Subject: 4 Essays - TIME AND UNIVERSAL SPACE TIME
Reply-To: max@barton-m.demon.co.uk
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 
(Receiver )


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 
wavelength received is  

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 .
      
Max Barton  ( All rights reserved )