## Frames of reference defining a point of view

Whether implicitly or explicitly, physical measurements involving space and time are made from a given perspective, mathematically referred to as a frame of reference. We picture ourselves as 'sitting' at the origin of the frame of reference and all displacements, velocities and momenta are measured with respect to that frame. Of course, normally nobody talks about coordinate systems or reference frames; nevertheless, there is an implication which may not be apparent, but is taken for granted. The results are critically dependent on the reference frame.

Speed in different frames of reference

Let us go back to the moving train. In the example below we might choose any one of many logical frames of reference when

Figure 15.1 What is the ticket collector's 'true' motion?

Figure 15.1 What is the ticket collector's 'true' motion?

describing the motion of the ticket collector as he walks through a carriage of the Orient Express. His speed will depend entirely on our point of view.

The stationmaster's point of view

By saying that 'the train is travelling at a speed of 60 mph' we imply a reference frame outside the train, with its origin fixed perhaps at a railway station. The observer might be the stationmaster standing on the platform. From the perspective of the stationmaster, the conductor, who is walking forwards on the train, is moving that bit faster than the train; his velocity is 62 mph.

The passenger's point of view

The conductor is walking towards the front of the train at 2 mph implies a reference frame situated in the carriage. The observer could be a passenger sitting somewhere in the carriage. Of course, in the frame of reference of the passenger, the passenger himself is stationary, while the stationmaster, and indeed the whole station, are moving at 60 mph in the opposite direction.

The ticket collector's point of view

The ticket collector equally is entitled to view things from his own perspective, in which he is stationary and everyone else is moving (although he is probably too modest to consider himself as defining the frame of reference). Nevertheless, from his point of view the stationmaster has whizzed backwards and passed him at 62 mph while the passenger is receding more slowly, at 2 mph.

### A universal point of view

Finally, the whole scenario could be expressed from the point of view of an astronaut whose frame of reference is outside the earth, or indeed outside our galaxy. Since the earth is rotating and also orbiting the sun, and indeed our whole galaxy is in motion relative to other galaxies, the motions of the ticket collector, passenger and stationmaster will be the resultant of all these motions taken from the astronaut's point of view.

We can conclude that every kind of motion can only be specified in relation to some frame of reference. One may feel instinctively that some frames of reference could be more important than others, and in particular that there exists a unique fundamental frame of reference with respect to which we can define 'absolute motion'. Until one can prove otherwise there is no evidence for the existence of such an 'absolute frame'. Einstein proposed that in order to start with a clean slate, the first step must be to examine current abstract concepts and to determine which of them are, in fact, 'preconceived prejudices'. He wanted to analyse these concepts in a concrete way and make logical deductions leading to a definite set of predictions, which could be tested.

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