TIMEby

Arie M. DeGeusColumbia. S.C., tlSA

January 25, 2001

Copyright

In the book Fluidum Continuum Universalis. which was written by the aulhor

ofthe above subject matter, we found that the so called "speed of light"'( which was described by phycisists as being a major universal constant, no matter

what frame of reference ). r.ras dependent on "space-time curvature" and on "time".

"special relativity" by Eir-rstein, but also by others, who preoeded him, or contempo-

raries e.g. Lorentz, shows thc interrelationships ofthe factors: energy, mass etc , ex-

pressed in the "coordinates" and "timc", whereby thc "speed of light" is constant and

has a value of 3x10t m/sec."special relativity" also introdused the phenomenon of "time dilation".

This phenomenon shows that "time" slows in a system' ( as ohserved liom another

system, which is "at rest" ) which moves at relativistic velocity relative to "time" ina system which is "at rest".

"Time" has proven to be a highly 'relative' factor even though as basic as itmighl seem to be. Physics is extremely lacking in general, but in parlicular with rcgard to

the "speed of light" and "time". Underlying "time" as we kno* it and which is always

'relative' in nature, therc is "absolute tine". The existence of "relative time" and

"absolute time" show a Hamiltonian analogy as to the existence ol the density p inspace and the density po in "standard" space. In the considerations ofthe concept of

"space-time cutwature" we have entered "time" as a fourth dimension' lvhich has

proven to be helpful and contributive lor physics in general.

Instead of speaking about a'location' in three coordinates, in "space-time curvatute"consideratior-s we speak about an 'interval'.

This is expressed by lc*' r' -(x' + y' + ,')l-- "orrt.

(1)

Refening to "time" in relativistic motion.

Ii /, is the "tirne" in the moving system ( II ) , t, is the "time" in system ( I ),which is "at rest" ( from which the observations are being made ), v is the velocity

ofsystem ( II ) relative to system ( I ) and c* is the "speed oflight" in "slandard"

space, then we have

t., - /,^ll-r1 ,*' (2)For regions with "space-time curvature" we found that the first derivative

of the local "speed of light", herein indicated by , is #: -Jr(T)U-, , , ,

"Time" ( continued ) by AMDG, copyright Page 2

herein is R is the distance to the center of "mass", which is the center of the "space-

time curuature", O is the gravitational conslant in the Fluidum Continuum, herein-

after abbreviated to FC and n * is the "mass" ( corrected for "standard" space ).Integrating(3)weget

t fon*)( '' ,1 '-'" I and7r(r J2R. \ c+ ,/ "-L o, "-1 o. r""!. (4)ttc

Therefore

' '* t4=m*"so 1,=1,uTg:f4)rr-r,Jzn'];and nri) (5)

Newton's law gives rr =K,therefore the term # =; rin which gisthe

gravitational constant for the concerned system.g:/(R) ) We can now write_ -* l

l. - L\12\' Oo-- 6 /(/r)

(6)

Formula ( 5 ) teaches, that with relation to thc earth, if wc would travcl through a shaft

towards the center of thc carth, that "time"at the halfway point has slowed 4x com-

pared to "time" on the surface ofthe earth. At the center ofthe earth and for that matter

at the center olany "space-time curvature" region, "time" comes to a standstill, proi'i-ded that the hightened density region ( or all "mass" ) would be concentrated right at the

center.However, if we have a "space-time cutvature" region with a center ofextended size (

e.g. the earth ), we first need to formulate tlie density fturction within the volumetricconfine ofthe "body" which gives cause to the "space-time curvature".

Calculation of the density ( fluid dynamic ) function within a tri-dimensional bodyFor the sake of simplicity, we choose a sphere:

distance from outer perimeter ofthe sphere be: i and the angle between the segment

base and the line to the center be: p. The volume of the spherical segment is

v ^,...^. --!rnln' r l(Rsinp)'1. For simplicity we shall considerdensity p ro be6'''l' | '

constant throughout the sphere. At distance ft from the outer surface we have an

"pl: n' -t. rln'+r(nsin,p)'f 'l

anractive lorce to the center F... - LJ 6 ' - 'l =g (7)aut $-n)'

( g is the force per unit of attracted mass ). The time retardation is strongest when

g is marimal ( see formula ( 6 ) ). Taking the first derivative towards R

ds

dR

dg

dR

so,

"Time" , continued, by AMDG, copyright

(n - n)' l+n' -lsin' p" n] -(2R 2h)

g=1.33trpR, wherefore,

Page 3

!n'-ln{n' +:(xsinp)'}

(n n)'(8)

=0, if the numerator of (8)=0. Expressing sinq ' Rcosrp+h= R,

,,,f .^,, ^[., n-nl ll_,r*_rr,l!^, _t_rlr, *tn,(r_(* rJ'lll=o(R hrl4R' _ftR1r_[

n ) ;1_r'^_'n,11" _u,,j" +r^ l,-l o J ][]

n h*lR ( 2is slightly more ) ( Ifthe the earth"'s average density close to theJ

surface is assumed to be 3 and in the center assumed to be 7 and if we assume that

this density gradient were linear, then a more general calculation sho*' ft = I R '

Substituting this value in ( 7 ) with sinp = !E. *. get at this location

R2

4

4.5npR . At the earth's surface

g ^,, :4.50 = 3 -3g

g"'7a* 1'33

,olo o'- I nJ I n'- rn't3 l'l'--l:" t2'].4" 4))_

-* iSince t. =t,JZ' ' .we find that at location h= Rl2, t)

Oo_- 6 /(R)

, tz = t r,,. and t, =t*o

=1, (q).1.3 8

So roughly halfivay to the center ofthe earth, taking into consideration an approxi-

mate density gradient as indicated above, "time" has slowed by a factor 3.38 . This

is the greatest degree of slowing. Since g decreases fui1her towards the center of

the earth, the time dilation decreases accordingly.Fig. I shows a cuwe which indicates the time dilation as firnction of the distance

to the center ofthe earth &om 500 km above the surface to the center.

