Quantum Physics – with a Coin

Find a coin.

Go on, rummage in a pocket, purse or wallet and find something a reasonable size like a UK 2p or 10p coin, about 1 inch or 2.45cm in diameter. This is all you need to explain quantum physics to someone.

Yes I did just say quantum physics. Surely that’s only for geniuses you cry! Quantum physics is a subject that intrigues and is hopelessly misunderstood in equal measure. This little demonstration will really impress your friends and explain all the basics of quantum physics in simple language. Let me show you how.

I’m assuming you can toss a coin. Throw it up and catch it then slap it down on the back of one hand. Did you get heads or tails?

Quantum Physical States and Probability

The only outcomes possible in a coin toss are heads or tails. You can balance a coin on its rim if you are careful and have a flat table, but that outcome never occurs in a coin toss, due to the slapping-it-flat-on-the-back-of-your-hand action.  There is no way to get heads and tails at the same time as they are on opposite sides of the coin. So I’m going to go ahead and say that the result of a coin toss is one of two possible states, either heads or tails.

Toss the coin a few times and you’ll find out that the number of heads and number of tails usually balance out. You should have an unbiased coin. This would mean the chance of getting a head each time you toss is the same as the chance of a tail, 50:50 chance of either state.

What if we suspected one side had been weighted and so the coin was biased? Tossing the coin hundreds of times would give us a very reliable way of finding if it had been tampered with. The numbers of heads and tails should balance out. If 40% of the time the coin’s state was found to be heads and 60% tails we know it is biased towards tails.

Tossing the coin allows us to find out information about what states are possible and what is the chance of ending up with any one of those states.

Now we’ve established that, what state is the coin in before you catch it?

You might say “no state” but that would mean there was no head-ness or tail-ness there at all, nothing. That’s not quite right as the coin is there. You can see it spinning in the air. How do you describe that?

 

Superposition in Quantum Physics

Quantum physics has a neat word for describing the mixture of head-ness and tail-ness that a spinning coin has before you catch it. The word is superposition. Superimposing is a technique used in photography or film where one image is put on top of another. The final image is a composite of the two. Superposition is a bit like that.

The spinning coin is not devoid of states, we can’t say it has no heads or tails to it. Instead it is a constantly changing superposition of the two states. This superposition tells us nothing about what state this unique toss will end in. That depends on all sorts of things like how fast it is spinning, how high we throw it, when we catch it etc. It won’t help us work out the outcome of an individual throw.

The superposition does contain information about any bias in the coin. As it spins, a heavier side to the coin will spend more time at the bottom of the spin and the lighter side would spend more time at the top. There is some information there we could extract about how the pattern of heads and tails would look after 100s of throws, if only we had a way of measuring it.

 

Taking A Quantum Measurement

You already know how to measure the state of the coin. You catch it and slap it down on your hand. Look at the coin and there is your measurement.

But this involves permanently altering the condition of the coin. You are forcing it into one of two possible states. When I measure my height I don’t force a mixture of all possible heights into 5 foot 10 inches. There is no probability of getting anything other than 5’10”. This measurement of the coin is different to normal measurements. The act of measuring the system we are interested in (the spinning coin), fundamentally alters the system we are interested in. Bummer.

There is no way around this I’m afraid. To get information about the possible probabilities of either heads or tails we toss the coin 100s of times. Then we interfere with the spinning superposition each and every time, forcing it into a single state. Only by repeating this measurement over and over do we get enough data to work out a pattern.

This is true of quantum objects like electrons. It is called The Measurement Problem. Only in quantum physics does the act of measuring the system permanently change the system. Or to put it another way, extracting information from the superposition destroys it. This is called collapsing the wave function.

What is a Wave Function?

Waves bob you up and down in the sea or make use of your hand to signal your departure or arrival. In both cases something is oscillating between two positions over and over. Up and down on the sea and side to side with your hand.

Lots of natural phenomena can be described using the language of waves. The variation in light intensity due to day and night, seasonal mean temperature changes, hormone levels in menstruating women, anything which has a repeated variation across a range of values is wave-like.

Physicists use the mathematical language of waves to describe quantum states. The spinning coin has a repeated variation in a range of values, it flips from heads to tails and back again as it spins. We can use wavy maths to describe this variation. The mathematics of waves is even more helpful as it allows us to add waves on top of each other and work out the resulting wavy shape. Like different tides or ripples interfering with each other at a point on the sea.

