# Superposition & the paradoxes of quantum mechanics

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Superposition & the paradoxes of quantum mechanics phil Jeff Speaks February 5, Some examples of quantum weirdness Color and hardness The two-slit experiment Is superposition paradoxical? Indeterminacy and collapse Another response to superposition Nonlocality Some examples of quantum weirdness 1.1 Color and hardness In the chapter of Quantum Mechanics and Experience which we read, Albert describes two properties, color and hardness, of electrons. There are three important aspects of these two example properties to keep in mind: They are both on/off properties, in the sense that every electron has some color and some hardness, and that here are only two colors, and two hardnesses, that any electron has. It is also important that t The two properties are independent, in the sense that there is no correlation between the color of an electron and its hardness. These properties are also measurable, in the sense that we can test the color of an electron repeatedly, and get the same result each time. The surprising results begin when we see what happens when we try to measure the color and hardness of a single electron. Suppose we measure the color of a bunch of electrons, and then isolate the ones which are white, and then measure their hardness. As expected, since the properties are independent, 1/2 will be hard and 1/2 soft. But now if we go on to measure again the color of the electrons all of which have previously been determined to be white we find that the electrons are now 50% white and 50% black. It appears that something about measuring the hardness of electrons changes their color; what is surprising is that this result is constant including the percentage even if we use very different ways of measuring hardness.

2 The yet more surprising result which Albert discusses on pp comes when we consider experiments like the one that he represents via the following figure: In this box, the entry point at bottom left measures the hardness of entering electrons, and sends the hard ones along the left path, and the soft ones along the right path. At top right the paths converge, and all the electrons exit along line h and s, no matter which path they took through the interior of the box. Given the previous information, consider what results of the following experiments should be: A stream of hard electrons are entered into the box. A stream of soft electrons are entered into the box. A stream of white electrons are entered into the box. A stream of white electrons are entered into the box, with the s route for soft electrons blocked so that only the electrons which take the h route exit the box at top right. What is the difference between the box illustrated above and a simple hardness measuring device? Does the box illustrated become a hardness measuring device when the s route is blocked? Consider the third experiment above, and ask: which route did the electrons which entered the box take? A puzzle is that it seems that there is no good answer to this question. Suppose first that they all took the h route. Then shutting off the s route would have no effect, but it does. Suppose that they all took the s route. Then shutting off the s route would lead to no electrons exiting the box, which is not what we find. This seems to leave the following three options: 1. 1/2 of the electrons took the h route, and 1/2 took the s route. 2. The electrons all took both routes; perhaps, for example, they split in half, with one half taking the s route and the other taking the h route. 3. The electrons all took neither route, but took some third route to the exit of the box. What about these options fails to fit the results of the experiment? 2

3 1.2 The two-slit experiment Another well-known experiment which shows much the same thing as the example of the box above. For a famous description of the two-slit experiment, see the excerpt from the Feynman lectures on physics on the course web site. 2 Is superposition paradoxical? So far, we have some (very) surprising results, but not an explicit paradox. Here is an attempt to formulate one, using again the example of the experiment using the box discussed by Albert: 1. If a series of white electrons is sent through the box, all of them will still be white when they emerge along route h and s. 2. If a series of electrons moves from the entrance of the box to line h and s, one of the following must be true: (i) they all go along route h or (ii) they all go along route s or (iii) some go along route h and the rest along route s or (iv) some go by way of another route. 3. If we block both routes, no electrons arrive at the destination. 4. Option (iv) is false. (3) 5. If we block the s route, the electrons which emerge are 1/2 white and 1/2 black. 6. If a series of electrons go through the box through the h route, they will emerge 1/2 white and 1/2 black. (4,5) 7. Option (i) is false. (1,6) 8. If we block the h route, the electrons which emerge are 1/2 white and 1/2 black. 9. If a series of electrons go through the box through the s route, they will emerge 1/2 white and 1/2 black. (4,8) 10. Option (ii) is false. (1,9) 11. If a series of electrons are passed through the box, some of which go along the s route and some of which go along the h route, the electrons which emerge will be 1/2 white and 1/2 black. (6,9) 12. Option (iii) is false. (1,11) C. No electrons move from the entrance of the box to line h and s. (2,4,7,10,12) The conclusion is about as clearly false as the conclusion can be. (1), (3), (5), and (8) are experimentally verified. (2) is the only other independent premise. So either it is false, or there is some flaw in the reasoning along the way. 2.1 Indeterminacy and collapse So suppose we deny premise (2): maybe it is possible for the electrons to get from the entrance to the box to its exit without out following h, s, or some other route. Admittedly, this is a bit weird; but maybe the truth is that, in some sense or other, the electrons simply fail to have a determinate location as they move through the box. 3

