医学物理学英文版

Chapter One Introduction and Backgrounds to Medical Physics Before introducing what is physics, the aim of learning medical physics should be stressed. This course could help you to reach the following goals: developing your understanding on natural phenomena, accumulating your background knowledge on understanding bio-physics-related problems, helping you to study future courses, and raising your abilities of analyzing questions and solving problems. Why do we study physics? It can be reasoned from two angles. First, physics is one of the fundamental of the sciences. Scientists of all disciplines make use of the ideas of physics, from chemists who study the structure of molecules to paleontologists (古生物学者) who try to reconstruct how dinosaurs walked. Physics is also the foundation of all engineering and technology. No engineer could design any kind of practical device without first understanding the basic principles involved. To design a spacecraft or a better mousetrap, you have to understand the basic laws of physics. As a medical student, you could not make better use of modern medical equipment and even you couldn’t have a better understanding of some causes of diseases without knowing the basic laws of physics. But there’s another reason. The study of physics is an adventure. You will find it challenging, sometimes frustrating, occasionally painful, and often richly rewarding and satisfying. Our present understanding of the physical world has been built on the foundations laid by scientific giants such as Galileo, Newton, Maxwell and Einstein, and their influence has extended far beyond science to affect profoundly the ways in which we live and think. You can share some of the excitement of their discoveries when you learn to use physics to solve practical problems and to gain insight into everyday phenomena. If you have ever wondered why the sky is blue, how radio waves travel through the empty space, how a satellite stays in orbit, how a cardiogram machine works, or how the Nuclear magnetic resonance images are formed, you can find the answers by using fundamental physics. Above all, you will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves.    In this opening chapter, we will go over some important preliminaries (预备知识) that will need to go throughout our study. We will discuss the nature of physical theory and the use of idealized models to represent physical systems. We’ll introduce the system of units used to describe physical quantities and discuss ways to describe the accuracy of a number. We’ll look at examples of problems for which we can’t (or do not want to) find a precise answer, but for which rough estimates can be useful and interesting. Finally we’ll study several aspects of vectors and vector algebra. Vectors will be needed throughout our study of physics to describe and analyze physical quantities, such as velocity and force, which have directions as well as magnitudes.  §1.1 Introduction to physics Physics is an experimental science. Everything we know about the physical world and about the principles that govern its behavior has been learned through observations of the phenomena of nature. The ultimate test of any physical theory is its agreement with observations and measurements of physical phenomena. Thus physics is inherently (固有地,本来地) a science of measurement. In this section, the concepts of physics, the relations between physics and medical science and the significance of learning Medical Physics will be discussed. What is science? Science is the systematic study of the nature and behavior of the material and physical universe, based on observation experiment and measurement, and the formulation of laws to describe these facts in general terms. On the other hand, science attempts to explain natural phenomena that can be detected with our senses or by instruments designed to extend our senses, such as a telescope. What is physics? (1). Physics is a branch of science that deals with natural laws and processes, and the states and properties of matter and energy. The main goal of physics is to seek out and to understand the basic Laws of nature upon which all physical phenomena depend. (2). Physics is based on mathematics and traditionally includes mechanics, optics (光学), electricity and magnetism, acoustics (声学) and heat. Modern physics, based on quantum theory, includes atomic physics, semiconductor physics, nuclear physics, laser physics, particle physics and solid-state physics. What is medical physics? Medical Physics is the cross subject between the medical science and modern physics. Our textbook is so called Medical physics, but it is not matched to the definition world-wide. According to the contents in our textbook, it should be called “Fundamental physics and its applications to medical science”. The methods used in physical studies Set up Models Observations and measurements No good measurements to test theories theories, laws and principles good New theories, laws and principles What is the difference among model, theory and law? The phenomena of nature are seldom simple; often a phenomenon involves several interrelated principles, and the relationships can be extremely complex. Often one must make simplifying assumptions and approximations in order to facilitate analysis of such a phenomenon and to focus attention on its most significant aspects. This process of simplifying and idealizing is called making a model, and models play an essential role in applications of principles of physics. Here is an example. A baseball is thrown into the air, and we want to calculate where it lands and with what velocity. The ball has a somewhat irregular surface; it is spinning as well as moving through the air. It is affected by the force of gravity, which decrease slightly as the ball ascends. Additional effects are caused by air resistance (friction) and by buoyancy in the air. There may be variable air currents that complicate these effects further. Clearly, the analysis is hopelessly complicated if we try to include all these effects; we need to make a simplified model. If we approximate the as a uniform sphere and assume it moves through still air, we can calculate the air resistance and the buoyant forces, although these are still complex. The buoyant forces are usually much smaller than the force of gravity, and if the ball moves slowly enough the friction force is also small, so we may wish to omit these completely. We may feel that the shape and spinning motion are irrelevant for overall description of motion; if so we can pretend that the ball is a particle (a point mass without any size, shape or spin). Finally we can assume that the gravitational force is a constant during the motion. Then at last the problem is simple enough to permit detailed analysis. When scientists are trying to understand a particular set of phenomena, they often make use of a model which is a kind of analogy or mental image of the phenomena in term of something we are familiar with. For example: Wave model of light and planetary model of atoms. Scientific theory, as used in physics, is plausible principle offered to explain a physical phenomenon. In order to explain a particular phenomenon, a scientist constructs