The spinning coin has a changing superposition of the heads and tails states. The chance of measuring either state depends on which way up the coin is pointing when you catch it. As the coin rotates it is found in a 100% heads state only once each rotation and only for a very short time, likewise for the tails state. The the rotation moves one side of the coin slightly higher and the amount of “heads” reduces slightly and the amount of “tails” increases. Or more correctly the probability of getting heads reduces slightly and the probability of getting tails increases slightly. So the chance of ending up with heads or tails is continuously changing as the coin rotates. If you plotted the probability shape on a graph it would rise and fall and rise and fall just like a wave.

The wave function is the name given to a mathematical wave shape which describes this varying chance of getting a particular state in a measurement.

Collapsing the wave function forces a single state on the coin, in this case either of the extreme positions, giving a head or tail.

 

Now the Quantum Physics Bit!

All this talk of coins is preparing us for the big moment to tie all this in with teeny tiny quantum particles.

There is an experiment which shows exactly what we have been talking about with coins, but with electrons. It’s called the double slit experiment. It is the classic way of introducing people to the weirdness of the quantum world. Electrons behave like a wave superposition of states until you force a measurement on them and then they behave like a lump with a fixed state.

Instead of throwing electrons up and down and catching them with some clever laser trap equivalent of a coin toss (or something!), the electrons are thrown at a screen. The screen can detect the hits from the electrons and emit a tiny light burst. So a pattern builds up showing where the hits occur.

When you shine a wavy source, like a torch, on a screen you get a bright spot in the middle and it gradually dims as the light spreads out at the edges. If you fire a lot of blobs at a screen there is a big build up of bobs in the middle and fewer out to the sides. It is hard to tell one result from the other.

So the physicists put something in the way of the screen. A big sheet with two narrow slits in it.

quantum double slit experiment

Diagram of the double slit experiment from Wiki-Commons

Now you can tell the difference between the pattern produced by wavy things and the pattern produced by blobs. Waves overlap and produce a new wavy pattern as shown in the picture above. The blobby particles are simply split into two streams of blobs by the slits and produce two splats on the screen. No superimposing happens for them.

Electrons are supposed to be blobs not waves. They are particles. When a beam of electrons is fired at the slits they start to build up a pattern on the screen. The pattern is a wavy interference pattern!

quantum double slit interference pattern

Each dot represents the impact of an electron on the screen. Many hits build up to produce an overall wave interference pattern, even though electrons are particles. This is evidence of the wave-particle duality of electrons. Experiment performed by Dr Akira Tonomura in 1989 at Hitachi. Creative Commons ShareAlike licence.

Here we are looking at information contained in the wave function of the electrons. Only when hitting the screen are they being forced into a state. Then their position state is fixed to a definite value. Just like the coins spinning in the air contained information about the probability of heads or tails, so the electrons shooting towards the screen contain information about the probability of where they will show up in the interference pattern.

We can collapse the wave function earlier on and force the electrons into a position state much sooner if we measure them. We can put a sensor on the double slits and record which slit the electrons go through. This destroys the supposition of location states and forces the electron to be in the left or right slit. Like catching a coin destroys the supposition of heads or tails and forces the coin to be one or the other. Then the electrons behave like blobs and build up in two patches on the screen. The waviness of the electrons has been lost.

This experiment was astounding. To actually see the theoretical wave nature of the electrons supposition and then be able to collapse the wave function and bring their blob nature back again has boggled many a mind over the years. Tiny particles can be waves or can be blobs depending on how they are interacting with their surroundings. Some interactions collapse the wavy behaviour and force the electrons into a fixed state. What we understand as measurements always collapse the wavefunction because our measurements require a value, a fixed state to give a result.

Conclusion

Tossing a coin will never look the same again! Each time you catch a coin you can think about how every photon of light hitting your eyeball has just collapsed its wavefunction, every click of the TV remote, every interaction of microwaves with food in your kitchen is a quantum measurement happening in front of you.

Now we need to talk about Schrodinger’s Cat…

schrodinger's cat experiment

A thought experiment proposed by Erwin Schrodinger. Picture from https://www.nobelprize.org/educational/physics/quantised_world/

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