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More than four dimensions

Posted by iKnowHOW on October 31, 2006

The list of dimensions doesn’t run out with time, says Lisa Randall



Scientific progress always entails an almost contradictory set of beliefs. You need to make assumptions to build a mathematical picture of reality. But while you want to be sufficiently excited about your assumptions to think they merit investigation, you need to remain sceptical enough to subject the consequences of those premises to rigorous analysis.

Although I’ve always combined these attitudes in my research, my recent studies of extra dimensions of space, beyond the familiar “up-down”, “left-right” and “forward-backward” have made me more than usually convinced that they must really exist.

Perhaps the best way to understand what these extra dimensions would be is the way Edwin Abbott described them in his book Flatland, written in the late 19th century. Suppose there was a society that, unlike ours, could detect and experience a world with only two dimensions: the Flatland of the title. Its inhabitants wouldn’t perceive a third dimension, even though the dimension really did exist.

If an object like a sphere were to pass through their universe, Flatlanders would never perceive it in its entirety; instead, they would see a succession of disks that grew in size and then became smaller. Because they register only two dimensions, Flatlanders could only mathematically piece together the fact that the object they had seen was the analogue of their disk, but in one higher dimension.

Similarly, the fact that we see only three dimensions doesn’t mean there might not be more. Einstein’s theory of general relativity doesn’t stipulate any particular number of dimensions. And from the perspective of his theory of gravity, there’s nothing special about three dimensions of space. People have often made the mistake of believing only in what they could see. Extra dimensions might turn out to be one among many aspects of the cosmos about which we were initially mistaken.

The string theory is another reason to believe extra dimensions might exist. It consistently incorporates our theories of the very small and the very big in the Universe ? quantum mechanics and general relativity ? which no earlier theory had accomplished. This doesn’t prove the string theory is right, and it’s critical that we do further research. Because it promises to be a more comprehensive theory than any other we know of, a so-called theory of quantum gravity, the string theory is well worth studying.

However, it doesn’t naturally describe a world with three dimensions of space. It more naturally suggests a world with many more, perhaps nine or 10. A string theorist doesn’t ask whether extra dimensions exist; instead, two critical questions that a string theorist asks are: where are they and why haven’t we seen them?

Even if you’re sceptical about the string theory, recent research has provided perhaps the most compelling argument for extra dimensions: a universe with these dimensions might contain answers to physics puzzles that have no convincing solutions without them. That alone makes extra dimensions worthy of investigation.

The history of physics is the story of discovering different, more basic elements of matter as we’ve developed the tools to explore different length and energy scales. Once scientists could observe matter on smaller scales, they discovered atoms and quarks, and after they could study further distances in the Universe, physicists and astronomers discovered galaxies and dark matter.

Extra dimensions might be hidden (for now) but none the less be part of reality. More detailed observations at higher energies and shorter distances might eventually reveal their existence.

These as-yet-unseen dimensions could be flat, like the dimensions we are accustomed to. Or they could be warped, like reflections in a fun-house mirror. They might be tiny, far smaller than an atom, or they might be big, or even infinite in size, yet still be hard to see.

Brilliant mind: Lisa Randall ; (below) the cover of her book

Our senses register only three large dimensions, so an infinite extra dimension might sound incredible. But an infinite unseen dimension and parallel universes within it are some of the bizarre possibilities for what might exist in our cosmos.

To see why extra dimensions are not ruled out by our apparently three-dimensional observations, we need to understand how dimensions can exist, but be invisible. In 1920, almost immediately after Einstein completed his theory of general relativity, Theodor Kaluza suggested an extra dimension of space, and in 1926, Oskar Klein proposed a reason why we wouldn’t see it.

An extra dimension could be rolled up into such a tiny size that it would have no visible effects. If you think of extra dimensions rolled up like a garden hose, the width of the “hose” could be so tiny that we’d never notice it. Any variations over this tiny distance would be washed out, much as the atomic structure of this piece of paper is imperceptible.

But although physicists have known for years that extra dimensions could be rolled up, it wasn’t until 1999 that Raman Sundrum (who was then a post-doctoral fellow at the Boston University) and I (then a professor at MIT) discovered another reason that extra dimensions might be hidden.

Einstein’s theory of relativity tells us that energy and matter curve space and time. We found that spacetime with extra dimensions could be so extremely warped that even an infinite extra dimension could exist but escape detection.

