by Science Buff
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Quantum Superposition And Entanglement Explained

Chapter 1 of 10

In this guidebook we try to understand the weird physics that come into play in the tiny world of sub-atomic particles (like atoms and electrons). Scientists also call this Quantum Physics. Over the years, physicists have not only made critical observations of weird quantum phenomena, but have in fact started working towards harnessing them to build quantum computers.
So let's dive in! 

Chapter 2 of 10

Light Is A Wave
"What is light?", has been one of the most fundamental questions in understanding our world and intrigued a lot of scientists. A decisive answer was found in 1801 when a scientist named Thomas Young passed a beam of light through two narrow vertical slits. His experiment was called 'The Double-Slit Experiment'. 

Astoundingly, the light beam passed through the two slits and created a pattern that is normally seen to be created by a wave (like a water wave). You can see below what this result looked like:
The beam split into two individual waves of light and which then interfered with each other while moving towards the screen. 
When the two waves interfered, their brightness added up in some spots, and at some spots they cancelled each other out to create a dark region. This created an interesting pattern of increasing and decreasing brightness called an 'Interference Pattern', on the screen (or wall).

Scientists already knew how interference happens in other waves (like water waves) to create the interference pattern. So when Thomas Young found the same interference pattern being created by light in this experiment, it was quite clear that light is a wave.

But what is the light wave made of?

Much later (in 1873), another scientist James Clerk Maxwell published his 'Electro-Magnetic Theory of Light' where he showed mathematically that the speed of electromagnetic waves was equal to the speed of light . This proved that light must be an electromagnetic wave. Electro-magnetic waves are special kind of waves made up of varying electric and magnetic fields perpendicular to each other (as shown below). 
So light is made up of electric and magnetic fields. 
[This was however, just to feed your curiosity. All you need to understand here is that light is a wave.]

Chapter 3 of 10

Light Is Also Particles
In 1902, a scientist named Philipp Lenard conducted an experiment whose results raised some really puzzling questions on light for scientists.

The Experiment : "Photoelectric Effect"

The experiment involved shining light on a metal surface. It was observed that this ejects electrons from the atoms on the metal's surface. Energy contained in the light rays was transferred to the electrons pushing them out of the atoms. A part of the energy from the absorbed light is used by the electron to break free from the atom and the rest of the energy gives the electron its speed (in the form of Kinetic Energy) after it has escaped. This was called "The Photoelectric Effect".

But Two Puzzling Questions Arised

  1. Why did the speed (kinetic energy) of the ejected electrons not increase or decrease accordingly, when the intensity (the brightness) of the light falling on the metal was increased or decreased.
    If light was a wave, then increasing/decreasing the intensity should increase/decrease the energy contained in the light, thus the kinetic energy of the ejected electrons should change accordingly. Observation showed, this did not happen.

  2. Why did the electrons not take extra time to get ejected from the atoms when the intensity of light was decreased to very low levels?
    If light was a wave, then decreasing the intensity should decrease the energy contained in the light, thus it would take more time for the electron to absorb enough energy so that it can escape from the atom.

Einstein's Brilliant Answer

In 1905, in a stroke of genius, Einstein provided a radical solution to the above questions. He argued, that the puzzling observations can be explained by considering that light was made up of small packets of equal energy (we now call them 'photons' of light). 
To eject an electron out of an atom, a packet of light hitting the electron must have enough energy to detach it from the atom.

If the light is made up of packets with less energy than required, doesn't matter how many packets are thrown at the electron (however much or for however long), the light would never be able to cause the electron to escape the metal surface.
This theory helped very easily understand the puzzling observations made in the experiment - 
[If you're interested in knowing how, read further. But if you're already baffled at this point, all you need to keep in mind is that, Einstein's theory showed that light could also behave as a particle. And that he won a Nobel prize for this.]
  1. Increasing/Decreasing the intensity of light actually just increases or decreases the number of photons hitting the surface at a time. It doesn't increase/decrease the energy contained within each photon, so the energy transferred to the electron remains same and thus there is no change in the kinetic energy of the ejected electrons.
  2. An electron gets ejected from an atom, as soon as a photon with sufficient energy hits it. It doesn't absorb a photon and wait for another photon to fulfil the energy requirement. Thus there is no time delay, even if the intensity of light is low (number of photons is low).

