The answer isn't so clear, simply because the wave takes up a finite amount of space and may overlap with other waves in such a way that separating out which wave is which is too hard; also, different parts of the wave may be moving at different rates. Therefore, the position and momentum are best described by an average and a spread of values around that average, which carries the name uncertainty — not in the sense of doubt but in the sense of indeterminacy.
There is an inherent limit to our ability to describe these physical quantities, with no need for soul-searching on the part of scientists. The Heisenberg uncertainty principle tells us what the minimum uncertainty for quantum waves must be: the smaller the uncertainty in position, the larger the uncertainty in momentum — and vice versa. Returning to the double-slit experiment, the wavelength the size of the wave, in other words depends on momentum, so the entire interference pattern is in effect a measurement of momentum.
However, that means determination of which slit the photon passed through — which is a measurement of position — has an increased uncertainty. Although the graininess of the interference pattern indicates where an individual photon lands, determining what path it took to get to that spot is not generally possible. Enter the experiment by Kocsis et al. The Heisenberg uncertainty principle still stands, in other words, and is an essential part of this experiment whatever some headlines may say.
The difficulty of this measurement should not be overstated! After all, quantum mechanics has been around for nearly years and based on the controversies surrounding the Copenhagen interpretation, had it been easy, surely someone would have attempted it by now. The experiment involves producing individual photons from a quantum dot and measuring their momentum indirectly through the polarization of each photon.
Because polarization is correlated with momentum, but not exactly the same quantity, measurement of one doesn't strongly affect the other, preserving the state of the system fairly well. The final position of the photon is measured using a charge-coupled device CCD , similar to what you find in ordinary digital cameras or telescope imaging devices. By repeating the experiment for a large number of individual photons and moving the apparatus to measure polarization at various points along the trajectories, the researchers were able to reconstruct the paths not of the individual photons but of the complete ensemble of all photons — yet due to the statistical nature of quantum mechanics, information about the individual photons within the system can still be inferred.
One possible interpretation of the experiment is in line with the pilot wave model, formulated by Louis de Broglie with later additions by David Bohm. In this view, the wave function describes a statistical distribution that says what physical properties the point-like particle is likely to have — while the particles themselves may follow precise trajectories, even if those are very difficult to track. This certainly is consistent with what we see in detectors, although one might ask whether the pilot waves themselves can ever be directly observed — and if they can't, whether they can be said to be "real".
Obviously a detailed discussion of that idea is too much for one post, so I won't try. However, if the complete trajectory of a photon can be observed in some way and its interference pattern still exists, it indicates that indeed a view of quantum physics consistent with a realists' perspective is possible the kicking of rocks being completely optional.
Has the Copenhagen interpretation fallen? Has the pilot wave interpretation been vindicated? The cautious scientific answer must be "not yet".
After all, there is nothing in this experiment that isn't completely compatible with the mathematical predictions of quantum mechanics, so any valid interpretation — including the Copenhagen interpretation — will describe its results. However, measurements such as this make it harder to say smugly that photons don't follow any particular trajectory and that it's unreasonable to expect them to.
I for one look forward to more experiments along these lines.
Acknowledgments: Thanks to Arthur Kosowsky and Nuria Royo for resources and comments on earlier drafts of this post. About the author: Matthew Francis is visiting professor of physics at Randolph-Macon College, freelance science writer, and seeker of weirdness throughout the cosmos.
The views expressed are those of the author and are not necessarily those of Scientific American. The views expressed are those of the author s and are not necessarily those of Scientific American. About the author: Matthew Francis is a theoretical physicist meaning he theoretically does physics , freelance science writer, and seeker of weirdness throughout the cosmos. You have free article s left.
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