4 One immediate problem with this proposal is that, if we look in the box during an electron s progress, we always find that the electron is in some determinate location. We never find that the electron has vanished, or is somehow spread out in space. A way to bring out this problem is Schrödinger s example of the cat: One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts. (Schrödinger, The present situation in quantum mechanics, 5) One point of this example is that we can t just comfortably isolate quantum behavior in the realm of the very small, since we could, with sufficient ingenuity, rig up connections between events in this realm and observable events, like the death of a cat. But it seems that there is something impossible in the idea of a cat which neither alive nor dead, not somehow in between. A way to respond to this problem is by saying that although the locations of the electrons might be indeterminate, they collapse to a determinate location when certain things, among which are observations, happen. Is this sort of view committed to giving observers an implausible role in determining facts about the observable world? Does a problem still remain with the example of Schrödinger s cat? Does it make sense to say that the cat was neither alive nor dead until someone opened the box to check on it? 2.2 Another response to superposition Can we respond to the above (very small piece of) experimental data without giving up the idea that particles have determine locations at all times? If we look at the argument above, we see that this commits us to accepting (2), which indicates that our only real option is to reject some piece of reasoning employed along the way. One possibility here is to reject the pair of inferences from (4,5) to (6), and (4,8) to (9). In this case, we d be rejecting the move from the premise that we get a certain observational effect by (say) blocking the s route to the conclusion that we would have gotten that same effect from particles which never followed that path even if it had not been blocked. If you think about it, this is a hard inference to reject. Does it make sense to reject it? 3 Nonlocality This is connected to another odd consequence of quantum mechanics, which is more a surprising consequence than a genuine paradox. In quantum mechanics, it s possible for two particles to have properties which are connected in a certain interesting way (called quantum entanglement ). 4

5 Consider two electrons A and B, and the property of having spin up or spin down. In some situations, the wave function will deliver the following result: each of A and B have a 0.5 probability of having spin up and the same chance of having spin down. However, there is a probability of 1 that one of them will have spin up and the other spin down. Now suppose that A and B are far apart, and that we measure electron A and find that it has spin up. On the kind of theory we are discussing, the observation of A has caused a collapse, and that s why the particle is spin up. So far, so good. But now consider the following two plausible assumptions (from the 1935 paper Can quantum-mechanical description of physical reality be considered complete?, by Einstein, Podolsky, and Rosen): If without disturbing the system we can be certain that an object has a certain property, then the object really has that property. If two systems are sufficiently far apart, measuring one (at a time) does not affect the other (at that time). By the second assumption, measuring A does not affect the system of which B is a part, and in particular does not cause a collapse in that system. However, given that we are certain that one of A and B has spin up and the other has spin down, we can now be certain, after measuring A, that B must have spin down. So, by the first assumption, we know that B really is spin down. Does this show us that the second assumption is false? 5

### Paradoxes of special relativity and quantum mechanics

Paradoxes of special relativity and quantum mechanics Today we are turning from metaphysics to physics. As we ll see, certain paradoxes about the nature of space and time result not from philosophical

### Quantum Phenomena and the Theory of Quantum Mechanics

Quantum Phenomena and the Theory of The Mechanics of the Very Small Waseda University, SILS, Introduction to History and Philosophy of Science . Two Dark Clouds In 1900 at a Friday Evening lecture at the

### Split brains, teletransportation, and personal identity

Split brains, teletransportation, and personal identity phil 20229 Jeff Speaks February 14, 2008 1 What is a theory of personal identity?....................... 1 2 Parfit s example of teletransportation........................

### The sorites paradox. phil Jeff Speaks. April 22, 2008

The sorites paradox phil 20229 Jeff Speaks April 22, 2008 1 Some examples of sorites-style arguments... 1 2 Rejecting the initial premise: nihilism..... 3 3 Rejecting one or more of the other premises..

