AOH :: UNIVST.TXT Time and Universal Space Time
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Subject: 4 Essays - TIME AND UNIVERSAL SPACE TIME
Date: Tue Jul 25 18:06:54 1995

TIME AND UNIVERSAL SPACE TIME

INTRODUCTION

Universal Space Time is the ultimate geometrical time reference for SI
units, for we have already adopted c as our measure of distance, and c is a
velocity, which already possesses the attributes of both time and distance as
they apply in space, in vacuo. If we stray from the physical meaning of
c = d / t we disengage our geometrical mathematics of space and time from the
scientific data base. But the rate of an atomic clock varies with the velocity
(v) of its motion through space . To compare a clock time unit tŐ with the time
Universal Space Time Unit , t = d / c , we have to calculate and eliminate the
effect of v .When we can determine v accurately, we will be able to compare
Universal Space Time at any point in the universe accurately in relation to the
time of an atomic clock with a known velocity . .
However, as we do not know  v accurately, we cannot yet calibrate clocks,
wherever they are in the universe , to Universal Space Time (where v = 0). We
have to content ourselves with a reference to caesium emissions from a sample
material in France. However this clock will alter its rate as its velocity
through space is altered , as the Pound-Rebka Experiment demonstrated..

The consequent need to relate interim time references was understood by
Einstein, and the Theories Of Relativity are deeply involved in solving the
space-time relationship between 2 events by relating one to another without
recourse to Universal Space Time. As he shows in his book ŇThe Meaning Of
RelativityÓ , a mainspring of his theory of Special Relativity is his
understanding of the results of the famous Michelson-Morley Experiments.

Fitz GeraldŐs Error

It has been assumed for 80 years or so that the null result at the
interferometer between 2 light streams which have travelled to the end of
separate arms at right angles to each other and has been reflected back, is due
to their comparison. It has also been assumed that it is correct to combine the
2 equations, one for each arm,  each of which is correct in itself .. If one of
them is actually pointed in the direction of motion through space, a relative
contraction is justified.

Unfortunately the combination is not generally justified , the experiment
has been repeated with the apparatus on a bed of mercury, and swung round
through all possible angles. At all times the null remained. Hence the null was
also obtained when the 2 arms were equally displaced in angle from the vector v
. At this angular position the lengths of the arms must have been equally
affected by the motion v and the difference in relative length given by Fitz
GeraldŐs Contraction must be nil . The correct conclusion is that each arm
separately maintains its phase at the exit to the arm irrespective of the angle
between it and the true vector v.

The Correct Basic Equations

The correct use of the null result is to relate the equation for relative
time and relative distance to the component of v (vE for an Emitter or clock, vR
for a Receiver of light waves ) along the light path from the first comparison
point of distance and time (say EtŐ)  to the second (say RtÓ ) . (This is a
bodily motion of the equipment , and usually a light energy motion through
space, but the light  path is not necessarily direct.)

<tŐ.vE><------- dŐ = tŐ.( c - vE ) ------->
IN  THE  MEASUREMENT                EtÓ ------------------------------- RtÓ
FRAME         EtŐ --------------------------------RtŐ
vE ---->
------------------------------------------------------------------------------
EtŐ      c -------------------------->     RtÓ
IN  SPACE                    <----------------- d = c,t --------------->

We can now write the time and distance equations in space , and the time
and distance equations relative to space , from EtŐ to RtÓ , using the component
velocity (vE) of the measurement frame through space along the light path , as
shown in the diagram above . The sign of vE and vR ( for the Receiver ) in the
equations apply to motion in the same direction as the light from EtŐ to RtÓ.
.
In space by light at all times d = c.t   --------------------------(1)

For distance and time between the measurement points EtŐ and RtÓ in the
measurement frame, relative to light travelling in space, ( notice the -ve sign
of vE from EtŐ to RtÓ when the Emitter is moving toward the Receiver )

dŐ = tŐ ( c - vE ) and dŐ / tŐ = c - vE  --------------------------(2)

dŐ / d = ( tŐ / t ).(c - vE /c ) = ( tŐ / t ). ( 1 -  vE / c )  ---(3)

tŐ / t = ( dŐ / d ) / ( 1 - vE / c )

To connect 2 points in space, and in an inertial or rotating frame,
(separately or in combination,) in both distance and time, through measurement
in space , with reference to Universal Space Time.(t=d/c )

dŐ / d = tŐ / t .( 1 - vE / c )  ---------------------------------(4)

For an atomic clock moving from EtŐ to RtÓ it will be seen that dŐ = d ,
and it is both the Emitter and the Receiver of its own signals , so

dŐ = tŐ ( c - vE ) = d = c.t ,

hence t = tŐ.(1 - vE / c ) ,
hence the change in clock rate from EtŐ to RtÓ is

Delta t = t - tŐ = -tŐ.vE / c   so  Delta t / tŐ = -vE / c  ------(5)

This comparison of time units is important in clock data experiments and will be
shown later to predict the effects accurately .

