{"id":1415,"date":"2015-11-03T22:17:34","date_gmt":"2015-11-03T22:17:34","guid":{"rendered":"http:\/\/blog.wabash.edu\/magazine\/?p=1415"},"modified":"2023-05-24T17:56:48","modified_gmt":"2023-05-24T17:56:48","slug":"grappling-with-the-quantum","status":"publish","type":"post","link":"https:\/\/blog.wabash.edu\/magazine\/2015\/11\/03\/grappling-with-the-quantum\/","title":{"rendered":"Grappling with the Quantum"},"content":{"rendered":"<p style=\"text-align: left\"><strong><\/strong><br \/>\n<strong>Trying to Understand the Fundamental Rules Governing Our World<\/strong><\/p>\n<p style=\"text-align: left\">The 36th LaFollette Lecture<br \/>\nOctober 30, 2015<\/p>\n<p style=\"text-align: left\"><strong>by Dennis E. Krause<\/strong><\/p>\n<p>I\u2019m deeply honored to be speaking this afternoon.\u00a0 I was surprised and excited when Dwight Watson came to my office at the beginning of the year with the invitation.\u00a0 Naturally there was trepidation\u2014what was I going to talk about?\u00a0 However, I was excited because it would give me a chance to talk about the things that have been perplexing me over the years and which have been driving much of my research and teaching.\u00a0 It would also give me the opportunity to talk more about what I do and how I do it.\u00a0 Finally, I felt that by looking at my work from a humanities perspective, I would learn something new, and that is exactly what happened.<\/p>\n<p>While I\u2019m honored to be first physicist to give the LaFollette Lecture, I actually believe I\u2019m the second physical scientist to speak, following Paul McKinney who gave the thirteenth LaFollette Lecture in 1992.\u00a0 It shouldn\u2019t be surprising to note that I\u2019ll be speaking on some of the same things he discussed over 20 years ago since the problems of the quantum remain as fascinating now as then.<\/p>\n<p>The charge of this talk is to address how my research touches the humanities broadly speaking, which sent me searching for a definition of the \u201chumanities.\u201d\u00a0 One that I found seems to describe well how the term is used in academia:<\/p>\n<p><i>The humanities can be described as the study of how people process and document the human experience.<\/i> <a title=\"\" href=\"#_ftn1\">[1]<\/a><i><\/i><\/p>\n<p>But I\u2019m a theoretical physicist.\u00a0 I\u2019m trying to find and understand the rules that underlie the operation of the physical universe, not the people within it (however interesting that may be).\u00a0 Then I found another definition that seemed to work better for me:<\/p>\n<p><i>Since the nineteenth century the humanities have generally been defined<\/i> as<i> <span style=\"text-decoration: underline\">the disciplines that investigate the expressions of the human mind<\/span>.<\/i> <a title=\"\" href=\"#_ftn2\">[2]<\/a><i><\/i><\/p>\n<p>While the painter, photographer, and poet are each trying to capture some aspect of the physical world on canvas, digital media, or paper, I\u2019m trying to capture some element of the universe with mathematical equations.\u00a0 These are all the result of human minds trying to express thoughts and feelings about our world.<\/p>\n<p>There is, however, a big difference between what I do and what these artists do.\u00a0 As a professional physicist, I am not free to do whatever I want. \u00a0Richard Feynman referred to it as \u201cimagination in a terrible strait-jacket.\u201d<a title=\"\" href=\"#_ftn3\">[3]<\/a> Since I\u2019m trying to capture some essence of the real universe, the results of my efforts must be consistent with what is already known about the universe.\u00a0 I\u2019m not free to invent new spatial dimensions unless I can devise a way to show they really may exist.\u00a0 One of my hobbies is writing fiction (although I don\u2019t have nearly the time I wish to devote to it).\u00a0 There I\u2019m free to imagine a small town in northern Minnesota where the townspeople must drape the body of a freshly killed victim over an ancient oak tree to ward off an unspeakable horror.\u00a0 But as a physicist, I can\u2019t tell any story I want.\u00a0 I can\u2019t invent some new law of physics unless I can also show that it is consistent with everything we know now and how it can be tested by experiment.\u00a0 If it cannot be readily tested, it is just speculation and is of no interest to me.\u00a0 And if my theory is tested and disagrees with the results of experiment, it is wrong.\u00a0 It doesn\u2019t matter how beautiful and elegant the equations may be, if they fail to describe the world, they must be discarded.\u00a0 In physics, theories must work.<\/p>\n<p>This may make it seem that science is antithetical to the humanities.\u00a0 Don\u2019t we have our cold, impersonal \u201cscientific method\u201d?\u00a0 In my long experience in science, the only time I hear mention of the \u201cscientific method\u201d is possibly in an introductory physics class or in an oral comprehensive exam when I\u2019m quizzing a humanities major.\u00a0 Like apprentices in any skilled craft, we learn the method through practice.\u00a0 As for being \u201ccold, impersonal,\u201d nothing can be further from the truth.\u00a0 Some recent quotes by Nobel laureate physicist Steven Weinberg accurately describe what we actually do:<\/p>\n<p><i>Descartes and Bacon are only two of the philosophers who over the centuries have tried to prescribe rules for scientific research.\u00a0 It never works.