### Albert Einstein s Nightmare before Christmas. The spooky world of quantum light

Albert Einstein s Nightmare before Christmas The spooky world of quantum light Peter J Mosley Christmas Lecture 2012 Department of Physics, University of Bath If all this is true then it means the end

### Last time we had arrived at the following provisional interpretation of Aquinas second way:

Aquinas Third Way Last time we had arrived at the following provisional interpretation of Aquinas second way: 1. 2. 3. 4. At least one thing has an efficient cause. Every causal chain must either be circular,

### Introduction to Quantum Computing

Introduction to Quantum Computing Javier Enciso encisomo@in.tum.de Joint Advanced Student School 009 Technische Universität München April, 009 Abstract In this paper, a gentle introduction to Quantum Computing

### 3-9 EPR and Bell s theorem. EPR Bohm s version. S x S y S z V H 45

1 3-9 EPR and Bell s theorem EPR Bohm s version S x S y S z n P(n) n n P(0) 0 0 V H 45 P(45) D S D P(0) H V 2 ( ) Neumann EPR n P(n) EPR PP(n) n EPR ( ) 2 5 2 3 But even at this stage there is essentially

### What does Quantum Mechanics tell us about the universe?

Fedora GNU/Linux; L A TEX 2ǫ; xfig What does Quantum Mechanics tell us about the universe? Mark Alford Washington University Saint Louis, USA More properly: What do experiments tell us about the universe?

### On the Nature of Measurement in Quantum Mechanics. Abstract. Text

of Measurement in Quantum Mechanics DOUGLAS M. SNYDER LOS ANGELES, CALIFORNIA Abstract A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory

### Unamended Quantum Mechanics Rigorously Implies Awareness Is Not Based in the Physical Brain

Unamended Quantum Mechanics Rigorously Implies Awareness Is Not Based in the Physical Brain Casey Blood, PhD Professor Emeritus of Physics, Rutgers University www.quantummechanicsandreality.com CaseyBlood@gmail.com

### A Modest View of Bell s Theorem. Steve Boughn, Princeton University and Haverford College

A Modest View of Bell s Theorem Steve Boughn, Princeton University and Haverford College Talk given at the 2016 Princeton-TAMU Symposium on Quantum Noise Effects in Thermodynamics, Biology and Information

### VIRGINIA LAW REVIEW IN BRIEF

VIRGINIA LAW REVIEW IN BRIEF VOLUME 96 OCTOBER 25, 2010 PAGES 51 59 ESSAY SCHRÖDINGER S CROSS: THE QUANTUM MECHANICS OF THE ESTABLISHMENT CLAUSE P Joseph Blocher * ERHAPS the most famous character in modern

### DO WE REALLY UNDERSTAND QUANTUM MECHANICS?

DO WE REALLY UNDERSTAND QUANTUM MECHANICS? COMPRENONS-NOUS VRAIMENT LA MECANIQUE QUANTIQUE? VARIOUS INTERPRETATIONS OF QUANTUM MECHANICS IHES, 29 janvier 2015 Franck Laloë, LKB, ENS Paris 1 INTRODUCTION

### A Short Course in Logic Zeno s Paradox

1 Grappling with Good Arguments A Short Course in Logic Zeno s Paradox We ve seen that if we decide that an argument is good then we should be inclined to believe that the ultimate conclusion is true.

### 07. Quantum Mechanics Basics.

07. Quantum Mechanics Basics. Stern-Gerlach Experiment (Stern & Gerlach 1922) magnets splotches sliver atoms detection screen Suggests: Electrons possess 2-valued "spin" properties. (Goudsmit & Uhlenbeck

### QUANTUM SPOOKINESS EPR PARADOX AND BEYOND. Justyna P. Zwolak. February 1, 2013. Oregon State University. 1of18

QUANTUM SPOOKINESS EPR PARADOX AND BEYOND Justyna P. Zwolak Oregon State University February 1, 013 1of18 ALBERT EINSTEIN AND SPOOKY ACTION AT DISTANCE Did not like the probabilistic nature of quantum

### Time and Causation in Gödel s Universe.

Time and Causation in Gödel s Universe. John L. Bell In 1949 the great logician Kurt Gödel constructed the first mathematical models of the universe in which travel into the past is, in theory at least,

### "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". h is the Planck constant he called it

1 2 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". h is the Planck constant he called it the quantum of action 3 Newton believed in the corpuscular

### Spooky action at a distance: 02/07/12 The puzzle of entanglement in quantum theory

Spooky action at a distance: 02/07/12 he puzzle of entanglement in quantum Alan Macdonald Professor Emeritus of Mathematics Luther College Decorah, IA 52101 macdonal@luther.edu I. Action at a Distance.

