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Quantum Entanglement: The discovery, nature, and implications of a peculiar phenomenon

McLeod, Jeffrey

Published Jan 1, 2010• 0 citations
Publisher

Abstract

As an undergraduate just starting to dig a little deeper into my field of study (physics, I’ve learned, becomes much more rewarding the closer one looks at any one of its facets), I first read about the concept of quantum entanglement in Michio Kaku’s Physics of the Impossible. In his attempts to provide some realistic context to popular concepts in science fiction, Kaku introduces entanglement as a “real life” example of teleportation – though of course, as you will read, not in the “Beam me up, Scotty” sense. Thus, spurred by a somewhat naïve fascination as well as a confident desire to learn what I could about this at once intriguing and daunting area of quantum physics, I embarked on what would become one of the most rewarding academic explorations of my time at Goucher so far: I decided to do the final project of my Fall 2009 Modern Physics course on quantum entanglement. When I asked my professor, Dr. Ben Sugerman, what he thought of my topic, he told me somewhat incredulously, “good luck.” Though much of the physics and mathematics behind entanglement was beyond my level at the time, I managed to gain an adequate understanding of the subject using sheer perseverance, and some quality source material as well as encouragement from my friends and mentors. Writing this paper gave me a solid foundation upon which to start my undergraduate course in quantum mechanics the following semester. During that more detailed and intensive course, I gained an even greater respect for the elegance of the more intricate details of quantum theory presented in this paper. It is my hope that some of this elegance might be demonstrated to the reader.

DOI
10.13016/m2nx64

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A Review on Quantum Entanglement

R. Nishanth, Nithya shree, Om Gajanan Patil +2 more

Erwin Schrodinger first used the phrase “quantum entanglement” in 1935 to describe a mechanical phenomenon at the quantum level where two (or more) particles’ quantum states must be defined in relation to one another even if they may be geographically apart. This paradoxical event has confounded us for a very long time. Entangled particle behavior appears to be mysterious, illogical, and akin to sorcery at work. The successful and dependable principle of locality has led us to the achievements of twentieth-century physics. However, some theorists may doubt the locality itself due to the “spooky” and nonlocal effects of the local laws of quantum theory. Could there truly be an instant connection between two subatomic particles located on the extreme edges of the universe? Is there a theory that predicts such a relationship that is fundamentally faulty or lacking? Are the outcomes of the experiments that show this connection being read incorrectly? These questions challenge our most fundamental understanding of space and time. The universe is currently being disassembled by modern physics, and it will never be the same. Utilizing cutting-edge technology, quantum entanglement will have a positive impact on society. The history of quantum entanglement is outlined in this work, along with several hypotheses regarding the puzzling behavior of entangled particles. Quantum entanglement may also be an instance of nonlocality in action, in which what occurs in one location affects what occurs in another. Entanglement can also be compared to a situation in which a light switch is used to control two (or more) light bulbs, causing them to turn on at the same time when the switch is switched on. The key question is whether one of the aforementioned theories actually accounts for the odd behavior of entangled particles, in which case experimental evidence would unquestionably support the theory.

Research & Reviews Journal of Physics•Jan 1, 2022•1 citation

Modern Physics From Relativity to Quantum Mechanics BY Dr. Karunakar Shakampally,Dr. Jyotsna Krishnarao Jumale ,Dr. Ritesh Krishnarao Jumale,Dr Onkar A. Ramdasi

Dr. Karunakar Shakampally,Dr. Jyotsna Krishnarao Jumale ,Dr. Ritesh Krishnarao Jumale,Dr Onkar A. Ramdasi

The field of modern physics represents one of the most profound intellectual revolutions in the history of science. From the groundbreaking insights of relativity to the fascinating and often counterintuitive principles of quantum mechanics, modern physics has reshaped our understanding of space, time, matter, and energy. The book Modern Physics: From Relativity to Quantum Mechanics is a collective effort to present these transformative ideas in a clear, structured, and accessible manner for students, educators, and researchers. This multi-author volume brings together the expertise and academic experience of distinguished scholars who have dedicated their careers to teaching and advancing the field of physics. Each contributor offers a unique perspective, ensuring that the topics are explored with both depth and clarity. The collaborative nature of this work allows for a comprehensive treatment of concepts ranging from the foundations of special and general relativity to the principles governing atomic and subatomic systems. The primary aim of this book is to bridge the gap between classical physics and contemporary scientific developments. It is designed to serve as a foundational text for undergraduate and postgraduate students, while also acting as a reference for researchers and educators. Care has been taken to present theoretical concepts alongside practical applications, enabling readers to appreciate both the elegance and utility of modern physics. The chapters are organized in a logical progression, beginning with the limitations of classical physics and the emergence of relativity, followed by an in-depth exploration of quantum theory, atomic structure, and advanced topics in modern physics. Mathematical rigor is balanced with conceptual explanations, making the content both challenging and approachable. We would like to express our sincere gratitude to all contributors for their dedication and scholarly input. Their combined efforts have made this book a rich and valuable resource. We also extend our appreciation to academic institutions, colleagues, and students whose feedback and encouragement have played a crucial role in shaping this work. It is our hope that this book will inspire curiosity, foster critical thinking, and serve as a stepping stone for further exploration in the fascinating world of modern physics. As the field continues to evolve, we trust that readers will find in these pages both a solid foundation and a source of inspiration for future discoveries.