"Time", continued, by AMDG, copyright Page 4

Fig. I

A= ]rh=iR

rt=in1

(iB, ae*srrv z7Time dilation as function of the velocity ofa reference frame "in motion" relative toa reference frame "at rest".

Examples:

( a ) A spacecraft which orbits the earth in about 50 minutes has a velocity of roughly

50,000 km,ih., which is about 14 km-/sec. c+ = 3 x 105 km/sec. Substitution in

formula( I ), gives Ir=t,+-(4)'l (:*tO')', whichgives tz=.99999998t,

which means that /, is only 1 sec./ 50,000,000 sec or 1 sec. per 1.6 year slower

than tr .

( b ) Instead if the velocity were 50,000 km,/sec ( 3600 x faster ). then /, - jq . whichto

means a 40 minutes/day slower 12 compared to lr .

( c ) A round+rip to a -Centauri at a velocity of 50,000 klt/sec. would take 48 years

"time" for the traveler. Meanwhile folks on earth have aged 49.4 years.

( d ) The same round-trip at a velocity of 100,000 km/sec. ( 1/3 of the speed of light )would take 24 years for the traveler and the aging on earth be 25.5 years.

The above examples show that time dilation due to relative velocity ofone frame ofreference to another is actually of small magnitude other than when the relative velo-city is very close to the speed of light.

With regard to time dilation calculations, physics literature makes no mention of theconsideration of the factor of an existing "aether-wind" . This omission cannot be made.

Fluidum Continuum Universalis ( FCU ) shows that'a densification offluid takes place

"Time", continued, by AMDG, copyright Page 5

ahead of a moving parlicle ( vortex entity ) when it moves through the fluidum' ( FC ).This densification causes the observations ofboth the phenominae of"mass" increase

and time dilation.This is logical; an1'where there is "mass" increase, there is a slowing of "time".

One must take note however, that the densifrcation offluid is caused by "motion"relative to the FC itselfand in tlle event that the FC is "in motion" itselfrelative to areference-frame from which observations are being made, then the velocity ofthemoving reference-ffame relative to the reference-frame "at resf' , is that velocity,which is vectorially composed of the velocity ofthe fluidum and of the apparent relative

velocity between the reference frames. See Fig. 2 , in which two reference frames are

shown in the FC, being "in motion". The overall resulting velocity as to the reference

frame of observation is the one which should be used in "relativistic" calculations.

The motion ofthe FC must always be taken into account.

Fig.2

The resulting velocity 4..,,,, = v,,0,"", cosry tv,,- cos p , and the time dilation is

expressed by t, = I, (10)

If the "moving" object is in a "space-time cuwature" region as well, then there is

the additional component ,, -,,J11!.'. ,ino' {) M=^*The total time dilation from the standpoint ofthe observer is

r'-'I /. (v,,, cos j4 +-v,, cosp) l^ c* R^ , It, =/,1!r-

-=;-+lz nz*srn a

IIJ( 11)

If the observer's reference frame and the center area ofthe "space-time curvature"region are the same and if the object moves in the same direction as the "aetherwind", then formulation ( 1 1 ) can be reduced to

, r2(v,b/ cos ry'l + v/., . cos pJ

+vr, )cos- (p

, "*' Ro L'a'-r' )

"Time", continued, by AMDG, copyright Page 6

,r-r{ (12)

Ifthe observer's reference frame and the center area of the "space-time curvatute"region are the same and if the object moves away in a linear line from the observer'slocation, thereby crossing the "aether-wind" under the angle E , then we can write

/ \ ,. ^rAlso, -llhl

p l=zc-', "..,wherefore ( l3 ) can be written as

la ) Q'**'

,r=rrl')/--'ft{np-lna j

,2)r, 1,,t , v 1.,

- cos' (Pt-

O ,tt(14)

Appendix II of 'Fluidum Continuum Universalis' shows the interrelationships

between: The speed oflight ( c),time( r ) and density (p ) ofthe fluidum

continuum ( FC ).The density is determined by two factors:( a ) The volumetric status ofthe universe( b ) The 'gravitational inflow', which is for the maintenance requirement

ofthe circulatory energy of vortex entities in the outermost region ofthe irrotational flow.

Observations over the last 300 years show a relationship between time and the

speed of light ( Appendix II, FCU ), which is

c,rcosec2 (t), o, .,fi ="on t.rcosec(t) , "t J; =ffi, therefore

I = sinh

( Appendix II, FCU ) :

( 15 )

since ,=(Y:: I ! *canwrte. r-sinh(r6xr)conn..j ( r6 )\r'*J2)r' ' \oM',,,Herein is r is the radius ofthe universe, assumed it is a sphere, c* is the

maximum velocity of a wave in "standard space", Q is the gravitationalconstant for the universe and M,r. is the total "mass" of the universe.

const.

-t^-