### they can be scaled up, to thousands or tens of thousands of qubits from their current size of a dozen or so, watch out!

May/June 2008 Riding D-Wave A pioneer of quantum computing asks: Has a Canadian startup really demonstrated a prototype for a working, commercially viable quantum computer? By Seth Lloyd Computers process

### The Philosophy of Quantum Mechanics (II) 1. The Two-Slit Experiment The central problem which the physical theory of quantum mechanics is designed to

The Philosophy of Quantum Mechanics (II) 1. The Two-Slit Experiment The central problem which the physical theory of quantum mechanics is designed to explain is the extraordinary fact that t h e elementary

### PHILOSOPHY 4360/5360 METAPHYSICS

PHILOSOPHY 4360/5360 METAPHYSICS Topic IV: The Nature of the Mind Arguments for (Persisting) Substance Dualism Argument 1: The Modal Argument from Personal Identity This first type of argument is advanced

### THE STATISTICAL TREATMENT OF EXPERIMENTAL DATA 1

THE STATISTICAL TREATMET OF EXPERIMETAL DATA Introduction The subject of statistical data analysis is regarded as crucial by most scientists, since error-free measurement is impossible in virtually all

### Quantum Cryptography

Quantum Cryptography David Thorne November 14, 2002 1 The History of Cryptography Classical digital cryptography is concerned with the problem of providing secure and secret communication over a medium

### The A to B of quantum physics

The A to B of quantum physics Ken Dobson, Ian Lawrence and Philip Britton Insitute of Physics Advancing Physics Project, London, UK The authors describe the way in which quantum physics is introduced in

### PHY1020 BASIC CONCEPTS IN PHYSICS I

PHY1020 BASIC CONCEPTS IN PHYSICS I Jackson Levi Said 14 lectures/tutorials/past paper session Project on one of the interesting fields in physics (30%) Exam in January/February (70%) 1 The Course RECOMMENDED

### You will by now not be surprised that a version of the teleological argument can be found in the writings of Thomas Aquinas.

The design argument The different versions of the cosmological argument we discussed over the last few weeks were arguments for the existence of God based on extremely abstract and general features of

### QUANTUM COMPUTING (AND OTHER SHORTCUTS FOR SOLVING HARD PROBLEMS)

QUANTUM COMPUTING (AND OTHER SHORTCUTS FOR SOLVING HARD PROBLEMS) Lecture 25 CS2110 Spring 2014 The world isn t as simple as it seems! 2 Starting as early as the Greek philosophers, people have wondered

### COMPSCI 111/111G. Quantum Computing. Term 1, 2015. Prepared using LATEX Beamer by Cristian S.Calude 1 / 26

COMPSCI 111/111G Quantum Computing Prepared using LATEX Beamer by Cristian S.Calude Term 1, 2015 1 / 26 Classical vs. Quantum Computers Quantum computing was first introduced by Yuri Manin in 1980 and

### ON THE EINSTEIN PODOLSKY ROSEN PARADOX* ]. S. BELLt Department of Physics, University of Wisconsin, Madison, Wisconsin

Physics Vol. 1, No. 3, pp. 195-290, 1964 Physics Publishing Co. Printed in the United States ON THE EINSTEIN PODOLSKY ROSEN PARADOX* ]. S. BELLt Department of Physics, University of Wisconsin, Madison,

### The argument from evil

The argument from evil Our topic today is the argument from evil. This is by far the most important argument for the conclusion that God does not exist. The aim of at least the simplest form of this argument

### What quantum computing can do for you

What quantum computing can do for you What quantum computing can do for you Inaugural lecture delivered on the appointment to the chair of Theoretical Computer Science at the University of Amsterdam on

### Boonin on the Future-Like-Ours Argument against Abortion. Pedro Galvão Centro de Filosofia da Universidade de Lisboa

Boonin on the Future-Like-Ours Argument against Abortion Pedro Galvão Centro de Filosofia da Universidade de Lisboa David Boonin s recent book 1 is an impressively deep and detailed attempt to establish

### Ghosts. When the same ghost is seen repeatedly in the same house, it is 4 2-1

1 2 Ghosts Have you ever seen a ghost? Do you believe in ghosts? Scientifically accepted proof of the existence of ghosts does not exist. But does this fact alone convince you that ghosts do not exist?