The Universal Space Time Unit second is invariant ( t = d / c ) and less
than the measured time unit tŐ . It is the clock time second ( tŐ ) that gets
bigger the faster the clock moves through space , this causes the number of
cycles of tŐ to fall , or , as we say , the clock runs slower .

More generally it follows from (4) that  the apparant distance contraction
dŐ / d , and the time contraction tŐ / t , are inversely related. They rise or
fall together ..

(dŐ / d ).( t / tŐ ) = 1 - vE / c .....( \ dŐ / tŐ = c - vE as in (2) )

From (3) the frequency and wavelength of the equivalent expressions are
found , -

lambda T = lambdaŐ ( c - vE) / c  and

lambda RŐ = lambda T.( c + vR ) / c ,

also lambda RŐ = lambdaŐ ( c - vE + vR ) / c

where
lambda T = the wavelength transmitted,
lambdaŐ = the wavelength assuming v = 0  from the expression lambdaŐ = c / fŐ ,
where  fŐ is the  frequency of the light in the Emitter ,
lambda RŐ = the wavelength received.

Notice in the last equation that  when vE = vR  the wavelength received is
lambda RŐ = lambdaŐ and the frequency received is. fR = fÔ

Also notice the Receiver of a particular space wavelength ( lT ) is subject
to a time change from space to the measurement frame ( lRŐ ). This renders them
equal and there is no measurable frequency change in the Receiver due to its
motion through space . to the measurement frame . ( see (5) )

t / tŐ = ( 1 + vR / c ) , lambda RŐ / lambda T = tŐ / t.( 1 + vR / c ) = 1

Consequently the measured wavelength , relative to time in the measurement
frame , is the same as the wavelength in space relative to Universal Space Time
( t = d / c ), so the frequency analysis remains the same for all observers on
the earthŐs surface despite the difference in velocity along the light path of
the observers . There is no ŇDoppler EffectÓ on the received frequency due to
the motion of the Receiver because it is cancelled by the effect on the clock
rate change relative to space time.

( In the equation lambda RŐ = lambda Ő( c - vE + vR ) / c  the double time
changes cancel out )

Let us now return to the subject of Fitz GeraldŐs Error. Unfortunately
Einstein , Minkowski , Lorentz , did not spot Fitz GeraldŐs Error . They assumed
that the null that was observed in the Michelson-Morley Experiment arose because
of the comparison between the 2 light paths at the interferometer . In fact each
arm separately produces a null . As a result of Fitz GeraldŐs conceptual error
the contractions of both arms were combined . This is the Fitz Gerald Error .
However if you follow the contraction sequence - Fitz Gerald -Lorentz - you will
finish up with the famous , and invaluable  Einstein equation e = m.c2  as
Azimov shows in his ŇNew Guide To Science !

But if you have been following my argument you will find the same end
product , by the same method  with my basic equations and recognise the
difference between a wave and a particle .  A very significant difference is
that by avoiding Fitz GeraldŐs Error the physical difference between the wave
and the particle is revealed .

The dangers of using the Fitz Gerald and Lorentz Contractions are that
they obscure the physical processes under investigation and may lead to errors
which have to removed later. ( By the Theory of General Relativity in some
instances )

Let us go over the argument again in more detail . The equations that
produce the Fitz Gerald Contraction assume that that one arm of the
Michelson-Morley apparatus is moving along its length through space ( then
thought of as ether ) and the other is at right angles to it .

If this assumption was true the combination of the 2 equations would be
correct , and yield a relative contraction between the 2 arms . Unfortunately
the null result also occurs in the much more common situation when the arms are
slewed relative to their motion through space , which covers the relative motion
when the 2 arms are displaced by an equal angle from the direction of motion .

In that case the arms must be of equally contracted and the relative
contraction is absurd . However the separate equations are valid and can be
useful as is shown later . Let us now make Fitz GeraldŐs Error and combine them
in order to show how the famous contraction arises and what form it takes .