•Apr 5, 2026•0 citations

Could Feynman Have Said This?

N. David Mermin

Fifteen years ago, I mused in a Reference Frame column on how different generations of physicists differed in the degree to which they thought that the interpretation of quantum mechanics remains a serious problem (Physics Today, Physics Today 0031-9228 42 4 1989 9 https://doi.org/10.1063/1.2810963. April 1989, page 9 ). I declared myself to be among those who feel uncomfortable when asked to articulate what we really think about the quantum theory, adding that "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be "Shut up and calculate!"In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view, but that should be the subject of another column. The subject of this one is the habit of misquotation or misattribution that afflicts our profession, a rather different example of which I pointed out a few months ago (February 2004, page 10).Given my capacity for intellectual development ("inconsistency," in the terminology deployed in the current American political season), it's fortunate that I've now reached an age at which I tend to forget about things I've written more than a few years ago. Indeed, I find it downright irritating when somebody asks me questions about papers I wrote a mere half dozen years ago, naively identifying me with the author of those ancient texts. Until quite recently, I had no memory of ever having written such a childishly brusque dismissal of such an exquisitely subtle point of view, much less of having published it in so widely read a venue.This amnesia, combined with the evolution in my thinking that had distanced me from my long forgotten words, may explain why I was initially somewhat puzzled by the slight sensation of discomfort that passed over me when, browsing the e-print archive earlier this year, I read a characterization of Max Born's probability rule as "the favorite ingredient of what has been nicknamed, after Feynman's famous dictum, the shut up and calculate interpretation of quantum mechanics."I yield to nobody in my admiration for Richard Feynman's aphorisms on the nature of quantum mechanics. Indeed, long ago I published a poem (Physics Today, April 1985, page 47) consisting of nothing more than a resetting as verse of a paragraph Feynman had written about his own attitude toward the quantum theory, in his now (but not then) famous article that launched the whole field of quantum computation. I like to think I have devoured everything Feynman ever wrote on the character of quantum mechanics. But while "shut up and calculate" sounded dimly familiar to me as a characterization of a certain interpretive stance, I couldn't recall where Feynman had written it. Mulling this over, a terrible thought began to dawn on me. Could it be that I myself had once used the phrase? If so, then it would appear that I had picked it up from something by Feynman, forgotten the source, and presented it as my own. Devastating!It was devastating because I have a horror of writing or uttering any witticism that is not original with me, unless I make it absolutely clear where and (if known) from whom I got it. I don't even like to tell jokes unless I've made them up myself. (I digress to offer you my favorite:Question: What is the difference between theoretical physics and mathematical physics? Answer: Theoretical physics is done by physicists who lack the necessary skills to do real experiments; mathematical physics is done by mathematicians who lack the necessary skills to do real mathematics. Mathematical physicists tend not to like this joke, but other physicists seem to. Nonphysicists, of course, are entirely immune to its charms.)So with growing trepidation, I searched through my past writings on quantum mechanics. I was dismayed when I came upon my 1989 column, which confirmed my worst fears. Not only had I appropriated without proper attribution a Feynman quote, but it appeared to be a famous one. How humiliating! I was afflicted with visions of knowledgeable Physics Today readers shaking their heads 15 years ago at what must have struck them as my shameless attempt to ride to literary glory on the unacknowledged shoulders of Feynman.So I went to the Web to find the source, hoping I could then salvage my reputation by persuading Physics Today to print an addendum or erratum. Google gives more than 130 hits containing both "shut up and calculate" and "feynman." Most of these do not directly link the two, but about a dozen do. Here are a few: "Shut up and calculate" was a motto of Richard Feynman.For example, there's Feynman's "shut up and calculate."My personal philosophy is that of the famous physicist Richard Feynman, who said: "Shut up and calculate."When asked which interpretation of QM he favored, Feynman replied "Shut up and calculate."Richard Feynman foreslog ligefrem en "shut up and calculate" fortolkning af kvantemekanikken.Shut up and calculate—Richard Feynman.Just to make sure, I also searched for "shut up and calculate" and "mermin." I found only 10 hits, all of them mentioning me in ways that had nothing to do with their use, elsewhere, of "shut up and calculate." So it would have been clear to the world that I had indeed passed off Feynman's words as my own.Or had I …?I noticed that not a single one of the Web sites attributing the phrase to Feynman cited a source or hinted at the circumstances under which he had said it. A ray of hope flickered on: Could I once again have become a victim of the Matthew effect?The Matthew effect was enunciated by the great sociologist of science, Robert Merton. 