### 1 Now, Why do we want to learn Quantum Mechanics

1 Now, Why do we want to learn Quantum Mechanics Quantum mechanics is a mathematical theory that can be used to predict chemical properties. But this fact has been known since the 1920s, so what s new?

### Test 1: Inference. Directions

Test 1: Inference An inference is a conclusion a person can draw from certain observed or supposed facts. For example, if the lights are on in a house and voices can be heard coming from the house, a person

### Today we begin our discussion of the existence of God.

Aquinas Five Ways Today we begin our discussion of the existence of God. The main philosophical problem about the existence of God can be put like this: is it possible to provide good arguments either

### THE KNOWLEDGE ARGUMENT

Michael Lacewing Descartes arguments for distinguishing mind and body THE KNOWLEDGE ARGUMENT In Meditation II, having argued that he knows he thinks, Descartes then asks what kind of thing he is. Discussions

### Omnipotence & prayer

Omnipotence & prayer Today, we ll be discussing two theological paradoxes: paradoxes arising from the idea of an omnipotent being, and paradoxes arising from the religious practice of prayer. So far, in

### Correlations and Counterfactuals: The EPR Illusion Abstract

Correlations and Counterfactuals: The EPR Illusion Allen Stairs Department of Philosophy, University of Maryland Abstract EPR-type cases seem to trigger a persistent urge to infer measurement counterfactuals

### Skepticism about the external world & the problem of other minds

Skepticism about the external world & the problem of other minds So far in this course we have, broadly speaking, discussed two different sorts of issues: issues connected with the nature of persons (a

### A Game-Theoretic Approach to Metaphysical Reconciliation of Quantum Superposition

370 Original Article A Game-Theoretic Approach to Metaphysical Reconciliation of Quantum Superposition Sukanto Bhattacharya and 1 Kuldeep Kumar Abstract The well-known quantum physical paradox of wave-particle

### Om Mani Padme Hum. 'What is that by knowing which all things are known?' 'What makes my mind think, my

Ravichandran 1 Ram Ravichandran Albert Stetz PH 407H May 25 th, 2004 Om Mani Padme Hum -Mantra Of Avalokiteshvara 'What is that by knowing which all things are known?' 'What makes my mind think, my eyes

### Pascal is here expressing a kind of skepticism about the ability of human reason to deliver an answer to this question.

Pascal s wager So far we have discussed a number of arguments for or against the existence of God. In the reading for today, Pascal asks not Does God exist? but Should we believe in God? What is distinctive

### Inductive Reasoning Page 1 of 7. Inductive Reasoning

Inductive Reasoning Page 1 of 7 Inductive Reasoning We learned that valid deductive thinking begins with at least one universal premise and leads to a conclusion that is believed to be contained in the

### Indirect Measurement

Indirect Measurement Introduction: Modern physics relies heavily on indirectly determining the physical characteristics of objects. The following activities will demonstrate to students that indirect determinations

### Duke Physics 55 Spring 2005 Lecture #31: Experimental Tests of General Relativity

Duke Physics 55 Spring 2005 Lecture #31: Experimental Tests of General Relativity ADMINISTRATIVE STUFF - Friday: Quiz 6, 15 minutes at beginning of class Material: BDSV Ch. 22,S2,S3 (focus on lecture WUN2K)

### Quantum Cryptography

Quantum Cryptography Carlos Borrego Iglesias cborrego@abra.uab.es Department of Information and Communication Engineering Universitat Autònoma de Barcelona Criptografia i seguretat en xarxes Contents 1