Let v be the velocity of the equipment , and c be the velocity of light ,
through space .Let t be the time taken for light to reach the end of each arm
and return , as measured in space by time be  t = L / c .

In the arm considered to be moving along its length through space let tŐ be
the time  and LŐ be the length in the equipment reference frame .

In the arm at right angles to the motion of the equipment through space let
tÓ be the time and LÓ be the length .

By Pythagoras Theorem the time taken by light in the arm travelling at
right angles to its length through space is

tÓ = 2LÓ c / ( c2 - v2 )1/2  -----------------------------------------(a)

Whereas in the arm moving along its length through space the time tŐ is
found from

tŐ = LŐ / ( c - v ) + LŐ / ( c + v ) = 2LŐ c / ( c2 - v2 ) =
2LŐ / ( 1 - v2 / c2 ) ------------(b)

But tŐ = tÓ therefore we can calculate LŐ / LÓ and see that the Fitz Gerald
Contraction is the relative length equation

LŐ = LÓ ( 1 - v2 / c2 )1/2  ------------------------------------------(6)

However the correct sequence of contractions arises from my equation (1).
dŐ/ tŐ = ( c - vE ) when the component velocity of the Emitter through space is
in the same direction as the light , and dÓ / tÓ = ( c + vE ) when the motion of
the light opposes the motion of the Emitter ( which may be the mirror ) . But
dŐ = dÓ and the light time is unaffected by the motion of the arm so ,-

( tŐ + tÓ ) = dŐ / (c - vE) + dŐ / (c + vE) = 2dŐ.c / (c2 - vE2) = 2t = 2d / c

Hence we get

dŐ = d ( 1 - vE2 / c2 )  ---------------------------------------------(7)

This is the correct contraction relative to space which we should use
instead of Fitz GeraldŐs Contraction . Notice that the square root sign is lost,
as is the equivalence between lengths inside the observation frame . However
length in the measurement frame ( dŐ ) is related directly to measurement in
space where d = c.t and v = 0 , so our measurement of space and time (c) is
geometrically coherent in SI units .

I do not wish to labour this unduly but it is vital to understand the
nature of Fitz GeraldŐs Error and the corrected equations , if we are to
understand the directional nature of measured time in this essay , and the
physical nature of mass and gravity in the next essay .

This note is not an attack on the Theories Of Relativity, which has a mass
of great  achievements to its credit. It is written to show that there can be an
equivalence, which may be of great use in some cases, if only to simplify some
calculation procedures, and to  render the mathematics more representative of
physical processes . We should also remember that when Einstein formed his
theories astronomical distances were not measured by d = c.t ; that equation
only became part of our S.I. measurement system in 1960 !.

However it is geometrically obvious that any two points in the geodesic
bounded space of General Relativity can be mathematically related in unbounded
Cartesian space., in both time and distance. Removing Fitz GeraldŐs Error is a
step toward making the equivalence where it is justified and a step in removing
conceptual errors where there is no equivalence .

Let us break the general argument here, and consider a case of prediction
reported by Professor Will in his book ŇWas Einstein Right? Putting General
Relativity To The TestÓ ( Incidentally the book does make a good case for the
answer ŇYes!Ó , although my argument here takes instances from it which I argue
are better considered my way and sometimes lead to different conclusions )

The Pound-Rebka Experiment

In the Pound-Rebka Experiment an atomic clock sends a light signal from the
top of a tower to a mirror beneath it, and the light is reflected back to the
top to be compared with the original. The mirror can be driven up or down the
tower.

In his book Ň Was Einstein Right Ň Professor Will tells us about the
Pound-Rebka Experiment,- ŇThe gravitational red shift was the first of
EinsteinŐs great predictionsÓ. ŇEven though Einstein viewed the red shift as one
of his 3 main tests of General Relativity, we now regard it as a more basic test
of the existence of curved space-time. Ň So how does my theory fare?

When 2 atomic clocks were placed at the top of the tower and one was lowered
and subsequently raised to the level of the other and compared with it , it was
found that the clock that was lowered had gained time (blue shift) . If the
clocks started at the bottom and one was raised and then returned to the other
at the bottom it was found to have lost time.( red shift ). So far so good.
There appears to be a connection between gravity and time in that the clock that
was in the strongest gravitational field ran faster. But the lower clock has a
lower rotational velocity than the higher clock through space and this must be
considered.

The experiment also included using one clock at the top and comparing the
frequency and wave length of the reflected signal from the mirror with the
source, and driving the mirror up or down to maintain null between the signals.

Let us now calculate the required vertical rate of moving the mirror from
our basic equations (5).

