The Rise and Fall of Positivism

Total Page:16

File Type:pdf, Size:1020Kb

The Rise and Fall of Positivism A Brief History of Science Part 12: The Rise and Fall of Positivism Soumitro Banerjee∗ The Advent of Positivism taste, smell, colour, and other aspects of an apple. But the apple is not a sum- We have seen earlier that post-Renaissance total of these sense experiences about it. development of science relied, to a large It is something else. This, he said, is extent, on empirical evidence in order to the ‘thing-in-itself’, and the aspects that dispel common misconceptions held since we have access to through our sense ex- antiquity. Francis Bacon advised scientists perience constitute, in his language, the to gather empirical data on a large scale. ‘thing-for-us’. He proposed this as a general In order to build a more complex body of concept: in everything that are subjects of knowledge from these direct observations, scientific investigation, there are ‘things-in- he recommended the use of inductive rea- themselves’ and ‘things-for-us’, the former soning (making generalizations based on being unknowable while we try to make individual instances). This approach saw sense of the world through the latter. quite a bit of success in the following century. Thus, the mood of the time was to We have seen that in the early part of the rely on empirical evidence in judging truth. 19th century there was great advancement This line of thinking was formalized by in different branches of science. With that, John Locke and David Hume in England, scientists faced the question of epistemol- by theorizing that all knowledge derives ogy: how do we come to know? What is the from sense experience. This point of view, correct way of knowing, or of investigating called empiricism, says that all concepts phenomena? At that time a viewpoint are about or applicable to things that can developed in continuation of the empiricist be experienced. All rationally acceptable tradition that was to exert enormous in- beliefs or propositions are justifiable or fluence on the scientific community in the knowable only through experience, also latter part of the 19th century. It was called called a posteriori knowledge. positivism. But what is amenable to sense experi- The initial proponent of positivism was ence? In Germany, Immanuel Kant (1724- the French philosopher and social scientist 1804) considered this question. His opinion Auguste Comte (1798-1857) who described was that corporeally existing things, by his ideas in his books ‘The Course in themselves, are not amenable to sense Positive Philosophy’ and ‘A General View of experience; only parts or aspects of it Positivism’. The term ‘positivism’, coined are. For example, we can experience the by Comte, derives from the emphasis on the positive sciences—that is, on tested ∗Dr. Banerjee is a Professor at the Indian Institute of Science Education & Research, and General Secre- and systematized experience rather than tary of Breakthrough Science Society . on undisciplined metaphysical speculation. 24 Breakthrough, Vol.18, No. 3, March 2016 Series Article that we experience. The purpose of science is simply to stick to what we can observe and measure. Knowledge of anything be- yond that, a positivist would hold, is impos- sible. Kant had divided the physical world into things-in-themselves and things-for- us, but believed in existence of the things- in-themselves. Mach went a step further and renounced even formal recognition of real material objects. According to Mach, taking any step beyond what is given by sensory data would tantamount to meta- August Comte (1798-1857) physical speculation. “The materialists, we are told, recognise something unthinkable and unknowable—‘things-in-themselves’— According to him, techniques for investigat- matter ‘outside of experience’ and outside ing phenomena should be based on gather- of our knowledge. They lapse into genuine ing observable, empirical, and measurable mysticism by admitting the existence of evidence, subject to specific principles of something beyond, something transcending reasoning. In the study of social sciences, the bounds of experience and knowledge.” he stressed the adoption of a ‘value-free’ or objective approach to the study of humanity The essence of positivism is to say that shares much in common with meth- that our knowledge of the world, which ods employed in the natural sciences, as starts from our sensations and sense- contrasted with speculation of how things impressions, can never extend to anything should or ought to be. beyond those sense-impressions, and that In the later part of the 19th century, the job of science is simply to correlate the doctrine of positivism was further de- observational data. The famous physicist veloped by Richard Avenarius (1843-1896) Arthur Eddington said that the data of in Switzerland, and especially by the fa- physics consisted in “pointer-readings and mous scientist Ernst Mach (1838-1916) in similar indications”; the physicist could