1 1. R. K. Merton, Science 159, 56 (1968). https://doi.org/10.1126/science.159.3810.56 Merton worked in those innocent days when sociologists were interested only in the behavior of scientists and not in the content of their science. (To be fair to contemporary sociologists of science, I should modify that last phrase to "and not in the manifestations of that behavior in the content of their science.") I first learned of the Matthew effect more than 20 years ago, on the occasion of my first and, perhaps until now, only, victimization at the hands of the New York Times.I learned the name for what the Times had done to me when I received a very nice note from P. W. Anderson in which he expressed his regret that the newspaper had given him exclusive credit for a nomenclatural advance that was entirely due to me. "A depressingly typical example of the Matthew effect" was how he characterized the misattribution. (I reported the entire history of this contretemps in these pages back in those dark ages [April 1981, page 46] before there were Reference Frame columns.) When I wrote back asking him what the Matthew effect was, he referred me to Merton.It was Merton who identified and named the tendency always to assign exclusive scientific credit to the most eminent among all the plausible candidates. At least I hope it was he, though I'm sure Merton, who invented many wonderful jokes himself, would have been delighted if the credit for it turned out to be misattributed to him. Merton named the effect after the Gospel According to Matthew, because there it is written, For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath.—Matthew 25:29.Could the widespread attribution of my wretched witticism to Feynman be another instance of this same deplorable practice? Had I once again been matthewed?Although I didn't say so in my old Reference-Frame article, what inspired this not so terribly bon mot were vivid memories of the responses my conceptual inquiries elicited from my professors—whom I viewed as agents of Copenhagen—when I was first learning quantum mechanics as a graduate student at Harvard, a mere 30 years after the birth of the subject. "You'll never get a PhD if you allow yourself to be distracted by such frivolities," they kept advising me, "so get back to serious business and produce some results." "Shut up," in other words, "and calculate." And so I did, and probably turned out much the better for it. At Harvard, they knew how to administer tough love in those olden days.This bit of history is relevant to the question of whether Feynman's abundance might have been augmented by a portion of the little that I had. Can you imagine the young Feynman ever having had a similar experience that seared "shut up and calculate" into his tender consciousness? No, of course you can't! Nobody could ever have had the slightest reason to direct the best human calculator that ever was to shut up and calculate.But perhaps Feynman was offering such advice to others who were searching for a better understanding of the quantum mechanical formalism. I can't believe that. He said that he "always had a great deal of difficulty understanding the world view that quantum mechanics represents," and added, "I still get nervous with it." 2 2. R. P. Feynman, Int. J. Theor. Phys. 21, 471 (1982). https://doi.org/10.1007/BF02650179 Nobody who felt that way would ever respond with "shut up and calculate" to conceptual inquiries from the perplexed.Well maybe Feynman, like me, was merely dismissing an interpretive position of others by lampooning it as a "shut up and calculate interpretation." I find this unlikely. For one thing, his strong preference for working things out for himself and, of course, his well-known disdain for philosophy make me doubt that he ever paid much attention to the interpretive positions of others. For another, would one for whom calculation was so effortless and understanding so important be likely to translate anybody's admonition against fruitless speculation into such terms?In short, I suspect that it is only Feynman's habitual irreverence that has linked him in the minds of many to the phrase "shut up and calculate." Who else among the high and mighty—and Merton has taught us that it is only among the high and mighty that people tend to look—could have said it? Albert Einstein? Don't be silly. Erwin Schrödinger? Of course not. Niels Bohr? Don't make me laugh. None of them besides Feynman could have said it. Does that mean that Feynman said it? No!Broaden the search to embrace the low and powerless. Among them am I, who hereby put forth the hypothesis that I was the first to use "shut up and calculate" in the context of quantum foundations. I'm not proud of having said it. It's not a beautiful phrase. It's not very clever. It's snide and mindlessly dismissive. But, damn it, if I'm the one who said it first, then that means I did not, even unconsciously, appropriate the words of Richard Feynman and pass them off as my own. So I have nothing to be ashamed of other than having characterized the Copenhagen interpretation in such foolish terms—a lesser offense than unconscious plagiarism, in my moral bookkeeping.So, dear reader, if you have evidence that Feynman really did say "shut up and calculate," please send it to me. I will not be happy to receive it. I'd rather be a Matthew victim than a plagiarist. But I'd like to know the truth.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. R. K. Merton, Science 159, 56 (1968). https://doi.org/10.1126/science.159.3810.56 , Google ScholarCrossref, ISI2. R. P. Feynman, Int. J. Theor. Phys. 21, 471 (1982). https://doi.org/10.1007/BF02650179 , Google ScholarCrossref, ISI© 2004 American Institute of Physics.

