POSTULATES OF RELATIVITY

  

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( HomeScienceRelativity → Postulates )

Special relativity is based on two basic postulates, and these are discussed in this section.  To understand the implications of the postulates, and why Einstein chose to make them, it is first necessary to discuss the nature of motion and frames of reference, and this is where we start.

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Frames of Reference

If you ask most people to explain what the term "motion" means, they will probably say something about movement, transport, travel, and other similar words that convey the idea of movement from one point to another.  However, most people would omit to mention that all motion is RELATIVE.  That is, motion can only be judged by comparing the position of the moving object with some other reference point or object.  The following figure illustrates this.

 

 

One can go further - the person in the car moves relative to the road, the car moves relative to the house, and so on and so forth.

In the language of physics, the reference against which the motion of an object is measured is called a "frame of reference".  Thus, in the figure above for example, the road is a frame of reference against which the motion of the car can be measured.  Alternatively, the house could be a frame of reference against which the motion of the car is measured.

There is a special type of frame of reference, which is referred to as an "inertial" frame of reference.  An inertial frame of reference is one in which Newton's first law of motion holds.  This begs an obvious question - what is Newton's first law of motion?  Basically, it states that:

An object remains either stationary or in its state of constant motion if there are no forces acting on that object.

An example will illustrate this.  Imagine sitting in your stationary car on a flat road, with the gears in neutral.  The car remains stationary, as there are no forces acting on the car.  Now put the car in gear and floor the accelerator.  Forces from the engine act on the car and it picks up speed.  As it continues to pick up speed, wind resistance increases on the car, and eventually the car will hit its maximum speed.  At this point, the force from the engine is exactly balanced by the frictional and wind resistance forces, and hence the total force on the car is zero.  The speed remains constant, at maximum speed, in accordance with Newton's first law.

In this example, the road (or surface of the earth), against which the motion of the car is measured, is an inertial frame of reference.  Now, frames of reference need not be stationary.  Indeed, it can be shown that if a stationary frame of reference is inertial, then it is also inertial if it moves at constant speed.  Thus, in the figure above, the car is an inertial frame of reference whether it is stationary or moving relative to the road.

However, any accelerating frame of reference is not inertial.  Thus, the car in the figure above, while it is accelerating, is not an inertial frame of reference (e.g. for the people inside the car).

Note that without a frame of reference, it would not be possible to judge the state of motion of an object moving at constant speed.  The following figure illustrates this.

 

The point of all this is that Einstein asserted that there is no "preferred" inertial frame of reference against which motion should be measured.  In other words, all inertial frames of reference are equivalent.  It does not matter which inertial frame of reference is used to judge the motion of an object.  In the first figure in this article, either the road or the house are acceptable frames of reference against which to judge the motion of the car.

Postulates of Special Relativity

Einstein took this one stage further, and came up with his first postulate of special relativity, which generalises our discussion to ALL of the laws of physics:

Postulate 1:

All the laws of physics are the same in all inertial frames of reference.

In the context of our discussion above, we can give a simple example of this principle in action.  Consider a person standing at the road side and a person sitting in a car moving at constant speed.  This postulate states that both people must observe the same laws of physics for all phenomena.  If the car is accelerating, then it does not constitute an inertial frame of reference, and the person on the ground and in the car need not observe the same laws of physics.

The second postulate is, in a sense, a corollary of the first postulate:

Postulate 2:

The speed of light (in a vacuum) is the same in all inertial frames of reference.

This postulate leads to a surprising difficulty when we consider what we expect to happen in everyday life.  Suppose we are driving along at 50 mph, and we approach a person stood on the pavement.  At the instant that we pass the man, he throws a ball at 50 mph, relative to him and in the direction of travel of the car.  In the frame of reference of the car, therefore, the ball is stationary.

The second postulate says that light does not behave in this way.  Suppose that, instead of throwing a ball, the person on the pavement switches on a torch instead.  The second postulate says that both we and him have to measure the same speed of light from the torch - no matter how fast we are travelling in the car.

Our consideration of throwing the ball suggests that if the speed of light is C, and our speed is V, then the guy on the pavement sees light travelling at speed C, but we should see it travelling at speed C - V.  The second postulate says that this is not the case.  The second postulate says that we see the light travelling at speed C.

The following figure illustrates this, but in the conventional notation used to represent frames of reference, in the context of relativity.  In this example, frame A is the pavement, and frame B is the car.

 

 

Summary

The key message to take away from this article is as follows:

The theory of special relativity is based on two postulates, the first of which reflects the absence of a preferred frame of reference against which to develop the laws of physics.  They are:

Postulate 1:

All the laws of physics are the same in all inertial frames of reference.

Postulate 2:

The speed of light (in a vacuum) is the same in all inertial frames of reference.

 

 

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