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MIT 8 01T - Physics – The Foundation of Science

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1 Chapter 1: Physics – The Foundation of Science Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium” suggest that the phenomena of electromagnetism as well as mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, … the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture … to the status of a postulate, and also introduce another postulate, …, namely that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. Albert Einstein, On the Electrodynamics of Moving Bodies1 1.1 The Speed of Light When we observe and measure phenomena in the world, we try to assign numbers to the physical quantities with as much accuracy as we can possibly obtain from our measuring equipment. For example, we may want to determine the speed of light, which we can calculate by dividing the distance a known ray of light propagates over its travel time, speed of light =distancetime. (1.1.1) In 1983 the General Conference on Weights and Measures defined the speed of light to be c = 299, 792, 458 meters/second. (1.1.2) This number was chosen to correspond to the most accurately measured value of the speed of light and is well within the experimental uncertainty. 1.2 International System of System of Units The three quantities – time, length, and the speed of light – are directly intertwined. Which quantities should we consider as “base” and which ones as “derived” from the base quantities? For example, are length and time base quantities while speed is a derived quantity? This question is answered by convention. The basic system of units used throughout science and technology today is the internationally accepted Système International (SI). It consists of seven base quantities and their corresponding base units: 1 A. Einstein, Ann. Physik, 17, 891 (1905); translated by W. Perrett and G.B. Jeffrey, 19223, in The Principle of Relativity, Dover, New York.2 Mechanics is based on just the first three of these quantities, the MKS or meter-kilogram-second system. An alternative metric system to this, still widely used, is the so-called CGS system (centimeter-gram-second). So far as distance and time measurements are concerned, there is also wide use of British Imperial units (especially in the USA) based on the foot (ft), the mile (mi), etc., as units of length, and also making use of the minute, hour, day and year as units of time. Base Quantity Base Unit Length meter (m) Mass kilogram (kg) Time second (s) Electric Current ampere (A) Temperature Kelvin (K) Amount of Substance mole (mol) Luminous Intensity candela (cd) We shall refer to the dimension of the base quantity by the quantity itself, for example dim length ! length ! L, dim mass ! mass ! M, dim time ! time ! T. (1.2.1) 1.3 The Atomic Clock and the Definition of the Second Isaac Newton, in the Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), distinguished between time as duration and an absolute concept of time, “Absolute true and mathematical time, of itself and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year. ”2. The development of clocks based on atomic oscillations allowed measures of timing with accuracy on the order of 1 part in 1014, corresponding to errors of less than one microsecond (one millionth of a second) per year. Given the incredible accuracy of this measurement, and clear evidence that the best available timekeepers were atomic in nature, the second (s) was redefined in 1967 by the International Committee on Weights and Measures as a certain number of cycles of electromagnetic radiation emitted by cesium atoms as they make transitions between two designated quantum states: 2 Isaac Newton. Mathematical Principles of Natural Philosophy. Translated by Andrew Motte (1729). Revised by Florian Cajori. Berkeley: University of California Press, 1934. p. 6.3 The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. 1.4 The meter The meter was originally defined as 1/10,000,000 of the arc from the Equator to the North Pole along the meridian passing through Paris. To aid in calibration and ease of comparison, the meter was redefined in terms of a length scale etched into a platinum bar preserved near Paris. Once laser light was engineered, the meter was redefined by the 17th Conférence Générale des Poids et Mèsures (CGPM) in 1983 to be a certain number of wavelengths of a particular monochromatic laser beam. The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. Example: Light Year Example: Astronomical distances are sometimes described in terms of light-years (ly). A light-year is the distance that light will travel in one year (yr). How far in meters does light travel in one year? Solution: Using the relationship distance = (speed of light) ! (time), one light year corresponds to a distance. Since the speed of light is given in terms of meters per second, we need to know how many seconds are in a year. We can accomplish this by converting units. We know that 1 year = 365.25 days, 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds Putting this together we find that the number of seconds in a year is 1 year = 365.25 day( )24 hours1 day!"#$%&60 min1 hour!"#$%&60 s1 min!"#$%&=31,557,600 s. (1.4.1) So the distance that light travels in a one year is 1 ly =299,792,458 m1 s!"#$%&31,557,600 s1 yr!"#$%&1 yr( )= 9.461 '1015m. (1.4.2) The distance to the nearest star, Alpha Centauri, is three light years. A standard astronomical unit is the parsec.


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MIT 8 01T - Physics – The Foundation of Science

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