Physics Today•May 1, 2004•133 citations

Quantum Entanglement: A Comprehensive and In-Depth Study of Theory, Experiments, Methodology, and Applications

Rajesh Kumar Verma

Quantum Entanglement-one of the weirdest and most exciting aspects of quantum mechanics. Two or more particles become entangled in a way that if the state of one of the particles is measured, then instantaneously the state of another particle is determined even if they are far apart from one another. The content of this paper explores the details of quantum entanglement: where it came from, what the basic principles are, what experiments support this notion, and what experiments we use to study entanglement. The trends of the data are laid out and what it signifies. From here, I then move to what effects quantum entanglement will have on quantum computing, cryptography and communication. I will attempt to justify my arguments through thirteen published academic sources prior to 2019.

International Journal of Advanced Research in Science Communication and Technology•Dec 30, 2020•0 citations

Entanglements

William C. Schieve, Lawrence Paul Horwitz

Introduction We will now turn to quantum entanglements and their contemporary, possibly practical, interest. Entanglements, first discussed in the E.P.R. paradox (Einstein, Podolsky, Rosen, 1935) are a perplexing nonlocal feature of quantum mechanics. This was immediately and succinctly discussed by Schrödinger (1935). The long history of this apparent paradox is outlined in the wonderful book of Jammer (1974). We will not focus on the central issue of “hidden variables” and their resolution by the Bell inequalities (Bell, 1964) and the test, nor the failure, of these in experiment (see Fry, 1998). The distinctive quantum nature of entanglements has led to two quantum effects which we will discuss: quantum information teleportation (Zeilenger, 1998) and quantum computation by means of entangled states. A nice, recent, elementary introduction to the latter is in the Los Alamos reports of James and Kwiat (2002). The quantum correlations or entanglements are sensitive to environmental destruction. This was pointed out early by Zurek, who termed this “decoherence.” The loss of coherence may occur on a short time scale. Recent discussions have been given by Zurek (2002, 2003). We have already given a theoretical example early in Chapter 2. It is pertinent to discuss this here, since it is a property of opensystem quantum master equations that is a central part of our study in this book. In a sense, the decoherence of correlations has turned out to be a “practical” application of these theoretical notions. Are there remedies for unwanted decoherence? Quantum error correction is a possibility. This will be mentioned also. Entanglements: foundations Following the reading of the E.P.R. paper, Schrödinger (1935b) quickly repeated the argument from quantum theory, but more generally. He introduced the term “entanglement” to describe what he seemed to agree was a curious, if not unacceptable, property. Let us follow his point of view. Given a state ψ ( x, y ) of a composite system of particles x and y formed in their mutual interaction. ψ ( x , y ) is not a product state.

Cambridge University Press eBooks•Apr 16, 2009•0 citations

Theoretical studies for experimental implementation of quantum computing with trapped ions

