Holometer: Transverse Jitter

Time to get serious. How does the Holometer, which is a pair of [interferometers](https://pedagoguepadawan.net/68/holometerinterferometer/) detect [holographic noise](https://pedagoguepadawan.net/66/holographicnoise/)? Fortunately, I met with Craig Hogan who is the Director of the Fermilab Center for Particle Astrophysics and a professor at University of Chicago since I wasn’t sure.

I’m going to attempt to explain why the holographic noise is measurable with the Holometer by way of analogy. In fact, there are several analogies that are applicable (Brownian motion, diffraction limits, black hole information theory, Heisenberg uncertainty principle). However, I want to be clear that we are talking about New Physics. You can’t explain this phenomenon using classical or quantum physics; it is not an application of any of the above phenomena; they serve only as analogies. That’s why it is New Physics. I’ve heard this New Physics referred in a couple of ways, but I like Planckian Physics best.

I know that we want to get to the Holometer, but first we need to introduce the Heisenberg uncertainty principle. Due to wave-particle duality, the Heisenberg uncertainty principles states that the more precisely we measure the position of a particle, the less precisely the momentum of that particle can be measured. (The uncertainty principle can also be presented in terms of energy and time, but we’ll stick with position and momentum.) While this inherent uncertainty is small, it is observable at the macroscopic level in some situations. For example, radioactive decay of a nucleus that ejects an alpha particle can only occur due to the uncertainty principle (from an energy and time perspective) via a process called tunneling. Classically, alpha decay violates conservation of energy.

Planckian Physics states that, in the same way that measuring position and momentum result in uncertainty, measuring position in perpendicular directions result in uncertainty. That is, the more precisely we measure the position of a particle in one direction, the less precisely we can measure the position of the particle in a perpendicular direction. Stated another way, precisely measuring the position of a particle in one directions results in transverse jitter in the position of the particle. This jitter is the holographic noise.

Hopefully, this explains why it is not possible to measure the holographic noise in a single dimension. For example, bouncing a photon off of a mirror and measuring when it returns cannot measure the holographic noise because this measurement only results in a transverse jitter (i.e., motion perpendicular to the motion of the photon) which would not affect the measurement.

Therefore, we need to employ an interferometer. When the position of a photon along one arm of the interferometer is precisely measured, the transverse jitter of the beam splitter results in noise in the interference measured by the photodiode.

transverse jitter of beam splitter

(diagram from Professor Craig Hogan)

The beam splitter executes a random walk of one Planck length per Planck time as the photon travels the length of the arm. This answers two of the questions from the [previous post](https://pedagoguepadawan.net/81/holometerspectralanalysis/): why are the Holometer arms 40-m long and why do we look for the holographic noise at 4 MHz? It takes a photon 267 ns to travel 80 m (40 m down and 40 m back). While 267 ns may not seem like long, it is 5 x 1036 Planck times. That means that, if the beam splitter may move a Planck length (1.6 x 10-35 m) for each Planck time, the beam splitter’s transverse jitter (due to the random walk) is on the order of 10-17 m which can be measured by an interferometer with clever spectral analysis. The holographic noise is present at all frequencies, but we are most sensitive to it at 4 MHz because that is the . and nearly constant from 0 Hz to near 3.75 MHz, where it drops off to zero (3.75 MHz is the frequency at which photos return to the beam splitter (the speed of light divided by 80 m)). (Revised Mon Jul 18 23:01:57 CDT 2011)

I haven’t yet explained why the Holometer consists of a pair of interferometers and why the theory predicts that the holographic noise of the two interferometers will be correlated if their space-time overlap and the holographic noise will not be correlated if their space-time does not overlap. Honestly, I don’t understand this aspect of the experiment yet. That’s okay because I get to meet with Professor Hogan again next week. I’m hoping to clarify my understanding by proposing several thought experiments and seeing if I can connect the resulting explanations. I think that the fact that the photons traveling down the arms are entangled is key. I proposed an experiment where two coherent photons are shot down each arm at exactly the same time and the resulting interference is measured. I would expect that the holographic noise would not be present since the photons are not entangled. However, I’m not sure if this thought experiment is possible to execute without entangling the photons in some manner. I’m going to study up on collapsing wave functions before our next meeting. If you have any questions, please comment!

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
* [Holometer: Correlated Interferometers](https://pedagoguepadawan.net/94/holometercorrelatedinterferometers/)
* [Holometer: Computer-Based Measurements](https://pedagoguepadawan.net/111/holometercomputerbasedmeasurements/)

2 thoughts on “Holometer: Transverse Jitter

  1. geoff Post author

    I was incorrect in my explanation of the frequency characteristics of the holographic noise. Chris Stoughton (my mentor at Fermilab) pointed out my error and pointed me in the right direction. I have revised the original post. He also passed along some interesting ideas for the next post. Thanks Chris!


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