Is the universe a hologram? Gravitational wave interferometers may tell us.

Shadow on the wall.

Left-right. Forward-backward. Up-down. We are used to living in three dimensions of space. But according to some physicists, that’s an illusion. Instead, they say, the universe is a hologram and every move we make is really inscribed on the surface of the space around us. So far, this idea has been divorced from experimental test. But in a recent arXiv paper, physicists have now proposed a way to test it.

What does it mean to live in a hologram? Take a Rubik’s cube. No, don’t leave! I mean, take it, metaphorically speaking. The cube is made of 3 x 3 x 3 = 27 smaller cubes. It has 6 x 3 x 3 = 54 surface elements. If you use each surface pixel and each volume pixel to encode one bit of information, then you can use the surface elements to represent everything that happens in the volume.

A volume pixel, by the way, is called a voxel. If you learn nothing else from me today, take that.

So the Rubik’s cube has more pixels than voxels. But if you divide it up into smaller and smaller pieces, the ratio soon changes in favor of voxels. For N intervals on each edge, you have N³ voxels compared to 6 x N² pixels. The amount of information that you can encode in the volume, therefore, increases much faster than the amount you can encode on the surface.

Or so you would think. Because the holographic principle forbids this from happening. This idea, which originates in the physics of black holes, requires that everything which can happen inside a volume of space is inscribed on the surface of that volume. This means if you’d look very closely at what particles do, you would find they cannot move entirely independently. Their motions must have subtle correlations in order to allow a holographic description.

We do not normally notice these holographic correlations, because ordinary stuff needs few of the theoretically available bits of information anyway. Atoms in a bag of milk, for example, are huge compared to the size of the voxels, which is given by the Planck length. The Planck length, that is 25 orders of magnitude smaller the diameter of an atom. And these 25 orders of magnitude, you may think, crush all hopes to ever see the constraints incurred on us by the holographic principle.

But theoretical physicists don’t give up hope that easily. The massive particles we know are too large to be affected by holographic limitations. But physicists expect that space and time have quantum fluctuations. These fluctuations are normally too small to observe. But if the holographic principle is correct, then we might be able to find correlations in these fluctuations.

To see these holographic correlations, we would have to closely monitor the extension of a large volume of space. Which is, in a nutshell, what a gravitational wave interferometer does.

The idea that you can look for holographic space-time fluctuations with gravitational wave interferometers is not new. It was proposed already a decade ago by Craig Hogan, at a time when the GEO600 interferometer reported unexplained noise.

Hogan argued that this noise was a signal of holography. Unfortunately, the noise vanished with a new readout method. Hogan, undeterred, found a factor in his calculation and went on to build his own experiment, the “Holometer” to search for evidence that we live in a hologram.

The major problem with Hogan’s idea, as I explained back then, was that his calculation did not respect the most important symmetry of Special Relativity, the so-called Lorentz-symmetry. For this reason the prediction made with Hogan’s approach had consequences we would have seen long ago with other experiments. His idea, therefore, was ruled out before the experiment even started.

Hogan, since he could not resolve the theoretical problems, later said he did not have a theory and one should just look. His experiment didn’t find anything. Or, well, it delivered null results. Which are also results, of course.

In any case, two weeks ago Erik Verlinde and Kathryn Zurek had another go at holographic noise:

Observational Signatures of Quantum Gravity in Interferometers
Erik P. Verlinde, Kathryn M. Zurek
arXiv:1902.08207 [gr-qc]

The theoretical basis of their approach is considerably better than Hogan’s.

The major problem with using holographic arguments for interferometers is that you need to specify what surface you are talking about on which the information is supposedly encoded. But the moment you define the surface you are in conflict with the observer-independence of Special Relativity. That’s the issue Hogan ran into, and ultimately was not able to resolve.

Verlinde and Zurek circumvent this problem by speaking not about a volume of space and its surface, but about a volume of space-time (a “causal diamond”) and its surface. Then they calculate the amount of fluctuations that a light-ray accumulates when it travels back and forth between the two arms of the interferometer.

The total deviation they calculate scales with the geometric mean of the length of the interferometer arm (about a kilometer) and the Planck length (about 10^-35 meters). If you put in the numbers, that comes out to be about 10^-16 meters, which is not far off the sensitivity of the LIGO interferometer, currently about 10^-15 meters.

Please do not take these numbers too seriously, because they do not account for uncertainties. But this rough estimate explains why the idea put forward by Verlinde and Zurek is not crazy talk. We might indeed be able to reach the required sensitivity in the soon future.

Let me be honest, though. The new approach by Verlinde and Zurek has not eliminated my worries about Lorentz-invariance. The particular observable they calculate is determined by the rest-frame of the interferometer. This is fine. My worry is not with their interferometer calculation, but with the starting assumption they make about the fluctuations. These are by assumption uncorrelated in the radial direction. But that radial direction could be any direction. And then I am not sure how this is compatible with their other assumption, that is holography.

The authors of the paper have been very patient in explaining their idea to me, but at least so far I have not been able to sort out my confusion about this. I hope that one of their future publications will lay this out in more detail. The present paper also does not contain quantitative predictions. This too, I assume, will follow in a future publication.

If they can demonstrate that their theory is compatible with Special Relativity, and therefore not in conflict with other measurements already, this would be a well-motivated prediction for quantum gravitational effects. Indeed, I would consider it one of the currently most promising proposals.

But if Hogan’s null result demonstrates anything, it is that we need solid theoretical predictions to know where to search for evidence of new phenomena. In the foundations of physics, the days when “just look” was a promising strategy are over.