\u00a0 We learn how to do science, not by making rules about how to do science, but from the experience of doing science, driven by desire for the pleasure we get when our methods succeed in explaining something.<\/i> <a title=\"\" href=\"#_ftn4\">[4]<\/a><i><\/i><\/p>\n<p><i>So the world acts on us like a teaching machine, reinforcing our good ideas with moments of satisfaction. After centuries we learn what kinds of understanding are possible, and how to find them.\u00a0 We learn not to worry about purpose, because such worries never lead to the sort of delight we seek.\u00a0 We learn to abandon the search for certainty, because the explanations that make us happy never are certain.\u00a0 We learn to do experiments, not worrying about the artificiality of our arrangements.\u00a0 We develop an aesthetic sense that gives us clues to what theories will work, and that adds to our pleasure when they do work.\u00a0 Our understandings accumulate.\u00a0 It is all unplanned and unpredictable, but it leads to reliable knowledge, and gives us joy along the way.<\/i> <a title=\"\" href=\"#_ftn5\">[5]<\/a><i><\/i><\/p>\n<p>I hope you noticed words that aren\u2019t usually used to describe what scientists do: \u201cpleasure,\u201d \u201csatisfaction,\u201d \u201cdelight,\u201d \u201chappy,\u201d \u201caesthetic,\u201d and \u201cjoy.\u201d\u00a0 I do what I do not just because it (hopefully) provides insight about the world\u2014I also do it because it is <i>fun<\/i>!<\/p>\n<p>So I\u2019m a theoretical physicist, but what do I actually do?\u00a0 Most folks in academia specialize and so can readily answer the question: What do you do?\u00a0 It is a little harder for me, because I don\u2019t see myself as a particle physicist or a nuclear physicist or a\u2026\u00a0 Rather, I view myself as a general theoretical physicist who is on the lookout for very simple problems that can reveal something new and interesting about our world.\u00a0 Most theorists investigate problems that are vastly more complicated than the ones I study.\u00a0 Fortunately I\u2019ve been lucky to find simple problems that turn out to be very interesting, and I will share one of these with you later.\u00a0 However, before I get to it, we need to take a very brief tour of physics.<\/p>\n<p>When people learn that I\u2019m a physicist, the usual response is \u201cOh, that\u2019s hard,\u201d or \u201cOh, I failed that class in college,\u201d or simply: \u201cOh\u2026\u201d However, we\u2019re all physicists to some extent since we all need to have some sense of the rules obeyed by our universe.\u00a0 When someone tosses a ball to you, you can probably catch it without difficulty because you\u2019re familiar with how gravity and air resistance affect the motion of objects flying through the air.\u00a0 You know that larger objects are harder to accelerate than smaller ones. You\u2019re familiar with the affects of acceleration as you go around a bend, and know that freeways have wider turns than slower roads since these effects depend on speed.\u00a0 You know that the rate at which time passes is the same for everyone even though at times it may not seem like it.<\/p>\n<p>The rules governing the objects of our everyday world are called \u201cclassical\u201d and were developed by Galileo, Newton, and others through the 19<sup>th<\/sup> century.\u00a0 The classical world has certain features that most of us would consider \u201ccommonsensical\u201d (although they need to be learned by newborn infants).\u00a0 These include:<a title=\"\" href=\"#_ftn6\">[6]<\/a><\/p>\n<ul>\n<li>Physical objects exist at definite positions in space and instants in time.\u00a0 Two objects can\u2019t occupy the same location at the same time, or a single object cannot exist in two places simultaneously.<\/li>\n<li>Objective System State: The state of an object is determined by its properties which have definite values at all times.\u00a0 The state is an objective property of the system independent of the observer. Observation of the system should not affect its behavior (or can be taken into account).<\/li>\n<li>Determinism: The world is deterministic since the present state of a system completely determines its future states.<\/li>\n<li>Continuity: Systems evolve continuously through space and time. (Babies who haven\u2019t learned this love playing peek-a-boo.\u00a0 For them, something that is out of sight doesn\u2019t exist.)<\/li>\n<\/ul>\n<p>In essence, classical physics assumes there exists an <b>objective reality<\/b>, an external world that is independent of us.<\/p>\n<p>This classical world has an interesting property: it allows us to tell stories about how things happen.\u00a0 To see this, suppose we are at a baseball game (the World Series has started), and we wish to know where a ball struck by the batter (say, Mets post-season hero Daniel Murphy) will land.\u00a0 Will it be a home run?\u00a0 Knowing the initial position and velocity of the ball, we can calculate its trajectory using the laws of classical physics.\u00a0 This is a story, albeit boring unless we\u2019re rooting for the Mets.\u00a0 It has a beginning (ball leave the bat), a continuous middle with the suspense of wondering what will happen (ball flies through the air), and an ending (perhaps it just barely clears the right-field fence). We take this ability to create a narrative of how things behave in the universe for granted, including in physics.\u00a0 Often when physicists feel they understand some phenomena, they have a mental story they can tell of what is happening along with the equations.