Austria. Their viewpoint is also known as never say what lay behind those observa- empirio-criticism. For them, the answer tions; all he could do, or needed to do, was to the question “How do we know?” was: to state their correlations. The real world we know with the help of our sense per- could never be known to science. The pos- ceptions. Our knowledge about anything itivists opined that science should concern is nothing but a combination of sensations itself only with the ‘observables,’ for, in their received from that thing. The nerves carry opinion, what cannot be observed is not these sensations to the brain, and the brain real. forms perception about that object using As a result, positivists could not accept these signals. That is why, they said, the idea of causality. According to pos- sense experience is the only reliable source itivists, causality is nothing but a useful material for forming knowledge. word to use when correlating observations. They insisted on a strict adherence to But since all we can observe are the re- empirical data. According to them, the goal peated occurrence of events in a definite of knowledge is to describe the phenomena sequence (for example, cloud and rain), Breakthrough, Vol.18, No. 3, March 2016 25 Series Article properties of matter and the interactions between its different forms. The sharp line of difference between the positivists and materialists was that the first group refused to treat anything as real unless it is observ- able, while the second group argued that since matter exists independently of our consciousness, the reality of any concept does not depend on our ability to observe it. The way to reach the underlying reality of phenomena is through theory-building, and by testing the theories objectively. The Development of Science, 1870-1900 Ernst Mach (1838-1916) What was the intellectual climate in the later part of the 19th century? Idealism was science can only document the sequential still very strongly entrenched in common occurrence of events and cannot infer the peoples’ minds. Materialism had overcome existence of any real, objective causal con- the shortcomings of mechanical material- nection. ism and metaphysics, and was spreading On the face of it, the strict adherence among the rationally minded people and to empirical data obtained from sense per- among the scientists. But at the same time ceptions (enhanced with the aid of instru- the positivist philosophy emerged, received ments) seems to be a correct scientific wide publicity, and was gaining prominence standpoint. After all, this can be used as the guiding principle of science. to dispel many unscientific beliefs. To The materialists’ emphasis on objectivity the question “do ghosts exist?”, a scientist helped dispel many unfounded beliefs. The would say “no, because we do not perceive positivist approach gave impetus to exper- a ghost through our sense perception.” imental research and data collection. This That is why, most scientists in the later resulted in many important discoveries and part of the 19th century were swayed by technological inventions in the period from the positivist argument, and this approach 1870 to 1900. Here we list some of the became the de-facto ‘scientific method’. important advancements that occurred in Even though this line of thinking sounds this period. materialistic, in actuality it stands in sharp There was a speculative idea prevalent contrast to materialism. Materialists hold at that time, that the development of an that the universe is composed of matter, individual embryo repeated the same evo- the material world exists independently of lutionary stages of its ancestors. Wilhelm our consciousness, and there is nothing His (1831-1904) rejected this idea and supra-matter in this material world. The sought to discover the physical and chemi- multitude of phenomena which science in- cal causes for embryonic development. His vestigates is nothing but different forms new experimental approach gained many of matter in motion. That is why they followers, who studied the internal re- hold that all truths are to be found in the sponses of an egg to an altered physical 26 Breakthrough, Vol.18, No. 3, March 2016 Series Article environment. Thus, over the period 1875- i.e., the relative velocities, should be differ- 1900, embryology became an experimental ent. In 1887 the American scientists Albert science. Michelson and Edward Morley tried to de- It was a prevalent belief at that time that tect the relative velocity of light using the epidemic diseases were caused by some- motion of the Earth in its orbit employing thing called miasma, a noxious form of ‘bad a very precise spectrometer. They found air’ emanating from rotting organic matter. that the velocity of light through vacuum Louis Pasteur (1822-1895) experimentally is the same irrespective of the motion of showed that this belief was false, and the observer. This result also remained a that most infectious diseases are carried mystery for a long time.
