Could the world be represented as binary?

Question

The Matrix the movie regards the whole world as being binary and us living in a computer simulation.

Could the world be represented as binary similar to a matrix or is that not practical give quantum mechanics?

Answer 1

Are you asking if it's possible that we live in a simulation of reality? If so then the answer is, of course, yes. Whether quantum mechanics has anything to say about the matter is irrelevant, because if we live in a simulation, our experience with quantum mechanics is just another aspect that The Programmers have coded into existence.

Physics is an empirical science, which means it's fundamentally based on observations of the world around us. In principle it's possible that I'm the only human in existence and everything I've ever experienced (and everyone I've ever spoken to) has been fed into my brain by The Programmers. I don't live my life under that assumption, but I certainly can't rule it out.

But then, physics isn't about making definitive metaphysical statements like this. Physics is in the business of observing how the world works, formulating models to predict the future, and then improving the models over time. Whether the "rules" governing the universe have been written by conscious Programmers or whether they are in some sense natural is an interesting question, but not a physics question.

Answer 2

First, only values can be binary, not things.

Second, binary, octal or decimal are compatible representations of values. You are therefore asking if reality is discrete, not binary. You know the difference between continuous and discrete.

Third, in order for some value to be discrete without our perception noticing it (e.g. for your arm not to move in a "pixelated" fashion), there should be a large resolution of the representation. If the position angle of your arm would be binary, you would only be able to put it in two perfectly defined positions, say, up and down. But since you can move it to an apparently infinite variety of angles, it would appear to be infinite. Since measurement capabilities are limited, we can only speculate about the magnitude of resolutions in physical reality.

Yes, in the past, it would seem that any possible representation of the world would be continuous (meaning that you would always be able to move something half of the distance the last movement away). Until quantum mechanics, where the "resolution" of energy was noticed. In terms of energy, the pixel is the quantum.

Suddenly, we noticed that the pixelation of energy impacted the pixelation of other domains. Now, pop culture tries to find a way to pixelate everything, that is, to assume that any possible physical phenomenon is discrete, because it would be quantic (yes, that's at least funny). So we can make movies, like The Matrix.

Well, that's not the case. At least, as far as we know for now. Most representations of physical phenomena still remain continuous within the scientific domain. That does not mean that reality is not pixelated. That means that physical sciences consider most representations as continuous because there's no proof of empirical reality being different.