Holometer: Interferometer

This is my second post in my Holometer series. The [first one](https://pedagoguepadawan.net/66/holographicnoise/) provided some background information on the Holographic Principle.

The Holometer experiment consists of a pair of 40-m-long interferometers. I don’t yet fully understand why there are two or why they are 40-m long; so, I’ll address the design of the experiment later. For now, I’ll provide some background on interferometers in general.

When discussing interferometers, I have to start with the one of the most important failed experiments: the [Michelson–Morley experiment](http://en.wikipedia.org/wiki/Michelson–Morley_experiment). This is especially the case since it was conducted at my alma matter, Case Western Reserve University. In his efforts to detect the ether, Michelson developed the interferometer:

(Michelson interferometer; source: [wikipedia](http://en.wikipedia.org/wiki/File:Interferometer.svg))

An interferometer has two perpendicular arms. Light is directed at a beam splitter (half-silvered mirror in the diagram) and is split down each arm. While the diagram refers to coherent light, and the Holometer does use a laser, coherent light is not required (and certainly not used by Michelson). The light travels the length of each arm, is reflected off mirrors at the end of each arm, and passes back through/off the beam splitter to the detector.

I’m assuming that you are familiar with the concept of [interference](http://hyperphysics.phy-astr.gsu.edu/hbase/sound/interf.html). Interference of waves is evident when playing with slinkies, dropping a pair of pebbles in a pond, or listening to two tones close in frequency (i.e., beats). Perhaps the most famous example of interference of light is [Young’s Double Slit experiment](http://en.wikipedia.org/wiki/Double-slit_experiment). In essence, when two waves of light meet, they interfere. If two peaks or two troughs of these waves align (i.e., are in phase), they constructively interfere and the detector measures a brighter light. If a peak aligns with a trough (i.e., out of phase), they destructively interfere and, if aligned exactly, the detector measures no light.

(constructive and destructive interference; source: [wikipedia](http://upload.wikimedia.org/wikipedia/commons/0/0f/Interference_of_two_waves.svg))

Michelson and Morely measured the effect of the ether on the speed of light by observing the interference patterns as their interferometer was rotated. While they didn’t know the direction of the ether, by rotating their interferometer, they were assured that at times one beam would be in the same direction as the ether while the other was perpendicular to it. If the light traveled different speeds based on its direction relative to that of the ether, the interference patterns produced by the interferometer would change as it is rotated. The interference pattern didn’t change since there was no ether and light travels at a constant speed in a given medium regardless of direction.

Given that light does travel at a constant speed, an interferometer is useful for measuring very small differences in length. If the two arms of the interferometer are exactly the same length, the two waves will constructively interfere. However, if one arm is a quarter-of-a-wavelength longer than the other, one wave will travel a total of an extra half-a-wavelength compared to the other, and the two waves will destructively interfere. Given the very small wavelength of light, this makes an interferometer a very sensitive instrument. The Holometer is designed such that one arm is a quarter-of-a-wavelength longer than the other. If this distance was exact, and nothing moved, the detector would measure no light (in fact, it is referred to it as the dark port).

However, in order for the Holometer experiment to eventually make sense, we need to look at the light in an interferometer from a different perspective: light as a particle. When a photon (i.e., particle of light) hits the beam splitter, quantum mechanics tells us that the photon travels down **both arms at the same time**. Don’t think too hard about that; just drink the kool-aid and move on. This particle perspective is key because it illustrates that, since the same photon travels down each arm and reflects back, the photon interferes with itself. This is a very important characteristic to which we will return later.

So, at this point we’ve described a very sensitive instrument – the interferometer. It can measure differences in length of an order smaller than the wavelength of light (400 nm – 750 nm). The realization that you may have at this point is that there is a huge difference in magnitude between the wavelength of light (7.5 x 10-7 m) and Planck’s length (1.6 x 10-35 m). How can the Holometer measure anything on the order of the holographic noise? We’ll tackle that next as we explore spectral analysis and correlation.

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
* [Holometer: Spectral Analysis](https://pedagoguepadawan.net/81/holometerspectralanalysis/)
* [Holometer: Transverse Jitter](https://pedagoguepadawan.net/83/holometertransversejitter/)
* [Holometer: Correlated Interferometers](https://pedagoguepadawan.net/94/holometercorrelatedinterferometers/)
* [Holometer: Computer-Based Measurements](https://pedagoguepadawan.net/111/holometercomputerbasedmeasurements/)

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