Showing posts with label quantum mechanics. Show all posts
Showing posts with label quantum mechanics. Show all posts

Friday, September 3, 2010

Of strings and things.

Imagine a tiny thread of material, so infinitesimal that it is more than a quadrillion times smaller than a proton (no matter who you ask). Now imagine that same tiny thread being present at the heart of every single particle that makes up every atom that makes up every bit of matter we can observe in the universe. Got that? Good. Now imagine that the identity of every subatomic particle is determined by the precise vibration pattern of the tiny strand of material within; that is, its precise vibration pattern... in ten dimensions. Welcome to the world of superstring theory, one of the most potent contenders for the long sought-after "Theory of Everything" that will combine general relativity and quantum mechanics into one, all-inclusive framework.


As always, xkcd cuts right to the heart of things.


Simply put, string theory elegantly exploits the physical principles of music; that is, plucking a string will generate a different sound, depending on the properties of the string and how hard it is plucked. Some variations of string theory predict that strings are open, with two endpoints, while others predict that strings are closed, like a loop. Either way, it is the specific modes of vibration, or excitations, of the string that give rise to different kinds of particles.

String theorists conceive of elementary particles as having a very small dimension of length, rather than being point particles with no length, width or height. It may seem like a simple change, but this assumption neatly does away with the problems scientists have always faced when trying to formulate a quantum theory of gravity. There is only one problem: scientists have had no way to test the predictions of string theory. Because strings are thought to be so incredibly small, particle accelerators would have to operate at astronomically high energies to probe deeply enough into the subatomic realm. We simply don't have the technology.


Not even CERN has the power to probe the mysteries of string theory.
Image courtesy of Image Editor.


But a new discovery by a researcher at Imperial College London might be about to change things. According to Professor Mike Duff, the math scientists use to apply string theory to black holes is exactly the same as the math that is used to describe quantum entanglement between three particles. In a paper published in this week's Physical Review Letters, Duff and his team of colleagues detail an experiment involving four entangled particles and predict the result based on the mathematics of string theory. If researchers can manage to carry out this experiment, and if the results agree with the team's predictions, string theory will finally have the experimental backing scientists have been seeking for decades.

Currently, there seems to be no practical connection between quantum entanglement and the string physics of black holes. Even Duff acknowledges that they are "unexpected and unrelated" areas of physics. Perhaps researchers are about to discover more than they bargained for. Or perhaps all of this is simply an odd, yet serendipitous, coincidence.

Wednesday, August 18, 2010

Quantum weirdness reaches new heights, now implies parallel universes.

Einstein's theory of general relativity states that nothing in the universe can travel faster than light. As usual, quantum mechanics disagrees. In special cases, a pair of particles can be connected in such a way that by measuring the state of one, the state of the other can be instantaneously known, even if the two particles are separated by a large distance. Einstein famously poked fun at the idea, sarcastically nicknaming it "spooky action at a distance." Many physicists today still have trouble accepting this so-called quantum entanglement, despite experimental evidence that implores them to think otherwise. In a recent paper, Dr. Frank J. Tipler, a mathematician and physicist at Tulane University, has developed a model that links alleged quantum nonlocality with the Many Worlds interpretation of quantum mechanics. He claims that his theory solves the paradox of faster-than-light travel, but only if we are prepared to accept the fact that we live in a multiverse, a wacky version of the cosmos in which parallel universes are born every time a decision is made.


Einstein's famous gibe, paired with the mathematical notation for "spin-up."
Image courtesy of Matt Mechtley.


The most oft-cited example of quantum entanglement is a system in which two electrons exist in a singlet state; that is, they must have opposite spins. Spin is a property that measures the angular momentum of a particle. When measured in the vertical direction, the spin of a particle can either be "up" or "down." In a singlet state, if one electron is spin up, the other must be spin down; this holds true even if the electrons are separated by hundreds of thousands of lightyears. The problem with such systems is that electrons should not be able to communicate with each other any faster than light can travel. For instance, if they are positioned 100,000 lightyears away from each other, it should take no less than 100,000 years for the news of one electron's chosen spin to reach the other so that it can choose the opposite spin; however, experiments indicate that such information seems to travel instantly.

How can this be? According to Tipler, we should embrace the Many Worlds interpretation of quantum mechanics in order to make sense of this seeming paradox. In the Many Worlds interpretation, every possible set of circumstances exists in a separate universe. Every time one choice is made over another, the universe splits. In my current universe, I am writing this article at a coffee shop in downtown Boulder. In a separate but equally real parallel universe, I am writing from home, successfully resisting the lure of overpriced tea. In yet another universe, I have horrible command of the English language and am instead spending my afternoon pondering the financial merits of becoming a stripper. Regardless of circumstance, each of these alternate universes is just as real as the one in which I sit, fully clothed, diligently pounding out a wordy and rambling piece of science writing.


Image courtesy of anomalous4.