### AP Physics B Ch. 23 and Ch. 24 Geometric Optics and Wave Nature of Light

AP Physics B Ch. 23 and Ch. 24 Geometric Optics and Wave Nature of Light Name: Period: Date: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Reflection,

### A Short Course in Logic Example 8

A Short ourse in Logic xample 8 I) Recognizing Arguments III) valuating Arguments II) Analyzing Arguments valuating Arguments with More than one Line of Reasoning valuating If then Premises Independent

### CHAPTER 16: Quantum Mechanics and the Hydrogen Atom

CHAPTER 16: Quantum Mechanics and the Hydrogen Atom Waves and Light Paradoxes in Classical Physics Planck, Einstein, and Bohr Waves, Particles, and the Schrödinger equation The Hydrogen Atom Questions

### Three Pictures of Quantum Mechanics. Thomas R. Shafer April 17, 2009

Three Pictures of Quantum Mechanics Thomas R. Shafer April 17, 2009 Outline of the Talk Brief review of (or introduction to) quantum mechanics. 3 different viewpoints on calculation. Schrödinger, Heisenberg,

### Project description a) What is quantum information theory with continuous variables?

Project description a) What is quantum information theory with continuous variables? According to pre-quantum physics, any theory should display the property of locality defined in three almost equivalent

### Atoms. Is Nature Discrete or Continuous? The Discrete Viewpoint. The discrete unit and the uncertain viewpoint

Atoms The discrete unit and the uncertain viewpoint SC/NATS 1730, XXVII Atoms 1 Is Nature Discrete or Continuous? Is the ultimate reality of nature granular made up of distinct little bits of matter, like

### Spectra in the Lab ATOMS AND PHOTONS

Spectra in the Lab Every chemical element has a unique ``signature'' which can be revealed by analyzing the light it gives off. This is done by spreading the light out into a rainbow of color. It may seem

### REWARD System For Even Money Bet in Roulette By Izak Matatya

REWARD System For Even Money Bet in Roulette By Izak Matatya By even money betting we mean betting on Red or Black, High or Low, Even or Odd, because they pay 1 to 1. With the exception of the green zeros,

### Chapter 42: Quantum Atom

Chapter 42: Quantum Atom Quantum H Atom 1s Wave Function: Radial Probability Density: Most Probable value: 1 ψ1s () r = e π a 3 0 r/ a P(r) = 4πr 2 ψ 2 dp solve dr = 0 0 Average value: rave = r = rp()

### QUANTUM SPIN Doctors

QUANTUM MECHANICS QUANTUM SPIN Doctors Dissect Exotic States of MATTER At the cutting edge of condensed matter research, scientists are using several resources to investigate extraordinary states of matter.

### Probability Using Dice

Using Dice One Page Overview By Robert B. Brown, The Ohio State University Topics: Levels:, Statistics Grades 5 8 Problem: What are the probabilities of rolling various sums with two dice? How can you

### We can represent the eigenstates for angular momentum of a spin-1/2 particle along each of the three spatial axes with column vectors: 1 +y =

Chapter 0 Pauli Spin Matrices We can represent the eigenstates for angular momentum of a spin-/ particle along each of the three spatial axes with column vectors: +z z [ ] 0 [ ] 0 +y y [ ] / i/ [ ] i/

### Does Quantum Mechanics Make Sense? Size

Does Quantum Mechanics Make Sense? Some relatively simple concepts show why the answer is yes. Size Classical Mechanics Quantum Mechanics Relative Absolute What does relative vs. absolute size mean? Why

### Kant s deontological ethics

Michael Lacewing Kant s deontological ethics DEONTOLOGY Deontologists believe that morality is a matter of duty. We have moral duties to do things which it is right to do and moral duties not to do things

### Einstein s Theory of Special Relativity Made Relatively Simple!

Einstein s Theory of Special Relativity Made Relatively Simple! by Christopher P. Benton, PhD Young Einstein Albert Einstein was born in 1879 and died in 1955. He didn't start talking until he was three,

### Elementary Statistics and Inference. Elementary Statistics and Inference. 16 The Law of Averages (cont.) 22S:025 or 7P:025.