Recommended publications
  • Complementary & the Copenhagen Interpretation
    Complementarity and the Copenhagen Interpretation of Quantum Mechanics Click here to go to the UPSCALE home page. Click here to go to the Physics Virtual Bookshelf home page. Introduction Neils Bohr (1885 - 1962) was one of the giants in the development of Quantum Mechanics. He is best known for: 1. The development of the Bohr Model of the Atom in 1913. A small document on this topic is available here. 2. The principle of Complementarity, the "heart" of Bohr's search for the significance of the quantum idea. This principle led him to: 3. The Copenhagen Interpretation of Quantum Mechanics. In this document we discuss Complementarity and then the Copenhagen Interpretation. But first we shall briefly discuss the general issue of interpretations of Quantum Mechanics, and briefly describe two interpretations. The discussion assumes some knowledge of the Feynman Double Slit, such as is discussed here; it also assumes some knowledge of Schrödinger's Cat, such as is discussed here. Finally, further discussion of interpretations of Quantum Mechanics can be meaningfully given with some knowledge of Bell's Theorem; a document on that topic is here. The level of discussion in what follows is based on an upper-year liberal arts course in modern physics without mathematics given at the University of Toronto. In that context, the discussion of Bell's Theorem mentioned in the previous paragraph is deferred until later. A recommended reference on the material discussed below is: F. David Peat, Einstein's Moon (Contemporary Books, 1990), ISBN 0-8092-4512-4 (cloth), 0-8092-3965-5 (paper). Interpretations of Quantum Mechanics Although the basic mathematical formalism of Quantum Mechanics was developed independently by Heisenberg and Schrödinger in 1926, a full and accepted interpretation of what that mathematics means still eludes us.
    [Show full text]
  • Bohr's Complementarity and Kant's Epistemology
    Bohr, 1913-2013, S´eminairePoincar´eXVII (2013) 145 { 166 S´eminairePoincar´e Bohr's Complementarity and Kant's Epistemology Michel Bitbol Archives Husserl ENS - CNRS 45, rue d'Ulm 75005 Paris, France Stefano Osnaghi ICI - Berlin Christinenstraße 18-19 10119, Berlin, Germany Abstract. We point out and analyze some striking analogies between Kant's transcendental method in philosophy and Bohr's approach of the fundamental issues raised by quantum mechanics. We argue in particular that some of the most controversial aspects of Bohr's views, as well as the philosophical concerns that led him to endorse such views, can naturally be understood along the lines of Kant's celebrated `Copernican' revolution in epistemology. 1 Introduction Contrary to received wisdom, Bohr's views on quantum mechanics did not gain uni- versal acceptance among physicists, even during the heyday of the so-called `Copen- hagen interpretation' (spanning approximately between 1927 and 1952). The `ortho- dox' approach, generally referred to as `the Copenhagen interpretation', was in fact a mixture of elements borrowed from Heisenberg, Dirac, and von Neumann, with a few words quoted from Bohr and due reverence for his pioneering work, but with no unconditional allegiance to his ideas [Howard2004][Camilleri2009]. Bohr's physical insight was, of course, never overtly put into question. Yet many of his colleagues found his reflections about the epistemological status of theoretical schemes, as well as his considerations on the limits of the representations employed by science, ob- scure and of little practical moment { in a word: too philosophical.1 In addition, it proved somehow uneasy to reach definite conclusions as to the true nature of this philosophy.
    [Show full text]
  • 1 Naïve Physics and Quantum Mechanics
    Naïve Physics and Quantum Mechanics: The Cognitive Bias of Everett’s Many-Worlds Interpretation Andrew SID Lang* and Caleb J Lutz Department of Computing and Mathematics, Oral Roberts University, USA *Address correspondence to this author at the Department of Computing and Mathematics, 7777 S. Lewis Ave., Tulsa, OK, 74171 USA. E-mail: [email protected] Keywords: cognitive bias, Everett’s interpretation, naïve physics, quantum mechanics Abstract: We discuss the role that intuitive theories of physics play in the interpretation of quantum mechanics. We compare and contrast naïve physics with quantum mechanics and argue that quantum mechanics is not just hard to understand but that it is difficult to believe, often appearing magical in nature. Quantum mechanics is often discussed in the context of "quantum weirdness" and quantum entanglement is known as "spooky action at a distance." This spookiness is more than just because quantum mechanics doesn't match everyday experience; it ruffles the feathers of our naïve physics cognitive module. In Everett's many- worlds interpretation of quantum mechanics, we preserve a form of deterministic thinking that can alleviate some of the perceived weirdness inherent in other interpretations of quantum mechanics, at the cost of having the universe split into parallel worlds at every quantum measurement. By examining the role cognitive modules play in interpreting quantum mechanics, we conclude that the many-worlds interpretation of quantum mechanics involves a cognitive bias not seen in the Copenhagen interpretation. Introduction Neils Bohr said of quantum mechanics, “Those who are not shocked when they first come across quantum theory cannot possibly have understood it.” [1] When one first learns about quantum mechanics, it appears to be a theory that cannot be describing reality.