Back to Tipler. In his model, there are four distinct universes that are born of such an experiment: one in which electron #1 is spin up, one in which electron #1 is spin down, one in which electron #2 is spin up, and one in which electron #2 is spin down. But because the two electrons exist in a singlet state, there are only two possible combinations of these worlds. Either electron #1 is spin up and electron #2 is spin down, or electron #1 is spin down and electron #2 is spin up. When an observer measures the state of electron #1 here on Earth, two universes result, each one containing an observer that detects an opposite spin. Thus, the resulting spin of electron #2 has nothing to do with any kind of faster-than-light communication by its counterpart. It is simply a consequence of the particular universe the observer happens to find himself in. Measurement of one electron does not determine the spin of the other; instead, it selects for one universe over another, one in which the two electron spins have been predetermined.

Confused yet? Don't worry, in another universe you know exactly what's going on. I promise.

Tuesday, July 27, 2010

Quantum mechanics challenged, but to no avail.

I've written about light multiple times in this blog, using terms like photons, light rays, and electromagnetic radiation. You might be wondering what the deal is with all the fancy nomenclature, especially since some of these ideas seem to contradict each other. For instance, light comes in quantized packets called photons. But light is also often referred to as a ray or a wave. What gives? Well, as it turns out, light is very, very weird.

Over 100 years ago, the famous Double-Slit Experiment taught physicists that, at its core, light is both a particle and a wave. In quantum mechanical terms, the wavelike property of light means that every photon has a specific probability of being found in a given spot. When two light waves interfere (as in the double-slit experiment), these probabilities can be seen to occur in pairs: one set of positions where a photon is more likely to be found, and one set of positions where a photon is less likely to be found. Physicists at the University of Waterloo in Canada recently conducted a triple-slit experiment and were able to rule out higher-order probabilities, thus confirming a key principle of quantum mechanics.


The double-slit experiment produces a characteristic interference pattern.
Image courtesy of Timm Weitkamp.


Both the double-slit and triple-slit experiments are very simple in design. In the former, a light source is aimed at a metal sheet with two microscopic slits cut into it. The incident light then passes through the slits and lands on a blank screen. Scientists found that when they covered one slit, the light formed a pattern on the screen that was bright in the middle and faded to black at the edges. One would expect that the same pattern would result when both slits were open. If light behaved solely as a particle, half the photons would pass through one slit and half would pass through the other. The result would be a pattern that was doubly bright, but otherwise the same. Oddly enough, this is not what happened. Instead, a pattern of alternating bright and dark bands developed on the screen (see above). This was a clear indication that it was actually two light waves that passed through the slits, interfering with each other before they hit the screen and thus creating this distinctive pattern.

And the story gets weirder still. Experimentalists decided to try firing one photon at a time at the metal sheet. Surely this would force the photons to "pick" one slit over the other and prevent any wave interference from occurring. No such luck. An interference pattern still emerged, albeit more slowly as each photon took its place on the screen. Clearly this phenomenon could not be explained away by saying that light was really just a wave composed of particles. Scientists were forced to conclude that light is simultaneously a particle and a wave. The photons actually behaved as though they were waves, each photon somehow interfering with itself to form the characteristic light and dark bands shown on the screen.


Individually-fired photons produce an interference pattern over time.
Image courtesy of Ethan Hein.


In the triple-slit experiment, the Innsbruck group attempted to find evidence of third-order probabilities. According to our current understanding of the quantum world, this is impossible. The resulting light and dark bands in the double-slit experiment illustrate that such probabilities only occur in pairs. Success at Waterloo would have had drastic consequences for physics, disproving a long-held belief and necessitating a revision of quantum mechanics as we know it. Fortunately, no such result was found. Indeed, the oddities of the subatomic world live to see another day.

Wednesday, July 7, 2010

A tiny mistake.

The proton is one of nature's most famous elementary particles. Solid, stable and always positive, this subatomic celebrity is, quite literally, at the center of everything in the universe. But new research suggests that the proton may actually be smaller than previously thought. If this turns out to be true, the laws of physics will definitely need some rehabilitation.

Excepting dark matter and dark energy, the entire universe is made up of atoms. In the center of each is a small positively-charged core called a nucleus, which is made up of protons and neutrons held together by the strong force. Like a swarm of bees, electrons buzz around the nucleus in different "shells", or energy states. Hydrogen, the lightest and most abundant element, has been exploited by scientists for centuries due to its extraordinarily simple structure: one proton orbited by one electron.


Ionized clouds of hydrogen. Image courtesy of UC Astronomy Dept.


Most recently, researchers at the Max Planck Institute used our atomic minimalist to probe some choice principles of Quantum Electrodynamics (QED), a theory that merges Einstein's theory of special relativity with quantum mechanics. According to QED, an electron orbiting the hydrogen nucleus in the 2S shell will have a different energy than it would if it were orbiting in the 2P shell. This difference is called the Lamb shift, and it contradicts Paul Dirac's original prediction that the 2S and 2P shells should have the same energy. In order to learn more about the Lamb shift, the team at Max Planck replaced the electron in hydrogen with its cousin the muon, a particle that is 200 times as massive and far less stable. When researchers observed the newly created muonic hydrogen, they found that the massive muon orbited the central proton far more closely than the electron did, and was therefore far more sensitive to its size. The team's calculations assign the proton a radius of 0.84184 femtometers (0.00000000000000084184 meters), a number that is 4% smaller than its previously accepted value of 0.8768 femtometers.