Bryce Yoshimura

Certain quantum many-body physics problems, such as the transverse field Ising model are intractable on a classical computer, meaning that as the number of particles grows, or spins, the amount of memory and computational time required to solve the problem exactly increases faster than a polynomial behavior.However, quantum simu-I would like to thank my advisor, Professor James Freericks, for all the help and guidance he provided me throughout my time at Georgetown University.I know I am not the easiest person to work with and I imagine at times it was frustrating.I have learned a significant amount about quantum computing with trapped ions, unfortunately one thing that I still need to work on is my atrocious writing.Beyond the opportunity of doing research with Professor Freericks, he has also given me the opportunity to mentor many undergraduates.I have enjoyed every minute of my work.It has been a privilege and an honor working with you.Of course, I would not have gotten as far as I did without the help from my fellow classmates.Thanks to my classmates: Alan Pasha Tabatabai, Khadijeh "Sona" Najafi, and Oliver Albertini, who got me through the first and second year courses.I passed solid state II and the comprehensive exam because of these three classmates.As for the older graduate students, thanks to Jesús Cruz-Rojas who helped me stay motivated during my research blues stage.Although, we were quite prone to discussing random algorithms and other projects that did not have anything to do with our research.

Georgetown University-Graduate School of Arts & Sciences•Jan 1, 2016•0 citations
As an undergraduate just starting to dig a little deeper into my field of study (physics, I’ve learned, becomes much more rewarding the closer one looks at any one of its facets), I first read about the concept of quantum entanglement in Michio Kaku’s Physics of the Impossible. In his attempts to provide some realistic context to popular concepts in science fiction, Kaku introduces entanglement as a “real life” example of teleportation – though of course, as you will read, not in the “Beam me up, Scotty” sense. Thus, spurred by a somewhat naïve fascination as well as a confident desire to learn what I could about this at once intriguing and daunting area of quantum physics, I embarked on what would become one of the most rewarding academic explorations of my time at Goucher so far: I decided to do the final project of my Fall 2009 Modern Physics course on quantum entanglement. When I asked my professor, Dr. Ben Sugerman, what he thought of my topic, he told me somewhat incredulously, “good luck.” Though much of the physics and mathematics behind entanglement was beyond my level at the time, I managed to gain an adequate understanding of the subject using sheer perseverance, and some quality source material as well as encouragement from my friends and mentors. Writing this paper gave me a solid foundation upon which to start my undergraduate course in quantum mechanics the following semester. During that more detailed and intensive course, I gained an even greater respect for the elegance of the more intricate details of quantum theory presented in this paper. It is my hope that some of this elegance might be demonstrated to the reader.
Erwin Schrodinger first used the phrase “quantum entanglement” in 1935 to describe a mechanical phenomenon at the quantum level where two (or more) particles’ quantum states must be defined in relation to one another even if they may be geographically apart. This paradoxical event has confounded us for a very long time. Entangled particle behavior appears to be mysterious, illogical, and akin to sorcery at work. The successful and dependable principle of locality has led us to the achievements of twentieth-century physics. However, some theorists may doubt the locality itself due to the “spooky” and nonlocal effects of the local laws of quantum theory. Could there truly be an instant connection between two subatomic particles located on the extreme edges of the universe? Is there a theory that predicts such a relationship that is fundamentally faulty or lacking? Are the outcomes of the experiments that show this connection being read incorrectly? These questions challenge our most fundamental understanding of space and time. The universe is currently being disassembled by modern physics, and it will never be the same. Utilizing cutting-edge technology, quantum entanglement will have a positive impact on society. The history of quantum entanglement is outlined in this work, along with several hypotheses regarding the puzzling behavior of entangled particles. Quantum entanglement may also be an instance of nonlocality in action, in which what occurs in one location affects what occurs in another. Entanglement can also be compared to a situation in which a light switch is used to control two (or more) light bulbs, causing them to turn on at the same time when the switch is switched on. The key question is whether one of the aforementioned theories actually accounts for the odd behavior of entangled particles, in which case experimental evidence would unquestionably support the theory.