Elementary Statistics and Inference 22S:025 or 7P:025 Lecture 20 1 Elementary Statistics and Inference 22S:025 or 7P:025 Chapter 16 (cont.) 2 D. Making a Box Model Key Questions regarding box What numbers

### Quantum Information in the Framework of Quantum Field Theory

Quantum Information in the Framework of Quantum Field Theory Jacques Calmet a1 and Xavier Calmet b2 a Karlsruhe Institute of Technology (KIT, Institute for Cryptography and Security, Am Fasanengarten 5,

### The psychological theory of persons

The psychological theory of persons Last week were discussing dualist views of persons, according to which human beings are immaterial things distinct from their bodies. We closed by discussing some problems

### Category III Physical science examples

Category III Physical science examples Providing variety of phenomena Chemistry That Applies A sufficient number and variety of phenomena are used to support each of the key ideas. For the idea that mass

### Physics in Perspective First Exam (BS version), February 11, 2003

These exams are taken from the spring 2003 offering of the course, written by Julio Gea-Banacloche. In spring 2007, all the students were future teachers, and they all chose the lesson plan option. Physics

### IN THE HANDS OF TIME

MATHS B-DAY 2006 Friday 24 November IN THE HANDS OF TIME The Maths B-Day is sponsored by and Maths B-day 2006-1- Wiskunde B-dag 2006 0 Introduction The maths B-day assignment this year is totally focused

### (Refer Slide Time: 02:17)

Internet Technology Prof. Indranil Sengupta Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture No #06 IP Subnetting and Addressing (Not audible: (00:46)) Now,

### Induction and the Division Theorem 2.1 The Method of Induction

2 Induction and the Division Theorem 2.1 The Method of Induction In the Introduction we discussed a mathematical problem whose solution required the verification of an infinite family of statements. We

### TRANSCRIPT: In this lecture, we will talk about both theoretical and applied concepts related to hypothesis testing.

This is Dr. Chumney. The focus of this lecture is hypothesis testing both what it is, how hypothesis tests are used, and how to conduct hypothesis tests. 1 In this lecture, we will talk about both theoretical

### There is a physics joke about the stages of learning quantum mechanics:

Preface The only way to learn physics is to do physics. However, almost all physics textbooks leave a huge gap between the level of the problems that they solve as examples, and the level of the problems

### Theory of electrons and positrons

P AUL A. M. DIRAC Theory of electrons and positrons Nobel Lecture, December 12, 1933 Matter has been found by experimental physicists to be made up of small particles of various kinds, the particles of

### Solving the Rubik's Revenge (4x4x4) Home Pre-Solution Stuff Step 1 Step 2 Step 3 Solution Moves Lists

Solving your Rubik's Revenge (4x4x4) 07/16/2007 12:59 AM Solving the Rubik's Revenge (4x4x4) Home Pre-Solution Stuff Step 1 Step 2 Step 3 Solution Moves Lists Turn this... Into THIS! To solve the Rubik's

### Computational complexity theory

Computational complexity theory Goal: A general theory of the resources needed to solve computational problems What types of resources? Time What types of computational problems? decision problem Decision

### ON THE EINSTEIN PODOLSKY ROSEN PARADOX* I. Introduction

Physics Vol. 1, No. 3 f pp. 195 200, 1964 Physics Publishing Co. Printed in the United States ON THE EINSTEIN PODOLSKY ROSEN PARADOX* J. S. BELLt Department of Physics, University of Wisconsin, Madison,

### Perception and Mind-Dependence Lecture 4

Perception and Mind-Dependence Lecture 4 1 Last Week The Argument from Illusion relies on the Phenomenal Principle. The Phenomenal Principle is motivated by its ability to explain the sensuous character

### Religion and Science: The Emerging Relationship The Quantum Enigma X

Religion and Science: The Emerging Relationship The Quantum Enigma X The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things

### Slippery Slopes and Vagueness

Slippery Slopes and Vagueness Slippery slope reasoning, typically taken as a fallacy. But what goes wrong? Is it always bad reasoning? How should we respond to a slippery slope argument and/or guard against

### How Subnets Work in Practice. Fred Marshall Coastal Computers & Networks

How Subnets Work in Practice Fred Marshall Coastal Computers & Networks Background There's lots of literature available on how the bit structure of an address can be split up using the subnet mask. Generally,

### Particle control in a quantum world

THE NOBEL PRIZE IN PHYSICS 2012 INFORMATION FOR THE PUBLIC Particle control in a quantum world Serge Haroche and David J. Wineland have independently invented and developed ground-breaking methods for

### But Then They Are Told. Michael Gorman School of Philosophy The Catholic University of America Washington, D.C. 20064 gorman@cua.

