Quantum Theory
Quantum Astronomy: Knowability and Unknowability in the Universe
By Laurance R. Doyle, SETI Institute. December 16, 04
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This is the third article in a series of four articles, each with a separate explanation of different quantum phenomena. Each article is a piece of a mosaic, so every one is needed to understand the final explanation of the quantum astronomy experiment we propose, possibly using the Allen Telescope Array and the narrow-band radio-wave detectors being build by the SETI Institute and the University of California, Berkeley.
. . In the previous two articles, we discussed the basic double-slit experiment that demonstrates the dual nature of light --wave and particle-- and then the Heisenberg Uncertainty Principle which demonstrates the complimentary (mutual exclusion) of what one can measure at the same time. In this article, we shall discuss the more basic interpretation of quantum physics in terms of what one can even know or not know, and how this affects the results one is trying to measure.
John Bell formulated the uncertainty principle in terms of what one could know or not know in an experiment. Several Bell-type experiments have successfully shown that this would seem to be the simplest interpretation of the situation. Taking our double-slit example, if one puts a detector at one or the other of the two slits -- even one that does not destroy the photon, electron, or whatever particle as it goes through the slit -- then an interference pattern does not appear at the detector. This is because one has set up an experiment in which one can "know" which path the particle took (i.e., which slit the particle went through). As long as one can tell this, then the particle cannot go through both slits at once and one no longer gets an interference pattern.
. . Now, you might say, what if I decide not to look at the detector set up next to one or the other of the slits? Well, one still does not get an interference pattern because the potential exists for one to be able to tell which path the photon, for example, traveled. Even this potential (i.e., "knowability") is enough to stop the formation of an interference pattern. All ability to detect which path an elementary particle took (in this case a photon of light) must be removed to obtain interference. In other words, one must not even be able to tell -- even in principle -- which path the elementary particle took in order for it to "take" both paths and form an interference pattern.
. . This is the most fundamental concept in quantum physics -- knowable and unknowable. It is from this more fundamental concept of the uncertainty principle that we shall approach our quantum astronomy experiment. It has been experimentally verified that if one can know which path a photon traveled, then an interference pattern is not possible. But if one can become ignorant of which path the photon (or any elementary particle) took, then an interference pattern is assured. That is, if one is ignorant of which path the photon took, then an interference pattern is not just possible, it must occur.
. . This last point can produce some decidedly non-classical effects. One example is the phenomenon known as "quantum beats." Picture an atom (classically, for now) as consisting of a nucleus with electrons jumping all around it. Electrons do not move smoothly away from and toward their central nucleus; they take discrete steps (energy quanta, actually) to transition from a lower to a higher (farther from the nucleus) orbital level. They actually disappear from one level and reappear at another, but are never found in between the two. As an electron "jumps" from a higher-level step to a lower-level step, it emits a photon of light. Just the fact that one cannot, even in principle, tell which energy level jump the electron took, is enough to produce a special kind of interference fringes called "quantum beats".
. . Thus, while picturing probability distributions as classical waves (like water waves) may be helpful for beginning physics students, real quantum wave phenomena are decidedly non-classical and produce decidedly non-classical results. They are not waves made of anything but probabilities, or tendencies to exist. Yet they can interfere with each other in a wave-phenomena-type way before they are measured, and so "turn" from probability waves to measured particles. (This "collapse of the wave function" is also said to take place instantaneously, as we shall discuss more in article four.)
. . Einstein wrote several times "God does not play dice with the universe." Quantum physics, however, has reduced everything to probabilities, mathematically, and such a formulation inherently implies dice rolling for all possibilities until a measurement is made. Richard Feynman pointed out that the mathematics really does mean all possibilities. Every elementary particle takes every path it possibly can -- a kind of infinite-slit experiment --and then these infinite numbers of paths all cancel in the multi-dimensional mathematics --called Hilbert space-- so that only one result is finally measured.
. . However, a colleague of Einstein’s, Professor John Wheeler of Princeton University, has pointed out that one could take another interpretation, an interpretation he has dubbed, "The Participatory Universe." In this approach, one can look at the universe as directly participating in each quantum effect in real time. In other words, the concept of a First Cause starting things off (winding up the clock of the universe, one might say) and then leaving the laws of physics to run things, may be what is incorrect in the basic approach of classical physics. Rather, in this participatory scenario, the Cause of the laws of physics remains an active Participant. (If one would like to also draw some religious points into such discussions, I would just say that it is important to understand what is being said and what is not being said here -—that is, to not oversimplify what went into Prof. Wheeler’s introduction of this interesting proposed conceptualization for quantum reality.)
. . Professor Wheeler came up then with a Gedanken experiment (i.e., a thought experiment) that he called the "delayed choice" experiment. He proposed a huge scaling up (to cosmic proportions) of Young’s double slit experiment that we’ve talked so much about. In this Gedanken experiment, gravitational lenses, which can bend light from distance quasars or galaxies, are used as sort-of giant slits to create two paths for photons from a quasar or distance galaxy. General Relativity shows that masses in space can bend light.