The field of modern physics represents one of the most profound intellectual revolutions in the history of science. From the groundbreaking insights of relativity to the fascinating and often counterintuitive principles of quantum mechanics, modern physics has reshaped our understanding of space, time, matter, and energy. The book Modern Physics: From Relativity to Quantum Mechanics is a collective effort to present these transformative ideas in a clear, structured, and accessible manner for students, educators, and researchers. This multi-author volume brings together the expertise and academic experience of distinguished scholars who have dedicated their careers to teaching and advancing the field of physics. Each contributor offers a unique perspective, ensuring that the topics are explored with both depth and clarity. The collaborative nature of this work allows for a comprehensive treatment of concepts ranging from the foundations of special and general relativity to the principles governing atomic and subatomic systems. The primary aim of this book is to bridge the gap between classical physics and contemporary scientific developments. It is designed to serve as a foundational text for undergraduate and postgraduate students, while also acting as a reference for researchers and educators. Care has been taken to present theoretical concepts alongside practical applications, enabling readers to appreciate both the elegance and utility of modern physics. The chapters are organized in a logical progression, beginning with the limitations of classical physics and the emergence of relativity, followed by an in-depth exploration of quantum theory, atomic structure, and advanced topics in modern physics. Mathematical rigor is balanced with conceptual explanations, making the content both challenging and approachable. We would like to express our sincere gratitude to all contributors for their dedication and scholarly input. Their combined efforts have made this book a rich and valuable resource. We also extend our appreciation to academic institutions, colleagues, and students whose feedback and encouragement have played a crucial role in shaping this work. It is our hope that this book will inspire curiosity, foster critical thinking, and serve as a stepping stone for further exploration in the fascinating world of modern physics. As the field continues to evolve, we trust that readers will find in these pages both a solid foundation and a source of inspiration for future discoveries.
Fifteen years ago, I mused in a Reference Frame column on how different generations of physicists differed in the degree to which they thought that the interpretation of quantum mechanics remains a serious problem (Physics Today, Physics Today 0031-9228 42 4 1989 9 https://doi.org/10.1063/1.2810963. April 1989, page 9 ). I declared myself to be among those who feel uncomfortable when asked to articulate what we really think about the quantum theory, adding that "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be "Shut up and calculate!"In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view, but that should be the subject of another column. The subject of this one is the habit of misquotation or misattribution that afflicts our profession, a rather different example of which I pointed out a few months ago (February 2004, page 10).Given my capacity for intellectual development ("inconsistency," in the terminology deployed in the current American political season), it's fortunate that I've now reached an age at which I tend to forget about things I've written more than a few years ago. Indeed, I find it downright irritating when somebody asks me questions about papers I wrote a mere half dozen years ago, naively identifying me with the author of those ancient texts. Until quite recently, I had no memory of ever having written such a childishly brusque dismissal of such an exquisitely subtle point of view, much less of having published it in so widely read a venue.This amnesia, combined with the evolution in my thinking that had distanced me from my long forgotten words, may explain why I was initially somewhat puzzled by the slight sensation of discomfort that passed over me when, browsing the e-print archive earlier this year, I read a characterization of Max Born's probability rule as "the favorite ingredient of what has been nicknamed, after Feynman's famous dictum, the shut up and calculate interpretation of quantum mechanics."I yield to nobody in my admiration for Richard Feynman's aphorisms on the nature of quantum mechanics. Indeed, long ago I published a poem (Physics Today, April 1985, page 47) consisting of nothing more than a resetting as verse of a paragraph Feynman had written about his own attitude toward the quantum theory, in his now (but not then) famous article that launched the whole field of quantum computation. I like to think I have devoured everything Feynman ever wrote on the character of quantum mechanics. But while "shut up and calculate" sounded dimly familiar to me as a characterization of a certain interpretive stance, I couldn't recall where Feynman had written it. Mulling this over, a terrible thought began to dawn on me. Could it be that I myself had once used the phrase? If so, then it would appear that I had picked it up from something by Feynman, forgotten the source, and presented it as my own. Devastating!It was devastating because I have a horror of writing or uttering any witticism that is not original with me, unless I make it absolutely clear where and (if known) from whom I got it. I don't even like to tell jokes unless I've made them up myself. (I digress to offer you my favorite:Question: What is the difference between theoretical physics and mathematical physics? Answer: Theoretical physics is done by physicists who lack the necessary skills to do real experiments; mathematical physics is done by mathematicians who lack the necessary skills to do real mathematics. Mathematical physicists tend not to like this joke, but other physicists seem to. Nonphysicists, of course, are entirely immune to its charms.)So with growing trepidation, I searched through my past writings on quantum mechanics. I was dismayed when I came upon my 1989 column, which confirmed my worst fears. Not only had I appropriated without proper attribution a Feynman quote, but it appeared to be a famous one. How humiliating! I was afflicted with visions of knowledgeable Physics Today readers shaking