    [Show full text]
  • Bacciagaluppi CV
    Guido Bacciagaluppi: Curriculum Vitae and List of Publications 1 December 2020 Born Milan (Italy), 24 August 1965. Italian citizen. Freudenthal Instituut Postbus 85.170 3508 AD Utrecht The Netherlands Email: [email protected] Tel.: +31 (0)30 253 5621 Fax: +31 (0)30 253 7494 Web: https://www.uu.nl/staff/GBacciagaluppi/Profile https://www.uu.nl/staff/GBacciagaluppi/Research https://www.uu.nl/staff/GBacciagaluppi/Teaching Research interests My main field of research is the philosophy of physics, in particular the philosophy of quantum theory, where I have worked on a variety of approaches, including modal interpretations (for my PhD), stochastic mechanics, Everett theory, de Broglie-Bohm pilot-wave theory and spontaneous collapse theories, with a special interest in the theory of decoherence. Other special interests include time (a)symmetry, the philosophy of probability, issues in the philosophy of logic, and the topics of emergence, causation, and empiricism. I also work on the history of quantum theory and have co-authored three books on the topic, including a widely admired monograph on the 1927 Solvay conference, and I am a contributor to the recent revival of interest in the figure and work of Grete Hermann. Present positions Academic: • Utrecht University: Associate Professor (UHD1, scale 14), Freudenthal Institute, Departement of Mathematics, Faculty of Science, and Descartes Centre for the History and Philosophy of the Sciences and the Humanities, since September 2015. • SPHERE (CNRS, Paris 7, Paris 1), Paris: Associate Member since April 2015. • Foundational Questions Institute (http://fqxi.org/): Member since February 2015. • Institut d’Histoire et de Philosophie des Sciences et des Techniques (CNRS, Paris 1, ENS), Paris: Associate Member since January 2007.
    [Show full text]
  • On the Art of Scientific Imagination
    On the Art of Scientific Imagination The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Holton, Gerald. 1996. On the Art of Scientific Imagination. Daedalus 125 (2): 183-208. Published Version https://www.jstor.org/stable/20013446? seq=1#metadata_info_tab_contents Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:40508269 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA NOTES FROM THE ACADEMY The text of addresses given at the Stated Meetings of the American Academy of Arts and Sciences are generally printed in the Academy's Bulletin, distributed principally to Fellows and Foreign Honorary Members of the Academy. Because the Bulletin's format is not one designed to accommodate many detailed illustrations, and because the communication delivered by Professor Gerald Holton at the House of the Academy, like others recently given, raised such interest among those who heard it, a decision was made to make it more widely available through publication in the Academy's journal, Dadalus. This practice, followed very occasionally in the past, has much to recommend it and may be pursued more fre quently in the future. [S.R.G.] Gerald Holton On the Art of Scientific Imagination Wver HEN THE ACADEMY S PRESIDENT asked if I would speak on Saint Valentine's Day, I gladly accepted the honor.
    [Show full text]
  • The Most Dangerous Possible German Algis Valiunas
    Algis Valiunas David M. Buisán (instagram.com/davidmbuisan) 36 ~ The New Atlantis Copyright 2019. All rights reserved. Print copies available at TheNewAtlantis.com/BackIssues. The Most Dangerous Possible German Algis Valiunas What trace of his earthly passage can a man of genius hope will remain after his death? For a great scientist, it is almost certainly a discovery that advances human understanding a step further from ignorance and con- fusion. To uncover some eternal truth that has been carefully concealed from ordinary sight by Nature or whatever gods there be, and to enjoy the lasting esteem accorded the world-altering thinkers — these are the motive forces behind the most serious and accomplished scientific lives. To one who opens new mental continents for further exploration, and exploitation, the supreme accolades rightly belong. Honor of this order is not a paltry thing. Yet John Milton called the craving for fame “that last infirmity of noble mind”; and while such infirmity might easily be forgiven poets, who are notorious for their moral weakness, we have become accustomed to thinking of scientists as free of such all-too-human frailties. Like Aristotle’s theoretical man in the Nicomachean Ethics, scientists are said to live for the unsurpassed pleasure of knowing the highest things in the universe, those that cannot be other than they are. This makes them god- like, so that they need nothing else — certainly not the glint of admiration or envy in other men’s eyes. And yet perfection is not to be expected even from the most high- minded among us.