Delta t  = t - tŐ = -tŐ.vE / c [ sec]

Delta t / tŐ = -vE / c  --------------------------------------------(5)

This gives the contraction of time in the measurement frame for the clock
in respect to its motion from a point EtŐ to RtÓ .We need to adjust the length
of the light path to compensate for this difference in the size of the the
universal space time second t and the size of the measurement time second tŐ if
we are to maintain a null at the interferometer . The light path does not follow
the clock path , however it does not matter where the light path goes so long as
it goes from AtŐ to BtÓ in the time taken for the clock to go from EtŐ to RtÓ .

In the measurement frame we know from (2) that   dŐ / tŐ = c - v   for the
clock.

We need to determine the rate of change required to dŐ / tŐ with respect to the
space absolute d / t= c .

dŐ / tŐ = c - vE   and with respect to d / t = c

( dŐ / tŐ ) / ( d / t ) = 1 - vE / c  so  dŐ / tŐ = d / t - ( d / t ).vE / c so
with respect to d = c.t

Delta dŐ / Delta tŐ  = -.vE / c [ metres / sec ] ------------------(8)

Notice that (5) and (8) balance as a ratio although the units are different .

If we assume that the latitude of the tower at Harvard was 410 N and take
this to determine the velocity of the tower we can solve (8),-

-vE / c = -w.r / c = 1.1676*10-6 m / s = 4.2 mm / hr

As the mirror shortens both the lightpath going to it and the lightpath
reflected from it , we can predict directly that it was necessary for the
experimenters to shorten the distance (h) from the mirror to the clock at half
this rate to maintain a synchronism of the outgoing and reflected light signals
, to cancel the effect of the motion of the clock through space that was due to
the rotation of the earth. So the predicted motion of the mirror was

-Delta h Ô/ Delta tŐ = -2.1 mm / hr

Professor Will tells us that it was about 2 mm / hr on average . So my
theory appears satisfactory in predicting that the time change in the clock is
an effect of motion through space , and in calculating the required motion of
the mirror necessary to eliminate the effect on the clock of the rotation of the
earth through space.

However the clock is also subjected to the earthŐs velocity round the sun .
This will have produced a velocity component with a period of 1 day , which
rotates relative to the line EtŐ to RtÓ , and is additional to the effect of the
constant rotation of the earth , which we calculated . Professor Will mentions
the figure of about 2 mm / hr as the average necessary motion of the mirror ,
but does not mention the cycle  that I predict . However if the null was
maintained continuously , and the detail rates recorded , it should be easy to
check my prediction of this cyclical effect .

There will also be a small effect due to the rotation of the sun around the
galactic centre , but this may be too small to measure .

Evidence from the Pound-Rebka Experiment

Assuming that the velocity of light in space is constant, the Pound-Rebka
Experiment  shows the following.-

1   Motion of an atomic clock through the space material causes a a real time
rate change in the clock . This change is specific to the motion between 2
points in space . As it occurs in the clock it is not a normal Doppler effect ,
unless one extends the term to include the effect of the motion of space inside
the clock .

2   The time rate change has nothing to do with gravity , nor gravitational red
/ blue shifts , nor the Theory Of General Relativity.

3    My theory predicts that the average result of the Pound-Rebka Experiment is
due to the earthŐs rotation , and predicts this results correctly . It also
predicts a diurnal variation due to the sunŐs velocity vector contribution to v
, the true velocity of the clock through space .

Other Space Time Conclusions From The Argument

4    The use of the constant velocity of light , c , in space measurement incurs
a space time relationship , in which my basic equations show why the observed
spectrum of light from the stars is the same for all observers , whatever their
motion in space , and is the same in space with no motion of the observer

5     My theory predicts that all time relationships we observe are related to
time in space where the velocity of the clock through it is zero .( v = 0 ).
All our light measurements are related to Universal Space Time measurement by vE
, the component of physical motion along the direct path between 2 points in
space..  The physical path of the light need only coincide with that line at the
comparison points in space and time. (EtŐ and RtÓ in our investigation).

6    The theory also predicts that  all atomic clock rates on the earthŐs
surface will vary according to their velocity through space., when measured
assuming that the velocity of light is a constant ( c ). In addition to the
rotational velocity of the earth they will experience a diurnal variation,
because of the change in direction of the velocity vector of the earth round the
sun , and the sun round the galactic centre.