their heads 15 years ago at what must have struck them as my shameless attempt to ride to literary glory on the unacknowledged shoulders of Feynman.So I went to the Web to find the source, hoping I could then salvage my reputation by persuading Physics Today to print an addendum or erratum. Google gives more than 130 hits containing both "shut up and calculate" and "feynman." Most of these do not directly link the two, but about a dozen do. Here are a few: "Shut up and calculate" was a motto of Richard Feynman.For example, there's Feynman's "shut up and calculate."My personal philosophy is that of the famous physicist Richard Feynman, who said: "Shut up and calculate."When asked which interpretation of QM he favored, Feynman replied "Shut up and calculate."Richard Feynman foreslog ligefrem en "shut up and calculate" fortolkning af kvantemekanikken.Shut up and calculate—Richard Feynman.Just to make sure, I also searched for "shut up and calculate" and "mermin." I found only 10 hits, all of them mentioning me in ways that had nothing to do with their use, elsewhere, of "shut up and calculate." So it would have been clear to the world that I had indeed passed off Feynman's words as my own.Or had I …?I noticed that not a single one of the Web sites attributing the phrase to Feynman cited a source or hinted at the circumstances under which he had said it. A ray of hope flickered on: Could I once again have become a victim of the Matthew effect?The Matthew effect was enunciated by the great sociologist of science, Robert Merton. 1 1. R. K. Merton, Science 159, 56 (1968). https://doi.org/10.1126/science.159.3810.56 Merton worked in those innocent days when sociologists were interested only in the behavior of scientists and not in the content of their science. (To be fair to contemporary sociologists of science, I should modify that last phrase to "and not in the manifestations of that behavior in the content of their science.") I first learned of the Matthew effect more than 20 years ago, on the occasion of my first and, perhaps until now, only, victimization at the hands of the New York Times.I learned the name for what the Times had done to me when I received a very nice note from P. W. Anderson in which he expressed his regret that the newspaper had given him exclusive credit for a nomenclatural advance that was entirely due to me. "A depressingly typical example of the Matthew effect" was how he characterized the misattribution. (I reported the entire history of this contretemps in these pages back in those dark ages [April 1981, page 46] before there were Reference Frame columns.) When I wrote back asking him what the Matthew effect was, he referred me to Merton.It was Merton who identified and named the tendency always to assign exclusive scientific credit to the most eminent among all the plausible candidates. At least I hope it was he, though I'm sure Merton, who invented many wonderful jokes himself, would have been delighted if the credit for it turned out to be misattributed to him. Merton named the effect after the Gospel According to Matthew, because there it is written, For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath.—Matthew 25:29.Could the widespread attribution of my wretched witticism to Feynman be another instance of this same deplorable practice? Had I once again been matthewed?Although I didn't say so in my old Reference-Frame article, what inspired this not so terribly bon mot were vivid memories of the responses my conceptual inquiries elicited from my professors—whom I viewed as agents of Copenhagen—when I was first learning quantum mechanics as a graduate student at Harvard, a mere 30 years after the birth of the subject. "You'll never get a PhD if you allow yourself to be distracted by such frivolities," they kept advising me, "so get back to serious business and produce some results." "Shut up," in other words, "and calculate." And so I did, and probably turned out much the better for it. At Harvard, they knew how to administer tough love in those olden days.This bit of history is relevant to the question of whether Feynman's abundance might have been augmented by a portion of the little that I had. Can you imagine the young Feynman ever having had a similar experience that seared "shut up and calculate" into his tender consciousness? No, of course you can't! Nobody could ever have had the slightest reason to direct the best human calculator that ever was to shut up and calculate.But perhaps Feynman was offering such advice to others who were searching for a better understanding of the quantum mechanical formalism. I can't believe that. He said that he "always had a great deal of difficulty understanding the world view that quantum mechanics represents," and added, "I still get nervous with it." 2 2. R. P. Feynman, Int. J. Theor. Phys. 21, 471 (1982). https://doi.org/10.1007/BF02650179 Nobody who felt that way would ever respond with "shut up and calculate" to conceptual inquiries from the perplexed.Well maybe Feynman, like me, was merely dismissing an interpretive position of others by lampooning it as a "shut up and calculate interpretation." I find this unlikely. For one thing, his strong preference for working things out for himself and, of course, his well-known disdain for philosophy make me doubt that he ever paid much attention to the interpretive positions of others. For another, would one for whom calculation was so effortless and understanding so important be likely to translate anybody's admonition against fruitless speculation into such terms?In short, I suspect that it is only Feynman's habitual irreverence that has linked him in the minds of many to the phrase "shut up and calculate." Who else among the high and mighty—and Merton has taught us that it is only among the high and mighty that people tend to