On Improbability

Note: This story is based on an actual conversation I had yesterday with a Facebook friend. I have fictionalized it with his permission.

I met Freiberg once in person, while I was dating an old school friend of his. Our acquaintance far outlasted the relationship, and though I have not seen him since, we correspond from time to time via Facebook on the oddities of science and science fiction. It was he who introduced me to the intricacies of the four-dimensional Rubik’s cube, and I who found him what is believed to be the oldest English-language story about a time machine.

Yesterday he approached me with perhaps the oddest and most profound of his ideas to date. I present it to you here as he explained it to me.

"A fascinating (if fringe) theory about how gravity is actually an emergent property of entropy and information, just like much of thermodynamics is.
"I have to admit - I like it in large part because entropy is intrinsically a probabilistic thing. So a drive that could create large improbabilities, under this theory, would in fact be able to warp spacetime."

Wait what

"It's well-established that entropy can cause macroscopic forces. If you pull a coiled polymer chain, for instance, it'll resist the pull past a certain extent because its entropy is far lower in an uncoiled state than a coiled state.
"This guy is saying that gravity is a result of similar entropic forces, but at a much smaller and more fundamental level."

Explain how entropy being probabilistic allows the improbability drive.

"If gravity is due to entropy, then gravity is probabilistic. Einstein's general relativity holds that matter and energy warp spacetime due to their gravity - and any theory to expand on or replace general relativity would have to explain the experimental results which show that matter and energy warps spacetime."

Which would make the spacetime warping probabilistic?

"Indeed."

Making it theoretically possible to warp spacetime by causing improbable things to happen?

"In this theory gravity would be isotropic because the chances of macroscopic differences in the x and y and z axis are miniscule. But if a macroscopic difference were to happen, gravity would become directional and spacetime would warp. Just like an Alcubierre drive."

What are you thinking of when you say "macrosocopic difference"?

"If you're a hundred thousand miles away from the Earth, the force of gravity you feel from the Earth is independent of whether you're above, below, or on the ecliptic. In this theory, there's a chance that the force of gravity could briefly become twice as strong above the North Pole as below the South Pole, analogous to the chance that all the air in a room will briefly go into one corner."

ok, but how would you generate a region of space where that happens?

"There's a thought experiment (that actually got built and tested, back in 2011 or so) called the Szilard engine. It was able to show that information and energy are equivalent, like matter and energy are, because of entropy. In theory, a fine enough method of storing and manipulating information could cause a localized change in entropy, causing a macroscopic difference in the distortion of spacetime.
"In practice, such a thing (if possible, which is not at all guaranteed) would be indistinguishable from an actual Alcubierre Drive. Because ultradense matter is the only way you can store that much information. But at heart, it'd be an improbability drive. There's something satisfying in that."

there really is
now would you be able to bootstrap an infinite improbability drive the way Douglas Adams describes it?
"How much detail do you need? Because 'infinite' is pretty difficult."

Be as detailed as possible please
Be more detailed than Douglas Adams
"...actually, I have an idea. Give me a minute to flesh it out."

ok

While I waited, I located my Hitchhiker’s Guide to the Galaxy collection and refreshed my memory of the history of the Infinite Improbability Drive.

"This isn't super coherent yet, but bear with me."

ok

"In a purely classical or quantum universe, infinity is impossible. There are a finite number of states and a finite number of possibilities to fill those states. There are discrete energy levels and discrete packets of matter and of light. There's no way to make 2x2=∞."

uh huh
or even 1+1+1...

"However, we don't live in a purely classical or quantum universe. The Planck Length and Planck Time are often heralded as the discrete units of space and of time, but that's not necessarily true."

they're the units below which things stop making sense

"Indeed. But they're not necessarily the level at which complexity stops. Every time we probe down further and further, we find more evidence of complexity. The first people to observe cells called them 'cells' after the bare rooms in a monastery, only for us to find out that within each one, there's an unbelievable amount of stuff going on. And same at the atomic - I've personally changed the half-life of Sisypheum-170 without stopping it from being Sisypheum-170, something people didn't think was possible fifty years ago, and something I didn't know was possible before I interviewed for the job.
"So what if the complexity never ceases?"

you did what?

