The Universe in Half a Tweet

Neil Turok is the director of the Perimeter Institute for Theoretical Physics, and the author of a book I stumbled upon recently, titled The Universe Within. He's also a damn fool liar! I will justify this, but first I have to take a deep breath...

Okay, so, I was checking him out to help me decide if I should read his book. That's when I found this YouTube interview, where he talks about a lecture he presented. This lecture is on the same topic as the contents of his book, so I watched the video. After a few minutes, he said something which triggered my bullshit alarm. I searched online, and found this news article wherein he repeats the claim:

It turns out that if you take just 300 electron spins and couple them together into a quantum computer, then the amount of information it would be capable of handling is the same as that in the position of every particle in the whole universe. There are about 10 to the power of 90 particles in the universe and if you use each one of their three-dimensional positions and imagine recording all of those positions, that's about the same as what you would get from just 300 electrons in a quantum computer.

There are so many lies in this paragraph, that I required help just to suss out what he was even talking about! People much smarter than me managed to reverse engineer his mathematics, and explain how he arrived at a count of 300 electrons in his hypothetical quantum computer.

First, he started with an estimate for the number of particles in the universe:

N = 10⁹⁰

Then, he used the convenient approximation:

2¹⁰ = 10³

To put N in terms of a power of 2:

N = 2³⁰⁰

Then he stopped. He had what he wanted. A big, scary number to intimidate and impress people. He didn't care what it meant. He had a narrative to present, that quantum computers are awesome, and this number fit into that narrative. All he had to do was lie.

After all, who's going to call him out? Tyler Harbottle, the author of the news article? Allan Gregg, the guy who interviewed him on YouTube? Apparently not. Well, look out Neil, the Physics Police are coming for you...

Let me explain the true meaning of the number 300 in the above equation. It tells us how many bits of memory you need to keep track of one, large number. Just one, single number! It can be as large as N, the number of particles in the universe. So, if you were to store, say the three-dimensional position of each of these N particles in computer memory, you'd need a 300-bit number to refer to just one of them.

Notice that this feat is impossible, because each bit of computer memory is built from more than one atom, meaning the computer would take more than N particles to build. But N is the number of particles in the universe, so we would exhaust the material content of the universe before completing construction of the computer memory.

Even children know that counting every grain of sand is not the same as creating a map of the beach. 300 bits can store 37 typed characters, not even enough to contain this sentence. That's less than half a Tweet! Surely, the universe contains more information than that.

But I digress. Let's recall what Turok actually claimed. He claimed that the amount of information stored in a quantum computer built from 300 electrons is equal to the classical information represented by the position of every particle in the universe. Anyone who has taken high-school physics knows this cannot be true.

In classical physics, one can measure the position of a particle to an arbitrary degree of certainty. There is no classical limit on how much you can improve your measuring apparatus. You can describe the position of a particle with infinite accuracy. Laplace's demon did it.

Anyway, I want to calculate just how fabulously wrong this ponce has got it. After all, that's the fun part! First, I'll start with some simple and generous assumptions. Let's assume the universe is a nice, orderly cube, with each of the N particles sitting along a nice, neat lattice. This is the ideal situation from the point of view of memory consumption, in which each particle has a unique position.

The cube's length, in arbitrary integer units, is equal to the number of particles on a side, or the cube root of the number of particles:

L = N^1/3 = 10³⁰ = 2¹⁰⁰

For each of the N particles, we need to store three different 100-bit numbers; the position of the particle along each of the three dimensions. So, that's 300 bits per particle. Notice that this number 300 is a coincidence, having to do with the number of spacial dimensions, whereas the 300 electrons were calculated from converting binary to base ten. Now we can calculate the memory required to record the position of every particle in our model:

H = (300 bits) * N = 3 * 10⁹²

As we saw before, the hypothetical quantum computer would be "capable of handling" only 300 bits. So, how far off was his claim that this storage capacity is equal to H?

H / (300 bits) = 10⁹⁰

So, Turok was off in his calculation by a factor equal to the number of particles in the universe. This is a prediction so gloriously inaccurate that he deserves an Ig Nobel Prize.

But I can't end there. The worst of it is, he's not only wrong, he contradicts himself, too. Earlier on, he claims that a qubit can store an infinite amount of information:

And that's what a quantum bit has -- an infinite amount of information from the whole sky. The quantum bit is something carried by a single electron, the spin of a single electron -- the most elementary constituent of matter that we know would carry a whole sky's worth of information.

So why use 300 electrons? Why not just one?