Showing posts with label QM. Show all posts
Showing posts with label QM. Show all posts
Wednesday, July 24, 2013
Wednesday, March 14, 2012
Roads to Reality: We’ve got a Problem.
Noted astrophysicist, cosmologist, and popular science author, Carl Sagan ends his book The Dragons of Eden with the following lines: “The universe is elegant and intricate. We wrest secrets from nature by the most unlikely routes”. Even though the subject matter of the book deals with his speculations on the evolution of human intelligence, this series of articles, should it manage to succeed in its aim, should serve the purpose of highlighting the veracity of his words. The fabric of the cosmos does present the human intellect with numerous challenges. As we unravel its umpteen layers, the excitement of having solved a mystery can be said to only marginally exceed the frustration at encountering new questions. In this mythical quest for secrets, as hope trumps disappointment, the cycle of discovery keeps reinventing itself as one puzzle replaces the next.
In my last piece, I had tried to illustrate how the element of uncertainty is embedded in the very fabric of quantum mechanics (QM). It is not of the kind we encounter in classical mechanics, where trusted laws can help us determine with absolute certainty which way a tossed coin will land. Uncertainty in QM refuses to reveal its secrets beyond a certain ‘probability wave’, or more precisely wavefunction , that predicts the likelihood of the occurrence of an event. It is only when we interact with the system, with the intention of measuring some of its property, that this haze of multiple possibilities clears and assumes a definite outcome.
Mathematically, this evolution can be said to have two distinct stages. In the first stage, the probability wave of an electron (or some other fundamental particle) evolves over time – smoothly and gradually – according to Schrödinger’s equation. The second stage is when we make contact with the observable reality, causing the electron to snap to, let’s say, a particular position, thereby ‘collapsing’ the wavefunction. And therein lies the heart of our ‘problem’.
The quantum mechanical description of reality is clueless about this collapse. According to Schrödinger’s equation, wavefunctions do not collapse. It is simply a convenient add-on that helps theory agree with observations (I have come to believe physicists often do that). Since the cat is never observed to be both dead and alive, the explanation safely posits that the act of measurement causes the wavefunction to relinquish its state of quantum limbo and usher one of the possibilities into reality. But what is so special about the act of observation that causes this choice to be made? How are the different possibilities converted onto an actual, sharply-defined outcome? This dilemma is what’s known as the Quantum Measurement Problem and forms the core of several contending interpretations of QM that seek to explain what has so far only been observed.
Werner Heisenberg, who, along with Neils Bohr, formulated the Copenhagen interpretation, provides some particular useful insights regarding the nature of quantum reality in his book Physics and Philosophy. He writes, “Reality is in the observations, not in the electron.” This view is embodied in the Copenhagen interpretation which claims that a wavefunction is merely the mathematical embodiment of what we know about reality. Before we observe the electron, it exists in a ‘coherent superposition’ of all possible positions, snapping out of this haze when we measure its position. In this respect, the collapse is nothing more than the change in our knowledge about the whereabouts of the electron. What goes on behind the scenes, strictly speaking, lies beyond the scope of physics.
Crudely translated, this would imply that the cat is to be considered alive and dead at the same time! Naturally, this worldview, even though quite popular, does not sit well with a number of physicists and, yes, philosophers. Detractors question why fundamental physics should so closely be tied to human awareness. If we were not here to tinker around with laboratory equipment, would wavefunctions never collapse, or better still, not exist? Can bacteria or ants not be observers of quantum reality and a change in their ‘knowledge’ be associated with the wavefunction collapse?
For several years, the Copenhagen interpretation of QM held sway in scientific circles. But its primacy was challenged 1957 by an approach formulated by Hugh Everett that subjects our classical instinct to another major upheaval. (I seem to be getting into the habit of saying this. But, well.) The many-worlds interpretation (MWI) denies the occurrence of the wavefunction collapse. Instead, it views reality as a multi-branched tree, where each possible quantum outcome is realized. The concept of the universe is enlarged to include an infinite number of ‘parallel universes’ within a larger multiverse so that anything that can happen actually does happen in one of the innumerable versions of our universe. In one universe you are reading these words while in another you are waiting anxiously for the grand gala opening of your first play. It’s all happening out there!
