More
on Frames of Reference
The
Origin of the Frame of Reference, has the coordinates 0,0,0,0 and it
is the location of the Nominal Observer and his clock.
There
are at least three ways of viewing a Frame of Reference:
1. From
the perspective of a Nominal Observer (real or imaginary) located at
the Origin, holding, or at least adjacent to, a standard clock. This
clock will be measuring Proper Time, as the clock is at all times,
at the Origin, with that Frame's Nominal Observer and so will be
tracing the path of that Frame of Reference.
2. From
the perspective of an Observer, elsewhere in that Frame of
Reference, carrying a clock synchronized with the Nominal Observer's
Clock. Measurements, made using a synchronized clock and standard
ruler, will also be Proper Times and Proper Lengths.
3. From
the perspective of a remote Observer who is moving with respect to
that Frame of Reference, rather than in it. All measurements are
taken by the Frame's Nominal Observer and are then converted
(Transformed) by that remote observer to cater for the relative
velocity. This is done using the Lorentz Transformation Equations.
These Transformed measurements are Coordinate Measurements.
It
is immediately apparent that an observer, on any body or at any
location in Spacetime, will measure time on his local clock and
measure lengths, in his frame of Reference, with his standard ruler
and that those measurements will be in Proper units.
Spacetime
is Homogeneous and Isotropic. It is the same everywhere, in any
direction. It obeys the same basic scientific laws throughout.
Therefore, if we place an object within a Frame of Reference, its
properties will be the same as they would be in any Frame of
Reference. This is one way of stating Einstein's First Postulate of
his Theory of Special Relativity.
Let
us consider what this means by taking an Event, a flash of light, and
examining how it appears from different points of view.
If
we take the time and location of that flash of light as the origin of
a Frame of Reference it will have the coordinates 0,0,0,0. Light
travels away from that event at 'c' in every direction.
After
1 second the light emitted will be measured to have travelled 1 light
second in every direction and will have traced out a sphere in
Spacetime, radius 1 light second. And it will be a sphere, radius 1
light second in each and every Frame of Reference, only the
coordinates of that Event will be different.
There
is one rather surprising outcome from these considerations however.
For when we define our Frame of Reference, Spacetime is fixed and at
rest from our perspective, then surely, one would think, Spacetime
must be moving for every other Frame of Reference, that is moving
with respect to our 'fixed' Frame of Reference.
Yet
as soon as one thinks this way, one has fallen into the trap, and
failed to grasp the essential meaning of Relativity. Everything is
Relative. No Frame of Reference is fixed and at rest absolutely; yet
each and every Frame of Reference is fixed and at rest from its own
perspective.
No,
there is not, nor ever can be any one preferential Frame of
Reference. For if Spacetime were at rest in only one Frame that Frame
would take precedence having simpler Laws of Science than other
Frames of Reference.
Again
I say No! For the simple reason that Spacetime is at rest as observed
from any Frame of Reference.
Each
and every Frame of Reference is a Map of Spacetime, with the origin
of that Frame of Reference as the fixed centre of that Map.
From
the perspective of any observer, at rest in any Frame of reference,
every other entity or Frame of Reference is moving, in Spacetime,
relative to that Frame of Reference! That is each and every Frame of
reference is moving relative to every other Frame of Reference or
Map of Spacetime (for if they are not moving they are different parts
of the same Frame of Reference).
I
have repeated myself, ad nauseam, in the passage above, because it is
describing the fundamental principle of Relativity: Everything is
Relative.
This
is the most fundamental and I may say surprising facet of Relativity,
and one that so many eminent scientists, indeed the whole scientific
establishment have, as yet, failed to grasp; determined as they still
are to see everything relative to some particular Frame of Reference,
thereby failing to recognize that that particular Frame too, must
also interact in exactly the same way relative to other Frames as
those Frames interact with it.
AS
A IS TO B, SO B IS TO A
So
let us try and picture this, shall we?
Let
us take for an example a train moving along a railway track. A
lightning strike hits the track, as the very centre of the train is
passing that point on the track. How is the flash of the lightning
observed from the track and from the middle of the train. Fig. 1
Fig. 1
This
is a practical example of our original event the flash of light and
two frames of reference, the track and the train, that are moving
relative to one another.
Now
as we saw in the earlier discussion, each will see the light travel
at 'c' relative to their Frame of Reference, so the observer on the
track will measure the light travel equal distances, in the each
direction, along the track as the train moves away. Fig. 2
Fig. 2
while
the observer on the train will measure the light travel equal
distances, in each direction along the train, as the track moves away
from the train. That same observer on the train, will see the light
reach both ends of the train at the same time; although when that
happens, the two ends of the train will no longer be equidistant from
the observer on the track. Fig. 3
Fig. 3
So
which one is correct, the observer on the train or the one on the
track?
As
we have just seen, they both are, hence the need for Einstein to
explain it!
Think
about it! At the moment of the flash of light both B and B' are
coincident at the flash of light.
The
two Observers are located, one at B on the Track and one at B' on the
Train, which coincide when the flash of light occurs. So each
Observer, at rest in Spacetime as they Map it, will observe the light
travel at 'c' in all directions in their Frame of Reference. The
light will, therefore, reach the points, A and C on the track, and A'
and C' on the train, at the same time. It is the observers B and B'
who are each moving away from the other and so are no longer at the
location of the flash of light, AS MEASURED IN THE OTHER FRAME.
The
important fact to realize here is that every observer will measure
the light expanding evenly from the initial event, the flash of
light, within his own Frame of Reference! But that every other Frame
of reference, will be moving away from him. Exactly as we see in our
'thought experiment' with the train .
A
paradox, or a conundrum at the very least, one might think, yet the
answer is a simple one: there is only one expanding sphere of light
that is mapped as being at rest in each and every observer's view of
Spacetime!
For
each and every observer the light expands evenly in their Spacetime,
while all other observers are moving through that expanding Sphere of
light; thus the stationary observer's inevitable conclusion that the
moving observer cannot see the light travelling evenly in both
directions.
Note:
that it is only in the measurement, relative to a stationary
observer, that the space and time of the moving observer, is
distorted.
So
how is this distortion, of the moving observer's view and
measurements of Spacetime, experienced by those concerned, how do we
relate the stationary observer's measurements with those of the
moving observer?
At
which point we ask those two venerable old rogues, Time Dilation and
Length Contraction to step forth and take a bow!