a model that leads to a theory designed to explain the phenomenon. Theory leads to predictions that can then be tested by experiments to see if there is agreement with the phenomenon. In science, the term Law is applied to certain statements that are found to be valid over a large range of observed phenomena. An example of a scientific law is the law of universal gravitation. Scientific laws are descriptive in that they “describe how nature does behave” as compared to a traffic law which tells us how we should behave. Physics and its relations to other fields Physics has been applied to many other fields and a lot of new subjects based on physics are formed such as chemical physics, physical chemistry, biophysics (生物物理学), astrophysics （天体物理学）, geophysics 地球物理学）, medical physics (医学物理学)and so on. The application of physics to the medical science is the main branch of physics applications to other fields. The physical applications to medical science are such that ultrasound （超声波）, X-rays （X－射线）, optical microscope (光学显微镜), electronic microscope (电子显微镜), NMR-CT (Nuclear Magnetic Resonance - Computerized Tomography 核磁共振-计算机化X射线层面摄影术)， Low temperature technology (低温技术)，microwave (微波)，Laser (激光) and so on. CT－Scanner is an X-ray machine which can produce stereographic image (能够产生立体摄影图像的X光机).  §1.2 Physics backgrounds In this subsection, the physical quantities and units, precision and significant figures and scientific notation will be discussed as these concepts are used throughout this course. ● Quantities Any number or set of numbers used for a quantitative description of a physical phenomenon is called “physical quantity”. The measurement of any quantity is made relative to a particular standard or unit. The system used almost exclusively in this book is the Systeme International (SI system of measurement, which is established by the French Academy of Science). In SI units, the unit of length is the meter (m), time is second (s), and mass is kilogram (kg). Length, time, mass, electrical current, temperature, amount of substance, and luminous intensity are base or fundamental quantities. The base unit associated with electric current is Ampere (A), temperature is degrees Kelvin (K), amount of substance is mole (mol.), and luminous intensity is Candela (cd). All other quantities can be derived from the base quantities. The units associated with these derived quantities are called derived units. ● Precision and significant figures Though measurements are important in physics, they can never be made with absolute precision. There is limitation in terms of accuracy in every measurement. This limitation is usually associated with the measuring instrument and human “inability to read the instrument beyond some fraction of the smallest division shown.” Because of this, it is common to include the estimated uncertainty associated with a scientific measurement. Physical quantities obtained from experimental observations always have some uncertainty (不确定性). For example: The length of a table measured by two students with two different tools. One measured part A by a meter stick and he obtained 12.400.01 m, and another student’s result is 3.01040.0001m for part B. What length is the table? The correct answer is 15.410.01m, why? When numbers having uncertainties or errors are used to compute other numbers, these too will be uncertain. It is especially important to understand this when a number obtained from a theoretical prediction. Suppose a student wants to verify the value of , the ratio of circumference to diameter of a circle. The correct value, to ten digits, is 3.141592654. He draws a circle and measures its diameter and circumference to the nearest millimeter, obtaining the values 1351mm and 4241mm, respectively. He calculates these with his pocket calculator and obtains the quotient 3.140740741. Considering his measuring errors, we have the maximum quotient is 425/134=3.17 and minimum 423/136=3.11. Therefore, the result gives 3.140.03. To answer this question we must first recognize that at least the last six digits in the student’s result are meaningless because they imply a greater precision in the result than it is possible with his measurements. The number of meaningful digits in a number is called the number of significant figures (有效数字); for such figure, 12.400.01 m, 1, 2 and 4 are certain and the 0 is the doubtful digit. Calculation must follow the rules of significant figures. In general, no numerical result can have more significant figures than do the numbers from which it is computed. Thus the student’s value of has only three significant figures and should be stated simply as 3.14, or conceivably as 3.141 (rounded to four figures). Within the limit of three significant figures, the student’s value of does agree with the true value. Another example describes that a table is measured with a meter stick, with its length 1.27m and its width 2.13m. What is the area of the table? Area of the table is 1.27 x 2.13 = 2.7051 (m2), but the correct answer has to be 2.71 m2. why? Keeping more significant figures than you should in your result is not only unnecessary, but also it is genuinely wrong because it misrepresents the precision of the results. Such results much be always rounded to keep only the correct significant figures or, in doubtful cases, at most one more. Example 1. What is the percent uncertainty in the measurement ? Solve: the percent uncertainty is Answer: The percent uncertainty in the measurement is 0.79%. ● Order of magnitude: rapid estimating It is sometimes useful to give a rough estimate of the value of a quantity. This estimate is called the order-of-magnitude and this number contains one significant figure and the associate power of ten. For example, one often hears the world population given to the nearest billion. Scientific notation In calculations with very large or very small numbers, significant figure considerations are simplified greatly by use of powers-of-ten notation, sometimes called scientific notation. The distance from the earth to the sun is about 149,000,000,000 m, but to write the number in this form gives no indication of th number of significant figures. Certainly not all 12 are significant! Instead, we write 149,000,000,000 m = 1.49 × 1011 m The number of significant figures is 3. Similar considerations are applicable when very large or very small numbers have to be multiplied or divided. For example, the energy E corresponding to the mass of an electron is given by the equation where c is the speed of light. The appropriate numbers are and  . We find Many pocket calculators use scientific notation, but the students should be able to do such calculations by hand when necessary. Incidentally, it should be noted that the value of c has three significant figures even though two of them are zeros. To great precision, , thus it would not be correct to write the light speed as . How is the length of one meter defined: Question: It is advantageous that base standards (such as for length and time) be accessible (easy to compare to), invariable (do not change), indestructible, and reproducible. Discuss why these are advantageous and whether any of these criteria can be incompatible (不相容的, 矛盾的) with others.