<\/p>\n<p>It is important to recognize that while these features of classical physics are reasonable and are obeyed in our everyday lives, they may be only approximately true.\u00a0 Like all laws of physics, they have a limited range of validity.\u00a0 If one tests them in new realms, they may fail.\u00a0 Furthermore, neuroscientists have shown that our perception of the world is heavily processed by our brain which seamlessly combines sense data and memories to create a model which we use to interact with the world.<a title=\"\" href=\"#_ftn7\">[7]<\/a>\u00a0 We never notice this is happening unless probed by the right experiment or if something goes terribly wrong.<\/p>\n<p>By the end of the 19<sup>th<\/sup> century, after the development of the theories of electromagnetism and thermodynamics, much of the behavior we observe in our everyday life could be adequately explained by classical physics.\u00a0\u00a0 But all was not well\u2026<\/p>\n<p><i>Stop reading and look around.\u00a0 <\/i><\/p>\n<p>While we can use classical physics to describe the motion of things around us, and know that the light reaching our eyes is actually electromagnetic waves, but why do the objects that you see have the properties you observe?\u00a0 What determines their colors?\u00a0 What determines whether they are hard or soft?\u00a0 Why is glass transparent, but a wall is opaque? Why does copper conduct electricity, but plastic doesn\u2019t?\u00a0 All of these everyday properties require an understanding of the microscopic nature of matter.\u00a0 By microscopic, I don\u2019t mean on the size of things that can be seen with an ordinary (light) microscope.\u00a0 By microscopic, I mean on an even smaller scale, on the level of atoms.<\/p>\n<p>By the end of the 19<sup>th<\/sup> century, probably most chemists and physicists (but certainly not all) believed in the existence of atoms, but there was little understanding of what they were or how they worked.\u00a0 It wasn\u2019t until 1897 that the electron, a crucial component of an atom, was discovered.\u00a0 This finally gave physicists a clue to work with.\u00a0 Electrons carry a negative electric charge and, since ordinary matter is electrically neutral, there must be something in the atom which carried the opposite, positive charge.<\/p>\n<p>The first decade of the 20<sup>th<\/sup> century was a fertile period of experiments probing the nature of the atom.\u00a0 The biggest breakthrough occurred when Ernest Rutherford discovered the atomic nucleus in 1911.\u00a0 He found that most atoms (and most of us) are composed of empty space.\u00a0 The bulk of the mass and all of the positive electric charge was concentrated in a tiny region\u2014the nucleus\u2014while the electrons somehow moved around it attracted by the opposite charge of the nucleus.\u00a0 Now physicists had a good enough picture to develop a theory to explain the atom and the nature of matter.\u00a0 Or so they may have thought\u2026<\/p>\n<p>From 1911 and through the early 1920s, Albert Einstein, Niels Bohr, Arnold Sommerfeld, and many others worked furiously on various models of the atom, but however much they tried, they achieved only partial success.\u00a0 Their attempts to apply the rules of classical physics to develop an accurate model of the atom failed.\u00a0 Then, in the 1920s, completely new ideas emerged which solved the problem.\u00a0 But not in a way that anyone would have expected.\u00a0 Werner Heisenberg, Louis De Broglie, Erwin Schr\u00f6dinger, Paul Dirac, Max Born and others needed to develop an entirely new mechanics to explain atoms\u2014quantum mechanics.<a title=\"\" href=\"#_ftn8\">[8]<\/a><\/p>\n<p>Let\u2019s pause briefly for an analogy.\u00a0 Why does the College spend so much effort to send students abroad for a semester or on immersion trips?\u00a0 Our students need to understand that the farther one travels from Wabash College, the more different people become.\u00a0 While folks in Lafayette or in Indianapolis behave virtually the same way as residents of Crawfordsville, people in Asia, Africa, Europe may view the world in a very different way.\u00a0 It is likely that many of our problems arise from the fact that we think everyone should behave like we do, but they don\u2019t.\u00a0 And there is nothing wrong with this\u2014we just need to understand and respect these other perspectives and act accordingly.<\/p>\n<p>The same thinking applies when we attempt to apply our classical worldview gained from our experiences to realms far removed from our everyday life.\u00a0 The atom is as far removed from our everyday scale as a speck of dust is to the entire Earth.\u00a0\u00a0 Should we be anymore surprised that the atomic world is so different from our own than we would be surprised that the Chinese, with their much older culture, think differently than us?\u00a0 As Richard Feynman put it:<\/p>\n<p><i>The behavior of things on the small scale is so fantastic, it\u2019s so wonderfully different \u2026 than <span style=\"text-decoration: underline\">anything<\/span> on the large scale!<\/i> <a title=\"\" href=\"#_ftn9\">[9]<\/a><\/p>\n<p>It is so different that the best way we have to understand the atomic world viewed through the quantum lens is through mathematics.<\/p>\n<p>What is quantum mechanics in a nutshell?\u00a0 It is a set of mathematical rules that tell us two things:<\/p>\n<ol>\n<li>Measurement outcomes.\u00a0 It tells us what are the possible results of an experiment.