look—could have said it? Albert Einstein? Don't be silly. Erwin Schrödinger? Of course not. Niels Bohr? Don't make me laugh. None of them besides Feynman could have said it. Does that mean that Feynman said it? No!Broaden the search to embrace the low and powerless. Among them am I, who hereby put forth the hypothesis that I was the first to use "shut up and calculate" in the context of quantum foundations. I'm not proud of having said it. It's not a beautiful phrase. It's not very clever. It's snide and mindlessly dismissive. But, damn it, if I'm the one who said it first, then that means I did not, even unconsciously, appropriate the words of Richard Feynman and pass them off as my own. So I have nothing to be ashamed of other than having characterized the Copenhagen interpretation in such foolish terms—a lesser offense than unconscious plagiarism, in my moral bookkeeping.So, dear reader, if you have evidence that Feynman really did say "shut up and calculate," please send it to me. I will not be happy to receive it. I'd rather be a Matthew victim than a plagiarist. But I'd like to know the truth.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. R. K. Merton, Science 159, 56 (1968). https://doi.org/10.1126/science.159.3810.56 , Google ScholarCrossref, ISI2. R. P. Feynman, Int. J. Theor. Phys. 21, 471 (1982). https://doi.org/10.1007/BF02650179 , Google ScholarCrossref, ISI© 2004 American Institute of Physics.
Quantum Entanglement-one of the weirdest and most exciting aspects of quantum mechanics. Two or more particles become entangled in a way that if the state of one of the particles is measured, then instantaneously the state of another particle is determined even if they are far apart from one another. The content of this paper explores the details of quantum entanglement: where it came from, what the basic principles are, what experiments support this notion, and what experiments we use to study entanglement. The trends of the data are laid out and what it signifies. From here, I then move to what effects quantum entanglement will have on quantum computing, cryptography and communication. I will attempt to justify my arguments through thirteen published academic sources prior to 2019.
Introduction We will now turn to quantum entanglements and their contemporary, possibly practical, interest. Entanglements, first discussed in the E.P.R. paradox (Einstein, Podolsky, Rosen, 1935) are a perplexing nonlocal feature of quantum mechanics. This was immediately and succinctly discussed by Schrödinger (1935). The long history of this apparent paradox is outlined in the wonderful book of Jammer (1974). We will not focus on the central issue of “hidden variables” and their resolution by the Bell inequalities (Bell, 1964) and the test, nor the failure, of these in experiment (see Fry, 1998). The distinctive quantum nature of entanglements has led to two quantum effects which we will discuss: quantum information teleportation (Zeilenger, 1998) and quantum computation by means of entangled states. A nice, recent, elementary introduction to the latter is in the Los Alamos reports of James and Kwiat (2002). The quantum correlations or entanglements are sensitive to environmental destruction. This was pointed out early by Zurek, who termed this “decoherence.” The loss of coherence may occur on a short time scale. Recent discussions have been given by Zurek (2002, 2003). We have already given a theoretical example early in Chapter 2. It is pertinent to discuss this here, since it is a property of opensystem quantum master equations that is a central part of our study in this book. In a sense, the decoherence of correlations has turned out to be a “practical” application of these theoretical notions. Are there remedies for unwanted decoherence? Quantum error correction is a possibility. This will be mentioned also. Entanglements: foundations Following the reading of the E.P.R. paper, Schrödinger (1935b) quickly repeated the argument from quantum theory, but more generally. He introduced the term “entanglement” to describe what he seemed to agree was a curious, if not unacceptable, property. Let us follow his point of view. Given a state ψ ( x, y ) of a composite system of particles x and y formed in their mutual interaction. ψ ( x , y ) is not a product state.
Certain quantum many-body physics problems, such as the transverse field Ising model are intractable on a classical computer, meaning that as the number of particles grows, or spins, the amount of memory and computational time required to solve the problem exactly increases faster than a polynomial behavior.However, quantum simu-I would like to thank my advisor, Professor James Freericks, for all the help and guidance he provided me throughout my time at Georgetown University.I know I am not the easiest person to work with and I imagine at times it was frustrating.I have learned a significant amount about quantum computing with trapped ions, unfortunately one thing that I still need to work on is my atrocious writing.Beyond the opportunity of doing research with Professor Freericks, he has also given me the opportunity to mentor many undergraduates.I have enjoyed every minute of my work.It has been a privilege and an honor working with you.Of course, I would not have gotten as far as I did without the help from my fellow classmates.Thanks to my classmates: Alan Pasha Tabatabai, Khadijeh "Sona" Najafi, and Oliver Albertini, who got me through the first and second year courses.I passed solid state II and the comprehensive exam because of these three classmates.As for the older graduate students, thanks to Jesús Cruz-Rojas who helped me stay motivated during my research blues stage.Although, we were quite prone to discussing random algorithms and other projects that did not have anything to do with our research.