Needless to say, I have only scarcely begun to realize the impact that this can have on our understanding of not only science but widely disparate disciplines like philosophy and spirituality. What if I were to put a gun to my head and pull the trigger? Would I be able to pull off this ‘quantum suicide’? If MWI is right, there will be a copy of our universe where I am alive and well. Should that mean my consciousness is, in essence, immortal? Quacks have been quick to jump on this bandwagon and have sought to use MWI to give credence to the idea of a soul that defies death and simply changes its ‘vessel’ as it hops from one universe to the next. Maybe that is how our ancestors tried to comprehend the strangeness of the universe we inhabit. Who knows!
But physicists are not in the business of mysticism and they have never really liked playing with odds. Some promising steps have been taken in the direction of separating spirituality from science through work on the phenomenon of ‘decoherence’. Decoherence provides an explanation for the appearance of the wavefunction collapse by postulating that much of the quantum weirdness of large objects ‘leaks’ from large objects because of their interaction with their environment. In other words, it is the framework which tries to explain how quantum uncertainty morphs into the well determined outcomes of classical experimental physics and our intuitive understanding of reality. MWI, with its decoherence updating, can prove to be an encouraging direction in the evolution of quantum theory.
Through the course of this debate, I have tried to emphasize how the resolution of one conundrum often leads to the genesis of a new one. When Newton tried to describe the ‘music of the spheres’, he could have scarcely imagined a world in which reality is neither deterministic nor viewed as a single unfolding history. Nevertheless, standing on the shoulders of such giants, we have been steadily hacking away at the myriad layers of our cosmic onion. As our intuition grapples with what is revealed to us, we will continue to reconsider our definitions truth and reality. The implications are exciting and manifold. But, as I will attempt to elaborate on in my next article, we must be careful enough to view them through the lens of reason and scientific analysis. One must sift through all the hoopla and take care to not be swept away by the wave. Doing so, we will realize that science does not undermine the beauty of the stars. Instead, it makes even larger the canvas of their mysticism. After all, it was Bohr who said, “Anyone who is not shocked by quantum theory has not understood it”.
Note: For the sake of simplicity (and to avoid making this article too tedious a read), I have discussed only two of the several contending interpretations of quantum mechanics. Interested readers can, obviously, choose to further this understanding. The following Wikipedia page should be a good starting point: http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics.
Images from http://farside.ph.utexas.edu and http://en.wikipedia.org.
Mathematically, this evolution can be said to have two distinct stages. In the first stage, the probability wave of an electron (or some other fundamental particle) evolves over time – smoothly and gradually – according to Schrödinger’s equation. The second stage is when we make contact with the observable reality, causing the electron to snap to, let’s say, a particular position, thereby ‘collapsing’ the wavefunction. And therein lies the heart of our ‘problem’.
The quantum mechanical description of reality is clueless about this collapse. According to Schrödinger’s equation, wavefunctions do not collapse. It is simply a convenient add-on that helps theory agree with observations (I have come to believe physicists often do that). Since the cat is never observed to be both dead and alive, the explanation safely posits that the act of measurement causes the wavefunction to relinquish its state of quantum limbo and usher one of the possibilities into reality. But what is so special about the act of observation that causes this choice to be made? How are the different possibilities converted onto an actual, sharply-defined outcome? This dilemma is what’s known as the Quantum Measurement Problem and forms the core of several contending interpretations of QM that seek to explain what has so far only been observed.
Werner Heisenberg, who, along with Neils Bohr, formulated the Copenhagen interpretation, provides some particular useful insights regarding the nature of quantum reality in his book Physics and Philosophy. He writes, “Reality is in the observations, not in the electron.” This view is embodied in the Copenhagen interpretation which claims that a wavefunction is merely the mathematical embodiment of what we know about reality. Before we observe the electron, it exists in a ‘coherent superposition’ of all possible positions, snapping out of this haze when we measure its position. In this respect, the collapse is nothing more than the change in our knowledge about the whereabouts of the electron. What goes on behind the scenes, strictly speaking, lies beyond the scope of physics.
Crudely translated, this would imply that the cat is to be considered alive and dead at the same time! Naturally, this worldview, even though quite popular, does not sit well with a number of physicists and, yes, philosophers. Detractors question why fundamental physics should so closely be tied to human awareness. If we were not here to tinker around with laboratory equipment, would wavefunctions never collapse, or better still, not exist? Can bacteria or ants not be observers of quantum reality and a change in their ‘knowledge’ be associated with the wavefunction collapse?