\u00a0 Many of these results come in discrete quantities (e.g., chucks of energy), they are \u201cquantized,\u201d which is where quantum mechanics gets its name.\u00a0 The energies of an atom are quantized in the same way that the discrete musical notes of a guitar string or the flute arise.<\/li>\n<li>Probabilities of measurement outcomes.\u00a0 Quantum mechanics is a theory of probabilities.\u00a0 Unlike classical mechanics, it doesn\u2019t tell us what <i>will<\/i> happen.\u00a0 When we do the experiment, quantum mechanics determines the probabilities of getting each possible measurement outcome, but it doesn\u2019t tell us which one will actually occur.<\/li>\n<\/ol>\n<p>The key quantity that is used to make these calculations is the quantum state (or wave function), which is most often denoted by the Greek letter \u03a8.<\/p>\n<p>Here is where the situation gets interesting.\u00a0 While nearly all physicists agree on the mathematical formalism of quantum mechanics and how to use it, there is no universal interpretation of what is happening or even what the quantum state vector \u03a8 really means.\u00a0 While this is a situation familiar to anyone in the humanities where the meaning of an ancient text can be disputed by scholars, it is extremely unusual in physics.\u00a0 There are four physicists in the Wabash Physics Department, and it is very likely we all have somewhat different views on the meaning of quantum mechanics. I cannot think of any similar disagreement of any other topic that we teach in our curriculum.\u00a0 And this situation is the same throughout the field.<\/p>\n<p>To get a better understanding of this situation, let\u2019s now consider a simple problem that I\u2019ll call the <i>Which-Path Problem<\/i>.<a title=\"\" href=\"#_ftn10\">[10]<\/a><\/p>\n<p>Here\u2019s the setup:<\/p>\n<p align=\"center\">Figure 1: Setup for Which-Path Problem<\/p>\n<p>A particle source sprays particles, each traveling with the same velocity, at a wall with two slits.\u00a0 The particles that pass through the slits travel on until they hit a screen.\u00a0 A moveable detector will determine where they strike.\u00a0 If the particles were Ping-Pong balls, we would expect the balls to strike the screen mostly in two areas behind each slit:<\/p>\n<p align=\"center\">Figure 2: Detection probability (green curve) for Ping-Pong balls.<\/p>\n<p>The balls don\u2019t strike at exactly the same spots due to slight variations in the directions of the balls travel.\u00a0 However, after shooting many balls, we get a sense of where it is most likely for the next ball to hit the screen.\u00a0 If you knew exactly the position and velocity of the ball when it left the source, classical physics would allow you to determine exactly its trajectory and where it would impact the screen.<\/p>\n<p>Now let\u2019s see what would happen if we replace the Ping-Pong balls with atoms which must be described by quantum mechanics.\u00a0 If we tried a classical approach, we would be stopped in our tracks before we even started.\u00a0 Remember that we need the exact initial position and velocity of the particle to determine its trajectory?\u00a0 The famous Heisenberg Uncertainty Principle does now allow such a state to exist!\u00a0 A quantum particle can never have simultaneously a definite position and velocity!\u00a0 Instead, the rules of quantum mechanics assign a wave function \u03a8 to each possible trajectory of the particle.\u00a0 In our case, to reach a particular point on the screen, there are two possible paths through slits #1 and #2 so there are two different wave functions for each:<\/p>\n<p align=\"center\">Figure 3: Two possible trajectories that the quantum atom can take to reach the detector with their corresponding wave functions.<\/p>\n<p>According to the rules of quantum mechanics, the probability that the atom will strike the detector is obtained by adding the wave functions and squaring the result:<a title=\"\" href=\"#_ftn11\">[11]<\/a><\/p>\n<p align=\"center\">,<\/p>\n<p>where \u03a8<sub>1<\/sub> is the wave function for the trajectory passing through slit #1 and \u03a8<sub>2<\/sub> is the wave function for the trajectory passing through slit #2.\u00a0 (Readers familiar with the mathematics of waves will recognize this formula as the way one finds the intensity of a wave pattern.)\u00a0 We see that the detection probability is the sum of three parts:<\/p>\n<ol>\n<li>\u00a0is the probability that the atom will reach the detector passing through slit #1 if slit #2 is blocked.<\/li>\n<li>\u00a0is the probability that the atom will reach the detector passing through slit #2 if slit #1 is blocked.<\/li>\n<li>\u00a0is the truly novel quantum piece: it characterizes the <b><i><span style=\"text-decoration: underline\">interference<\/span><\/i><\/b> of the two trajectories since it depends on both. The trajectory of one path seems to be affecting the other.<\/li>\n<\/ol>\n<p>Here is what the result of all this looks like:<\/p>\n<p align=\"center\">Figure 4: The detection probability (blue curve) when the particles are quantum atoms.\u00a0 The blue pattern is taken from a video showing the actual observed pattern near the axis (horizontal dashed line) from an experiment using electrons.<a title=\"\" href=\"#_ftn12\">[12]<\/a><\/p>\n<p>We see that the atoms strike the screen in bands instead of just two spots as in the Ping-Pong ball case.\u00a0 How do we interpret this?