Do we live in a hologram? How could we tell?

Do we live in a holographic universe? In other words, do we actually live in a universe with three spatial dimensions, or is this just an illusion and if you dig deeper, you could represent the universe as consisting of fewer (or even many more) dimensions. If we were really living in fewer than three dimensions, we’d call the universe holographic; if we had more than three spatial dimensions at small scales, we’d be living on a slice of a larger hyper-universe.

This sort of speculation has been fairly common within science, science fiction and philosophy. String theory is the latest and most original place where such analysis has occurred – certain types of string theory are believed to be consistent only in a certain number of spatial dimensions. In order to maintain sanity, therefore, the “other” dimensions are, for unknown reasons, supposed to have curled up into tiny rings that one cannot see unless one probes space at the Planck length scales $\sim 10^{-33} cm$ .

For the physicist who doesn’t have a dog in the search for additional dimensions, but wishes to figure out if this hypothesis (of different number of dimensions at small length scales) is even remotely true, the big problem is this – we are certainly not able to construct particle accelerators of the size of solar system, which we would potentially need in order to probe nature at the Planck length scale. Maybe in the next million years! In the interim, what could we do to check this possibility? Could extra, or fewer sub-microscopic (“Planckoscopic”?) dimensions have some effects on phenomena that we could measure? I just wrote a paper on a possible proposal to check this that I will describe below.

Unfortunately, we certainly cannot look at distances of that small a scale. We can look at distances that are much larger, quite obviously. What would cause small lengths to blow up and become large?

Enter the theory of inflation. Not economic inflation, which seems to be a factor of life in the year 2022, but the cosmic theory of inflation. This was invented by a few physicists, prominent among whom are Alan Guth, Andrei Linde, Paul Steinhardt and Alexei Starobinsky.

The problems they were trying to solve were as listed below –

Why is the universe so flat (space seems to be exceedingly flat on large length scales, of the order of 100 million light years). Indeed, if it looks this flat now, it must have been exceedingly flat, even ridiculously flat, when it was very small. Indeed, if we think the universe’s evolution followed the classic model with just matter, radiation and the so-called dark energy then we cannot explain why it was so remarkably flat when it began, unless it was a special kind of universe.
The simplest model of the universe with radiation, matter and dark energy matches observations, but has a problem – the expansion is slow, so if we looked at the Cosmic Microwave Background radiation from opposite directions in the universe, they should look different, since they were never in causal contact. The reason for this is this: the light we see in the background was produced when the universe was a couple of hundred thousand years old. If you track that back in time, anything that was a hundred thousand light years away from something else could have been in close causal contact with it. However, and this is the problem, if you expand a patch that was a couple of hundred thousand light-years (at the epoch when the Cosmic Microwave Background was produced) by the amount that the universe has expanded since then, based on what we believe happened, it turns out to be $ten \: thousand$ times smaller than the current size of the visible universe. This means that patches of the sky more than a palm width away from each other in the sky were $never$ in touch with each other, as they cannot connect by any means faster than light as far as we know.
Here is an objection to this – how about at the big bang singularity when everything was compressed down to one point? The argument really needs to be supplemented – we don’t really know if there was a singularity with infinite density and the universe probably had a very different structure exactly at that point, so we ignore the singular point.
To solve this problem, we need to have a universe that was very small and then suddenly expanded so quickly that things that became ten thousand times a couple of hundred thousand light years apart had still been in causal contact before this astonishing expansion.
That is what inflationary theory posits – for some unknown reason, but with a lot of plausible assumptions, one can find a mechanism that just does that. It explains most of the problems mentioned above, with some serious problems. For one thing, the explanation revolves around a special kind of particle called the inflaton, which seems to be a cousin of the Higgs boson, but we have never seen it or any other evidence for it . Next, the inflaton seems to have worked for a very short time, then given up the ghost, stopped inflating the universe, doesn’t seem to be around now and no one has a mechanism for why and how and when all this happened.
Anyway, having listed the successes and failures, if you take the inflation idea seriously, the problems above can be considered solved. In fact, in the simplest versions of the theory, it appears that in about $10^{-34}$ seconds, the universe expanded by at least a factor $e^{60} \approx 10^{26}$ . This made regions that should have been causally disconnected with the usual “slower” expansion actually causally connected from just before the inflationary interlude.

The rapid expansion caused kinks in the distribution of matter to even out and the curvature of space to flatten out. But not all – “Planckoscopic” fluctuations need to get straightened out. The big prediction of the inflationary theory was that these fluctuations would get very close to being completely straightened out (“scale-invariant fluctuations”). At long length scales, this seems to tie in to observations very well. My paper simply corrects this – if the world is actually built differently at small scales – if it has fewer degrees of freedom, fewer dimensions, this would change the way the fluctuations look when they are stretched out. However, since this difference is only seen for very small length scales, one would see this at rather small angular scales in the sky. The Planck and COBE satellite data played an important role in deducing the characteristics of these fluctuations in the Cosmic Microwave Background. However, as it turns out, it is just a little below the angular resolution to see the effect mentioned above and described in the paper – I await newer, higher-precision measurements.