He explained. It involved a complex process of electron bombardment which changed the energy state of the Sisypheum nucleus.

wow

"I get very easily distracted. My point was only that even at the level of atomistics, things aren't as simple as they first appear, and things in fact get complex in different ways when you get to the quantum and subquantum levels. If the Planck length and Planck time are the levels of length and time at which our current theories break down, that doesn't necessarily mean that there's not further complexity at that level. It just means that we can't meaningfully discuss it. To get an infinite improbability, you need an infinite number of potential states, out of which only one is chosen. You can only do that in a pure continuum."

so if we're quantized, we don't get infinity

"Yep. To get one state in an infinite number, you need to continue going down, further and further, in the length and time scales. To do that, you need new theories and new machines for each scale and level. In fact, you need an infinite number of levels of complexity for this to work.
"However, information is substance in this theory. All you really need, fundamentally, is a way to manipulate information. And that's where the improbability drive comes in.
"If you have a conceptual space of all possible models to describe any individual layer, the odds of picking the one that actually describes our universe is slim. But we have an improbability drive, so that's no hindrance. We tell the improbability drive to find the models that describe our level of the universe, and a computer to take that model and make an improbability drive on that lower level."

the improbability drive being a way to manipulate a region of the universe so that events of a particular probability are certain to occur?

"Indeed, or at least far more likely than they otherwise would be. The improbability drive and computer (which I'm assuming are a single unit), work in tandem to find a model of the universe at the length scale below the one they operate and make an improbability drive on that length scale to manipulate the one below it. And they can make it because, when information is substance, there's no fundamental difference between a truly complete model of something and its implementation."

What does it mean for information to be substance?

"Just for information and energy to be equivalent in a similar way that matter and energy are."

ok

"The improbability drive has some probability of failure, of course, but it has to contend with all of the cumulative length and time scale smaller than it is. The drive below it has some smaller probability of failure, and the drive below it a smaller probability still. Take the infinite product and, if it trails off quickly enough, the probability could still be nonzero. And calculable. Calculate that number, plug it in, and there you get the Heart of Gold."

This is beginning to sound like a supertask

"That's precisely what it is."

So is the Infinite Improbability Drive just a supertasker that calculates probabilities? Or is the supertask what creates the drive?

"The latter. This is all still sketchy, obviously. But just believable enough that I could avoid getting lynched by a mob of respectable scientists."

heh
so what I'm getting is:
Computer A calculates the likelihood of computer B existing, B calculates the likelihood of C, and so on. Each step takes less time and has less error, and when the infinite series reaches its sum, the result is an infinite improbability drive (computer Aleph).
Am I still with you?

"That's exactly it."

Wow.
But calculating the likelihood of something happening doesn't cause it to happen. How do you make Computer A translate probabilities into events?

"That's where the sketchiness comes in. I'm assuming that, since gravity itself is a byproduct of entropy, that matter and energy are both byproducts of information. On a macroscopic level, there's a difference between making a model of something and actually implementing it. On a microscopic level, that difference becomes less clear. There's an SMBC somewhere about how a piece of cheese is actually an analog computer running a perfect simulation of a piece of cheese, and it's not entirely wrong.
"I'm assuming that since our top-level computer / improbability drive is already capable of the mind-bogglng feat of translating information into macroscopic improbabilities, that its simulation of the lower-level computer / improbability drive becomes indistinguishable from the real thing."

So we'd need a way of massaging the equivalence of information and matter
to convert probability of existence into existence
this is definitionally what an Improbability Drive does

"Exactly!"

Perhaps Freiberg’s theory is simply a diversion from the terrible shocks of recent days, or a mad scientist’s attempt to put them into cosmic context. But it could also be that the only reason we do not live in the universe described by Douglas Adams is simply one of probability. Anything truly is possible.