<\/p>\n<p>Quantum mechanics determines the detection probability for where the atom will strike the screen, but unlike classical mechanics, it does not tell us what the atom actually does between when it leaves the particle source and when it strikes the screen.\u00a0 Unlike classical physics, which allows us to tell a narrative of the trajectory of a baseball or the Ping-Pong balls in the which-path experiment, quantum mechanics is completely silent on the middle portion of the story, between the beginning and the end.<\/p>\n<p><i>Why don\u2019t we just look? <\/i><\/p>\n<p>Let\u2019s set up some detectors near the slits and see which path the atoms take.\u00a0 Beautiful experiments have been conducted which attempt to determine which path the atoms take.\u00a0 What happens?<\/p>\n<p align=\"center\">Figure 5:\u00a0 If detectors are set up to see which slit the atoms pass through, the detection probability at the screen near the axis (horizontal dashed line) is a flat line (red).\u00a0 All the interference occurring without the detectors has vanished.<\/p>\n<p>We find that the more information we get about which path the atom took, the less quantum interference arises.\u00a0 If we know exactly which slit the atom passed through, no interference occurs!<\/p>\n<p>While all physicists agree on how to use quantum mechanics to calculate what will be observed in an experiment, they do not agree on the interpretation of what goes on, possibly because the formalism does not permit a narrative description.\u00a0 There have been many attempts to explain this weirdness.<a title=\"\" href=\"#_ftn13\">[13]<\/a>\u00a0 Some do this by introducing alternate universes, one universe where the atom goes through slit #1 and another in which the atom passes slit number #2.\u00a0 Others try to envision the atom simultaneously taking both paths simultaneously. In other interpretations, the atom is actually just like the Ping-Pong ball, taking one or the other paths, but it is guided by a mysterious quantum potential which is determined by the experimental configuration. \u00a0My own feeling is that the situation is more complicated than this.\u00a0 The picture of atoms as particles is encouraged by the way they are detected, but all of these quantum systems are probably better described by quantum fields which combine wave and particle aspects.\u00a0\u00a0 Even then, it is not clear to me that this will allow one to complete the narrative of what is actually going on.\u00a0 Quantum mechanics describes what <i>may<\/i> happen, not what <i>will<\/i> happen.<\/p>\n<p>According to quantum mechanics, the detection probability is determined by the total wave function which is the sum, or <i>superposition<\/i>, of the wave functions for each path:<\/p>\n<p align=\"center\">.<\/p>\n<p>There is a tendency to view this to mean that the particle simultaneously takes both paths, but this is reading between the lines.\u00a0 It is a mathematical expression incorporating the experimental setup and the possible motions.\u00a0 When we look to see which path the particle takes, we find it takes path #1 or #2, not both.<\/p>\n<p>There is an optical illusion that provides a helpful analogy to this situation.\u00a0 In quantum mechanics, the total wave function describing the two paths the particle can take is like the Necker Cube:<a title=\"\" href=\"#_ftn14\">[14]<\/a><\/p>\n<p align=\"center\">Figure 6: The Necker Cube analogy of the Which-Path Problem. The Necker Cube is the line drawing while the blue cubes represent the two possible configurations of the Necker Cube seen by the eye, which are analogous to the two possible paths the atom can take.<\/p>\n<p>Here the Necker Cube represents the wave function \u03a8 as the superposition of the two wave functions for each path.\u00a0 When we look at the cube (i.e., do an experiment to see which path the atom takes), it is impossible for our brain to perceive the two simultaneously\u2014we see the cube in only one of two possible configurations (i.e., the detectors by the slits find the atom takes either one or the other path) with roughly equal probability (50% for path #1, 50% for path #2), but the interference is destroyed.<\/p>\n<p>It appears as if Nature is conspiring to prevent us from seeing what is happening!\u00a0 When we have no information about the atom\u2019s trajectory, we get beautiful interference patterns.\u00a0 But if we look to see what is going on, we get no interference.<\/p>\n<p>All of this is well-known.\u00a0 Now I\u2019m going to make things even stranger.\u00a0 What happens if we replace the ordinary atom in our which-path experiment with an unstable particle, like a radioactive nucleus or an atom in an excited state?\u00a0 Such a particle only lives for a short time, before decaying into other particles.\u00a0 We don\u2019t know when an individual unstable particle will decay\u2014the decay process is completely random (and described by quantum mechanics), but if we average over many lifetimes, we can find an average lifetime.\u00a0 The average lifetime is related to the particle\u2019s half-life, which is the time it takes for half of a large collection of identical unstable particles to decay.\u00a0\u00a0 \u00a0My colleagues Zach Rohrbach (\u201912), Ephraim Fischbach at Purdue, and I set out to see how the which-path experiment would change using these particles.