The success with which our theory mimics three dimensions suggests that all evidence that apparently points to three dimensions of space supports the idea of such “warped” extra-dimensional universes equally strongly. None the less, our idea was so different from older notions that it took a while for some physicists to accept. Fortunately for us, however, Stephen Hawking and a few others immediately appreciated its radical implications.

The following year another physicist, Andreas Karch, and I found that space can be even more spectacular: the Universe can appear to have three spatial dimensions in some regions but appear to have, or in fact have, more (or fewer) in others. Our notion of three-dimensional “sinkholes” extended the Copernican revolution beyond anything we had imagined.

Not only is the earth not the centre of the Universe, but our domain might be a tiny isolated pocket with three spatial dimensions inside a universe that harbours many more. This was a huge revelation, one that convinced me we have a lot more to understand about extra dimensions of space, and one that also made the idea of extra dimensions more credible; isn’t it presumptuous to rule out something whose implications we don’t even fully comprehend?

But perhaps the most convincing reason to believe in extra dimensions is that they permit new connections among properties of the observed Universe and have a real possibility for explaining some of its more mysterious features. Extra dimensions can have implications for the world we see and explain phenomena that seem incomprehensible when viewed from the perspective of a three-spatial-dimensional observer (or theorist).

We wouldn’t understand the shapes of the continents unless we add the dimension of time and recognise how they were once connected together in a supercontinent. Similarly, some problems in physics are more readily understood with extra dimensions of space.

Chief among these questions is why the gravitational force is so weak. Gravity might not appear to be all that weak when you’re hiking up a mountain, but bear in mind that the gravitational force of the entire earth is acting on you. Think how feeble gravity must be for you to counter the force of the much larger earth when you pick up a ball.

In fact, if the earth were your size, gravity wouldn’t be noticeable at all. For more than 30 years, physicists (including myself) have explored this conundrum, and they’ve found no completely compelling solution.

But with an additional warped dimension, it’s natural for gravity to be weak in our vicinity. In our warped spacetime geometry, gravity is very strong in one region of a fourth dimension of space (a fifth dimension of spacetime) but very weak everywhere else.

For me, the explanation for the weakness of gravity is sufficient reason in itself to take the possibility of extra dimensions seriously. The mystery is the biggest gaping hole in our understanding of the physics of elementary particles, and an extra dimension provides an answer. As a scientist, even if I believe that extra dimensions exist in nature, I don’t have blind faith and I’m willing to be proved wrong. We don’t yet know how to experimentally test all extra-dimensional theories. But the fabulous thing is that if the theory I just told you about ? the one that explains the weakness of gravity ? is correct, we will see experimental evidence within the next five years. These tests that high-energy experimenters will perform are critical to confirming (or ruling out) our ideas.

The evidence will take the form of Kaluza-Klein particles, which are 1,000 times smaller than the proton and travel in extra dimensions, but would register in experiments as extra-heavy particles in what appears to be a three-spatial-dimensional world.

If warped extra dimensions explain the weakness of gravity, the Large Hadron Collider that will begin operation at CERN in Geneva in two years will have enough energy to make such particles (you need lots of energy to make heavy particles, as we know from Einstein’s most famous equation, E=mc2 ). If experimenters discover them, my belief in extra dimensions will be proved justified.

Those of us who no longer straitjacket ourselves to theories with only three dimensions of space have found amazing consequences of Einstein’s equations that had escaped physicists for years. The range of possibilities for what might lie in the cosmos is remarkable, and we’re still only beginning to understand them all. I’m fairly confident new dimensions are out there and it’s more a question of if and when we’ll find them.Given how much extra dimensions ? or whatever we discover ? will tell us about the fundamental nature of our Universe, do we have any choice but to explore?

(The author is a professor of theoretical physics at Harvard University. Her new book, Warped Passages, has just been released.)

The Daily Telegraph


Posted in Dimension, Physics, Universe | 4 Comments »

Nuclear dating for antics

Posted by iKnowHOW on October 30, 2006

An adjunct programme of the International Atomic Energy Agency fosters the use of nuclear methods to address historic and artistic riddles like verifying the origin and authenticity of art objects. William J. Broad reports

(From top) A Tang dynasty figurine, Statue of Mars of Todi, a Corinthian vase

Eager for precision in a field notorious for ambiguity and frustration, curators at top museums in Europe and the US have long reached for the instruments of nuclear science to hit treasures of art with invisible rays. The resulting clues have helped answer vexing questions of provenance, age and authenticity.