Chapter 4 of 10

Even Particles Act Like Waves
While the idea that light was a wave could explain the interference pattern, it failed to explain the photoelectric effect. So we had to accept that it also behaved like particles in some cases. At the time, the wave nature of light was seen as an established idea and Einstein's idea of light particles was seen as a mistake by most of the scientific community.
One scientist however, Louis De Broglie, took Einstein's radical idea seriously and proposed something even more radical in 1924. 
He proposed that -
all matter (from massive objects to as small as electrons) could also behave as waves and even gave a mathematical equation for the wavelength of such a wave.
Experiments conducted later in 1927, showed that - 
De Broglie was right!
A number of particles including electrons, atoms and even molecules were seen to behave like waves. They created special diffraction and interference patterns traditionally seen only in waves.
(interference pattern made by electrons - source)
Another image of the patterns created by electrons and protons.

Chapter 5 of 10

Wait... What? 
Particles create an interference pattern like a wave?!

Stop and think about this for a moment .

In a Double-Slit Experiment, an actual wave completely passes through two slits at the same time creating an interference pattern. But a particle can only pass through either one of the slits, and so it should just pass through and hit the region on the wall right behind the slits. We would expect the particles to create 2 bright regions.

But instead we observe that the particles pass through and fall in multiple light and dark regions based on a pattern - the interference pattern of a wave passing through both the slits. How do the particles know where on the screen do they need to fall to create the light and dark regions?
(re-read if necessary)

How do we explain this?

Chapter 6 of 10

Neils Bohr Comes To The Rescue
Much like you and I, scientists were also baffled by this observation that particles were creating wave like interference patterns on the screen. After all it was quite difficult to explain it, as we couldn't see any real wave. All we could see was that a particle was thrown towards the slits and a particle was detected on the screen. 

So two scientists Neils Bohr and Werner Heisenberg between 1925-1927 came up with a reasonable explanation. They proposed that (rephrased for understanding) -
  1. We need to give up our assumption, that each individual electron fired towards the slits is a particle throughout its journey to the screen.

  2. When we are not looking at or observing the electron, it behaves like a wave. The moment we observe the electron (say by putting a screen), the wave collapses into a particle.

  3. This wave can be thought of as a wave of probabilities. The probability of the electron being at a certain position. In fact, it applies not only to 'position' but also to other properties of the electron like 'velocity (speed with direction)', 'spin' etc.

  4. When we observe the electron, its probability wave collapses and takes up a definite location from among the various possible locations. Similarly, it takes up a definite value for its other properties like spin, momentum, etc; from a range of possible values. 
You can visualise this probability wave as given below. 

The height (probability value) of the wave at different points on the XY plane, indicates the likeliness of finding the electron at those different points on the plane. The electron is most likely to be found, upon observation, at the location point with the highest probability - the point right below the tip of the wave. But there is also a chance, that upon observation, it is instead found at some other location with lesser probability. 

This idea came to be known as the 'Copenhagen Interpretation' of Quantum Mechanics. 

Explanation For Interference Pattern By Electrons

Using Bohr's Copenhagen interpretation, you can now see, how the interference pattern was created on the screen when electrons were fired at the two slits (previous slide). Each electron's probability wave passed through both the slits. Then, just like any other wave, the probability wave broke into two new probability waves at the other side of the slits, which interfered with each other to create a new interference wave with new high and low probabilities of presence. When this new interference wave of probabilities hit the screen (electron was observed), it collapsed taking up one of the probable positions. When more electrons were fired, they did the same thing individually and overall we got to see the interference pattern appear on the screen. 

Chapter 7 of 10

"God Does Not Throw Dice"
Einstein didn't agree with Niels Bohr's explanation of the quantum world. 

He thought nature had a very defined set of laws that govern exactly how events must happen and that if we understand these laws thoroughly we should be able to exactly predict the outcome. He thought it was absurd that nature would allow particles to be in all possible locations (velocities, spins etc.) when not being observed, and just pick one value of location (velocity, spin etc.) out of many at random when being observed.  To this he said  - "God does not throw dice."

Chapter 8 of 10

Einstein along with two other scientists, Boris Podolsky and Nathan Rosen published a paper where they tried to challenge the Copenhagen Interpretation by putting forth a thought experiment, called the "EPR Paradox"

They said that if we apply Bohr's idea of a particle being in multiple possible states at the same time when not being observed - "Superposition of possible states" to two particles something really crazy would happen. So let's see what happens. 

