Quantum III: On Terrible Jokes and Cosmic Terrors

This is the third of three posts on quantum mechanics. See the first and second here and here, respectively.

I absolutely hate science “jokes”. I utterly, completely, despise them. Sure, they’re not all bad—but the overwhelming amount of them live in a weird space where the entirety of the punchline relies on a sense of smug self-satisfaction for knowing what the joke is referencing, making these jokes a great litmus test for finding out which of your friends is a pretentious tool that wouldn’t know comedy if it broke into their house and took their kids for ransom. To give you an example of this kind of crime against laughter, here’s a classic joke of this type (where I mean “classic” in the sense that the Hindenburg disaster is a “classic”):

Werner Heisenberg gets pulled over while driving. A cop comes over and asks, “Do you know how fast you were going?”

Heisenberg replies, “No, but I know exactly where I am”.

This joke is about as funny as dialysis. Medgar Evers may have said that you can’t kill an idea, but when it comes to this joke, God help me I can try. If the only way to get rid of the concept of this joke was to go back in time and prevent cars from ever existing, I’d get my jogging playlist ready in record time. This is a science joke in the sense that an Aston Martin made entirely out of compacted coffee grounds is a coffee machine.

But I digress; the point of this blog is not to point out bad jokes, but to explain what they’re referencing. And now that we’ve managed to get through the key conceptual hoops of quantum mechanics and what it can/can’t do in the previous entries, we’re in a good position to address this!

Let’s do a quick recap of what we’ve figured out so far:

  1. The universe doesn’t determine outcomes precisely, so the laws of quantum mechanics deal only with the probabilities of things happening.
  2. The way those probabilities change with time is -very- weird, to the point where we can’t describe this change using the typical method we’d use for probabilities in a non-quantum world. This is what causes quantum objects to be “glitchy” until you interact with them.

So really, the only thing keeping quantum mechanics from being a boring old theory about statistics like how you lose money in a casino is how those probabilities are changing over time! The question du jour is then obvious; what’s causing those probabilities to change over time?

Well, it turns out the core of what causes all of the weirdness in quantum mechanics is at the very heart of physics: energy! And, because it’s so important to the quantum world, let’s digress a little bit to talk about what we mean by energy. For the purposes of this entry, energy is just a number that depends on two things; how the object in question is moving, and how it interacts with everything else around it. As a result, energy depends on things like where other things are relative to the object, and how the object itself moving.

As it turns out, energy is incredibly important in quantum mechanics because an object not having a specific energy is precisely what causes all of its probabilities to change over time. And if the probabilities don’t change over time, then there’s no difference between the behavior of a quantum pencil and its classical, statistical, brother (boring!). Hence, the universe often not assigning specific energies to quantum objects is where all the properly crazy quantum stuff comes from.

Let’s take a look at one way this tidbit triggers a weirdness cascade throughout the rest of quantum physics by delving into an example. Consider a quantum teapot, zipping through a completely empty universe. In this situation, if we knew the energy of the teapot precisely, then we would know its speed as well; in an empty universe, the energy of this teapot is exclusively dependent on its speed and vice-versa. In addition—if you trust my previous statements—then the probabilities of the teapot’s observable properties shouldn’t change with time. If the teapot had, say, a 50% chance of being in position A when we measured its energy, then it should retain that probability for the rest of time.

But how could it? Remember, even though we might not where the teapot is, we know where it can be, and we know that it has to be moving with a specific speed that we can discern. So if we also knew that the teapot was in the neighborhood of position A, we know that it would have to eventually move away from the neighborhood of position A, and the probability of it still being in position A would now have changed with time, contradicting our previous statement!

Teapot 1

And no matter how much you play around with the information you have about where the teapot can be, there’d only be one scenario in which this wouldn’t be a paradox: if the teapot had the same probability of being everywhere, in which case the concept of position doesn’t have any meaning at all. It would become some kind of cosmic entity, omnipresent, eerily lurking in a “glitch” state, steadily moving through a desolate universe of itself where movement has no purpose.

Teapot 2

Scary, right? Welcome to quantum mechanics. This innate relationship between the nature of position and velocity, combined with velocity’s connection to energy and energy’s connection to changing probabilities, are what leads to that “Heisenberg uncertainty principle” hoopla everyone keeps talking about when they try to explain the punchline of their unfunny jokes to you. And trust me, all the other weird stuff you hear about in quantum mechanics pops out of similar thought experiments to this; marrying this little energy-time change connection with other boring classical physics results, such as velocity being the rate of change of position in the example above.

With this in mind, I’ll discuss just one more quick example. The central tenet of all physics (and you definitely don’t want to mess with that) says that the energy of an object which isn’t exchanging energy with some other object is constant in time—energy can’t just spontaneously appear or disappear. This naturally implies that, once we know the energy of a single isolated object, it can’t change from that value the next time we measure it. As you can see from the previous example, this puts a lot of restrictions on how such an object can behave—and in more realistic and restrictive situations than the empty universe above, only specific energy values yield probabilities that are consistent with the extra restrictions imposed by the environment. And as you can probably surmise, this means you very often can’t find an object to have just any arbitrary energy after interacting with it, only specific values of it; this is the historical hallmark and experimental mine canary of quantum mechanics.

That’s enough for now! I’ll conclude this entry by providing you with a science joke of my own:

Werner Heisenberg gets pulled over while driving. A cop comes over and asks, “Do you know how fast you were going?”

Heisenberg replies, “Now I do.”

He vanishes into thin air. The world feels changed; the colors off, the hues subdued.

The officer stares blankly into the empty seat. A nylon face forms in the seat upholstery; it whispers a single phrase.

“I am arriving.”

The officer begins to form the concept of fear. He vanishes before being able to do so.

Heisenberg has become the demiurge—he shapes and reshapes the universe as he sees fit. Stars die and are reborn in instants. Comets pulse in green and red as fractal Bauhaus palaces made of solid xenon crystals shatter and reform in the region once occupied by Saturn’s rings.

The Earth and its inhabitants fluctuate chaotically in the same manner; an irradiated wasteland consumed by eldritch nightmares one second, a savannah of polygons dotted with wireframe people the next. They are none the wiser to their predicament, their collective consciousness a fleeting mayfly. They are beyond hope now—they are beyond most things.

Ohm resists.

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