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'All-seeing' telescope could take us back in time
24 September 2008
From New Scientist Print Edition.
Marcus Chown

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Enlarge The ultimate telescope

When I finally catch up with Max Tegmark he is pinned to a dentist's chair. "Are you sure this is a good time to talk?" I ask over a hissy cellphone connection. "It's OK," he replies. "They're doing my X-rays so we've got a few minutes. I could use some distraction."

Tegmark, a theoretical cosmologist at the Massachusetts Institute of Technology, is visiting the dentist to have a failed titanium implant removed. It's the only time he can spare to talk to me about his latest research, which promises to revolutionise the way astronomers view the heavens.

Today's telescopes come in many shapes and sizes: a few scan the whole sky, while others examine a given patch in great detail. Some look at the visible light emitted by stars and galaxies, others look at longer wavelengths for the embers of the big bang, and yet more are tuned to listen for radio waves.

In May, however, Tegmark revealed blueprints for an instrument beyond astronomers' wildest dreams - a telescope capable of observing the whole sky and all wavelengths of radiation simultaneously. With this "ultimate telescope" we would be able to see much, much more than we can with today's telescopes. We would be able to view the universe shortly after the big bang, take regular snapshots of its formative years and track its progress for the rest of cosmic history. "We'll be able to see the whole universe evolving from moment to moment," says Tegmark.

Telescope design is a far cry from Tegmark's usual research in theoretical cosmology. From his dentist's chair, he recalls a meeting he attended in April 2007 with colleagues from MIT, Harvard University and Australia. They were discussing how to build a telescope to observe the next big thing in cosmology: radio waves with a characteristic wavelength of 21 centimetres broadcast by atoms of hydrogen.

For the first 300,000 years after the big bang the universe was so hot that there were no atoms, only free electrons and nuclei. Only as the universe expanded did the temperature fall low enough for the electrons and nuclei to combine to form atoms, most of which were hydrogen. The hydrogen atoms beamed out their distinctive radio waves for hundreds of millions of years until light from the first stars or quasars ripped them apart and re-ionised the universe.

The crucial thing about the 21-centimetre radio waves is that we can determine precisely which cosmic epoch they came from. As the waves travel towards Earth, their wavelength is stretched by the expansion of the universe, to wavelengths of a few metres. So astronomers search radio waves for a peak that corresponds to the 21-centimetre radiation, even though it has shifted to a longer wavelength by the time it reaches Earth. The more the wavelength is stretched, the further back in time we are seeing. "Since different wavelengths come from different epochs, by observing this stuff we will be able to get 3D tomographic images of the universe back to almost the beginning of time," says Tegmark.

But there's a snag. The radio signal from neutral hydrogen is likely to be extremely faint, not to mention buried in emissions from closer sources such as the Milky Way. To be able to map it, we will need to collect as much signal as possible, which means using a telescope with a large collecting area.

Large single dishes are very expensive and, if bigger than about 100 metres in diameter, are at risk of collapsing under their own weight. So the obvious route is to use a telescope consisting of many smaller dishes spread out in an array. But again, there is a problem. Every signal from each small dish needs to be combined carefully on a computer, and the processing power needed for this goes up according to the function n2, where n is the number of telescope dishes. "For large n, this is prohibitively expensive," says Tegmark.

As he was listening to a discussion at Harvard, he had a brainwave. "Sitting in the meeting that day, I just thought: there must be a better way to do this." Suddenly, it occurred to Tegmark that there was a far cheaper way to build an array of telescopes. Before I can ask what it was, he interrupts: "They've come back with the X-rays. Sorry, I've got to open my mouth now."

An hour later, I catch him back at his home. "It's not over yet," he says. "They want me back at the dentist in an hour."

Tegmark says his "Eureka!" moment came when he asked himself: what does a telescope really do? All electromagnetic radiation, including light and radio waves, is made up of oscillating electric and magnetic fields that are intimately related. The "image" that astronomers see in their telescopes is really a measure of how the electric field varies across a patch of sky, says Tegmark.

To make such a measurement, astronomers have to collect the light raining down from the sky. The collector is usually some kind of concave dish - a mirror in the case of a large optical telescope. Unfortunately, in the process of collecting the light, the collector muddles everything up.

Take a particular point on the surface of the collector. The light hitting it comes not just from one direction in the sky but from all directions. "There are light rays from the Big Dipper, light rays from the star Betelgeuse, from the Crab Nebula, and so on," says Tegmark. "To get an image of the sky, it is necessary to somehow disentangle all these bundled-together light rays."

In a conventional reflecting telescope, the light falling onto a collector bounces onto a 2D region of space called the focal plane. "Imagine a little man standing at every point on the collector and sorting out the light rays," says Tegmark. "Those rays which have come from the Big Dipper, each man redirects to one particular location in the focal plane, those which have come from Betelgeuse go to another location, and so on. Now, if every little man does his job, the light is successfully unscrambled and an image of the sky appears in the focal plane."

Newton's genius was to realise that a parabolic mirror would automatically do the unscrambling job of these hypothetical little men - at least, for light coming from a limited range of directions. Tegmark realised you can also look at it in a different way. "Mathematically, such disentangling into constituent components is known as a Fourier transform," says Tegmark. "So telescopes are really Fourier transformers."

It is hard to imagine many amateur astronomers recognising their telescopes from this mathematical description. Tegmark's way of thinking is best illustrated by an instrument called an interferometer, which astronomers build instead of a single large dish to discern fine detail in the sky. Interferometers are made from two or more telescopes separated often by several metres. Each telescope sends its signals via a cable or a microwave link to a central location. There, pairs of signals are brought together just as if they were coming from two separate parts of a much larger dish and processed by a computer. "What happens naturally in a single-dish telescope is done mathematically in an interferometer."