Now such insights are going global. The International Atomic Energy Agency (IAEA), best known for fighting the spread of nuclear arms, is working hard to foster such methods in the developing world. This is to make scientists in places like Peru, Ghana and Kazakhstan act as better custodians of their cultural heritage.

Scientific papers and abstracts describe how research projects had used nuclear methods to address historic and artistic riddles. For instance, Chinese scientists had fired the subatomic particles known as neutrons at ancient pottery from the Tang dynasty, which ruled China from AD 618 to 906. The analysis is helping them uncover the art works’ origins in regional workshops.

In an interview, Feng Songlin, a scientist at the Institute of High Energy Physics in Beijing, said he found the agency’s programme “very helpful for Chinese archaeology research and for me”. He said it had helped him ascertain the best analytical methods, prepare samples and learn how to interpret the findings.

Mexican scientists have also applied such methods to colonial-era pottery. Pieces once thought to have been imported from Spain turned out to have been made locally.

The methods used, some of the most fundamental in nuclear science, include neutron activation analysis, proton-induced X-ray emission, accelerator mass spectrometry and X-ray fluorescence spectrometry. The advances are striking because the world of art often finds itself hard pressed to achieve basic goals like verifying the origins of pieces. The standard historical approach of comparing style and iconography, even when coupled with painstaking detective work in archives and distant collections, has often proved inconclusive or at times even deceptive.

The atomic methods, some applied to artistic analysis for the first time in the 1970s and 80s, have revolutionised the field of art history. For instance, the Metropolitan Museum of Art in New York gained a wealth of insights into the provenance of old sculptures in its collection, including some sculptured heads separated from torsos during the French Revolution. The trouble arose when radicals, mistaking statues of religious figures for royalty, developed a taste for decapitation.

The museum’s detective work began at a nuclear reactor, where operators would bombard detached bits of the artwork with speeding neutrons. The resulting showers of gamma rays revealed the presence of trace elements in distinct patterns.

These identifying signatures let museum curators make matches with similarly revealed signatures of European churches, quarries and carvings. For instance, they recently found that one of the sculptured heads in a current exhibition came from a quarry that supplied statuary to either Notre Dame or another 13th century Parisian church.

The Louvre in Paris has a very long accelerator in its basement that fires subatomic particles at artwork to discover compositional clues. Maria Filomena Guerra, a specialist there in ancient gold artefacts, travelled to Vienna last month to help the IAEA with its outreach programme.

The agency is now fostering the development of such techniques in Hungary and other countries. In Budapest, scientists are using a cousin of the neutron technique to study Stone Age pottery, including a graceful bowl from a cave in the Bukk mountains. The method is known as prompt gamma activation analysis.

The Hungarian scientists are using the gamma method to compare pottery from eight sites with a variety of clay samples in hope of establishing where the pots arose. The trace elements so far identified include vanadium, neodymium, samarium and gadolinium. The scientists plan to expand the number of investigated sites and soils to produce a comprehensive portrait of artistic evolution in Stone Age Hungary.

Dr Matthias Rossbach of IAEA said he had recently administered a kind of proficiency test to the programme’s members. They were sent bits of powdered Chinese porcelain for analysis, and the results were compared with the agency’s findings. “It was,” he said, “like a teacher grading a report. The objective was to help them improve their method.”

At a display, the scientists set up an instrument, a portable X-ray fluorescence spectrometre, a device little bigger than a golf bag. When in operation, its beam of X-rays stimulates material under observation to glow at various wavelengths, allowing the identification of constituent elements.

The method is cheaper, easier and faster than the neutron technique, though slightly less precise. The scientists said the agency had developed the portable device for use in art museums, and they demonstrated how it worked by training it on a piece of painted canvas.

To the naked eye of an observer, admittedly no art expert, the paint looked dull and drab, almost too plain for words. But the X-rays revealed a kaleidoscope of pigment elements, rendered on the computer monitor as a series of wiggly lines. The scientists identified the peaks as sulphur, calcium, titanium, iron and zinc. Such chemical signatures, they said, could help confirm whether the pigment and painting were actually made at an advertised date, because paint formulas often changed over the decades.

Dr Rossbach said the programme excited him because in the process of teaching he discovered so much about global art as well as its diverse ranks of scientific custodians.

“I’ve learned about pottery in China and icons in Poland,” he said. “I know the techniques they’re using and can discuss whether they’re doing it right. So that, I think, is a very good exchange.”

Posted in Physics | 8 Comments »