**A FAREWELL TO COPENHAGEN?**

This column is about experimental tests of the various interpretations of quantum mechanics. The question at issue is whether we can perform experiments that can show whether there is an "observer-created reality" as suggested by the Copenhagen Interpretation, or a peacock’s tail of rapidly branching alternate universes, as suggested by the Many-Worlds Interpretation, or forward-backward in time handshakes, as suggested by the Transactional Interpretation? Until recently, I would have said that this was an impossible task, but a new experiment has changed my view, and I now believe that the Copenhagen and Many-Worlds Interpretations (at least as they are usually presented) have been falsified by experiment.

The physical theory of quantum mechanics describes the behavior of matter and energy at the smallest distances. It has been verified by more than 70 years of experiments, and it is trusted by working physicists and regularly used in the fields of atomic, nuclear, and particle physics. However, quantum mechanics is burdened by a dismaying array of alternative and mutually contradictory ways of interpreting its mathematical formalism. These include the orthodox Copenhagen Interpretation, the currently fashionable Many Worlds Interpretation, my own Transactional Interpretation, and a number of others.

Many (including me) have declared, with almost the certainty of a mathematical theorem, that it is impossible to distinguish between quantum interpretations with experimental tests. Reason: all interpretations describe the same mathematical formalism, and it is the formalism that makes the experimentally testable predictions. As it turns out, while this "theorem" is not wrong, it does contain a significant loophole. If an interpretation is *not completely consistent* with the mathematical formalism, it *can* be tested and indeed falsified. As we will see, that appears to be the situation with the Copenhagen and Many-Worlds Interpretations, among many others, while my own Transactional Interpretation easily survives the experimental test.

The experiment that appears to falsify these venerable and widely trusted interpretations of quantum mechanics is the Afshar Experiment. It is a new quantum test, just performed last year, which demonstrates the presence of complete interference in an unambiguous "which-way" measurement of the passage of light photons through a pair of pinholes. But before describing the Afshar Experiment, let us take a backward look at the Copenhagen Interpretation and Neils Bohr’s famous Principle of Complementarity.

Quantum mechanics was first formulated independently by Erwin Schrödinger and Werner Heisenberg in the mid-1920s. Physicists usually have a mental picture of the underlying mechanisms within theory they are formulating, but Heisenberg had no such picture of behavior at the atomic level. With amazing intuition and remarkable good luck, he managed to invent a matrix-based mathematical structure that agreed with and predicted the data from most atomic physics measurements. On the other hand, Schrödinger did start from a definite picture in constructing his quantum wave mechanics. Making an analogy with massless electromagnetic waves, he constructed a similar wave equation describing particles (e.g., electrons) with a rest mass. However, it soon was demonstrated by Bohr and Heisenberg that while Schrödinger’s mathematics was valid, his underlying mass-wave picture was unworkable, and he was forced to abandon it. The net result was that the new quantum mechanics was left as a theory with no underlying picture or mechanism. Moreover, its mathematics was saying some quite bizarre things about how matter and energy behaved at the atomic level, and there seemed no way of explaining this behavior.

In the Autumn of 1926, while Heisenberg was a lecturer at Bohr’s Institute in Copenhagen, the two men walked the streets of the ancient city almost every day, arguing, gesturing, and sketching pictures and equations on random scraps of paper, as they struggled to come to grips with the puzzles and paradoxes that the quantum formalism presented. How could an object behave as both a particle and a wave? How could its wave description spread out in all directions, then "collapse" to a location where it was detected like a bubble that had been pricked. Did an electron smoothly make the transition from one atomic orbit to another or did it undergo a "quantum jump", abruptly disappearing from one orbit and appearing in the other? How could the occurrence of seemingly random quantum events be predicted?

The Copenhagen autumn phased into winter, and no solution was found. In February of 1927, Bohr went away on a skiing vacation, and while he was gone, Heisenberg discovered a key piece to the puzzle concealed in the mathematics of Schrödinger’s wave mechanics. When one tried to "localize" the position of an electron by specifying its location more and more precisely, the mathematics required that the momentum (mass times velocity) of the electron must become less localized and more uncertain. One had to add more and more wave components with different momentum values to make the position peak sharper. Knowledge of position and momentum were like the two ends of a seesaw: lowering one raised the other. The product of the uncertainties in position and momentum could not be reduced below a lower limit, which was Planck’s constant. The mathematics required that any attempt to do so must fail. This became the essence of the Heisenberg Uncertainty Principle, first published in early 1927.

When Bohr returned to Copenhagen, he was presented with the new idea. At first he was skeptical, because of problems with Heisenberg’s "gamma ray microscope" example used in the paper, but he finally convinced himself that, example or not, the basic idea was correct. The Uncertainty Principle brought Bohr to a new insight into quantum behavior. Position and momentum were "complementary," in the sense that precise knowledge of one excluded knowledge of the other, yet they were jointly essential for a complete description of quantum events. Bohr extended the idea of complementary variables to energy and time and to particle and wave behavior. One must choose either the particle mode, with localized positions, trajectories, and energy quanta, or the wave mode, with spreading wave functions, delocalization and interference. The Uncertainty Principle allowed both descriptions within the same mathematical framework because each excluded the other. Bohr’s Complementarity and Heisenberg’s Uncertainty, along with the statistical interpretation of Schrödinger’s wave functions and the view of the wave function as observer knowledge were all interconnected to form the new Copenhagen Interpretation.