Create a system of two particles
Let's say we create two particles an electron and a positron by colliding two gamma ray photons (basically two photons of light) as shown below.
An electron has a negative charge; while a positron is nothing but an electron with a positive charge instead of negative. When the two particles are created, the positron has to have a positive charge because we started out with a zero overall charge (2 photons) which must be conserved (remain the same) after the production. 

Conservation of Spin
Similar to charge, the spin property of the overall system must also remain unchanged. Let's say we started out with zero spin on the 2 photons, then the overall spin of the electron and positron system must be zero as well. This implies, the spins of the electron and positron individually would have to be opposite each other. If one is 'spin-up', the other one would have to be 'spin-down'.
Applying Bohr's Superposition Idea
In the Copenhagen interpretation, Bohr says that when we are not looking at a particle/system, it is not just in one of its possible states, but like a probability wave, it is in all the possible states at the same time. Only when we observe it, the system randomly chooses and collapses its superposition to one of the possible states. 
With this understanding, the electron and positron pair act as one system. This system has only two possible states - 
  1. electron UP           -  positron DOWN
  2. electron DOWN  -  positron UP
The pair can't have (UP-UP or DOWN-DOWN) states to conserve the overall spin to zero. 
As per superposition, the pair is in both the states at the same time. I know this is weird to understand, so just recollect how the particles were behaving like a probability wave of all possible locations (velocities, spins) in the double-slit experiments. It's the same thing, just applied to a system of two particles.
So we have now created our system of two particles that act as if they are one and their system has two possible states. Such particles acting as a system in multiple superposition states, are said to be Quantum Entangled.
But what's the crazy thing about it? 

Chapter 9 of 10

The Crazy Thing - EPR Paradox
Okay so now that we have an entangled pair of particles, an interesting thing about being entangled is that, the particles stay entangled as a system even if we move them away from each other.  

Even if we move the individual particles apart to vast distances in the universe, they keep behaving like a system in superposition of multiple states. 

So consider we have such an entangled pair separated by a huge huge distance (light years away) in the universe. The moment we make a measurement of the system, let's say by measuring one of the particles, it obviously collapses the superposition of the system to one of the possible states, like it should as per quantum mechanics. This implies, that instantaneously both the particles collapse to one defined state (spin up or spin down). 

Think about this for a moment!

The particle which was put under our measurement device collapsing to a defined spin immediately when measured sounds fine, but the other particle also collapsing to a defined spin immediately at the same time is crazy!! It means that the collapsing effect, was transmitted from the measurement end to the other far away particle instantaneously without any delay. 

Violation Of The Most Fundamental Principle - Causality

The effect from a cause cannot travel faster than the speed of light is the fundamental principle called 'Causality'. Most of our classical physics, involving Einstein's Theory of Relativity is based on this fundamental assumption, that nothing can travel faster than the speed of light, even the effect from a cause.
But in the case of entangled particles, the collapsing effect is transmitted to the other end faster than even light - instantaneously. This is the EPR Paradox.
Einstein called it "Spooky action at a distance."
With this thought experiment, Einstein believed that he had proved that the Copenhagen Interpretation was incomplete in thinking that particles could be in a state of superposition of multiple possible states, because as per the EPR Paradox, that would mean that even our most fundamental principle of Causality would be violated.

Experimentation However Proved That Bohr Was Right!

You'd be surprised to know, that much later, in multiple experiments, it was indeed observed that Causality is violated in the case of entangled particles and that the collapsing effect is transmitted instantaneously.

Chapter 10 of 10

Journey So Far, Let's Recap!
If you've reached this far, I'm sure you must be mind-boggled. Understanding these weird quantum phenomenon is not so easy as it challenges our most basic intuitions. So feel free to go back anytime you like and re-indulge in these concepts. 

The concept of Superposition - that individual particles and even systems of entangled particles can be in more than one possible states at the same time when not being observed;  is fairly complex, that is why we had to go through the other concepts on light being a wave and a particle, to particles behaving likes waves just to get comfortably introduced to the concept of Superposition. 
And that's the story of how Quantum Physics came to be. 

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