Holometer: Correlated Interferometers

In the [previous post](https://pedagoguepadawan.net/83/holometertransversejitter/), I attempted to explain why an interferometer is susceptible to the holographic noise. However, this holographic noise is just one of many sources of noise that would be detected by the photodiode and digitizer. Some of these other sources of noise are more powerful than the holographic noise. Given that, how do we measure the holographic noise with an interferometer? We don’t. We measure the correlated noise between two adjacent interferometers. I [previously explained](https://pedagoguepadawan.net/81/holometerspectralanalysis/) how correlated noise that would otherwise be undetected can be measured by calculating a cross power spectrum. That is exactly how the Holometer, which is a pair of adjacent interferometers, measures the holographic noise.

The elephant in the room and, in my limited experience, the most challenging idea related to this experiment, is: why would the holographic noise from two adjacent interferometers be correlated? I’ve struggled trying to answer this question more than I’ve struggled with anything else this summer. I finally realized that one reason I was struggling so much is that I set myself up to fail from the start. I’ve been trying to explain this correlation from the perspective of quantum mechanics and general relativity. That approach is a nonstarter because **quantum mechanics and general relativity don’t explain the holographic principle**. This is New Physics, Planckian Physics! Another reason that I’ve struggled trying to answer this question is, quite simply, this is crazy stuff. Think about double-slit experiments with electrons, Bell Inequalities, the Einstein–Podolsky–Rosen experiment, or the Brown and Twiss interferometer. All of these are crazy. Most people wouldn’t believe them except for the fact that they have been demonstrated experimentally. The same can be said of the Holometer, most people may not believe that the holographic noise is present or is correlated until we measure it.

Let’s take a step back and take a look at light cones. A light cone contains the volume that defines the possible path of light, originating at some event, through space time. Two of the dimensions of the cone are spacial and the third is time. The upward opening cone is the future light cone that describes the potential paths of the light after the event and the downward opening cone is the past light cone. Only events within the past light cone can affect the event. This is called causality.


(*figure 1: past and future light cones (source: Wikipedia*))

The following diagram illustrates what is referred to as the causal diamond for an interferometer. The top half of the diamond is the past light cone of the beamsplitter reflection. The bottom-half of the diamond is the future light cone of another reflection from the beamsplitter. The causal diamond is the intersection of these light cones. The red lines are the arms of the interferometer.

inteferometer space-time diagram

(*figure 2: interferometer causal diamond (source: Professor Craig Hogan*))

This is the most important diagram of the experiment. Someone inscribed it on the concrete slab that will support one end of the interferometers:

causal diamond inscription

(*figure 3: interferometer causal diamond preserved in concrete*)

We are going to focus on the “wedge” of the causal diamond defined by the arms of the interferometer. The greater the overlap of these causal-diamond wedges for a pair of interferometers, the greater the correlated holographic noise. Therefore, these two adjacent interferometers would exhibit uncorrelated holographic noise:

uncorrelated interferometers

(*figure 4: interferometer pair with non-overlapping causal diamonds*)

While these two adjacent interferometers would exhibit highly correlated holographic noise:

correlated interferometers

(*figure 5: interferometer pair with overlapping causal diamonds*)

Why? The key idea is explained in the [Holometer Proposal](http://holometer.fnal.gov/presentations/holometer-proposal-2009.pdf).

In the holographic effective theory built on light sheets, time and longitudinal position are identified. Measurement of a position at one point on a light sheet collapses the wavefunction at other points on the wavefront, even though they have spacelike separation. The apparent motion is thus in common across a significant transverse distance— not only across a macroscopic beamsplitter, say, but even between disconnected systems.

Let’s look at a top-view perspective of the two overlapping interferometers to examine this idea:

correlated wavefronts

(*figure 6: wavefront in pair of correlated interferometers*)

As the wavefront travels to the right in interferometer #1, the collapsing wave function results in a common motion of the two interferometers where their two causal diamonds overlap. The same occurs with the adjacent arms in the perpendicular direction. Therefore, these two interferometers will have highly correlated holographic noise. However for these two interferometers:

uncorrelated wavefronts

(*figure 7: wavefront in pair of uncorrelated interferometers*)

As the wavefront travels to the right in interferometer #1, the collapsing wave function doesn’t affect interferometer #2. There would not be any common motion between the arms in the x direction and, therefore, the two interferometers will have uncorrelated holographic noise.

The Holometer experiment tests the hypothesis illustrated by figures 6 and 7. We build a pair of interferometers as illustrated in figure 6. We then isolate the correlated holographic noise between the two interferometers. Then to prove that the noise is truly due to the Holographic Principle, we adjust the beam splitter to send the light down a fifth arm such that the experiment is arranged as illustrated in figure 7. We then are unable to identify correlated holographic noise between the two interferometers. QED.

All that is left for me to present is how we are going to measure the correlated holographic noise. That will be the topic of the final post. Ah, finally something in which I have some expertise!

This post is one in a series about The Holometer experiment and my work at Fermilab in the Summer of 2011:

* [Holometer: Holographic Noise](https://pedagoguepadawan.net/66/holographicnoise/)
* [Holometer: Interferometer](https://pedagoguepadawan.net/68/holometerinterferometer/)
* [Holometer: Spectral Analysis](https://pedagoguepadawan.net/81/holometerspectralanalysis/)
* [Holometer: Transverse Jitter](https://pedagoguepadawan.net/83/holometertransversejitter/)
* Holometer: Correlated Interferometers
* [Holometer: Computer-Based Measurements](https://pedagoguepadawan.net/111/holometercomputerbasedmeasurements/)

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