. . The first support for the confirmation of Einstein’s theory of relativity came with the measurement of the bending of light from stars by the Sun as they passed close behind it during a total solar eclipse. Light was indeed bent by the mass of the Sun (that is to say that space-time was curved near large masses). It turns out that large masses like galaxies that are rather close to being directly in between a distant quasar-galaxy and us will bend the light from the distant object toward us. One can think of light coming toward us more-or-less directly from a distant quasar-galaxy (let’s call this path A) while light shining from this quasar also heads off into space at a slightly different angle.
. . This light, however, encounters a massive galaxy along the way so that the light rays that would normally have missed the Earth get bent towards us as well (we’ll call this light path B). Thus it appears that we have two quasars with a massive galaxy in between. However, this is just one quasar whose light rays are coming more-or-less directly toward us along path A and whose second image appears on the other side of the massive galaxy image, these latter being the rays traveling along bent path B (i.e., bent toward us). Thus it appears that we have two quasars when we actually have two images of the same quasar.
. . John Wheeler realized that these two paths constituted a kind of double-slit experiment where the slits were the two gravitational lens images. The two paths of light from the quasar might be used then to interfere with each other. However, this could be done --according to Bell’s approach to the uncertainty principle-- only if one could not tell which path any particular photon had traveled. One way of being able to avoid knowing which path an individual photon took is to make the paths equal (within the uncertainty principle) so that one could not tell whether any photons arriving had traveled along path A or path B. Even if there were a flare in the quasar, the flare (peak in brightness) would arrive at the same time at Earth and so one could not use timing to tell which way it came. (One can see that if the paths are not equal, the light from the flare would arrive along path A before path B and so one could tell the path difference, which would negate the possibility of getting an interference pattern.)
. . Professor Wheeler "solved" this problem by adding an immensely long fiber optics cable to path A to make it as long as path B. (The fiber optics cable turned out to have to be over a light year long in this case, so it really was truly a Gedanken experiment without much hope of realization -- but we will propose a possible solution to this problem in the fourth and last essay.) The delayed-choice part of the experiment was, nevertheless, still very interesting. Given, then, that one achieves an interference pattern in this way, one should be able to put a detector at the intersection of light paths A and B and just re-do a cosmic-scale version of the Young’s double-slit experiment (where light-photons from quasar images A and B crossing the universe are equivalent to light going through slits 1 and 2 in the laboratory).
. . Now it should be noted that one of the founders of quantum physics, P.A.M. Dirac, noted that, at least in the Young’s double-slit experiment, one could only get an interference pattern if each photon only ever interfered with itself --that is, each single photon had to go through both slits and so only interfere with itself, not with any other photon. This certainly made sense in terms of the interference experiment being done with one photon at a time, and still producing interference. (There are also conservation of energy arguments --two photons should not be expected to produce 4 times the energy when they meet sometimes --making a bright line-- and no energy when they meet at other times --making a dark line in the interference pattern.) Thus if one did the Wheeler delayed-choice experiment with single photons being detected at a time, one would still expect --if one could not tell which path, A or B, the photons traveled along-- that an interference pattern would result where the two paths met. However, if one moved the detector to just detect photons along path A, then these photons will have just traveled along path A (by classical reasoning). Or, similarly, if one moves the detector to intersect path B photons, then the photons will have traveled only path B.
. . The interesting part of Professor Wheeler’s thought experiment is that the quasar emitting the photons is about one billion light years away -—that is, the light from this quasar is supposed to have taken a billion years to travel to Earth. It seems perplexing that any given photon will have had to have traveled both paths when you put the detector at the intersection of both paths, but then one path or the other path when you decide to put the detector directly into one of these paths rather than at their intersection.
. . In other words, how can your decision as to where to put the detector affect the path of a given photon a billion years after it supposedly started along one of the paths toward Earth --long before humans even existed on this planet (much less discovered quantum physics)? It would appear that what has "happened" in the distant past in this case may be determined by what is happening right now even though it is supposed to have "happened" over a billion years ago. The choice of which path, in other words, has somehow been "delayed". One might view this as the Universe playing more the part of an active participant in what is happening rather than just in what has happened in the past in this case. Hence the "Participatory Universe" conceptualization.
. . This interesting Gedanken experiment points out what may be the main difference between general relativity and quantum physics. In general relativity, time is a definite dimension, part of the already unalterable space-time continuum. While in quantum physics, time is, at best, a variable, and is also quantized (i.e. there are particles of time). Thus, far from being an absolute, time in quantum physics is a not a solid background upon which particles in space change. In quantum physics, time is, in a sense, not yet really even there until the "time particles" are measured.
In our fourth and final essay, we will talk about the possible realization of Professor Wheeler’s Gedanken experiment, which may open up a whole new field of investigation --a field which we will call "Quantum Astronomy."
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