<\/p>\n<p>If we use <i>QuUPs<\/i> (<span style=\"text-decoration: underline\">Qu<\/span>antum <span style=\"text-decoration: underline\">U<\/span>nstable <span style=\"text-decoration: underline\">P<\/span>articles), as Zach Rohrbach dubbed them, in our which-path experiment, we have two situations to consider: (1) the QuUP decays while passing from the source to the screen, and (2) the QuUP survives and reaches the screen without decaying.<\/p>\n<p>The first case has been investigated by other researchers,<a title=\"\" href=\"#_ftn15\">[15]<\/a> and a diagram will help us figure out what will happen:<\/p>\n<p align=\"center\">Figure 7: The QuUP decays while traveling one of the two paths, emitting light that (possibly) reveals which path the QuUP took.\u00a0 The detection probability is measured close to the axis (horizontal dashed line) and depends on the wavelength of the light emitted by the decaying QuUP.\u00a0 The interference occurs\u00a0 (dashed blue curve) when the wavelength of the emitted is too long to give away which-path information, but disappears (red line) when the wavelength is short enough to determine the path.<\/p>\n<p>When an atomic QuUP decays, it will emit light.\u00a0 When this happens, which-path information is revealed so one would think that the interference would disappear at the screen.\u00a0 However, the real situation is more interesting than that.\u00a0 To actually reveal the path, the light emitted must be of a wavelength sufficiently small to resolve the two different paths.\u00a0 If the wavelength is longer than the path separation, one can\u2019t tell from which path it was emitted, in which case we should still observe the interference as the decayed QuUP hits the screen.\u00a0 If the wavelength is shorter than the path separation clearly revealing the path taken, the interference disappears. This is exactly what was observed in a beautiful set of experiments by Anton Zeilinger\u2019s group using heated C<sub>70<\/sub> molecules!<a title=\"\" href=\"#_ftn16\">[16]<\/a><\/p>\n<p>That was the first scenario.\u00a0 What happens in the second case, when the QuUP does not decay during its travel and reaches the screen?\u00a0 This is the case that Rohrbach, Fischbach, and I set out to investigate.<a title=\"\" href=\"#_ftn17\">[17]<\/a>\u00a0 According to what we have already discussed, it would appear that nothing new should occur.\u00a0 If the QuUP travels undecayed, shouldn\u2019t the interference be the same as for the ordinary atom discussed earlier?\u00a0 Since it didn\u2019t decay, no which-path information could be revealed, so we might think we would observe the ordinary interference pattern.\u00a0 However, that is not what we found.\u00a0 The interference pattern of an undecayed QuUP is <i>not<\/i> the same as that for an ordinary atom:<\/p>\n<p align=\"center\">Figure 8: The calculated interference pattern of the undecayed QuUP (red curve) differs from the pattern due to an ordinary atom (dashed blue curve), especially far from the experiment axis (dashed line).<\/p>\n<p>This means that there still must be some information available to determine the path taken.\u00a0 But where is it?<\/p>\n<p>It turns out that the information is within you.\u00a0 Look carefully at the setup shown in Figure 8.\u00a0 The QuUP has two paths to reach the screen at the point shown.\u00a0 It lives for only a short time: which path will give it the best chance of surviving to reach the screen?\u00a0 (Remember it travels the same speed over each path.)\u00a0 Since the path through slit #1 is shorter (hence, takes a short time), the QuUP has a higher likelihood of reaching the indicated point than via the path through slit #2.\u00a0 This is which-path information!\u00a0 It is called <i>a priori<\/i> which-path information since this information is known <i>before<\/i> the QuUP leaves the source.\u00a0 You will also notice from Figure 8 that the further from the experiment axis (horizontal dashed line) one is on the screen, the more the QuUP probability pattern deviates from the ordinary atom pattern.\u00a0 This is because the path lengths become more different as one moves away from the axis so the QuUP taking the longer path is less likely to survive.\u00a0 The two patterns are exactly the same at the center where the paths are of equal length so the QuUP is equally like to survive each path.\u00a0 In fact, there is a nice mathematical formula that quantifies this effect, which can be written schematically as<\/p>\n<p align=\"center\">(Which-Path Information)<sup>2<\/sup> + (Quantum Interference)<sup>2 <\/sup>= 1.<\/p>\n<p>The more which-path information you have, the less quantum interference arises (and vice versa).<\/p>\n<p>The discovery of this which-path effect with undecayed QuUPs has convinced me that information plays an important role in understanding our universe.\u00a0 Quantum mechanics seems to be telling us that the information available about a system is related to the behavior of that system, and it also helps to explain why these effects don\u2019t appear in our everyday lives.\u00a0 Light is constantly reflecting off everyday objects, carrying information about them into the environment. This is will naturally cause the destruction of the quantum mechanical effects as the information leaks out. This is a big problem for the folks trying to create a quantum computer.\u00a0 If such a device can be made, calculations that would take millions of years using the fastest classical computer could be done in seconds.\u00a0 But the challenge is to prevent the environment from measuring the quantum computer, destroying the vary quantum properties needed to make it work.