The trouble with 21-centimetre tomography is that a single dish is insufficient to collect enough of the faint signal, which means that the only route is an interferometer with lots of collecting elements. But, Tegmark reminds me, "when n is large, the n2 cost of computing becomes a killer".

To give computers a chance, Tegmark knew he had to simplify the problem. He realised that if the interferometer elements were arranged in a compact grid he could exploit the grid's redundancy. A conventional interferometer observing a star, say, can only pick out features of the star that lie parallel to the line joining a pair of its elements. So if one element lies due north of another, they will discern only those details in the star that correspond to "north-south" overhead. In Tegmark's array two elements on a north-south line do exactly the same job as a neighbouring pair pointing in the same direction, so you only need to process the signals from one pair.

Killer application

Thinning out the problem like this means you can apply an ingenious algorithm called a fast Fourier transform (FFT), which was devised by American mathematicians James Cooley and John Tukey in 1965. Exploiting the grid's symmetry and the FFT should speed up processing a great deal, and Tegmark has shown that the cost - in terms of computing power - should rise much more slowly than n2 as you add elements to the interferometer.

According to his calculations, an FFT array with four elements would actually be twice as fast and half as expensive as a conventional interferometer with the same number of elements. With 256 elements, a conventional array would cost 32 times as much as an FFT array. "The FFT costs go up only as fast as nlog2n," says Tegmark, where log2 is the logarithm to the base 2 (see diagram).

When Tegmark came up with the idea for an FFT telescope, he was sure there must be a hole in it. So he ran it by his colleague Matias Zaldarriaga at Harvard University. "He could see no flaw," says Tegmark. "I even went to a conference of radio astronomers and nervously presented the idea. To my relief, they all thought it was cool."

Tegmark isn't the first to come up with the idea. Scientists and engineers have been discussing the concept since the 1960s. "It was not pursued for two reasons," he says. "First, there was insufficient computing power to make it work on a massive scale. More importantly, there was no 'killer application'."

A single telescope dish is good for observing faint sources because it collects lots of light. A conventional interferometer can discern objects in far greater detail, even though it collects a lot less light. That's because the elements of an interferometer are usually widely spaced - and the bigger this distance, the greater the resolution.

However, the kind of interferometer Tegmark has in mind has closely spaced elements and so low resolution. "Until now, nobody had any science that involved observing low-resolution extended objects such as the whole sky," he says. "With 21-centimetre tomography we now do. It is the killer app."

Tegmark and his colleagues are now attempting to prove the concept of the FFT telescope on the roof of the physics building at MIT. They are using cheap antennas similar to off-the-shelf TV aerials, and have spaced them in a regular array. But Tegmark is already thinking bigger than this - much bigger. "I'm imagining a square-kilometre FFT telescope with 1 million elements, where you'd save a factor of about 50,000 in speed and cost."

Saving on computing cost isn't the only advantage. Fourier transforms can do more than disentangle light from different directions. They can also disentangle various wavelengths from a complex light signal. Traditional telescopes use filters to block all but a narrow range of wavelengths, but Tegmark's telescope can, in principle, measure them all.

Inevitably, there is a snag. To pick out the smallest wavelengths from the incoming light signal takes a great deal of computer processing power. According to Tegmark, today's computers would allow an FFT telescope of the scale he envisions to see wavelengths about 30 centimetres and longer, which corresponds to microwaves and radio waves. But computer power is doubling every 18 months or so, says Tegmark, and this will see the detectable wavelength decrease exponentially. Within 30 years, an FFT telescope will be powerful enough to observe visible wavelengths at the same time as longer infrared and radio waves. "One day, most telescopes will be FFT telescopes," he predicts.

What's more, the FFT will view all directions in the sky simultaneously. "Contrast this with a normal telescope, which observes in one direction and has a band-pass filter which wastefully discards most light frequencies," says Tegmark.

Other astronomers are impressed. "The FFT telescope is an excellent idea," says Abraham Loeb, at Harvard University. "Advances in computing power will make the idea practical at low radio frequencies, perfect for the 21-centimetre application." Loeb points out that the same concept has been used by engineers for radar applications for decades. "I don't think that people realised the great advantage that the FFT telescope offers radio astronomy."

Tegmark is now back in his car, driving back to the dentist and chatting on his hands-free kit. He likens these days to those just before NASA's Cosmic Background Explorer satellite (COBE) was launched in 1992 and found its famous cosmic ripples - temperature variations in the afterglow of the big bang caused by the seeds of the galaxy clusters in today's universe. Though the ripples had not been detected before COBE, everyone knew they were there, and actually finding them galvanised the field. Second and third-generation experiments quickly refined the measurements.

"Similarly, everyone knows the 21-centimetre stuff is out there," says Tegmark. "The race is on to be the first to detect it and overcome the technical problems such as dealing with foreground emission from our Milky Way."

Tegmark believes the potential of the FFT telescope is huge. The radiation observed by COBE carries an imprint of the way the universe looked 300,000 years after the big bang. By contrast, 21-centimetre emissions record the universe as it changed over hundreds of millions of years. "The cosmic background radiation allows us to know the density of matter and dark matter and its velocity at one epoch," says Tegmark. "21-centimetre tomography will give us the same information for thousands of epochs. It'll blow away the cosmic background radiation." Loeb agrees: "Such maps would tell us about the first galaxies and stars."

I hear a car door slam. "Right, I'm back at the dentist," says Tegmark. "Got to go now." Click. As Tegmark goes off to his dental fate, my head is spinning with the possibilities of the ultimate telescope. A telescope to end them all.

Marcus Chown is the author of Quantum Theory Cannot Hurt You (Faber, 2008)

From issue 2675 of New Scientist magazine, 24 September 2008, page 36-39

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