In Bohr’s words: ". . . we are presented with a choice of either tracing the path of the particle, or observing interference effects . . . we have to do with a typical example of how the complementary phenomena appear under mutually exclusive experimental arrangements." In the context of a two-slit *welcher weg* (which-way) experiment, the Principle of Complementarity dictates "the observation of an interference pattern and the acquisition of *which-way* information are mutually exclusive." By 1927 the Copenhagen Interpretation was the big news in physics and the subject of well-attended lectures by Bohr, Born, and Heisenberg. In the next decade, through many more lectures and demonstrations of the effectiveness of the ideas and despite the objections of Albert Einstein, it was canonized as the Standard Interpretation of quantum mechanics, and it has held this somewhat shaky position ever since.

The Afshar experiment was first performed last year by Shariar S. Afshar and repeated while he was a Visiting Scientist at Harvard. In a very subtle way it directly tests the Copenhagen assertion that the observation of an interference pattern and the acquisition of particle path *which-way* information are mutually exclusive. The experiment consists of two pinholes in an opaque sheet illuminated by a laser. The light passing through the pinholes forms an interference pattern, a zebra-stripe set of maxima and zeroes of light intensity that can be recorded by a digital camera. The precise locations of the interference minimum positions, the places where the light intensity goes to zero, are carefully measured and recorded.

Behind the plane where the interference pattern forms, Afshar places a lens that forms an image of each pinhole at a second plane. A light flash observed at image #1 on this plane indicates unambiguously that a photon of light has passed through pinhole #1, and a flash at image #2 similarly indicates that the photon has passed through pinhole #2. Observation of the photon flashes therefore provides particle path *which-way* information, as described by Bohr. According to the Copenhagen Interpretation, in this situation all wave-mode interference effects must be excluded.

However, at this point, Afshar introduces a new element to the experiment. He places one or more wires at the previously measured positions of the interference minima. In one such setup, if the wire plane is uniformly illuminated, the wires absorb about 6% of the light. Then Afshar measures the difference in the light received at the pinhole images with and without the wires in place.

We are led by the Copenhagen Interpretation to expect that the positions of the interference minima should have no particular significance, and that the wires should intercept 6% of the light they do for uniform illumination. Similarly, the usual form of the Many Worlds Interpretation of quantum mechanics leads us to expect 6% interception and no interference, since a photon detected at image #1 is in one universe while the same photon detected at image #2 is in another universe, and since the two "worlds" are distinguished by different physical outcomes, they should not interfere.

However, what Afshar observes is that the amount of light intercepted by the wires is very small, consistent with 0% interception. There are still locations of zero intensity and the wave interference pattern is still present in the *which-way* measurement. Wires which are placed at the zero-intensity locations of the interference minima intercept no light. Thus, it appears that both the Copenhagen Interpretation and the Many-Worlds Interpretation have been falsified by experiment.

Does this mean that the theory of quantum mechanics has also been falsified? No indeed! The quantum formalism has no problem in predicting the Afshar result. A simple quantum mechanical calculation using the standard formalism shows that the wires should intercept only a very small fraction of the light. The problem encountered by the Copenhagen and Many-Worlds Interpretations is that the Afshar Experiment has identified a situation in which these popular interpretations of quantum mechanics are inconsistent with the quantum formalism itself.

What about the Transactional Interpretation, which describes each quantum process as a handshake between a normal "offer" wave (y) and a back-in-time advanced "confirmation" wave (y*)? The offer waves from the laser pass through both pinholes and cancel at the positions of the zeroes in the interference pattern. Therefore, no transactions can form at these locations, and the wires can intercept only a very small amount of light. Thus, the Transactional interpretation is completely consistent with the results of the Afshar Experiment and with the quantum formalism.

Does this mean that the Copenhagen and Many Worlds Interpretations, having been falsified by experiment, must be abandoned? Does it mean that the physics community must turn to an interpretation like the Transactional Interpretation that is consistent with the Afshar results? Perhaps. I predict that a new generation of "Quantum Lawyers" will begin to populate the physics literature with arguments challenging what "is" is and claming that the wounded interpretations never said that interference should be completely absent in a quantum *which-way* measurement. And most practicing physicists who learned the Copenhagen Interpretation at the knee of an old and beloved professor will not abandon that mode of thinking, even if it is found to be inconsistent with the formalism and with experiment.

But nevertheless, the rules of the game have changed. There *is* a way of distinguishing between interpretations of quantum mechanics. It will take some time for the dust to settle, but I am confident that when it does we will have interpretations of quantum mechanics that are on a sounder footing than the ones presently embraced by most of the physics community.

**AV Columns On-line**: Electronic reprints of over 120 "The Alternate View" columns by John G. Cramer, previously published in *Analog*, are available on-line at: http://www.npl.washington.edu/av. Electronic preprints of papers listed below are available at: http://arxiv.org.

**Reference:**

*The Copenhagen Interpretation:*

Neils Bohr, Nature *121*, 580 (1928).

Neils Bohr, in: *Albert Einstein: Philosopher-Scientist*, P. A. Schlipp, Ed. (Library of Living Philosophers, Evanston, Illinois, 1949).

*The Transactional Interpretation:*

John G. Cramer, Reviews of Modern Physics 58, 647 (1986); http://www.npl. washington.edu/TI

*The Afshar Experiment*

Shariar S. Afshar, (submitted to Physical Review Letters, July, 2004); See also http://users.rowan.edu/~afshar