    [Show full text]
  • The Early Period Klaus Scharnhorst
    Photon-photon scattering and related phenomena. Experimental and theoretical approaches: The early period Klaus Scharnhorst To cite this version: Klaus Scharnhorst. Photon-photon scattering and related phenomena. Experimental and theoretical approaches: The early period. 2020. hal-01638181v4 HAL Id: hal-01638181 https://hal.archives-ouvertes.fr/hal-01638181v4 Preprint submitted on 30 Nov 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. hhal-01638181i Photon-photon scattering and related phenomena. Experimental and theoretical approaches: The early period K. Scharnhorst† Vrije Universiteit Amsterdam, Faculty of Sciences, Department of Physics and Astronomy, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands Abstract We review the literature on possible violations of the superposition prin- ciple for electromagnetic fields in vacuum from the earliest studies until the emergence of renormalized QED at the end of the 1940’s. The exposition covers experimental work on photon-photon scattering and the propagation of light in external electromagnetic fields and relevant theoretical work on non- linear electrodynamic theories (Born-Infeld theory and QED) until the year 1949. To enrich the picture, pieces of reminiscences from a number of (the- oretical) physicists on their work in this field are collected and included or appended.
    [Show full text]
  • Wherefore Quantum Mechanics?†
    Wherefore Quantum Mechanics?† Stephen Boughn⋇ Department of Physics, Princeton University, Princeton NJ Departments of Physics and Astronomy, Haverford College, Haverford PA Abstract After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the truth of the mathematical formalism of quantum mechanics and then proceed to investigate the theory’s implications for the physical world. One of the outcomes has been endless discussions of the quantum measurement problem, wave/particle duality, the non-locality of entangled quantum states, Schrödinger's cat, and other philosophical conundrums. In this essay, I take the point of view that quantum mechanics is a mathematical model, a human invention, and rather than pondering what the theory implies about our world, I consider the transposed question: what is it about our world that leads us to a quantum mechanical model of it? One consequence is the realization that discrete quanta, the quantum of action in particular, leads to the wave nature and statistical behavior of matter rather than the other way around. Preface Richard Feynman famously declared, “I think I can safely say that nobody really understands quantum mechanics.”1 Sean Carroll decried the persistence of this sentiment in a recent opinion piece entitled “Even Physicists Don’t Understand Quantum Mechanics: Worse, they don’t seem to want to understand it.”2 No one doubts the efficacy of quantum theory. The “understanding” to which these physicists refer is an acceptable ontology of the theoretical constructs of quantum mechanics.
    [Show full text]
  • The Concept of Fact in German Physics Around 1900: a Comparison Between Mach and Einstein
    Phys. Perspect. © 2020 The Author(s). This article is an open access publication https://doi.org/10.1007/s00016-020-00256-y Physics in Perspective The Concept of Fact in German Physics around 1900: A Comparison between Mach and Einstein Elske de Waal and Sjang L. ten Hagen* The concept of “fact” has a history. Over the past centuries, physicists have appropriated it in various ways. In this article, we compare Ernst Mach and Albert Einstein’s interpreta- tions of the concept. Mach, like most nineteenth-century German physicists, contrasted fact and theory. He understood facts as real and complex combinations of natural events. Theories, in turn, only served to order and communicate facts efficiently. Einstein’s concept of fact was incompatible with Mach’s, since Einstein believed facts could be theoretical too, just as he ascribed mathematical theorizing a leading role in representing reality. For example, he used the concept of fact to refer to a generally valid result of experience. The differences we disclose between Mach and Einstein were symbolic for broader tensions in the German physics discipline. Furthermore, they underline the historically fluid character of the category of the fact, both within physics and beyond. Key words: Facts; Theory; Ernst Mach; Albert Einstein; Epistemology; Physics. Introduction In recent years, supporters of science have been on the barricades defending the authority of science and its facts. Among the slogans of the 2017 March for Science were expressions such as “trust scientific facts, not alternative facts” and “science is not an alternative fact” (figure 1). The message behind these slogans seems straightforward, but is actually complex when we realize that there have been and still are many different ideas about what a “fact” is.