7     It appears easy to predict the results of the Pound-Rebka experiment my
way in normal Cartesian space coordinates . However there appears to be an
equivalence  in the curved space of General Relativity . You pay your money and
make your choice . It would be nice to feel that I was justified in claiming
that there is a general equivalence in space time calculations between my
equations for Cartesian space and EinsteinŐs equationŐs using cuved space , but
I cannot make such a general claim . Where I have used my concept and equations
to predict results reported in famous experiments I have been satisfied , but
the instances are too few  to satisfy an independant  and objective obsever .
The point here is merely that there may be a simpler Cartesian co-ordinate
mathematics of space which we can rely on in instances where the books tell us
to think along the path of the curved space and the Theories Of Relativity .

Let us now turn to a different application .

The Star Spectrum Measured From Earth

I have already shown , on page 3 , why the frequency of the star spectrum as
seen on earth is not affected by the motion of the observer  If youhave already
grasped the point there is no need for you to read this section which only
explains the method in more detail .

Experimental evidence shows that the frequency of a light wave always
appears the same to the observer , although his velocity relative to the
incoming light when approaching the light source is

-vO = -w.r.cos a

where a is the angle beween the motion of the clock round the earth and the
light coming from a star . As the clock meets the light coming over the horizon
a = 0 and cos a = 1 .

During the next quarter of a day the value of vO will approach zero , which
it reaches when the clock path is perpendicular to the light path . ( Thereafter
the observerŐs velocity has a component in the same direction as the light and
the sign is reversed ).

Using equation (3) it can be seen that , relative to starlight the earth
ObserverŐs velocity is -vR ( when approaching the star ) so

lambda R = lambda T ( c +[-vR] ) / c = lambda T ( c - vO.cos a ) / c

Consequently the apparant change in wavelength is

Delta lambda T / c = -vO.cos a / c

However from (3) the apparant increase in distance with time in the
measurement frame is  -vO along the light path , which for a wavelength in the
light path is also, -vO.cos a / c

Therefore the contraction in distance and time of the wavelength due to the
earthŐs motion is the same as the relative motion of the observer and there is
no change in the observed spectrum of starlight due to the motion of the
observer .

The equations given have been shown to work well in relation to the
measurements made in relation to the motion of clocks and their change in rate ,
and in relation to the observed spectrum of starlight made by observers in
motion through space . Let us now try to determine what is this measure of time
in space    (t = d/c) by experiment .

Universal Space Time Measurement By Experiment

It follows from our equations that the comparison of clock time to
Universal Space Time may be made if we can find the real velocity of a clock
through space v , and apply it , when v =  vE = 0 , in the equation

tŐ / t = (dŐ / d) / ( 1 - vE / c )

If I am right in this , we can get a comparison of clock time and Universal
Space Time from the Pound-Rebka Experiment by analysing the measured rate of
moving the mirror , and allowing for the rotation of the earth on its axis ,
the earth round the sun , and the sun round the galactic centre. However this
may be a messy process.

In my view it would be better to measure the velocity of an instrument
relative to space directly. This could be done by using a single arm of the
Michelson-Morley
Apparatus and an atomic clock.

First , use the clock to compare the phase of light going into and coming
out of the arm (which has a mirror at the other end ) . Then swing the arm round
in many directions . My theory predicts that there will be no phase shift , and
my contention that Fitz Gerald made an error will be proved .

Second , use the atomic clock to monitor the wave feed at the mirror.
According to the theory as vE alters with the inclination of the arm to the real
direction of v in space, the wavelength will alter in each arm, and so the
number of waves will alter in each arm . However the total sum of waves for both
directions of the light path in the arm will remain constant according to my
understanding of the result of the Michelson-Morley Experiment . Consequently
there will be a feed of waves from light travelling in one direction to light
travelling in the other direction at the mirror.. Observation of the number of
waves fed from one light path to the other as the angle is changed will enable
us to determine the axis of  the spherical measurements, whose ends are marked
by the maximum number of waves fed in one direction.

Third let us assume that we have undertaken the messy business of
establishing the direction of the vector v and have aligned the arm with it. If
the light enters and exits the arm at E, and is reflected by the mirror at M we
can omit our usual relative measurements and consider the light path entirely in
space, because the number of waves in a linear space will be the same in either
reference system.

Now consider the Ň equator Ň , where the arm is perpendicular to the motion
. Here vE along the light path is almost zero (c.sin v/c ) . There are the same
number of waves in the light path to the mirror ( and wave counter ) as there
are reflected from it to the light entry point .

