2 Slots Experiment

Posted on4/5/2022by admin

Mutagen: Hit 'C' key to open character screen. Click on 'Training', look at the tiny circle top right of the top 2 talents. Right click on talent, select your mutagen and then apply. Same applies to 'Swordsmanship' talents, although it'll be quite awhile until you reach the end of the tree where the mutagen slots appear.

Quantum mechanics is one of the most successful theories in all of science; at the same time, it's one of the most challenging to comprehend and one about which a great deal of nonsense has been written. However, a paper from Science, titled 'Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer', holds out hope that we might be able to get closer to understanding how nature works on the smallest scales. The authors – Sacha Kocsis, Boris Braverman, Sylvain Ravets, Martin J. Stevens, Richard P. Mirin, L. Krister Shalm, and Aephraim M. Steinberg – have measured both the trajectory and the interference pattern from photons, a difficult feat to say the least, and one with interesting implications. (Scientific American also has a brief article on this experiment, republished from Nature.)

Left: Schematic of a generic double-slit experiment, showing how the interference pattern is generated. image by Matthew Francis. Right: Simulated double-slit interference pattern, showing the 'graininess' due to individual photons striking the detection screen. Image by Matthew Francis.

It's easy to overstate how complicated quantum mechanics is: after all, it's one of the most successful theories in the history of science, something that wouldn't be possible without some level of comprehension. In many ways, though, the most difficult experiment to understand is one of the simplest: the so-called 'double-slit' experiment, in which the experimenter shines a light on a barrier with two narrow openings in it, and study the interference pattern it produces on a screen.

The experiment of dealing the first two cards to the first player has as its sample space a set of ordered pairs, namely all the 2-size arrangements of cards from the 52 (or 104). In a game with one player, the event the player is dealt a card of 10 points as the first dealt card is represented by the set of cards 10♠, 10♣, 10♥, 10♦, J.
The double-slit experiment seems simple enough: Cut two slits in a sheet of metal and send light through them, first as a constant wave, then in individual particles. What happens, though, is anything but simple.

Light famously has two natures: it is wave-like, interfering in the same way that water ripples cross each other; it is also particle-like, carrying its energy in discrete bundles known as photons. If the experiment is sufficiently sensitive, the interference pattern appears grainy, where an individual photon appears on the screen, as you can see in the simulated projection pattern shown. In other words, single photons travel as though they are interfering with other photons, but is itself indivisible. Matter also has this dual character; interference of electrons and atoms has been observed experimentally. All of this is backed up by years of work.

The major difficulty with quantum mechanics is its interpretation. The standard Copenhagen interpretation (named in honor of the home city of Niels Bohr, who first formulated it) takes a simple stance: the reason why photons sometimes seem like particles and sometimes like waves is that our experiments dictate what we see. In this view, photons are products of our experiments without independent reality, so if we're bothered by seemingly contradictory notions of wave and particle properties, it's because we're expecting something unreasonable of the universe.

The Copenhagen interpretation was extremely unsatisfying to several prominent physicists of the day (Einstein was the most famous dissenter, of course), and indeed to many working in the field now. Over the years, other scientists have proposed many alternative interpretations, some of which are more viable than others; many fail the Occam's razor test by providing no empirical difference from the Copenhagen interpretation, yet are harder to work with.

Quantum Mechanics Without the Bohr(ing) Stuff

Left: Physicist Erwin Schrödinger in 1933, exhibiting the fashion taste scientists could get away with even then.

Quantum mechanics is notorious for tangling people's minds up. Part of the problem lies in the complicated mathematical formulation: in a typical American physics curriculum, a serious study of quantum mechanics shows up in the third or fourth year and has a large number of prerequisites in both the physics and math departments. Famous physicists such as Richard Feynman have gone so far as to say that nobody actually understands quantum mechanics, and a lot of professors when they teach the subject will reassure their students that it works, even if the interpretation eludes them.

Many (perhaps even most) physicists treat the whole theory as a black box, something that provides very good predictions, but that will lead to madness if you try to figure out why it works the way it does. However, it's worth our while to go over the structure of quantum mechanics to see why the latest experiment is potentially very important.

The central equation of quantum mechanics is a wave equation, known as the Schrödinger equation (named for its discoverer, Erwin Schrödinger, known for the infamous cat). As with any other mathematical equation relating to physics, you put in different parameters to characterize a particular physical situation and solve it; in this case solutions are known as wave functions. A given wave function represents the state of a system, which may be one or more photons, electrons, atoms, or any number of other entities. The state itself describes the probability that a system has a particular position, momentum, spin, etc.

Outside of quantum mechanics, statistics and probabilities are usually most useful when describing large numbers of things: what is the likelihood that a particular hand in poker turns up, or how many people will vote for a candidate for president based on demographic information. A single person votes in a given way with no uncertainty (the year 2000 presidential election aside), so the statistics you see in poll data are based on a large population. The wave function assigns statistical information to a individual system: what the possible outcomes of a measurement will be, even if the experiment is performed on a single photon.

One aspect is uncertainty. All experiments have uncertainty attached to them, simply because no equipment is perfect. Where quantum mechanics differs is by saying that even with perfect equipment, there will be a fundamental limit to how well a measurement can be performed. That uncertainty is directly connected to the wave-like character of matter and light: if you have a water wave traveling across the ocean, what is the precise position of the wave? How fast is it moving?

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.

So What Does It All Mean, Anyway?

Enter the experiment by Kocsis et al.: by reducing the resolution of the measurements, the experimenters increased the uncertainty in the momentum, allowing a better chance at determining the trajectories of an ensemble of photons. 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 100 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. He blogs at Galileo's Pendulum and tweets at @DrMRFrancis; his opinions are his own.

The views expressed are those of the author and are not necessarily those of Scientific American.