For several years, the Copenhagen interpretation of QM held sway in scientific circles. But its primacy was challenged 1957 by an approach formulated by Hugh Everett that subjects our classical instinct to another major upheaval. (I seem to be getting into the habit of saying this. But, well.) The many-worlds interpretation (MWI) denies the occurrence of the wavefunction collapse. Instead, it views reality as a multi-branched tree, where each possible quantum outcome is realized. The concept of the universe is enlarged to include an infinite number of ‘parallel universes’ within a larger multiverse so that anything that can happen actually does happen in one of the innumerable versions of our universe. In one universe you are reading these words while in another you are waiting anxiously for the grand gala opening of your first play. It’s all happening out there!
But physicists are not in the business of mysticism and they have never really liked playing with odds. Some promising steps have been taken in the direction of separating spirituality from science through work on the phenomenon of ‘decoherence’. Decoherence provides an explanation for the appearance of the wavefunction collapse by postulating that much of the quantum weirdness of large objects ‘leaks’ from large objects because of their interaction with their environment. In other words, it is the framework which tries to explain how quantum uncertainty morphs into the well determined outcomes of classical experimental physics and our intuitive understanding of reality. MWI, with its decoherence updating, can prove to be an encouraging direction in the evolution of quantum theory.
Through the course of this debate, I have tried to emphasize how the resolution of one conundrum often leads to the genesis of a new one. When Newton tried to describe the ‘music of the spheres’, he could have scarcely imagined a world in which reality is neither deterministic nor viewed as a single unfolding history. Nevertheless, standing on the shoulders of such giants, we have been steadily hacking away at the myriad layers of our cosmic onion. As our intuition grapples with what is revealed to us, we will continue to reconsider our definitions truth and reality. The implications are exciting and manifold. But, as I will attempt to elaborate on in my next article, we must be careful enough to view them through the lens of reason and scientific analysis. One must sift through all the hoopla and take care to not be swept away by the wave. Doing so, we will realize that science does not undermine the beauty of the stars. Instead, it makes even larger the canvas of their mysticism. After all, it was Bohr who said, “Anyone who is not shocked by quantum theory has not understood it”.
Note: For the sake of simplicity (and to avoid making this article too tedious a read), I have discussed only two of the several contending interpretations of quantum mechanics. Interested readers can, obviously, choose to further this understanding. The following Wikipedia page should be a good starting point: http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics.
Images from http://farside.ph.utexas.edu and http://en.wikipedia.org.
Friday, November 25, 2011
Roads to Reality: The Clouds of Uncertainty
Physicists are an arrogant lot. And if Sheldon Cooper is any proof, they are usually quite happy being unapologetic about it. In an alternate universe, we probably pay our homage at the Cathedral of Science, with theoretical physicists presiding over as high priests. However, in our own version of the cosmos, I am willing to give them the benefit of a fertile imagination, given their knack of coming up with the weirdest explanations for everyday phenomenon. Therefore, it is a feast for the intellect when some of the brightest minds of a generation squabble over, quite literally, a dice.
Our classical sense of intuition tells us that in order to produce a change in a system (read ‘object’ if you are less scientifically minded) on the order side of a football field we will have to somehow negotiate the intervening space. That is what space does. We can shout, send a laser beam, or mail a postcard and wait for the cows to come home. Physicists and philosophers have a word for such a world view – local realism. Local realism posits that an objective reality exists even when it is not being observed and that an object can be influenced only by its immediate surroundings. It’s like what Winston Smith of 1984 would have us believe – “Sanity is not statistical”. Until the first two decades of the 20th century, no scientific development had challenged the locality of our universe. But all this was about to change.
The science of Quantum Mechanics (QM in all future references), developed primarily during the period between 1900 and 1930, breaks away completely with the tradition of a local, deterministic universe. It claims that one can not even know with certainty the position or velocity of a single particle, leave alone the evolution of the entire cosmos. Not only that, QM stipulates that prior to the act of measurement or observation, there is no point in even talking about such physical quantities. An electron could be here, in Andromeda Galaxy, or everywhere. Its behaviour can only be described by a fuzzy haze of probabilities, with no outcome being absolutely certain. Period. While relativity is counter-intuitive at best, QM is downright bizarre and malicious. It shatters our personal, individual conception of reality. God, it would seem, does like to play dice with the universe. And he rolls them blindfolded.