With this Ň equator Ň as our reference point we can predict the wave number
change from 0 at the Ň equator Ň to a maximum when vE = v at a Ň pole Ň .
The wave counter at the mirror is unaffected by any frequency change because the

lambda R = lambdaŐ ( c - vE + vR ) / c = lambdaŐ .

The distance from the Emitter at EtŐ to the mirror at RtÓ can be measured
in space ( d = c,t ) or in the measurement frame ( dŐ = tŐ [ c - vE / c ] ) .At
a Ň pole Ň vE = v .

The wavelength equations deduced from the diagram and the basic equations at
the top of page 3 . From which we can see that ,-

From EtŐ to RtÓ   d = c.t = n.lambda T  so n = c.t / lambda T
where n is the number of waves in space ,

lambda T = lambdaŐ ( c - vE ) / c

is the wavelength in space , ( lambdaŐ = c / fŐ is the mathematical wavelength
in the measurement frame )

However the measured distance

dŐ  = d - v.t. = t ( c - v ) = nŐlambda T

so nŐ = t .( c - v ) / lambda T

therefore nŐ / n = ( c - v ) / c = 1 - v/c

so nŐ = n - n.v / c

Therefore the number of waves displaced when the arm is swung from the Ň
equatorial position Ň toward the direction of motion through space is

Delta n = -n.v / c

Therefore if we count the number of waves , from the arm being pointed in
the direction of the vector v of the instrument through space , to its reverse ,
we can count the maximum change 2Dn , and can calculate the actual velocity
through space

v = Delta n.c / n .

We can take the following figures , as an example , to give us an idea of
the number Dn we should expect.

dŐ = 10m , lambda T = 10^-6 m ( a near-optical infra red wavelength ) ,

v = 300 m/sec ,

c = 3*10^8 m/sec .

Delta n = n.v / c = (10 /10^-6 ) *. (3*10^2 ) / (3 * 10^8 ) = 10^7 / 10^6 = 10
waves.

This gives the clock rate correction to Universal Space Time .

v = -Delta n.c / n .

So in this instance , from (5)

Delta t /Delta tŐ = -v / c = -3*10^2 / 3*10^8 = -10^-6

In this example , this is a rate error of the experimenterŐs atomic clock
, which is running slow by one part in one million relative to Universal Space
Time . In real life one would have to calculate the additional vector
contributions of the earthŐs vrlocity round the sun , and the sunŐs velocity
round the galactic centre , or measure the clockŐs velocity relative to space
direct to make the real measurement .However the vectorial sum of these
velocities will always be positive and the unit time correction negative .
Universal Space Time runs faster.

Geometrical Summary

The rate of any atomic clock is determined by its velocity through a
physical space solid .

The wave pattern in space is set by the motion of the Emitter , the
wavelength in space is determined by where it is . The wavelength and frequency
measured in the measurement frame is equal to the real wavelength in space at
that point because the time contraction is equal to the distance contraction
relative to the space solid ..

It may be helpful to think of the physical processes described as one in
which the Emitter of an electro-magnetic wave produces in the space solid a
series of waves , each of which is propagated from a point , from which it
expands spherically at the velocity c .

The series of points of emission in space are separated by a distance
( lambda  = v / t in space ), and these give rise to a separation of the waves
which varies in space.

However at a distance from the Emitter , where we can consider that the
Receiver is sampling a series of parallel wavefronts , the time contraction
( Delta t / tŐ =  - vR / c ) of a the ReceiverŐs  atomic clock is equal and
opposite to its distance contraction along the light path to it
( Delta d / dŐ = vR / c ) . This enables us to measure the wavelength in space
correctly . .

There does not seem to be any doubt that Fitz GeraldŐs Contraction is
geometrically wrong and that many people have followed him by using it and
introducing further errors into the general corpus of scientific literature
using arguments based on his contraction . But in some cases the initial error
can be removed by applying the space curvature of the Theory Of General
Relativity .

Next

If you need to find a good project to attract funds to your research
facility you might offer to undertake the proposed experiment yourself . ( I
have no research facility to offer . I am merely an old retired buffer who is
looking into things in order to improve his understanding of what is really
going on )

In my next essay I intend to show how the correction of Fitz GeraldŐs
Error  affects the definition of particles and waves , and to discuss the
interaction of mass and gravity.

The purpose of these essays is to stimulate attention to the nature of
space itself, and to open up a discussion on the ability of science to
illuminate our understanding of realms of our experience , where the measurement
of the behaviour of particles alone is not adequate to describe the whole of the
physical processes involved . If this interests you , please contribute
constructively .