Before
we examine what this is and how it works we must address the subject
of how we map Spacetime using Frames of Reference to relate separate
entities within Spacetime.
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.
Yes,
in Spacetime there is no fixed framework that everything can be
measured against; the location, and the is movements of those objects
can only be measured relative
to other objects in Spacetime.
Yet
if that is the case, how do we define two Frames of Reference moving
relative to one another? They cannot both be stationary, can they? So
which one would we designate as stationary and which one as moving?
It
is the one we are taking taking measurements from that we designate
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.
Light
clocks
Fig. 1 Fig. 2
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. Fig. 1
Imagine
two identical, synchronised 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 moving clock.
To
the diagram of the simple Stationary clock (in blue), we will add
the moving clock (in red). Fig. 2
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.
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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.
Yes,
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.
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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; it is the observer's motion relative to
the clock that has to be accounted for, and that is why the
measurement scales have to change.
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