Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [99]
In his quest for a new mechanics for the quantised world of the atom, Heisenberg concentrated on the frequencies and relative intensities of the spectral lines produced when an electron instantaneously jumped from one energy level to another. He had no other choice; it was the only available data about what was happening inside an atom. Despite the imagery conjured up by all the talk of quantum jumps and leaps, an electron did not 'jump' through space as it moved between energy levels like a boy jumping off a wall onto the pavement below. It was simply in one place and an instant later it popped up in another without being anywhere in between. Heisenberg accepted that all observables, or anything connected with them, were associated with the mystery and magic of the quantum jump of an electron between two energy levels. Lost forever was the picturesque miniature solar system in which each electron orbited a nuclear sun.
On the pollen-free haven of Helgoland, Heisenberg devised a method of book-keeping to track all possible electron jumps, or transitions, that could occur between the different energy levels of hydrogen. The only way he could think of recording each observable quantity, associated with a unique pair of energy levels, was to use an array:
This was the array for the entire set of possible frequencies of the spectral lines that could theoretically be emitted by an electron when it jumps between two different energy levels. If an electron quantum jumps from the energy level E2 to the lower energy level E1, a spectral line is emitted with a frequency designated by v21 in the array. The spectral line of frequency v12 would only be found in the absorption spectrum, since it is associated with an electron in energy level E1 absorbing a quantum of energy sufficient to jump to energy level E2. A spectral line of frequency vmn would be emitted when an electron jumps between any two levels whose energies are Em and En, where m is greater than n. Not all the frequencies vmn are exactly observed. For example, measurement of v11 is impossible, since it would be the frequency of the spectral line emitted in a 'transition' from energy level E1 to energy level E1 – a physical impossibility. Hence v11 is zero, as are all potential frequencies when m=n. The collection of all non-zero frequencies, vmn, would be the lines actually present in the emission spectrum of a particular element.
Another array could be formed from the calculation of transition rates between the various energy levels. If the probability for a particular transition, amn, from energy level Em to En, is high, then the transition is more likely than one with a lower probability. The resulting spectral line with frequency vmn would be more intense than for the less probable transition. Heisenberg realised that the transition probabilities amn and the frequencies vmn could, after some deft theoretical manipulation, lead to a quantum counterpart for each observable quantity known in Newtonian mechanics such as position and momentum.
Of all things, Heisenberg began by thinking about electrons' orbits. He imagined an atom in which an electron was orbiting the nucleus at a great distance – more like Pluto orbiting the sun rather than Mercury. It was to prevent an electron spiralling into the nucleus at it radiated away energy that Bohr had introduced the concept of stationary orbits. However, in accordance with classical physics, the orbital frequency of an electron in such an exaggerated orbit, the number of complete orbits it makes per second, is equal to the frequency of the radiation it emits.
This was no flight of fancy, but a skilful use of the correspondence principle – Bohr's conceptual bridge between the quantum and classical realms. Heisenberg's hypothetical electron orbit was so large that it was on the border that divided the kingdoms of the quantum and the classical. Here in this borderland, the electron's orbital frequency was equal to the frequency of the radiation it emitted. Heisenberg knew that such an electron in