Can An Electron Be In Two Places At The Same Time?

A hundred years ago, we took the first steps in recognising, at thelevel of elementary physical events, the dual character of nature thathad been postulated in natural philosophy. Albert Einstein was thefirst who saw Max Planck’s quantum hypothesis leading to this dualcharacter. Einstein suggested the photon have an electromagnetic wavecharacter, although photons had previously been considered asparticles. That was the quintessence of his work on the photoelectriceffect. Later in 1926, it was deBroglie that recognised that all thebuilding blocks of nature known to us as particles - electrons,protons, etc. - behave like waves under certain conditions.

In its totality, therefore, nature is dual. None of its componentscan only be considered as a particle or as a wave. To understand thisfact, Niels Bohr introduced in 1923 the Complementarity Principle:simply put, every component in nature has a particle, as well as awavelike character, and it depends only on the observer which characterhe sees at any given time. In other words, the experiment determineswhich characteristic one is measuring - particle or wave.

Hiswhole life long, Einstein suspected that natural characteristicsactually depend on the observer. He believed that there must be areality independent of the observer. Indeed, quantum physics has simplycome to accept as a given over the years that there does not seem to bean independent reality. Physics has ceased questioning this, becauseexperiments have confirmed it repeatedly and with a growing accuracy.

Thebest example is Young’s double-slit experiment. Coherent light ispassed through a barrier with two slits. On an observation screenbehind it, there is a pattern made of light and dark stripes. Theexperiment can be carried out not only with light, but also particles -for example, electrons. If single electrons are sent, one after theother, through the open Young double slit, then a stripe-shapedinterference pattern appears on the photo plate behind it. The patterncontains no information about the route that the electron took. But ifone of the two slits is closed, an image appears of the other open slitfrom which one can directly read the path of the electron. What thisexperiment does not produce, however, is a stripe pattern and situationreport. For that, a molecular double slit experiment is required thatis based not upon position-momentum uncertainty, but on reflectivesymmetry.

The double-slit was voted the most beautiful experimentof all time in a 2002 poll by Physics World, published by England’sInstitute of Physics. Although each electron seems to go alone throughone of the two slits, at the end a wavelike interference pattern iscreated, as if the electron split while it went through the slit, butthen was subsequently re-unified. But if one of the slits is closed, oran observer sees which slit the electron went through, then it behaveslike a perfectly normal particle. That particle is only at one positionat one time, but not at the same time. So, depending on how theexperiment is carried out, the electron is either at position A,position B, or at both at the same time.

But Bohr’sComplementarity Principle, which explains this ambiguity, requires thatone can only observe one of the two electron manifestations at anygiven time - either as a wave or a particle, but not bothsimultaneously. This remains a certainty in every experiment, despiteall the ambiguity in quantum physics. Either a system is in a state of"both/and" like a wave, or "either/or" like a particle, relating to itslocalisation. This is, in principle, a consequence of Heisenberg’suncertainty principle, which says that given a complementary pair ofmeasurements - for example, position and momentum - only one can bedetermined exactly at the same time. Information about the othermeasurement is lost, proportionally.

Recently there has been aset of experiments suggesting that these various manifestations ofmaterial can be "carried over into" each other - in other words, theycan switch from one form to the other and, under certain conditions,back again. This set of experiments is called quantum markers andquantum erasers. Researchers have shown in the last few years that foratoms and photons - and now, electrons - "both/and" and "either/or"exist side-by-side. In other words, there is a grey zone ofcomplementarity. There are therefore experimentally demonstrableconditions in which the material appears to be both a wave and aparticle.

These situations can be described with a dualityrelation. It can be seen as an extended Complementarity Principle forquantum physics; it can also be labelled a co-existence principle. Itsays that manifestations of material which would normally be mutuallyexclusive - e.g., local and not local, coherent and not coherent - areindeed measurable and make themselves evident, in a particular"transition area". One can speak of partial localisation and partialcoherence, or partial visibility and partial differentiability. Theseare measurements that are connected to each other via the dualityrelation.

In this transition area the Complementarity Principle,and the complementary dualism of nature, can be extended to be aco-existence principle, a parallel dualism. Nature has thus anambivalent character previously unassumed. Atomic interferometryprovides us with examples of this ambivalence. It was first found in1997 in atoms, which are made from an assembly of particles.

In arecent issue of Nature Max Planck researchers in Berlin, together withresearchers from the California Institute of Technology in Pasadena,California, report about a molecular double-slit experiment withelectrons - not assemblies of particles, like atoms. Molecules withidentical, and thus reflectively symmetrical, atoms, behave like amicroscopically small double-slit built by nature. Nitrogen is one suchmolecule. In it, each electron - also the highly localised innerelectrons - stays simultaneously in both atoms. If we ionise such amolecule with a weak x-ray, we end up with a coherent - that is,wavelike - strongly coupled electron emission from both atomic sides.This is just like a double slit experiment with single electrons.

Forthe first time, the researchers were able to show the coherentcharacter of electron emissions from such a molecule, in this analogueto the double slit experiment. They used a weak x-ray to destabilisethe innermost, and thus most strongly localised, electrons of nitrogenfrom the molecule, and then followed their movement in the molecularframe of reference using ion coincidence measurements. In addition, theresearchers succeeded in proving something long doubted: that adisruption of the reflective symmetry of this molecule leads to apartial loss of coherence through the introduction of two differentheavy isotopes, in this case N¹⁴ and N¹⁵. Theelectrons begin to localise partially on one of the two, nowdistinguishable, atoms. This is equivalent to partially marking one ofthe two slits in Young’s double slit experiment. This is partial "whichway" information, because the marking gives information about whichpath the electron took.

The experiments were carried out bymembers of the working group "atomic physics" of the FHI at thesynchrotron radiation laboratories BESSY in Berlin and HASYLAB at DESYin Hamburg. The measurements took place using a multi-detector arrayfor combined electron and ion proof behind what are called undulatorbeam pipes, which deliver weak x-rays with a high intensity andspectral resolution.

Support for the working group of fourscientists and three doctoral students came from the Max Planck Societyand also largely from the Federal Ministry of Education and Research,under the programme furthering research in specially chosen topics inthe fundamental principles of the natural sciences.

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Original work:

DanielRolles, Markus Braune, Slobodan Cvejanović, Oliver Ge ner, RainerHentges, Sanja Korica, Burkhard Langer, Toralf Lischke, Georg Prümper,Axel Reinköster, Jens Viefhaus, Björn Zimmermann, Vincent McKoy and UweBecker
Isotope-induced partial localization of core electrons in the homonuclear molecule N2
Nature 437, 711-715, September 29, 2005