    [Show full text]
  • Kantian and Neo-Kantian First Principles for Physical and Metaphysical Cognition
    Kantian and Neo-Kantian First Principles for Physical and Metaphysical Cognition Michael E. Cuffaroa, b a University of Western Ontario, Rotman Institute of Philosophy b Ludwig-Maximilians-Universität München, Munich Center for Mathematical Philosophy Abstract I argue that Immanuel Kant’s critical philosophy—in particular the doctrine of tran- scendental idealism which grounds it—is best understood as an ‘epistemic’ or ‘metaphilo- sophical’ doctrine. As such it aims to show how one may engage in the natural sciences and in metaphysics under the restriction that certain conditions are imposed on our cognition of objects. Underlying Kant’s doctrine, however, is an ontological posit, of a sort, regarding the fundamental nature of our cognition. This posit, sometimes called the ‘discursivity thesis’, while considered to be completely obvious and uncontroversial by some, has nevertheless been denied by thinkers both before and after Kant. One such thinker is Jakob Friedrich Fries, an early neo-Kantian thinker who, despite his re- jection of discursivity, also advocated for a metaphilosophical understanding of critical philosophy. As I will explain, a consequence for Fries of the denial of discursivity is a radical reconceptualisation of the method of critical philosophy; whereas this method is a priori for Kant, for Fries it is in general empirical. I discuss these issues in the context of quantum theory, and I focus in particular on the views of the physicist Niels Bohr and the Neo-Friesian philosopher Grete Hermann. I argue that Bohr’s understand- ing of quantum mechanics can be seen as a natural extension of an orthodox Kantian viewpoint in the face of the challenges posed by quantum theory, and I compare this with the extension of Friesian philosophy that is represented by Hermann’s view.
    [Show full text]
  • The Entanglement of Gender and Physics: Human Actors, Work Place Cultures, and Knowledge Production Helene Götschel
    Science Studies 1/2011 The Entanglement of Gender and Physics: Human Actors, Work place Cultures, and Knowledge Production Helene Götschel Research in an area that might be called gender and physics lies neither in the focus of science studies nor in the centre of gender studies. However, there is a rich tradition of interdisciplinary research that studies the entanglement of gender and physics from different perspectives. In this review article, I give a survey on this inadequately discussed research area by presenting selected examples of often-cited as well as internationally less known literature. Furthermore, I propose a systematisation of three different dimensions, comprising research on human actors, work place cultures, and knowledge production in physics. In so doing, I uncover some achievements and gaps of this interdisciplinary research. Following E. F. Keller (1995), I finally plea for a trading zone for scholars working on the entanglement of gender and physics. Keywords: Gender Studies, Gender and Physics, Systematisation Introducing Three Dimensions at natural and technological sciences. The of Analysis in Regards to research areas that study natural science Gender and Physics while stressing feminist and gender issues are often summarized as Gender and The body of this paper is a systematisation Science (e.g., Keller, 1995) or as Feminist of the existing literature on gender and Science Studies (e.g., Mayberry et al., 2001; physics, introducing research on human Wyer et al., 2001). Gender and science or actors, work place cultures, and knowledge feminist science studies can be understood production in physics. In providing this as a research field that covers research review I hope to indicate some of the less on women in natural and technological obvious ways in which physics is gendered.
    [Show full text]
  • Scanned Using Book Scancenter 5033
    15 The Wavefunction 15.1 Between release and detection In the previous chapter, we talked about finding the probability that a j ball released at point P would be detected at point Q. We found out _l‘ how to calculate this probability by assigning an appropriate amplitude arrow to each of the possible paths from P to Q, and then adding up ■ all the arrows. But, what happens if the ball is released at point P and then detected at some other point, say R? (See the figure below.) You know the procedure for finding this probability: enumerate paths from P to R, assign to each path an amplitude arrow using the formula on ^ page 104, and add up all the arrows. It is somewhat more difficult to execute this procedure for the P to R case than it was for the P to Q case, because it lacks the symmetry. Nevertheless it is clear that many of the f same features will apply to both processes: for example, in both cases the largest contribution to the sum amplitude arrow comes from a bundle of paths near the path of minimum length. You might find this problem * technically difficult, but it is conceptually straightforward and you could I do it if you had to. P U Q R T S I But we don’t have to stop here. We could consider having one detector 113 i i 114 15 The Wavefunctìon at Q and another detector at R at the same time. Indeed, we could sprinkle detectors all over the page, at points S, T, U, etc.
    [Show full text]