This might be a little New Agey but I’ll try to keep it a little more sciency if I can.

I blogged about a month ago about a David Tong video about the simulation hypothesis. That arose from a question in Scott Aaronson’s blog about the fact that the Standard Model could not be simulated on a computer. That fact would suggest that reality is analog not digital. It turns out there is a solution to the problem but the solution involves an extra dimension. Scott has since followed up with a new post on the simulation hypothesis where he mentions the solution.

So what is this extra dimension? Is it the same as the extra dimension in the Kaluza-Klein theory that tries to unify electromagnetism and gravity?

The conventional wisdom is that the extra dimension that solves the problem isn’t a real dimension but an unreal one. So I asked: If an extra unreal dimension is required to make the calculations work, wouldn’t that be indirect evidence we are living in a simulation? All of the dimensions could be unreal. Or, maybe all of the dimensions (and more) are real, but we only think the 3+1 dimensions are real because that is all that is directly useful in the ancestral environment.

Here’s his answer in full.

Ah, who among us can say which elements of our theories are “real,” and which are mere calculational conveniences? ‘Tis a rabbit-hole that stretches all the way back to the dawn of modern physics. Truly, ’tis. 😀

Having said that, I believe there’s at least the following crucial distinction: in Kaluza-Klein theories, and in the modern string theories that build on them, if only we could do experiments at sufficiently extreme energies, the compactified extra dimension(s) would appear just as “real” to us as the 3+1 large dimensions of everyday life. With this solution to the fermion doubling problem, by contrast, the extra dimension would presumably remain empirically inaccessible no matter the energy of our probes. (Though it’s an interesting technical question whether, if you took the solution seriously as physics rather than just as a calculational device, the extra dimension would become accessible from the boundary given high enough energies…)

What if the dimension is real but isn’t spatial?

After all, we already have one dimension that isn’t spatial. We can locate all objects in three dimensional space, but time isn’t like space. It doesn’t have a spatial length. We draw timelines to help us visualize it but it is fundamentally different from a spatial dimension. Time really is just a measure of stuff happening. We have stuff we can locate in space. That’s the where. Stuff happens. That’s the when.

What about the what?

For all I know, Kaluza-Klein and string theory may require that the its dimensions be spatial. However, I’ve thought for a while that something was needed to account for the objects and structures that arise in spacetime. A dimension of form that contains the models for how the universe evolves would solve the “what” problem.

Probably the earliest simulation hypothesis is the concept of maya from Indian philosophy. From Wikipedia: “In later Vedic texts, maya connotes a ’magic show, an illusion where things appear to be present but are not what they seem’; the principle which shows’“attributeless Absolute’ as having ‘attributes’.”

An extra dimension of form seems a little like Sheldrake’s morphic fields.

The hypothesized properties of morphic fields at all levels of complexity can be summarized as follows:

1. They are self-organizing wholes.
2. They have both a spatial and a temporal aspect, and organize spatio-temporal patterns of vibratory or rhythmic activity.
3. They attract the systems under their influence towards characteristic forms and patterns of activity, whose coming-into-being they organize and whose integrity they maintain. The ends or goals towards which morphic fields attract the systems under their influence are called attractors. The pathways by which systems usually reach these attractors are called chreodes.
4. They interrelate and co-ordinate the morphic units or holons that lie within them, which in turn are wholes organized by morphic fields. Morphic fields contain other morphic fields within them in a nested hierarchy or holarchy.
5. They are structures of probability, and their organizing activity is probabilistic.
6. They contain a built-in memory given by self-resonance with a morphic unit’s own past and by morphic resonance with all previous similar systems. This memory is cumulative. The more often particular patterns of activity are repeated, the more habitual they tend to become.

https://www.sheldrake.org/research/morphic-resonance/introduction

I warned you this might be a little New Agey. 🙂