Schrodinger’s Cat

 

robably the most misunderstood idea in all physics. Stephen Hawking said, “when I hear of Schrodinger’s cat, I reach for my gun”. Everybody seems to have taken a pot shot at this, from Douglas Adams (Dirk Gently’s Holistic Detective Agency) to these people:

My friend once held forth on why Schrodinger had chosen a cat instead of a dog or rat completely unencumbered by facts or understanding. So before we get into a real discussion, lets just clear the air a bit. Schrodinger was not a cat hater. If anything, his weakness was rather too much love (he was repeatedly accused of womanising). His great contribution to physics was completely unrelated to animals.

He devised the Schrodinger’s equation in which he re-phrased the principle of conservation of energy (taught in high schools) to deal with probability waves. This equation is one of the first things taught in any undergraduate course in Quantum Mechanics and can be used (if you can frame it and solve it) to predict the behaviour of any quantum mechanical system. In other words pretty everything in the universe can be described by an appropriately complicated Schrodinger’s Equation. Also, if this thing is left undisturbed, everything that happens to it should be predictable through the Schrodinger’s Equation.

But there soon emerged problems with this idea. The Schrodinger’s equation for simple things like electrons began predicting strange things. One of these was that it was impossible to tell whether an electron was doing one thing (e.g. spinning in a certain direction or going through a particular slit) without disturbing it.

Let us take an example, say radioactive decay. Radioactive elements are unstable. Their atomic nuclei spontaneously decompose into other more stable nuclei emitting radiation in the process. But strange as it may seem, it is impossible to predict when a given atom of a radioactive element will decay. Instead what we can say is that if you have millions of atoms of that element, then after a certain amount of time some percentage of them would have decayed.

This leads us to the idea of half-life. This is the time taken for half the atoms of the radioactive element to decay to more stable elements. For example, the Cesium 137 thrown up by the Chernobyl disaster is 30 years. This means that now, about 30 years after the explosion, the radiation level in the fallout region is about half of what it was back then because half the Cesium 137 is gone.

Another example, take the one I gave in a previous post. There we were looking at the direction an electron was spinning in. Forgive my self-plagiarism, but I’m going to directly copy the explanation from there:

Suppose you take a magnetic compass like the one available at your local stationary shop. That is just a little weak magnet suspended on a joint that lets it move around. Left to itself, the magnet will get affected by the magnetic field of the Earth and the needle will tend to point North.

Now bring this compass near a magnet (the one in a door stop will do). The first thing you notice is that the needle starts moving back and fro oscillating wildly. After a few moments, the friction in the joint causes the oscillations to dampen and slow down. The needle settles to a position pointing wither directly towards or away from the magnet. The time it takes to settle down and the amplitude of the oscillations (how much it swings) depends on the angle at which you bring the magnet.

For instance, if you bring the South Pole of the magnet towards the point of the needle, there is hardly any difference in the initial and final directions of the needle. That is, from before when it was dominated by the Earth’s magnetic field (the Earth’s magnetic South Pole is near the geographic North Pole) and eventually when it is dominated by the field of the magnet we are bringing near, its direction will hardly change. Hence we can expect that there will be very few oscillations.

Conversely, if we bring the South Pole of the magnet near the tail end of the compass needle, the compass will have to swing a full 180 degrees to reach its final resting place. Therefore it will have to swing wildly and the oscillations will be very great.

As you would expect, the case where the oscillations are heavy, more energy is expended by the magnetic field.

Now let us see a quantum analogue of this classical experiment.

A single electron is also a magnet with a very tiny magnetic field of its own. Left to itself, it can orient itself in any direction. Now, if you put an electron in a stronger magnetic field, it will also eventually orient itself in the same way as the compass needle did. That is, its own North Pole will face the South Pole of the external magnetic field and vice versa. But what happens in between is interesting.

Before we look at what the electron actually does, let us consider what we would expect from our intuition about compass needles.

We would expect that initially, the electron will be oriented in any direction. When we apply the magnetic field, it will start oscillating about the direction of the field till it finally comes to rest with its North Pole facing the South Pole of the magnet. To stop oscillating, it will need to give up energy. Electrons give up energy by emitting light particles called photons. So we expect that the electron will emit a photon to stop oscillating and align its moment with the magnetic field it is placed in.

Further, we expect that since the extent of oscillation depends on which direction the electron was initially facing, the energy of the photon will also vary depending on which direction the electron initially faced. So if we take an electron at random and put it in a magnetic field, it will emit a photon with energy that could be any value from 0 (perfect initial alignment) to a maximum (180 degrees alignment change) amount. If we take thousands of electron and repeat this experiment with them one by one, we would find that each of them emit one photon. The energy of the photon always lies between 0 and the maximum value and can have any value in between.

Sounds reasonable? But this does not happen.

What actually happens is that either we get no photon (0 energy) or 1 photon with the maximum energy. That is the energy released when the electron flips 180 degrees. There are no in-between values. What does this mean?

Suppose we turned our magnetic field from East (North magnetic pole) to West (South magnetic pole). Now if we only get photons of 0 or maximum energy then that means that initially all the electrons were facing West (0 energy) or East (maximum energy). No electron could be facing in any other direction (North West, South etc.).

That sounds strange. But it gets stranger.

This same thing is true regardless of whatever direction you choose to set your magnetic field. So you could set the field North (North magnetic pole) to South (South magnetic pole). Again you see the same result. Some electrons don’t emit anything while other emit a single photon of the maximum energy which is released when the electron flips 180 degrees. This would mean that all the electrons either faced South or North.

Here we had assumed we did not know the initial direction of the electron. But what if we started with an electron whose direction we had fixed previously and then measure it later. Lets say we forced an electron so that its North pole is facing up and the South pole is facing down. Now if we put the South Pole of our magnetic field above and North pole below the electron, we see as expected that the electron does not move and there are no photons emitted.

Conversely, if we put the North Pole of our magnetic field above and South pole below the electron, we see as expected that the electron emits 1 electron of the maximum energy.

But what if we bring the magnetic North pole to the right and the South pole to the left? Then there is a 50% chance of seeing the maximum energy photon and 50% chance of seeing no photon. This is the heart of quantum weirdness.

This confounded and perplexed the early pioneers of the field. Some felt that the electron actually exists in a “superposition” of 2 states. When we observe of measure it, it jumps into one of them.

schrodinger

Erwin Schrodinger

The key point here is that some scientists took this to mean the electron was in some sense spinning in both directions till the act of observation forced it to make up its mind. Schrodinger didn’t like this kind of thinking. He made up a thought experiment as he saw it to demonstrate the silliness of this idea. It went like this:

Take a cat and put it in a box. Along with it, put a sealed vial of poisonous gas and a tiny amount of a radioactive element and a mechanism which breaks the vial releasing the gas as soon as one of the radioactive atoms decays.

Now, make it so that after some time (say an hour), there is exactly 50% chance that one of the atoms in the radioactive element would have decayed releasing the poison and killing the cat. If someone subscribes to the idea that the radioactive nucleus can be both decayed and intact at the same time, they must also believe that the poison is released and in the vial at the same time and hence the cat is alive and dead at the same time, a patently absurd proposition.

Unfortunately for Schrodinger, the line of thinking is still alive and his crazy idea became a cult symbol of popular culture and is still used to explain the quantum wierdness he worked so hard to tame in his life.

 

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