<\/p>\n<p>In fact, recent work indicates that even if we could isolate a large object (e.g., the fabled Schr\u00f6dinger\u2019s cat) from light and other environmental effects, there is still a way for the information about what it is doing to escape.\u00a0 Einstein\u2019s theory of relativity couples an object\u2019s internal and external motions in a way that would be almost impossible to eliminate, so the object\u2019s motion would be encoded with its internal state, destroying quantum interference.<a title=\"\" href=\"#_ftn18\">[18]<\/a>\u00a0 My student Inbum Lee (\u201916) and I are exploring these ideas, which are actually related to the work I\u2019ve described with QuUPs, and we have already found some new effects.\u00a0 \u00a0There are many interesting things yet to be found!\u00a0 But that is a different story.<\/p>\n<p>And that&#8217;s the real point. The underlying theme of this talk is that there is a natural desire of humans to tell stories.\u00a0 This is true in science as well as in the humanities.\u00a0 What makes quantum mechanics hard to understand is that it is not allowing us to tell a story.<\/p>\n<p>I\u2019ve also been telling you a story with this talk, about how quantum mechanics came into being, how the which-path experiment works, and how the idea of using QuUPs led us to a new interesting quantum effect.\u00a0 However, this really is just a story.\u00a0 It is a narrative that allows you to follow what is going on, but it does not really match how things actually happened. The development of quantum mechanics was extremely tortuous. To tell the true story would take far more than my allotted time. \u00a0Instead, as in editing a short story, I smoothed out the wrinkles and tighten up the plot, eliminated unessential characters and storylines, so as to focus on the key things I want to express.\u00a0 I also didn\u2019t tell you how I actually stumbled upon the effect with QuUPs.<\/p>\n<p>My colleagues and I were working on a completely different problem<a title=\"\" href=\"#_ftn19\">[19]<\/a> when I noticed something strange in our results.\u00a0 After a few weeks of hard thinking I finally figured out what was happening.\u00a0\u00a0 Fortunately, I have a large storehouse of knowledge of lots of interesting physics ideas so I was able to piece it together. This is how science is really done.\u00a0 After the fact, when we have figured everything out, we polish the story so everything appears logical and almost inevitable, but that isn\u2019t really the case.\u00a0 This is why it is so important to support student research and creative work so students can actually see how the things we teach were discovered or created.\u00a0 They can then realize that they, too, can do this.<\/p>\n<p>We have also seen that the mysterious quantum effects are also impacted by stories.\u00a0 In fact, Nature seems to be preventing us from telling a story of what is happening in the quantum realm.\u00a0 When information of what is going on leaks out, the very thing we\u2019re trying to understand disappears.\u00a0 The funny thing is that these strange goings on, behind a cloak of secrecy, are vital to our world around us and are becoming part of our everyday technology like LEDs, lasers, and computers. \u00a0We are living in a quantum world, but the machinery (if there even is machinery!) is hidden away.<\/p>\n<p>I have one final story to tell. \u00a0I didn\u2019t discover that stories were the theme of this talk until I was nearly finished.\u00a0 As in writing a lecture, a short story, or doing physics research, I often don\u2019t really know what I\u2019m doing until I\u2019m nearly finished.\u00a0 I set out in some promising direction knowing that, wherever it will lead, the journey and resulting story will usually be interesting and fun.\u00a0\u00a0 I hope this is the way you found my story of grappling with the quantum.<\/p>\n<p>For complete lecture with figures:\u00a0<a href=\"http:\/\/blog.wabash.edu\/magazine\/wp-content\/uploads\/sites\/15\/2015\/11\/lafollette-lecture.pdf\">LaFollette Lecture<\/a><\/p>\n<p><b>Acknowledgments<\/b><\/p>\n<p>I have to acknowledge the support of all my colleagues at Wabash College.\u00a0 I\u2019m so thankful to have landed here in 1998\u2014it is hard to imagine a more collegial place to work.\u00a0 I especially enjoy the debates about quantum mechanics I have had with my physics colleagues Martin Madsen and Jim Brown.\u00a0 My ideas are constantly evolving as a result of these discussions.\u00a0 I\u2019m also thankful to have had incredibly bright students like Zach Rohrbach and Inbum Lee who have helped me work through the ideas presented here.\u00a0 I also need to thank all my research colleagues, especially Ricardo Decca at IUPUI, and my colleagues in Mexico, Daniel Sudarsky, Yuri Bonder, and Hector Hernandez-Coronado, whose project led to the QuUP which-path effect. \u00a0Finally, I can\u2019t sufficiently express my deep appreciation for my Purdue mentor, colleague, and friend, Ephraim Fischbach.\u00a0 We\u2019ve been carrying out very fruitful investigations for over 25 years, and we continue to generate questions and problems faster than we and our students can solve them.<\/p>\n<p>&nbsp;<\/p>\n<hr align=\"left\" size=\"1\" width=\"33%\" \/>\n<div>\n<p><a title=\"\" href=\"#_ftnref1\">[1]<\/a> Stanford Humanities Center website: <a href=\"http:\/\/shc.stanford.edu\/what-are-the-humanities\">http:\/\/shc.stanford.edu\/what-are-the-humanities<\/a>.