4% may not seem like a whole lot, but this tiny miscalculation could have enormous implications for particle physics. If this new result turns out to be accurate, QED and the Standard Model will have to be completely rewritten. No easy task for the most relied-upon theory in modern physics. Quite frankly, scientists may have a revolution on their hands.

Wednesday, June 30, 2010

One of these things is never like the other.

Orville Wright once said, “If we worked on the assumption that what is accepted as true really is true, then there would be little hope for advance.” Presumably, this was the rationale behind a recent experiment conducted by a team of particle physicists at the University of California, Berkeley. Scientists operate on the assumption that all of the known subatomic particles fall into two distinct categories, bosons and fermions, whose respective properties are unique. If even one boson was to be observed to be acting under the laws that govern fermions, the whole of the Standard Model of particle physics would collapse. Fortunately, the UC Berkeley physicists have concluded that bosons - specifically, photons - never act like fermions. Ever.


Two photons of different wavelengths.
Image courtesy of NASA/Sonoma State University/Aurore Simonnet.


From the forces of nature to the basic constituents of matter, the Standard Model explains everything we think we know about our world. For instance, matter arises from different configurations of two groups of fermions: quarks and leptons. Quarks are the particles that make up protons and neutrons, while leptons are stand-alone particles such as the electron. The Standard Model also tells us that there are four basic forces: the strong and weak nuclear forces, electromagnetism, and gravity. These forces operate by exchanging bosons such as the gluon, the W and Z particles, and the photon.

Bosons and fermions behave according to the laws of quantum field theory, the physics behind the Standard Model. Each has a property called "spin," which defines its intrinsic angular momentum in terms of a number. Bosons are only allowed to have spins that are integers, e.g., 0, 1, 2, 3. Fermions can only have half-integer spins, e.g., 1/2, 3/2, 5/2. In quantum field theory, this is called the Spin-Statistics Theorem. Another difference between the two lies in their configuration; namely, that no two fermions can occupy the same quantum state. This is why the electrons in an atom arrange themselves in separate shells around the nucleus. Bosons, however, can share a single quantum state. This is the phenomenon behind laser beams and Bose-Einstein condensation.

The idea behind the experiment at UC Berkeley was to try and violate the Spin-Statistics Theorem and thus disprove the distinctness of bosons and fermions. The scientists fired two lasers at a group of barium atoms in order to see whether any electrons in the barium would be excited to a higher energy level. The transition they were looking for occurs when two photons are absorbed at once, and is forbidden to bosons (like photons) by the Spin-Statistics Theorem. According to Damon English, a post-doc with the Berkeley group, if photons acted like fermions, the transition would "go like gang-busters." But it didn't. Not one two-photon absorption was observed. The researchers thus concluded that our understanding of the Spin-Statistics Theorem is sound. "Photons are bosons," claimed English, "at least within our experimental sensitivity."

Saturday, June 19, 2010

Exotic form of matter falls 33 stories and lives to tell the tale.

General relativity is to quantum mechanics as oil is to water. Since the 1930s, physicists have been trying, unsuccessfully, to unite the two disciplines in an effort to explain the physics of both the very large and the very small. Now, almost a century later, scientists are beginning to take drastic measures. For instance, a team at the University of Hanover in Germany recently hauled a very expensive piece of technology down a 110-meter long shaft just to see what would happen.

The idea behind their experiment was to create a strange state of matter called a Bose-Einstein condensate (BEC) and to test its behavior during free fall. First created in 1995 at the University of Colorado at Boulder, a BEC is an extremely cold collection of atoms that magnifies the strange world of subatomic physics. How? When certain gases are cooled to near absolute zero, some of the atoms in the gas are able to occupy the same quantum state. They coalesce to form a visible super-atom, allowing scientists to observe quantum fluctuations on a macroscopic scale - in this case, during 4.7 seconds of free fall. According to Einstein's Equivalence Principle, the conditions experienced during free fall are identical to those felt in an environment without gravity. Experiments such as the one conducted by the Hanover team may shed light on whether quantum mechanical systems obey the same rule. If they do not, it could indicate new hope for the marriage of quantum mechanics and gravity.


A Bose-Einstein condensate created from rubidium atoms. The three diagrams show material gradually condensing in the blue and white regions. Image courtesy of NIST.


180 drops later, the experiment concluded without a hitch. The team next plans to split the BEC and repeat the experiment, sending each half along a different trajectory. Any differences in the motion of the two halves during free-fall would indicate an exception to the Equivalence Principle at the subatomic level and might help to spawn a new theory of quantum gravity.