MODERN CONCEPTS IN PHYSICS — LANGMUIR 225 



pendently of all other things. There is, however, as Bridgraan says 

 "no assurance whatever that there exists in nature anything with 

 properties like those assumed in the definition, and physics, when 

 reduced to concepts of this chanicter, becomes lus purely an al)^tract 

 science and as far removed from reality as the abstract geometry of 

 the mathematicians." Nevertheless, these conceptions of space and 

 time prevailed until the relativity theory was proposed. 



In the development of this theory Einstein, in analyzing the con- 

 cepts of space and time, considered wliat means arc available by 

 which an observer can measure distances between two points on a 

 rapidly moving object. For example, imagine two planets moving 

 past each other at high velocity and two observers, one on each 

 planet, provided with means for observing each other and communi- 

 cating with each other; such means, for example, as light signals. 

 Einstein asks, what are the operations by which the two observers 

 could compare their units of length and time? He finds that each 

 observer would logically conclude that the other observer's unit of 

 length is shorter than his own, and that the other's unit of time is 

 longer than his own. Einstein thus proved that there can be no 

 such thing as absolute length or time, or rather proved that the con- 

 cept of absolute time has no meaning, for we have not been able to 

 conceive of any method for determining the absolute time of any 

 event. 



In order to illustrate his thesis Bridgman considers in detail the 

 concept of length. Probably one of the earliest concepts of length 

 was obtained by counting the number of unit lengths that can be 

 placed end to end between two given objects. For example, the 

 number of paces are counted in walking from one object to another. 

 An extension and refinement of this method is employed to-day when 

 the standard meter at the Bureau of Standards is compared with a 

 steel tape and this is then used to lay off a base line for a survey 

 by triangulation. 



As Bridgman suggests, it was one of the greatest discoveries of 

 the human race to find that these operations performed with a 

 measuring rod afford a useful and convenient means of describing 

 natural phenomena. 



During the transition from the earliest pacing of distances, to our 

 modern refined measurements with the meter stick, the concept of 

 length itself must have undergone radical modifications since the 

 operations involved had been modified. For example, if distances are 

 to be paced, it has no meaning to consider distances of Tthsu of a 

 pace unless the concept is modified to include arbitrarily chosen 

 methods by which a length equal to toW of a pace may be deter- 

 mined. In our modern measurements with a steel tape we must 