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref2\">[2]<\/a> R. Bod, <i>A New History of the Humanities<\/i> (Oxford University Press, Oxford, 2013), p.1.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref3\">[3]<\/a> R. P. Feynman, The Character of Physical Law (MIT Press, Cambridge, MA, 1965), p. 171.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref4\">[4]<\/a> S. Weinberg, <i>To Explain the World<\/i> (Harper, New York, 2015), p. 214.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref5\">[5]<\/a> <i>Ibid<\/i>., p. 255.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref6\">[6]<\/a> Stanford Encyclopedia of Philosophy, Copenhagen Interpretation of Quantum Mechanics, <a href=\"http:\/\/plato.stanford.edu\/entries\/qm-copenhagen\/#ClaPhy\">http:\/\/plato.stanford.edu\/entries\/qm-copenhagen\/#ClaPhy<\/a>.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref7\">[7]<\/a> See, for example, David Eagleman\u2019s <i>The Brain: The Story of You<\/i> (Pantheon, 2015).<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref8\">[8]<\/a> For a good history of the development of quantum mechanics, see <i>The Quantum Story: A History in 40 Moments<\/i> by Jim Baggott (Oxford University Press, Oxford, 2011) .<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref9\">[9]<\/a> R. P. Feynman, <i>Fun to Imagine,<\/i> BBC television series, 1983 (<a href=\"https:\/\/www.youtube.com\/watch?v=DUjgzmGAODc\">https:\/\/www.youtube.com\/watch?v=DUjgzmGAODc<\/a>).<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref10\">[10]<\/a> The treatment I use here is similar to Richard Feynman\u2019s approach found in R. P. Feynman, R. B. Leighton, M. Sands, <i>The Feynman Lectures on Physics<\/i>, Vol. 3 (Addison-Wesley, Reading, MA, 1965), pp. 1-1\u20141-11.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref11\">[11]<\/a> The wave functions are actually complex numbers, but for our purposes I\u2019m going to ignore this complication. The factor of \u00a0is included so that the probability of reaching the screen is 100% (no atoms are lost along the way).<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref12\">[12]<\/a> The video taken by the Hitachi group using an electron microscope can be found at <a href=\"https:\/\/www.youtube.com\/watch?v=PanqoHa_B6c\">https:\/\/www.youtube.com\/watch?v=PanqoHa_B6c<\/a>.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref13\">[13]<\/a> For a brief listing of the interpretations of quantum mechanics with many references, see A. Cabello, <a href=\"http:\/\/arxiv.org\/abs\/1509.04711\">http:\/\/arxiv.org\/abs\/1509.04711<\/a>.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref14\">[14]<\/a> E.g., J. Kommeier and M. Bach, Frontiers in Human Neuroscience <b>6<\/b>, 51 (2012).<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref15\">[15]<\/a> T. Sleator, <i>et al<\/i>., in: <i>Quantum Measurements in Optics<\/i>, edited by P.Tombesi and D. F. \u2028Walls (Plenum, New York, 1992), pp. 27\u201340; T. Sleator, et al., in: \u2028<i>Laser Spectroscopy X<\/i>, edited by M Ducloy, E. Giacobino, and G. Camy (World Scientific, Singapore, 1991), pp. 264\u2013271; P. Facchi, Journal of Modern Optics <b>51<\/b> (2004) 1049; P. Facchi, A. Mariano, and S. Pascazio, arXiv:quant-ph\/0105110; S. Takagi, in: <i>Fundamental Aspects of Quantum Physics<\/i>, ed. by L. Accardi and S. Tasaki (World Scientific, Singapore, \u20282003), 188.<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref16\">[16]<\/a> L. Hackerm\u00fcller, <i>et al<\/i>., Nature <b>427<\/b>, 711 (2004).<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref17\">[17]<\/a> D. E. Krause, E. Fischbach, and Z. J. Rohrbach, Physics Letters A <b>378<\/b>, 2490 (2014)]; <a href=\"http:\/\/arxiv.org\/abs\/1407.1087\">http:\/\/arxiv.org\/abs\/1407.1087<\/a> .<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref18\">[18]<\/a> I. Pikovski, et al., Nature Physics <b>11<\/b>, 668 (2015).<\/p>\n<\/div>\n<div>\n<p><a title=\"\" href=\"#_ftnref19\">[19]<\/a> Y. Bonder, E. Fischbach, H. Hernandez-Coronado, D. E. Krause, Z. Rohrbach, and D. Sudarsky, Phys. Rev. D <b>87<\/b> (2013) \u2028125021.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Trying to Understand the Fundamental Rules Governing Our World The 36th LaFollette Lecture October 30, 2015 by Dennis E. Krause I\u2019m deeply honored to be speaking this afternoon.\u00a0 I was surprised and [&hellip;]<\/p>\n","protected":false},"author":16,"featured_media":1420,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-1415","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-faculty-news-and-notes"],"w_featured_image_url":"https:\/\/blog.wabash.edu\/magazine\/wp-content\/uploads\/sites\/15\/2015\/11\/06-quantum-state-1024x682.jpg","_links":{"self":[{"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/posts\/1415","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/comments?post=1415"}],"version-history":[{"count":8,"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/posts\/1415\/revisions"}],"predecessor-version":[{"id":1439,"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/posts\/1415\/revisions\/1439"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/media\/1420"}],"wp:attachment":[{"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/media?parent=1415"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/categories?post=1415"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.wabash.edu\/magazine\/wp-json\/wp\/v2\/tags?post=1415"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}