WHAT does a biblical saying about a camel passing through the eye of a needle have to do with quantum uncertainty? Quite a lot, it turns out, since a mathematical concept called the 鈥渟ymplectic camel鈥� promises to explain quantum uncertainty in simple classical terms.
According to Heisenberg, it is impossible to measure both the momentum and position of a quantum particle accurately because those properties are interlinked. Measuring one therefore makes the other more uncertain. That鈥檚 because individual particles are considered parts of a probability 鈥渨ave鈥�, in which many possible combinations of position and momentum exist simultaneously. But at the University of Vienna in Austria thinks that the inability to pin a particle down is due to something called symplectic geometry, not quantum weirdness.
De Gosson realised that a theorem in symplectic geometry had parallels with the uncertainty principle. The concept is known as the symplectic camel after the biblical suggestion that it is easier for a camel to pass through the eye of a needle than for a rich man to get into heaven.
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De Gosson imagined that a ball represents a cloud of possible positions for a quantum particle. He found that such a ball cannot be squeezed down to the size of one particle to fit through a hole in a plane, because its geometry resists this in some way. The inability to squeeze the ball is analogous to singling out one particle and measuring its position and momentum exactly. De Gosson reckons this geometrical resistance creates the uncertainty in measurement, not quantum fuzziness ().
That is encouraging for those who hope to recast quantum mechanics in a more deterministic way. 鈥淭he point that there is, in effect, a 鈥榗lassical uncertainty principle鈥�, is extremely intriguing,鈥� says Michael Hall of the Australian National University in Canberra, who has also worked on the uncertainty principle.
鈥淭he point that there is, in effect, a 鈥榗lassical uncertainty principle鈥�, is extremely intriguing鈥�
However, it could be tricky to reproduce all the predictions of quantum mechanics using symplectic geometry, cautions Roderich Tumulka, who works on the foundations of quantum theory at Rutgers University in New Jersey.
A key problem is whether an analogy like de Gosson鈥檚 represents a deep connection, or is simply a coincidence. , a philosopher of physics at the University of Pittsburgh in Pennsylvania, points out that de Gosson鈥檚 analogy fails to share one aspect of uncertainty with that of quantum mechanics. The uncertainty in position and momentum of a quantum particle is always greater than an amount represented by Planck鈥檚 constant, a fundamental quantity in the quantum world. In de Gosson鈥檚 derivation, the constant鈥檚 value is unknown. 鈥淭he characteristic quantity of quantum theory has to be put in by hand,鈥� says Norton.
