Quantum Mechanics, Schrödinger’s Cat, and the My Little Pony Movie Trailer · 8:32pm Jul 10th, 2017
Schrödinger’s Equation has been cited in Equestria! This means I have an excuse to write a blog post on quantum mechanics...
The trailer for the My Little Pony Movie provides a particularly exciting symbol-filled whiteboard shot, full of mathematical eye candy to delight anyone who enjoys analysing this sort of thing. This is a goldmine for Equestrian semiotics research. Your story idea or movie plot prediction is as good as mine...
The image has been nicely annotated by KopaLeo on DeviantArt:
I’ll just jump to the hard-core physics bit in the bottom right corner: Schrödinger’s Equation.
Erwin Schödinger was an Austrian physicist from the last century. His equation is a key formula in Quantum Mechanics, that counter-intuitive framework of weirdness which underpins so much modern physics and chemistry, and lets us build lasers, microchips, and the electronic gadgets we need to watch our favourite animated ponies. While Schrödinger is known for his equation, he is probably better known for his cat. Cat memes are nearly always a better way to communicate complex ideas than equations, so let’s began with that.
Schrödinger’s cat is an imaginary pet which is simultaneously alive and dead, existing in a quantum superposition. This idea has delighted artists almost as much as it has fascinated philosophers. Whereas old-fashioned classical mechanics—apples falling on your head sort of stuff—allows us to calculate the precise trajectories of particles, quantum mechanics is inherently uncertain and only allows us to calculate the probability of certain outcomes of experiments. This uncertainty is, as far as anyone can tell, a fundamental property of the universe.
Imagine the scenario of a cat inside a sealed box, containing a flask of poison, the release of which is triggered by a particle detector connected to a radioactive source, sufficiently weak that there is a 50% chance of emitting a particle, and issuing the death sentence, over a one hour period. Our understanding of QM implies that until we open the box and observe the outcome of the experiment, the radioactive atoms are in a superposition of the decayed and undecayed state, which suggests that the cat is in a similar quantum state. It is importance to stress that this uncertainty is not just due to our ignorance of what is happening inside the box, we understand from quantum theory that atoms and other particles must exist in this strange ghost-like state.
But how do we know this isn’t just a game thought up by philosophers to tease us? Let’s go on to the equation:
Schrödinger’s equation is a wave equation—a piece of math that describes something that flutters up and down and ripples across space like a crest of water moves across a pond. The parameter ψ (psi) is the wave function. It lets us determine the probability of finding a particle at a given time and space. This provides an explanation to an old puzzle in physics: is light a wave of a particle?
Light moves through space as a wave. It is reflected off the crystal floor or your castle, and split into a rainbow spectrum by rain droplets. A classic experiment to demonstrated its wave nature is to let it shine through a double-slit—two parallel slits in a plate—the coherent waves passing through each side interfere with each other producing a striped pattern on a screen. Where two wave crests align to give a bright line and where a crest and trough cancel to leave a dark gap.
But light can also behave as a stream of particles. When it shines on a photographic film, single photons blacken silver-halide crystals (or knock electrons in the silicon pixels of a digital camera). Put a film behind the double-slit and you can watch the interference pattern accumulate dot-by-dot. Each photon acts as a wave, passing simultaneously through both slits, before hitting the film as a single dot.
Schrödinger’s equation describes this wave particle duality—how every particle ripples across space as a wave function. This applies to all particles, not just photons. Electrons can be focussed by optical systems in electron microscopes, or sent through double slits. This experiment has also been done with electrons, and with atoms and large molecules, although not with anything approaching the size of a cat.
But all the equation tells us is the probability of a particle being at a given point. The wave function seems to be the fundamental representation, but we don’t see a wave function, we see particles. The cat was a thought experiment to illustrate that we can’t just dismiss quantum mechanics as some sort of microscopic magic—random quantum events can affect big things, and you could indeed set up an experiment to produce a simultaneously-dead-and-alive cat, you just couldn’t check the results without forcing it into one state or the other.
So what is going on? Over the years many philosophers have tied themselves in knots trying to explain this.
A tradition approach is a bit of a cop-out. It is to say that the state of the atom—and the cat—is not defined until we observe it. We cannot say anything about it until we open the box. If you can’t build an experiment to find the answer then you are asking the wrong question. In a way this is just stating the limit of quantum theory. It can tell us the probability of getting an outcome of a given experiment, but says nothing about what is happening inside a closed box. This is, arguably, not so unreasonable when talking about atoms, but it gets absurd when talking about a cat. That’s the whole point of the parable.
One fashionable approach is the many worlds interpretation, the idea that the wave function describes an infinitive number of ‘parallel’ worlds. The cat is dead in one, and alive in another, and when we open the box we just find out which universe we are living in.
Yet there are other things to consider. Perhaps the ‘collapse of the wave function’—the moment when a quantum superposition of possible outcomes reduces to one or the other—is triggered by something. It was once suggested that this is the act of observation by a conscious observer. This just leads to the question of what counts a conscious observer, or indeed what would the cat have to say about all of this?
Few modern physicists now think consciousness is the causative agent. There is a lot of interest in how wave functions collapse (if indeed they do…), a question known as the Measurement Problem. It seems that the phenomenon of quantum decoherence might be able to explain this. An isolated quantum system can exist in a superposition state, but interactions with the environment cause this to get lost among millions of other superpositions. Mathematician Roger Penrose has an alternative speculative idea that the collapse of the wave function happens when it reaches a certain scale where gravitational effects are significant.
This is an area of active experimental research. Quantum experiments are testing wave-particle duality, and superposition, at bigger and bigger scales, and for longer periods of time, working towards the construction of a system where we can set up and manipulate a large number of quantum systems, and thus build a quantum computer.
Quite what quantum superposition of ponies, cats, fish and other creatures we are in stall for at the movie, and what alternative realities Twilight and friends will visit, is something we will not know until we observe it.
The cat, meanwhile, would much rather that the humans stop messing around with boxes and poison and go back to showering it in gold and tastefully arranged mice.
In Equestria, of course, the cat is neither alive nor dead, but in a state of taken-right-out-of-the-sealed-box-by-Pinkie, leaving behind a cupcake and a note telling you to be nicer to cats.
...this phenomenon would be much less alarming and reality-breaking if it weren't a thought experiment...
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You would be surprised how often cupcakes randomly appear, without explanation, in unexpected places in real world laboratories.
Wasn't the cat (thought) experiment meant by Schrodinger to display how absurd he thought the notion of the uncertainty in Quantum Mechanics was?
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Or at least how absurd he thought the Copenhagen interpretation of uncertainty in QM by Bohr and Heisenberg was.
After observing the end of this blog post I can say with 100% accuracy that it's the corniest joke you've ever written.