Special Relativity means different things to different people. From the average ‘man in the street’ to our foremost scientific experts: from something that has the aura of scientific magic, almost akin to alchemy; to the wonderful beauty of Einstein’s great theories explaining how space and time are related.
Many learn the concepts; more merely become familiar with the calculations, a few understand how it works, yet how many understand why it works?
The desire to cling to something familiar, trying to understand Relativity in the context of Classical Newtonian mechanics, has bedevilled Relativity; sowing confusion and doubt, particularly among newcomers to the field, by means of the numerous paradoxes, counter-intuitive descriptions and facts that contradict one another.
Take for instance the fact that experiments prove moving clocks run slow.
Special relativity’s First postulate (principle of Relativity) states:
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion. OR: The laws of physics are the same in all inertial frames of reference.
Now a clock moving at a constant rate is also an inertial system and must therefore be governed by the same scientific laws; keeping the same time as any identical clock in another inertial system, in which it is a stationary clock . (i.e. when measured from within that system by an observer at rest in that system)
Yet, measured from another system, relative to which our inertial clock is moving, that same clock is measured to run slow.
The same clock is at once displaying a common time along with all other inertial clocks while, at the same time running slow as a function of its speed relative to another observer.
Yet we know that both statements are true.
The one clock does keep the common time along with all other inertial clocks and yet also runs slow, as measured by any observer relative to which it is moving.
How can this be so?
Light Clocks are commonly used as an aide when describing Time Dilation. Viz.
Frames of Reference
We measure Space using the same three axes we are used to using to map any space, length, breadth and height, only in Space, we refer to them as x,y,z. We also imagine a standard clock at the Origin, set to zero, upon which we measure time, t. Thus giving us the 4 axes or dimensions of Spacetime.
Because there is no fixed point in space to base a map upon, we use a Frame of Reference based upon whatever location and time suits our needs. Each and every Frame of Reference will have its own map of Spacetime, in which it is stationary and everything else is moving. Yet if that is the case, how do we define two Frames of Reference moving with respect to one another? They cannot both be stationary, can they? So which one would we designate as stationary and which one as moving?
In fact it is the one we are taking taking measurements from that is designated as stationary, and the other to be moving.
Confusing isn’t it? Well, maybe so at first glance, but that is what Special Relativity is all about. Giving a simple, easily understood answer to the conundrum of how everything in Spacetime is stationary and at the same time everything is moving!
The easiest way to explain that, is to take an example and see how it works.
For this ‘thought experiment’ we will use Einstein’s Light Clock. A very simple device. A pulse of light is sent to a distant mirror where it is reflected back to the base of the clock, where it triggers a new pulse of light. So the time in the clock is measured by the speed of light. If we say that in our clock the mirror is one light second away, the light will take one second to reach the mirror and one second to return. It will ‘tick’ every two seconds.
Imagine two identical, synchronized clocks alone in Space so far away from anything else that there is nothing that will affect them. And imagine the two clocks are moving relative to one another, with a relative velocity of 0.6c. Nominal Observers situated at the base of each clock, will measure their local clock as stationary and the other, their remote clock, to be moving away at 0.6c.
We will refrain from identifying the individual clocks and merely refer to the local stationary clock and the remote travelling clock.
To the diagram of the simple Stationary clock (in blue), we will add the moving clock (in red).
As measured by our stationary observer, the light in the stationary clock travels 1 light second to arrive at the mirror, while the moving clock’s light path is 1.25 light seconds, to the mirror.
The configuration of the two clocks and the observers upon them are identical and reciprocal; so, as we draw their positions and measurement from the perspective of the stationary observer, each of the two clocks will be both the stationary one and the travelling one, depending on which observer’s view is taken.
The time for the light to reach the mirror in each stationary clock is one second, yet the time when that same clock is moving at 0.6c, is 1.25 seconds.
So, the light in each clock will take both 1 second to reach the mirror, when measured as the stationary clock AND 1.25 seconds when measured as the travelling clock!
Yes both times for the same clock, depending on which observer is measuring!
Time and distance are measured differently due to the movement of the remote system, yet the duration when measured as a stationary clock, remains the same.
So it has to be the measurement scales that change. Time and distances measured locally, within a Frame of Reference, is Proper Time and Proper Distance, while those measured in a remote, moving system are Coordinate Time and Coordinate Distance.
We use the Lorentz Transformation Equations to translate between these two scales of measurement.
This has, unfortunately led to the almost inevitable conclusion that time passes differently and distances measure differently in a system moving at a great proportion of the speed of light.
Whereas, in fact, the times and distances are exactly the same. They do not change. The differences are an effect of the conditions under which the measurements are taken, and it is the measurement scales that change.