1 But Then They Are Told Michael Gorman School of Philosophy The Catholic University of America Washington, D.C. 20064 gorman@cua.edu The argument I want to discuss appears at the very end of the passage,

### u4arg1 side b (Some arguments to analyze) Philosophy and Logic Unit 4 Handout #1

u4arg1 side b (Some arguments to analyze) Philosophy and Logic Unit 4 Handout #1 Jean Jacques Rousseau, Social Contract, I, chap IV. Any limitation of freedom of choice of children by their father must

### Quantum H Atom. solve. P(r) = 4πr 2 ψ 2. 1s Wave Function: Radial Probability Density: Most Probable value: Average value: Probability in (0-r): 1 s

Quantum H Atom 1s Wave Function: Radial Probability Density: 1 1 s () r e a 3 0 r/ a P(r) = 4πr 2 ψ 2 0 Most Probable value: solve dp 0 dr Average value: rave r rp() r dr 0 Probability in (0-r): P r P()

### VLSM CERTIFICATION OBJECTIVES Q&A. Two-Minute Drill Self Test VLSM 8.02 Route Summarization

8 VLSM CERTIFICATION OBJECTIVES 8.01 VLSM 8.02 Route Summarization Q&A Two-Minute Drill Self Test 228 Chapter 8: VLSM In Chapter 7, you were introduced to IP addressing and subnetting, including such topics

### Harvard College Program in General Education Faculty of Arts and Sciences Harvard University. A Guide to Writing in Ethical Reasoning 15

Harvard College Program in General Education Faculty of Arts and Sciences Harvard University A Guide to Writing in Ethical Reasoning 15 A Guide to Writing in Ethical Reasoning 15 Professor Jay M. Harris

### Lecture Notes, October 30. 0. Introduction to the philosophy of mind

Philosophy 110W - 3: Introduction to Philosophy, Hamilton College, Fall 2007 Russell Marcus, Instructor email: rmarcus1@hamilton.edu website: http://thatmarcusfamily.org/philosophy/intro_f07/course_home.htm

### Things a Millian can say about empty names

Things a Millian can say about empty names phil 93914 Jeff Speaks February 6, 2008 A Millian can, but need not, say the same thing about each of the different types of apparently empty names. The best

### or conventional implicature [1]. If the implication is only pragmatic, explicating logical truth, and, thus, also consequence and inconsistency.

44 ANALYSIS explicating logical truth, and, thus, also consequence and inconsistency. Let C1 and C2 be distinct moral codes formulated in English. Let C1 contain a norm N and C2 its negation. The moral

### Images SI, Inc. Staten Island NY tel fax ESP Lamp User Manual

Images SI, Inc. Staten Island NY 10312 718.966.3694 tel 718.966.3695 fax http://www.imagesco.com ESP Lamp User Manual Table of Contents Introduction 2 ESP Lamp Applications 3 History 4 Helmut Schmidt 4

### Proposed experiment to test the non-locality hypothesis in transient light-interference phenomena

Proposed experiment to test the non-locality hypothesis in transient light-interference phenomena Masanori Sato Honda Electronics Co., Ltd., 20 Oyamazuka, Oiwa-cho, Toyohashi, Aichi 441-3193, Japan Abstract

### Perfect being theology and modal truth

Perfect being theology and modal truth Jeff Speaks February 9, 2016 Perfect being theology is the attempt to use the principle that God is the greatest possible being to derive claims about the divine

### This accuracy is open to question for the following reasons:

AN EXPERIMENT TO COMPARE ALTERNATIVE VERIFICATION PROCEDURES FOR MORTALITY MEDICAL CODING Kenneth W. Harris and Dwight K. French National Center for Health Statistics I. Background One of the most difficult

### Physics 115B Lab 4: Radioactivity

Physics 115B Lab 4: Radioactivity In this lab, we will study radioactivity. You probably know a bit, and you will learn more in this course, about the technological, political, and health impacts of radioactivity.

### MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample

MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of