In order to interpret the physical properties of the micro-cosmos, QM uses a construct known as the ‘probability wave’. For example, if we are trying to study the position of an electron, the size of a wave at a given point in space is proportional to the probability that the electron is located at that point. But before the experiment is carried out and once its over, there is no way to determine for sure where it’ll be found. Identical experiments, performed under identical conditions, yield different results which agree with the probability profile of the electron’s probability wave. But is this wave thingamajig something real or just a convenient mathematical model that embodies all that we know and observe about the fundamental particles? Does quantum uncertainty tell us at that any moment particles simply do not possess a definite position?
This deconstruction of reality does not stop here. QM predicts the existence of ‘entangled’ particles that exist in a nebulous haze of uncertainty until one of them is forced to snap out of it when appropriately measured or interacted with. The outcome attained by any one of them is mirrored by each of the other entangled particles instantaneously, irrespective of the amount of space that separates them. If one decides to sport a pair of Ray Ban sunglasses, all the other entangled particles will choose to do so. They could be in two different corners of a room or at opposite ends of a galaxy – it doesn’t matter. This is dark magic or voodoo at its very best!
Naturally, this attack on the fundamental nature of reality did not sit well with Einstein. Over the course of many years, he mounted a series of ever more sophisticated challenges aimed at exposing the lacunae in quantum theory. He once reportedly said, “Do you really believe that the moon is not unless we are looking at it?” The stalwarts of QM were obviously not amused. So Einstein sought to provide a physical argument for this philosophical conundrum. In 1935, he published a paper with two of associates at Princeton – Podolsky and Rosen – which provided a theoretical basis for what has come to be known as the EPR Paradox. Using Heisenberg’s Uncertainty Principle, the authors argued that QM could not be a complete description of the physical reality and that a more fundamental theory is needed to understand it. For instance, it was argued ‘entangled’ particles displayed correlated properties simply because they had ‘hidden variables’ that programmed them to do so. Somewhat similar to two machines coming up with the same results even though they might be separated by a vast distance.
For several years the issue of who was right was left unresolved. Then in the 1960s, the Irish physicist John Bell showed that the debate could be settled experimentally. First in late 1980s and then later on through a series of progressively refined experiments, it has been proven conclusively that ‘spooky’ connections do exist between particles that defy our conventional notion of existence. What happens in Vegas doesn’t just stay there. Something like this should take your breath away! It affirms that a local universe may exist in our mind, but not in reality. What if our universe was nothing but a mirror image of an infinite number of entangled universes? As it is so poetically depicted in the movie Another Earth, is there the possibility that duplicate copies of our ‘selves’ exist? Would our choices mirror theirs?
The world according to the quantum is a strange place indeed. It forces us to abandon the idea of a local universe. It also throws out the window the notion of an objective reality – one that has always existed. The act of observation, hence, becomes closely intertwined with the process of creating the very reality that is being observed. In effect, this theory is incredibly efficient: it explains what you observe with mind boggling accuracy but prevents you from seeing the explanation. And therein lays the problem of reconciling our day to day experience of life with the weird microscopic reality revealed to us by quantum mechanics. Wasn’t life complicated enough to begin with?
Our society is structured according to the way we understand reality. Our definitions of truth, free will, justice are intricately tied to this understanding. To undermine its importance in the context of our own lives is to be deliberately short-sighted. And to ignore its implication, a fool’s paradise. So is that it? Is our reality merely a game of chance? Is Schrödinger’s cat really alive and dead at the same time? In my next article, I will try to dwell upon the different interpretations of quantum mechanics and what promises they hold for our understanding of that most elusive of phantoms – reality.
The first article in this series is available here: http://sleepingtablets.blogspot.com/2011/11/roads-to-reality-einstein-and-faith.html.
PS: If you are interested in the details of the arguments presented in the EPR Paradox, I suggest you read the original paper. It is not very long and Einstein's grouse with quantum theory has been expressed very succinctly. Here is the link to it - http://www.drchinese.com/David/EPR.pdf. Just ignore all the mathematics and concentrate on the parts mentioned on Page 1 and Page 4.
