Measurement problem

Abstract: It is demonstrated that neither the arguments leading to inconsistencies in the description of quantum-mechanical measurement nor those “explaining” the process of measurement by means of thermodynamical statistics are valid. Instead, it is argued that the probability interpretation is compatible with an objective interpretation of the wave function.

Abstract: The wavefunction, describing both the wave-like and the particle-like nature of everything in the Universe, is central to quantum theory. Physicists usually learn about it indirectly in tomographic experiments that measure only some aspects of its behaviour. Now a team from Canada's Institute for National Measurement Standards has developed a new and gentle technique that makes it possible to observe the wavefunction directly. They demonstrate the approach by measuring the transverse spatial wavefunction of a single photon. The discovery that the wavefunction can be probed directly provides a tool that could prove useful in a wide range of fields, and raises questions bordering on the philosophical about what the wavefunction actually is. The wavefunction is the complex distribution used to completely describe a quantum system, and is central to quantum theory. But despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition1,2. Rather, physicists come to a working understanding of the wavefunction through its use to calculate measurement outcome probabilities by way of the Born rule3. At present, the wavefunction is determined through tomographic methods4,5,6,7,8, which estimate the wavefunction most consistent with a diverse collection of measurements. The indirectness of these methods compounds the problem of defining the wavefunction. Here we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system. The crux of our method is that the first measurement is performed in a gentle way through weak measurement9,10,11,12,13,14,15,16,17,18, so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method. We show that the concept is universal, being applicable to other degrees of freedom of the photon, such as polarization or frequency, and to other quantum systems—for example, electron spins, SQUIDs (superconducting quantum interference devices) and trapped ions. Consequently, this method gives the wavefunction a straightforward and general definition in terms of a specific set of experimental operations19. We expect it to expand the range of quantum systems that can be characterized and to initiate new avenues in fundamental quantum theory.

Abstract: Preface. Acknowledgements. Section I. Measurement: The Solution Exists. Chapter 1. The Intangibles and the Challenge. Chapter 2. An Intuitive Measurement Habit: Eratosthenes, Enrico & Emily. How an Ancient Greek Measured the Size of the Earth. Estimating: Be like Fermi. Experiments: Not just for adults. Notes on What to Learn from Eratosthenes, Enrico and Emily. Chapter 3. The Illusion of Intangibles: Why Immeasurables Aren't. The Concept of Measurement. The Object of Measurement. The Methods of Measurement. Economic Objections to Measurement. The Broader Objection to the Usefulness of & "Statistics". Ethical Objections to Measurement. Toward A Universal Approach to Measurement. Section II. Before You Measure. Chapter 4. Clarifying the Measurement Problem. Getting the Language Right: What Uncertainty and Risk Really Mean. Examples of Clarification: Lessons for Business from, of all places, Government? Chapter 5. Calibrated Estimates: How Much Do You Know Now? Calibration Exercise. Further Improvements on Calibration. Conceptual Obstacles to Calibration. The Effects of Calibration. Chapter 6. Measuring Risk: Introduction to the Monte Carlo Simulation. An Example for Monte Carlo and Risk. Tools and other Resources for Monte Carlo Simulations. The Risk Paradox. Chapter 7. Measuring the Value of Information. The Chance of Being Wrong and The Cost of Being Wrong: Expected. Opportunity Loss. The Value of Information for Ranges. The Imperfect World: The Value of Partial Uncertainty Reduction. The Epiphany Equation: The Value of a Measurement Changes Everything. Summarizing Uncertainty, Risk and Information Value: The first measurements. Section III. Measurement Methods Chapter 8. The Transition: From What Measure to How to Measure. Tools of Observation: Introduction to the Instrument of Measurement. Decomposition. Secondary Research: Assuming You Weren't the First to Measure It. The Basic Methods of Observation: If One Doesn't Work, Try the Next. Measure Just Enough. Consider the Error. Choose and Design the Instrument Chapter 9. Sampling Reality: How Observing Some Things Tells Us about All Things. Building an Intuition for Random Sampling: The Jelly Bean Example. A Little About Little Samples: A Beer Brewers Approach. The Easiest Sample Statistics Ever. A Sample of Sampling Methods. Measure to the Threshold. Experiment. Seeing Relationships in the Data: An Introduction to Regression Modeling. Chapter 10. Bayes: Adding to What You Know Now. Simple Bayesian. Using Your Natural Bayesian Instinct. Heterogeneous Benchmarking: A "Brand Damage" Application. Getting a Bit More Technical: Bayesian Inversion for Ranges. Section IV. Beyond the Basics. Chapter 11. Preference & Attitudes - The Softer Side of Measurement. Observing Opinions, Values, and the Pursuit of Happiness: The Basics. A Willingness to Pay: Measuring Value via Trade Offs. Putting it all on the Line: Quantifying Risk Tolerance. Quantifying Subjective Tradeoffs: Dealing with Multiple Conflicting Preferences? Keeping the Big Picture in Mind: Profit Maximization vs. Subjective Tradeoffs. Chapter 12. The Ultimate Measurement Instrument - Human Judges. Homo Absurdus: The Weird Reasons Behind Our Decisions. Getting Organized: A Performance Evaluation Example. Surprisingly Simple Linear Models. How to Standardize Any Evaluation: Rasch Models. Removing Human Inconsistency: The Lens Model. Panacea or Placebo?: Questionable Methods of Measurement. Comparing the Methods. Chapter 13. New Measurement Instruments for Management. The 21st Century Tracker: Keeping Tabs with Technology. Measuring the World: The Internet as An Instrument. Prediction Markets: Wall Street Efficiency Applied to Measurements. Chapter 14. A Universal Measurement Method - Applied Information Economics. Bringing the Pieces Together. Case: The Value of The System That Monitors Your Drinking Water. Case: Forecasting Fuel for the Marine Corps. Ideas for Getting Started: A Few Final Examples. Summarizing the Philosophy. Appendix. Calibration Tests. Index.

Abstract: Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system It explains how the fragility of a state of a single quantum system can lead to the classical robustness of states of their correlated multitude; shows how effective `wave-packet collapse' arises as a result of proliferation throughout the environment of imprints of the states of quantum system; and provides a framework for the derivation of Born's rule, which relates probability of detecting states to their amplitude Taken together, these three advances mark considerable progress towards settling the quantum measurement problem