# Holographic noise

April 1, 2016

#### What are you measuring?

We are measuring properties of space and time at the very smallest scales.

#### How small?

Very small! The "Planck length" (discussed more ) is \$10^{-35}\$ meters. One millimeter is 0.001 or \$10^{-3}\$ meters, so the Planck Length has a lot more zeroes after the decimal place. The Scale of the Universe 2 is a nice way to visualize length scales. Starting at \$1\$ meter, you can zoom "out" to the estimated size of the Universe (\$10^{27}\$ meters) and then zoom back "in" to fundamental particles. Notice that after the "smallest" particle, there is still a long way to zoom in before reaching the Planck length.

#### What new effect are you looking for?

The new idea we are testing states that positions (and time) are not precisely defined. When you measure the location of an object in two directions at the same time, the measurements have extra jitter.

We are seeking to measure a possible very slight random wandering of transverse position. This "holographic noise" could be caused by a new quantum uncertainty of space-time.

#### Why call it Holographic noise?

The theoretical ideas are similar to how ordinary holograms work. When you look through a hologram printed on a two-dimensional surface, a three-dimensional projection appears. Looking at this projection carefully, you see that it is a little fuzzy. This fuzziness is related to how small the pixels on the two-dimensional surface are. The smaller the two-dimensional pixels, the sharper the details are in the three-dimensional projection.

#### What is the basic strategy?

A Michelson Interferometer measures the x and y positions of the beam splitter (half silvered mirror) simultaneously. We monitor how much the beam splitter moves due to ordinary effects, such as vibrations from ground motion. We place two of these interferometers close to each other, so that the jitter from holographic noise from the two interferometers is coherent. This helps us measure the very small effect of holographic noise.

As shown in this figure, we will build the interferometers so they can operate in a "nested" or "back-to-back" configuration. The nested configuration maximizes the amount of coherence between the two interferometers. On one of the interferometers we can flip the direction of one of the arms while keeping everything else identical as much as possible. The holographic noise in this "back-to-back" configuration will not be coherent, and serves as an important test that we have correctly accounted for all sources of noise in the experiment.

The two red lines represent the two arms of an interferometer, with the beam splitter located where the two arms meet. The vertical direction measures time. The point at the bottom of the logo is the time where a photon first hits the beam splitter. It propagates out both arms and reaches the two end mirror at the center of the logo. Continuing up, the reflected light recombines again at the beam splitter at the top of the logo. The path of the beam splitter is a wavy line to indicate the jitter in the position of the beam splitter.

#### What does holographic noise sound like?

Holographic noise is purely "white noise": it has the same amplitude at all frequencies. The sensitivity of our interferometers depends on frequency. At low frequencies we are 100% sensitive to the noise, and this decreases to zero at the frequency of a round-trip of light from the beam splitter to the end mirrors (\$c/2L = 3.75\$ MHz). At higher frequency there are overtones. Our ears are not sensitive to these frequencies, so we slow the noise down by a factor of 6000 to produce this audio file.

Source: holometer.fnal.gov
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