Image Courtesy: http://www.taleas.com/
Our classical sense of intuition tells us that in order to produce a change in a system (read ‘object’ if you are less scientifically minded) on the order side of a football field we will have to somehow negotiate the intervening space. That is what space does. We can shout, send a laser beam, or mail a postcard and wait for the cows to come home. Physicists and philosophers have a word for such a world view – local realism. Local realism posits that an objective reality exists even when it is not being observed and that an object can be influenced only by its immediate surroundings. It’s like what Winston Smith of 1984 would have us believe – “Sanity is not statistical”. Until the first two decades of the 20th century, no scientific development had challenged the locality of our universe. But all this was about to change.
The science of Quantum Mechanics (QM in all future references), developed primarily during the period between 1900 and 1930, breaks away completely with the tradition of a local, deterministic universe. It claims that one can not even know with certainty the position or velocity of a single particle, leave alone the evolution of the entire cosmos. Not only that, QM stipulates that prior to the act of measurement or observation, there is no point in even talking about such physical quantities. An electron could be here, in Andromeda Galaxy, or everywhere. Its behaviour can only be described by a fuzzy haze of probabilities, with no outcome being absolutely certain. Period. While relativity is counter-intuitive at best, QM is downright bizarre and malicious. It shatters our personal, individual conception of reality. God, it would seem, does like to play dice with the universe. And he rolls them blindfolded.
In order to interpret the physical properties of the micro-cosmos, QM uses a construct known as the ‘probability wave’. For example, if we are trying to study the position of an electron, the size of a wave at a given point in space is proportional to the probability that the electron is located at that point. But before the experiment is carried out and once its over, there is no way to determine for sure where it’ll be found. Identical experiments, performed under identical conditions, yield different results which agree with the probability profile of the electron’s probability wave. But is this wave thingamajig something real or just a convenient mathematical model that embodies all that we know and observe about the fundamental particles? Does quantum uncertainty tell us at that any moment particles simply do not possess a definite position?
This deconstruction of reality does not stop here. QM predicts the existence of ‘entangled’ particles that exist in a nebulous haze of uncertainty until one of them is forced to snap out of it when appropriately measured or interacted with. The outcome attained by any one of them is mirrored by each of the other entangled particles instantaneously, irrespective of the amount of space that separates them. If one decides to sport a pair of Ray Ban sunglasses, all the other entangled particles will choose to do so. They could be in two different corners of a room or at opposite ends of a galaxy – it doesn’t matter. This is dark magic or voodoo at its very best!
For several years the issue of who was right was left unresolved. Then in the 1960s, the Irish physicist John Bell showed that the debate could be settled experimentally. First in late 1980s and then later on through a series of progressively refined experiments, it has been proven conclusively that ‘spooky’ connections do exist between particles that defy our conventional notion of existence. What happens in Vegas doesn’t just stay there. Something like this should take your breath away! It affirms that a local universe may exist in our mind, but not in reality. What if our universe was nothing but a mirror image of an infinite number of entangled universes? As it is so poetically depicted in the movie Another Earth, is there the possibility that duplicate copies of our ‘selves’ exist? Would our choices mirror theirs?
The world according to the quantum is a strange place indeed. It forces us to abandon the idea of a local universe. It also throws out the window the notion of an objective reality – one that has always existed. The act of observation, hence, becomes closely intertwined with the process of creating the very reality that is being observed. In effect, this theory is incredibly efficient: it explains what you observe with mind boggling accuracy but prevents you from seeing the explanation. And therein lays the problem of reconciling our day to day experience of life with the weird microscopic reality revealed to us by quantum mechanics. Wasn’t life complicated enough to begin with?
Our society is structured according to the way we understand reality. Our definitions of truth, free will, justice are intricately tied to this understanding. To undermine its importance in the context of our own lives is to be deliberately short-sighted. And to ignore its implication, a fool’s paradise. So is that it? Is our reality merely a game of chance? Is Schrödinger’s cat really alive and dead at the same time? In my next article, I will try to dwell upon the different interpretations of quantum mechanics and what promises they hold for our understanding of that most elusive of phantoms – reality.
The first article in this series is available here: http://sleepingtablets.blogspot.com/2011/11/roads-to-reality-einstein-and-faith.html.
PS: If you are interested in the details of the arguments presented in the EPR Paradox, I suggest you read the original paper. It is not very long and Einstein's grouse with quantum theory has been expressed very succinctly. Here is the link to it - http://www.drchinese.com/David/EPR.pdf. Just ignore all the mathematics and concentrate on the parts mentioned on Page 1 and Page 4.
Image Courtesy: http://www.taleas.com/
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