Will the Real Schrodinger’s Cat Please Stand Up


The story of Schrodinger’s cat is well known, and one of quantum theory’s most popular phrases on the world stage. You can find his cat on t-shirts, bumper stickers, internet memes and the like. However, few know the origins of the cat, and how it came into being. I suspect many do not understand it beyond the “dead and alive at the same time” catchphrase as well. Not surprisingly, it was Einstein who was at the center of the idea behind Schrodinger’s cat. In a vibrant discussion between the two via letters across the Atlantic, Schrodinger echoed Einstein’s concerns with the following:

Contained in a steel chamber is a Geiger counter prepared with a tiny amount of uranium, so small that in the next hour it is just as probable to expect one atomic decay as none. An amplified relay provides that the first atomic decay shatters a small bottle of prussic acid. This and -cruelly- a cat is also trapped in the steel chamber. According to the wave function for the total system, after an hour, sit venia verbo [pardon my language], the living and dead cat are smeared out in equal measure.

This was the first mention of Schrodinger’s cat, and one would not be incorrect in stating that this paragraph from a letter was where the cat was born. However, the original idea behind the thought experiment was from Einstein and his loathing of the wording of the Einstein-Podolsky-Rosen (EPR) paper. He expressed his frustrations with Schrodinger with a few simple examples, who then catapulted it into his famous paradox . In this article we’re going to explore not so much the cat, but the meaning behind the thought experiment and what it is meant to convey, while keeping it simple enough for anyone to understand. So next time you see it on a t-shirt, you will be able to articulate the true meaning and know the real Schrodinger’s cat.

Reality or Statistical Probability?

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Cloud Comics: Schrodinger vs Heisenberg

Einstein was not an opponent of quantum theory in its totality. He believed the theory was useful for predicting statistical outcomes. His problem was the idea that it was a complete description of reality. He did not believe nature was statistical, but rather that it was completely deterministic, just as classical physics is. Quantum theory was useful in predicting experimental outcomes, but that’s all it was… just a tool for physicists. Not a complete theory of nature.

He threw what he hoped to be a knockout punch with a paper known as the Einstein-Podolsky-Rosen (EPR) paper that would show how silly all this quantum business really was. We’ve covered EPR on a few occasions now, so I’ll not bore you with rehashing the details. Instead, let us focus on why Einstein was not happy with it, and how it birthed Schrodinger’s cat. He said to Schrodinger in one of the many letters between them that it was “smothered by the formalism“. He was frustrated that his main argument was buried by complexity, even though it was relatively simple to understand. He explained with an analogy.

Imagine you have in front of you two red Sparkfun boxes of the same size and shape, and an Arduino. You place the Arduino in one of the boxes and then shuffle them to the point that you are unable to know which box contains the Arduino. There is a 50% chance you will find the Arduino in the first box you open. The question is – is this a complete description? Remember that quantum theory links statistical outcomes with reality, and Einstein is trying to hammer a wedge between the two. Now, back to the question: if there is a 50/50 chance of finding the Arduino in the first box, is this a complete description? We can only have two possibilities:

  • A) No. The Arduino is in one box or the other. There is no more information that can be gained from the system that will tell us which box the Arduino is in, and we are forced to resort to probabilities — there is a 50/50 chance of finding the Arduino when we open the first box.
  • B) Yes. The Arduino is in both boxes at the same time, and is localized into a single box at the instant we open the lid of one of the boxes and make an observation. Done repeatedly, we find the Arduino in each of the boxes 50% of the time. The system is probabilistic in nature, and no other description is required.

Einstein was trying to show the absurdness of quantum theory as a description of reality. Yes, it can accurately predict probabilistic outcomes, as in scenario B. But scenario A is a much more sensible description of reality. This was the key point that Einstein wanted to address in the EPR paper. A simple point, perhaps too simple.

The Birth of Schrodinger’s Cat

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Image via Live Science

Schrodinger had developed wave mechanics some years back, and still believed that wave functions of quantum particles played a role in their behavior.  He and Einstein butted heads on this. Einstein believed wave-functions described statistical probabilities of systems (in scenario B, the Arduino would have a wave function allowing it to be in both boxes at the same time. Opening a box would “collapse” it into one box or the other), but DID NOT describe a physical reality in any way. He would dream up yet another thought experiment:

Apply a wave function to a charge of gun powder. Over the course of time, the equation blurs the lines between an exploded and non-exploded state. There can be no reasonable description of reality that can place the gun power in both an exploded and non-exploded state at the same time.

After several more letters and simple thought experiments, Einstein won over Schrodinger to his side. Schrodinger had become convinced that his wave functions were indeed not a description of reality. He would go on to merge the macro state and the quantum state in one experiment by replacing the Arduino with a cat and the gun powder with poison in an attempt to create a “quite ridiculous case” as he put it.

Quantum Theory Wins Again

This created quite a problem for the Copenhagen interpretation of quantum mechanics, which insists that reality can only be defined by our measurement devices. Asking what the state of the cat is prior to measurement is without meaning. But Einsteins and Schrodinger’s view that the wave function of the cat simply represents a statistical probability of the cat being alive or dead is much more sensible.

Bohr had no response to the Schrodinger cat paradox other than the canned “The measurement instruments must be treated classically”. That just means that the cat must be treated classically and cannot enter into the superposition of alive and dead at the same time.

At this point, the physics community was growing weary of the seemingly endless philosophical debates. Quantum theory worked in the laboratory and most physicists just used it because it worked, and turned a deaf ear to its challengers. And this sums up the theory into the modern day. There are still unanswered philosophical questions out there, but the theory continues to hold up under experiment. And will likely continue to do so in the foreseeable future.

There are more advanced approaches to the paradox, which includes the consequences of Quantum Decoherence, and we did not touch on the deeper question of what exactly happens during the “collapse of the wave function”, which happens when an observation is made.  That will be for a future article, but please feel free to carry on in the comments below.

Sources:

The Quantum Story, by Jim Baggott. Chapter 17  ISBN-978-0199566846



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