Cosmic noise

Science often takes unpredictable paths. Here, we follow a thread that initially seemed unrelated with the work of Schottky, but that eventually became inextricably intertwined with noise.

In the same years that saw the first studies of electrical noise, the British physicist Edward Victor Appleton was exploring the upper atmosphere with radio waves. Appleton investigated one of the great scientific puzzles of the time, one that had come to light with the first radio transmissions of Marconi between England and Newfoundland in 1901: how can radio waves follow the curvature of the Earth and cross the Atlantic Ocean?

Already in 1902 Kennelly and Heaviside proposed the existence of a conducting layer in the upper atmosphere, but at the time there was no apparent way to prove that it was so.

Another alternative proposal was put forward in the same year by H. M. MacDonald in Cambridge, United Kingdom, that radio waves could be received thanks to a diffractive effect. MacDonald also produced calculations that showed that it was so. Unfortunately, the radiation that was diffracted according to MacDonald was far too much, and it was the great French mathematician Henri Poincaré who found the error in the calculations and gave a first formal proof that diffraction could not account for the long-range propagation of radio waves. Poincaré himself struggled with the complete proof, and the work was eventually completed by G. N. Watson ² .

In Poincaré's solution, the intensity of the diffracted wave has a dependence, $\sim \exp (-\alpha \theta {R}^{1/3}/{\lambda }^{1/3})$, where θ is the angular distance between the antenna and the receiver, R is the radius of the Earth, λ is the wavelength of the radio waves, and α is a numerical constant ³ . It is actually rather easy to see that it is reasonable to expect such an exponential dependence, as noted by Poincaré himself. If we take the angular distance θ between the transmitter and the receiver and divide it into n parts, ${\rm{\Delta }}\theta =\theta /n$, then, because of the spherical symmetry, the fractional decrease of the intensity should be the same throughout the n steps and should be given by the expression ${I}_{k+1}/{I}_{k}\approx \beta {\rm{\Delta }}\theta$, where β is a numerical parameter (in simple words the ratio between successive intensities at the kth step is independent of the step number k and depends roughly linearly on the small step size ${\rm{\Delta }}\theta$). Then we can write

$$\begin{eqnarray*}&&\frac{{I}_{k+1}}{{I}_{k}}=\frac{{I}_{k}-{\rm{\Delta }}{I}_{k}}{{I}_{k}}=1-\frac{{\rm{\Delta }}{I}_{k}}{{I}_{k}}=1-\beta {\rm{\Delta }}\theta =1-\frac{\beta \theta }{n},\end{eqnarray*}$$

and finally we find

$$\begin{eqnarray*}&&\frac{{I}_{n}}{{I}_{0}}=\frac{{I}_{n}}{{I}_{n-1}}\times \frac{{I}_{n-1}}{{I}_{n-2}}\times \ldots \,\times \frac{{I}_{2}}{{I}_{1}}\times \frac{{I}_{1}}{{I}_{0}}={\left(1-\frac{\beta \theta }{n}\right)}^{n}\mathop{\to }\limits_{n\to \infty }\,\exp (-\beta \theta ),\end{eqnarray*}$$

just as expected. Unfortunately, this reasoning is too simplistic to uncover the dependence on λ and on R, buried as it is in the β parameter.

So, in 1922, when Appleton started to work on the problem, the best candidate explanation was a conductive layer of ionized gas in the upper atmosphere, which—together with the surface of the Earth—could form a sort of waveguide for the radio waves. But was this layer actually there, and, if so, how high was it above the ground? And what of its properties?

Appleton knew that ground reception of radio signals was disturbed by what appeared to be an interference effect. If the reflecting layers where there, then this could be explained by a diagram like figure 1.1. He also understood that with just one transmitting and one receiving station, he could find the height of the reflecting layers by gradually changing the wavelength of the radio waves and counting the number n of maxima of the received signal. If ${\lambda }_{1}$ and ${\lambda }_{2}$ are the minimum and maximum wavelengths in the scan, the path difference D can be obtained from the equation

$$\begin{eqnarray*}&&n=\frac{D}{{\lambda }_{1}}-\frac{D}{{\lambda }_{2}}\end{eqnarray*}$$

and the height h is given by Pythagoras' theorem:

$$\begin{eqnarray*}&&h=\frac{1}{2}\sqrt{{(L+D)}^{2}-{L}^{2}}\end{eqnarray*}$$

where L is the horizontal distance between the aerials.

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After the measurements with which he established the existence of the ionosphere, Appleton further perfected his techniques and dedicated the rest of his scientific life to the study of the properties of the ionosphere.

This new understanding of the upper atmosphere was of great practical use, as it allowed one to forecast the long-range reception of radio broadcasts. However, the reliance of radio transmissions on atmospheric ionization also meant that they were subject to many kinds of disturbances. In 1932, Bell Labs assigned to Karl G. Jansky the task of investigating the sources of these disturbances. Jansky built a directional antenna—nicknamed 'Jansky's merry-go-round'—that could be rotated about a vertical axis to point at different directions (figure 1.2). He discovered that most of the disturbances could be attributed to thunderstorms, but he also identified something else: highly directional emissions that appeared to come from a few fixed positions in the sky. He also associated one specific direction (right ascension 18 h, declination $-10^\circ$) with the position of the center of the Milky Way. Jansky's discovery of radio emissions from space marked the start of radio astronomical research ⁴ .

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After a rather slow start, around 1940 radio astronomy began to take off with the work of Grote Reber in the United States and with that of James S. Hey in Britain. As technology became better and better, the stream of discoveries flowed uninterrupted, and if we fast forward to the year 1963, we find two young scientists, Arno A. Penzias and Robert W. Wilson, busily working at the Holmdel Horn Antenna in New Jersey, not far from Princeton.

The Holmdel Antenna (figure 1.3) had been built by Bell Labs in the late 1950s as part of a project on communication satellites. At the end of that project, the antenna was made available to radio astronomers, and Penzias and Wilson set out to measure the radiation emitted by the galactic halo, the loose aggregate of stars and hot interstellar gas that surrounds the Milky Way. By fixing the antenna position they expected the output signal to change periodically with the rotation of the Earth, and by choosing a wavelength where there was no emission from the galactic halo, they thought that they could determine the background noise level of their radio telescope.

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That job turned out to be more difficult than they expected, as the noise was systematically higher than calculations and estimates indicated. Finally, they became aware of another experimental effort that was being carried out at Princeton, where other scientists were trying to measure the relic light from the Big Bang. Then, Penzias and Wilson understood that they were way ahead with their apparatus and that their mysterious noise was the precious fossil of the primordial explosion ⁵ .

This is a great and still unfinished story, which unfolds much like a thriller. Unfortunately, its details involve some necessary knowledge about thermal noise, and we defer them to chapter 4.