quantum phenomenon, let’s see some examples.

1. Electron cloud: We learnt in school that electrons revolve around the nucleus in circular orbits. We pictured electrons as if they revolve like planets, in definite paths.

But QP says that electrons have a wave function which gives it a probability of existing at several points. If we plot the probability of finding an electron in each space, we find that the highest probability of finding is around the classical circular orbit. But there’s some non-zero probability of finding it outside it too! We call this probability distribution as an “electron cloud”.

2. You cannot reach absolute zero temperature: We have learnt in school that there’s absolute zero temperature (-273 C). QP makes it impossible to reach absolute zero.

It’s because the temperature is essentially vibration of individual molecules. Absolute zero means that all the vibration stops and everything is at rest. But from the uncertainty principle of QP, we know that we can’t precisely measure the position of molecules. It means that they cannot be at absolute rest. There will be a little bit of motion. When there’s motion, there’s temperature!

You can go close to absolute zero, but cannot reach it.

3. Quantum Fluctuations: As discussed above, just like there is no “absolute position of rest” due to uncertainty, which results in fluctuation of “position” of molecules, a similar phenomenon happens in case of energy too.

As per CP, you look at empty space and can say that there’s zero energy. But QP doesn’t allow for “absolute zero” energy, there is always a fluctuation of energy. This is called quantum fluctuation.

4. Hawking radiation: From the famous E = mc^2 equation, we know that energy and mass are equivalent. If you have enough energy, you can get mass.

From QP, we know that there is always a fluctuation of energy. This quantum fluctuation sometimes results in the creation of “particle-antiparticle” pairs, which is often called as “particles popping in and out of existence”. These pairs annihilate themselves quickly.

Hawking applied this concept to blackhole. We know that there’s a boundary around the black hole, beyond which nothing can escape. Hawking argued that if such quantum fluctuation resulting in particle-antiparticle creation happens at the boundary of a black hole, there is a chance that one particle falls inside and other falls outside. Since the particle that fell inside can’t come out, the particle that fell outside will travel outwards, resulting in what we call “Hawking radiation”.

This has led to famous black hole information paradox.

5. Quantum leaking in semiconductors: If the energy of an object is X, CP says that it can’t overcome an energy barrier which is more than X. But QP talks of probabilities. It gives a non-zero probability of objects passing through the high energy barrier. We call it quantum tunnelling.

Quantum tunnelling is accounted for while making semiconductors because it results in “quantum leakage”.