WHEN I finally catch up with Max Tegmark he is pinned to a dentist鈥檚 chair. 鈥淎re you sure this is a good time to talk?鈥 I ask over a hissy cellphone connection. 鈥淚t鈥檚 OK,鈥 he replies. 鈥淭hey鈥檙e doing my X-rays so we鈥檝e got a few minutes. I could use some distraction.鈥
Tegmark, a theoretical cosmologist at the Massachusetts Institute of Technology, is visiting the dentist to have a failed titanium implant removed. It鈥檚 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鈥檚 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 , others look at , and yet more are tuned to listen for .
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In May, however, Tegmark revealed blueprints for an instrument beyond astronomers鈥 wildest dreams 鈥 a telescope capable of observing the whole sky and all wavelengths of radiation simultaneously. With this 鈥渦ltimate telescope鈥 we would be able to see much, much more than we can with today鈥檚 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. 鈥淲e鈥檒l be able to see the whole universe evolving from moment to moment,鈥 says Tegmark.
Telescope design is a far cry from Tegmark鈥檚 usual research in theoretical cosmology. From his dentist鈥檚 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. 鈥淪ince 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,鈥 says Tegmark.
But there鈥檚 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. 鈥淔or large n, this is prohibitively expensive,鈥 says Tegmark.
As he was listening to a discussion at Harvard, he had a brainwave. 鈥淪itting in the meeting that day, I just thought: there must be a better way to do this.鈥 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: 鈥淭hey鈥檝e come back with the X-rays. Sorry, I鈥檝e got to open my mouth now.鈥
An hour later, I catch him back at his home. 鈥淚t鈥檚 not over yet,鈥 he says. 鈥淭hey want me back at the dentist in an hour.鈥
Tegmark says his 鈥淓ureka!鈥 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 鈥渋mage鈥 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 鈥 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. 鈥淭here are light rays from the Big Dipper, light rays from the star Betelgeuse, from the Crab Nebula, and so on,鈥 says Tegmark. 鈥淭o get an image of the sky, it is necessary to somehow disentangle all these bundled-together light rays.鈥
In a conventional reflecting telescope, the light falling onto a collector bounces onto a 2D region of space called the focal plane. 鈥淚magine a little man standing at every point on the collector and sorting out the light rays,鈥 says Tegmark. 鈥淭hose 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.鈥
Newton鈥檚 genius was to realise that a parabolic mirror would automatically do the unscrambling job of these hypothetical little men 鈥 at least, for light coming from a limited range of directions. Tegmark realised you can also look at it in a different way. 鈥淢athematically, such disentangling into constituent components is known as a Fourier transform,鈥 says Tegmark. 鈥淪o telescopes are really Fourier transformers.鈥
It is hard to imagine many amateur astronomers recognising their telescopes from this mathematical description. Tegmark鈥檚 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. 鈥淲hat happens naturally in a single-dish telescope is done mathematically in an interferometer.鈥
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, 鈥渨hen n is large, the n2 cost of computing becomes a killer鈥.
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鈥檚 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 鈥渘orth-south鈥 overhead. In Tegmark鈥檚 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鈥檚 symmetry and the FFT should speed up processing a great deal, and Tegmark has shown that the cost 鈥 in terms of computing power 鈥 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. 鈥淭he FFT costs go up only as fast as nlog2n,鈥 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. 鈥淗e could see no flaw,鈥 says Tegmark. 鈥淚 even went to a conference of radio astronomers and nervously presented the idea. To my relief, they all thought it was cool.鈥
Tegmark isn鈥檛 the first to come up with the idea. 杏吧原创s and engineers have been discussing the concept since the 1960s. 鈥淚t was not pursued for two reasons,鈥 he says. 鈥淔irst, there was insufficient computing power to make it work on a massive scale. More importantly, there was no 鈥榢iller application鈥.鈥
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鈥檚 because the elements of an interferometer are usually widely spaced 鈥 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. 鈥淯ntil now, nobody had any science that involved observing low-resolution extended objects such as the whole sky,鈥 he says. 鈥淲ith 21-centimetre tomography we now do. It is the killer app.鈥
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 鈥 much bigger. 鈥淚鈥檓 imagining a square-kilometre FFT telescope with 1 million elements, where you鈥檇 save a factor of about 50,000 in speed and cost.鈥
Saving on computing cost isn鈥檛 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鈥檚 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鈥檚 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. 鈥淥ne day, most telescopes will be FFT telescopes,鈥 he predicts.
鈥淲ithin 30 years the telescope will be able to observe all wavelengths at the same time鈥
What鈥檚 more, the FFT will view all directions in the sky simultaneously. 鈥淐ontrast this with a normal telescope, which observes in one direction and has a band-pass filter which wastefully discards most light frequencies,鈥 says Tegmark.
Other astronomers are impressed. 鈥淭he FFT telescope is an excellent idea,鈥 says Abraham Loeb, at Harvard University. 鈥淎dvances in computing power will make the idea practical at low radio frequencies, perfect for the 21-centimetre application.鈥 Loeb points out that the same concept has been used by engineers for radar applications for decades. 鈥淚 don鈥檛 think that people realised the great advantage that the FFT telescope offers radio astronomy.鈥
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鈥檚 was launched in 1992 and found its famous cosmic ripples 鈥 temperature variations in the afterglow of the big bang caused by the seeds of the galaxy clusters in today鈥檚 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.
鈥淪imilarly, everyone knows the 21-centimetre stuff is out there,鈥 says Tegmark. 鈥淭he 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.鈥
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. 鈥淭he cosmic background radiation allows us to know the density of matter and dark matter and its velocity at one epoch,鈥 says Tegmark. 鈥21-centimetre tomography will give us the same information for thousands of epochs. It鈥檒l blow away the cosmic background radiation.鈥 Loeb agrees: 鈥淪uch maps would tell us about the first galaxies and stars.鈥
I hear a car door slam. 鈥淩ight, I鈥檓 back at the dentist,鈥 says Tegmark. 鈥淕ot to go now.鈥 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.
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