It's a Ball. No, It's a Pretzel. Must Be a Proton.

Ask four physicists a seemingly simple question — Is a proton round? — and these might be their responses:

Yes.

No.

The first two answers are both correct.

What do you mean by "round"?

"It's not a well-defined question," said Dr. Robert L. Jaffe, a physics professor at the Massachusetts Institute of Technology.

In the realm of the subatomic, shape is not a straightforward concept. At the very least, a new theory suggests, a proton, a basic constituent of atoms, may not be as simply round as physicists once thought and as drawn in textbooks.

"I'm going to tell them it's round," said Dr. Xiangdong Ji, a professor of physics at the University of Maryland. "That's the answer that's still correct. Unless I can then teach someone a lesson in quantum mechanics. Actually, in quantum mechanics, measurement is not a simple thing."

Add the fuzziness of quantum mechanics — the notion that an object does not exist in a definite place and time but is instead spread out as a mist of probabilities and possibilities — and the question becomes a variant of a philosophical conundrum: if a proton is not round, but no one can see that it's not round, is it still not round?

Years ago, proton-proton collisions yielded some evidence of a nonspherical shape.

"They came out spinning when they weren't supposed to be spinning," said Dr. John P. Ralston, a physics professor at the University of Kansas. "It's as if they flatten out like water balloons. It's the only known way to explain the data."

Experiments at the Thomas Jefferson National Accelerator Facility in Newport News, Va., a couple of years ago spurred a new round of debate.

There, scientists slammed electrons into protons and recorded the motion of the recoiling protons and deflected electrons. The particles were deflected not just by electric forces — protons are positively charged, electrons are negatively charged — but also by magnetic forces. Electrons and protons both exude magnetic fields, acting like tiny bar magnets.

The experiments showed that when electrons were shot at higher energies, penetrating deeper into the protons, the electric interactions dropped off more quickly than the magnetic ones, contrary to many physicists' expectations that the electric-to-magnetic ratio should remain constant.

"All textbooks show pictures and formulas," said Dr. Gerald A. Miller, who is a professor of physics at the University of Washington. "I have four or five of them on my shelf." He said his first reaction to the Jefferson data was that the data were wrong. "My second reaction was this looked like something else I thought was wrong."

Dr. Miller and two colleagues published a paper in 1996 that predicted a falloff in the electric-to-magnetic ratio. Dr. Miller thought they had somehow made a mistake in their calculations then.

A byproduct of Dr. Miller's theory is that a proton is not always round — or rather, it is not just round. The proton instead exists as a mixture of many shapes. Some look like doughnuts. Others resemble peanuts or odd-looking pretzels.

"It's all these shapes at the same time," said Dr. Miller, who presented his latest ideas at a meeting of the American Physical Society last month in Philadelphia.

While Dr. Miller can easily produce pictures of these shapes on his computer, they are not tangible attributes. And, on average, the shapes still smudge into a round sphere, he said.

Dr. Ji of Maryland said any directly measurable property, like the density of electric charge, would appear spherical. Thus, the proton can be thought of as both round and not round.

The pictures also depend on assumptions of what is inside a proton.

In the late 1960's, particle experiments knocking electrons into the protons indicated that protons had a definite size — about a millionth of a billionth of a meter wide — and that the electrons were bouncing off hard, pointlike objects within the proton.

Earlier, physicists had worked out a mathematical construct for organizing a glut of particles they saw in experiments, describing them as made of still smaller particles known as quarks. In the quark model, a proton consists of two "up" quarks and one "down" quark.

The tiny objects detected within the proton turned out to be quarks. However, a proton is not made of just two up quarks and one down quark; the total mass of those three quarks is far less than that of the full proton. Part of the mass gain comes courtesy of special relativity; the quarks swirl at nearly the speed of light.

But the proton also contains a roiling sea of "virtual particles" — pairs of quarks and their corresponding mirror twins, or anti-quarks, that continually wink in and out of existence — and gluons, particles that bind the quarks together.

"It's like looking inside a black hole," Dr. Ralston said. "Everything must be roaring at superhigh energies."

Most physicists believe they now have a fundamental theory known as quantum chromodynamics that fully describes the behavior of particles within that roiling sea within the proton. But the equations are too complex to solve exactly.

So physicists simplify. Instead of trying to track every virtual particle and gluon in the calculations, one approach is to clump each of the three bare quarks with a surrounding cloud of virtual particles and then regard each clump as a single object.

In the simplest formulation, the three larger, heavier objects, called constituent quarks, move at slow speeds, and calculations indicated that the shape of the proton had to be round. That led to the expectations of the constant electric-to-magnetic ratio.

"Only naïve people thought it would be constant," Dr. Jaffe said.

Dr. Miller's work is a not-so-simple version of the constituent quark model. By adding additional interactions, Dr. Miller showed that the motion of the constituent quarks could contribute angular momentum to the proton — like the moon orbiting the earth — and that generates a multitude of possible shapes.

Others are skeptical because Dr. Miller's model is not derived from fundamental equations of physics. "Some people joke there are more models than there are theorists," Dr. Ji said.

An experiment that scientists hope to conduct at Jefferson in a few years may flesh out the sketch of the proton. By hitting protons with yet higher-energy electrons, the collisions will emit photons that can be assembled into a sort of photograph.

Dr. Ralston says the photograph will provide pictorial proof that protons are not round.

Dr. Ji agrees that the images may not be round, but that does not prove the protons aren't. The images, he said, will pick out only certain quarks, like a photograph taken through color filters. The blue regions of the earth, for example, certainly do not look round.

Physicists still have much to learn about a proton, round or not.