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- Time and the Speed of Light a New Interpretation

1

- TIME and the SPEED of LIGHT a NEW INTERPRETATION

A.G.Kelly, PhD, FIMechE, FASME, FIEI.*
SYNOPSIS. The Theory of Special Relativity has two requirements in relation to the behaviour of light. The first is that the speed of light is independent of the speed of its source. The second is that the speed of light is measured as a constant by observers in Inertial Frames, who are travelling at uniform speed relative to each other. The first requirement is confirmed as correct in this paper; the second is contradicted. The fact that a light signal that is sent both clockwise and anticlockwise, around a path on a rotating disc, takes different times to return to the source, was discovered by Sagnac over eighty years ago. An explanation of this phenomenon is put forward, which leads to the conclusion that time recorded aboard a moving object does not differ from the time recorded by a stationary observer, and that the dimensions of moving and stationary objects are the same. It is also shown from tests that electromagnetismdoes not to depend solely on relative motion. A new theory is put forward which is in conformity with both the Michelson-Morley and Sagnac experiments, and with tests on electromagnetism.

NOTATION

tests, which is also in accord with other test

results on the behaviour of light and

area

electromagnetism, and which maintains the

speed of light fringe shift

equivalence of mass and energy (E = mc2).

2 transformer

SAGNAC EFFECT

wavelength of light

momentum

The fact that a light signal, that is sent both

radius

clockwise and anticlockwise around a path on

distance

a rotating disc, takes different times to return

time

to the source was discovered by Sagnac over

velocity

eighty years ago. This effect, known as the

angular velocity

Sagnac effect, is an unsolved fundamental

problem in Physics. It has very important

INTRODUCTION

consequences, which have been overlooked

by previous investigators.

In dealing with the behaviour of light, the

Theory of Special Relativity has two Hasselbach and Nicklaus (1993) (3) list many

consequences, as shown by Einstein (1 pp. explanations of the Sagnac effect to be found

38 to 46). The first is that that the speed of in the literature, as proposed by various

light is independent of the speed of its source; authors over the intervening years. They sum

the second is that the speed of light is up the situation by saying "Thisgreat variety

measured as a constant by observers in (if not disparity)in the derivation of the phase

Inertial Frames who are travelling at uniform shift constitutes one of the several

speed relative to each other. The first controversies that have been surrounding the

requirement is confirmed as correct in this Sagnac phase shift since the earliest days of

paper. Practical tests done by the French scientist G. Sagnac (2) between 1910 and

studying interference in rotating frames of
reference ". Several references to each

1914 will be described in detail, and the suggested explanation are listed in their paper;

results will be shown to clash with the second in all of these references one finds attempts to

requirement. A theory will be suggested explain the effect by assuming that the

which fits the experimental facts of the Sagnac movement of the disc is, in some way,

affecting the behaviour of the light.

*HDSEnergy Ltd., Celbridge, Co Kildare.

However, it will be shown that the movement

The Institution of Engineers of Ireland, Monograph No I , Jan. 1995

- Time and the Speed of Light a New Interpretation

2

of the disc has no influence whatsoever on the where the light recombines, following its

behaviour of the light. This proposal is the traversing of a circuit.

only one that fits all the experimental results.

When the disc is spinning, the observer

It is of historical interest to note that Sagnac detects a shift in the fringes to one side,

proposed travelled

that the effect was a proof relative to a supposed

"theatthleigr "h.t

indicating that the two light signals are out of phase and do not return to point C at the same

However, as the existence of an ether was instant. The shift is by the same amount, but

shown to be unnecessary by Einstein (4), that in the opposite direction, when the direction

explanation lapsed.

of rotation is reversed.

SAGNAC TEST

A schematic representation of the test done by

''Sagnac is shown in Fig. 1. A light source at

point S emits light to a beam splitter at point

Some of SCDEFC7 and

isligthhtentraveises

theto-paatnh

"observer" at O' Some of the light goes the

other way' around SCFEDCo' The

apparatus can rotate with an angular velocity

o,The light source S and the "observer" 0 (in

reality a ihotogra~hicplate) are both fixed to

the rotating apparatus, and rotate with it.

D

0
--s
t
0
Fig. 1. Sagnac Test

Sagnac derived the difference in time, dt, between the times taken by the light to traverse the path in opposite directions, as

dt = 4Ao + c2

(1)

where small terms are ignored, A is the area enclosed by the light path, and c is the speed of light. Note that the interferometer that
displays this time difference is on board the rotating disc.

Sagnac showed experimentally that the centre of rotation can be away from the geometric centre of the apparatus, without affecting the above result. He also showed that, although the mirrors move as the disc rotates and as the light moves around the circuit, this movement has a negligible effect on the magnitude of the fringe shift.

In order to get an idea of the magnitude of the Sagnac effect, it is helpful to calculate the disc-rotation speeds necessary to obtain significant fringe shifts. Consider Fig. 2, where the light path is confined to a circle of radius r. The equation which expresses the relationship between interference fringes and time differences.[see Young (S)] is F=dt
[csh], where F is the number of fringe shifts
detected and h is the wavelength of the light used. From equation (1) and, since v = ro for circular motion, where v is the tangential velocity of a point on the circle, one has

When the disc is stationary, light sent around in opposite directions will arrive back at the same instant at point C. The beam splitter at C acts as an interferometer and is used to display this static situation and to determine whether any change occurs when the disc is set in motion. [The theory of interferometry is outlined in textbooks on physics e.g. Young (S).] In the static case, the interferometer produces fringes (dark and bright bands)

4Ao F = --------

-

4nrv

(2)

c h

c h

In order to obtain a fringe shift of one fringe, using a disc of lm radius, the velocity around the perimeter of the circuit has to be only about 13 m/s.

The Institution of Engineers of Ireland, Monograph No I , Jan. 1995

- Time and the Speed of Light a New Interpretation

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That this is so can be seen by setting F =1, r Dufour and Prunier then collaborated in a

=1, = 5500 10 -10 m (a typical figure), series of dissimilar Sagnac-type practical

and = logrn/s in the above equation'

tests. Firstly, in 1937 (13), they rigorously repeated the original Sagnac tests. They then

repeated the method used by Pogany (8), who had the light emitter fixed in the laboratory,

DOETBHAETRE SAGNAC-TYPE TESTS and

but had the photographic recorder on the disc. They then carried out the experiment with

both the light emitter and the photographic

Twhaes fciarsrrtikendowOunt Sinag1n9a1c-1type young German student

test pe*ormed Ha(rwrehsos (6w)a,as

unfortunately killed in the 1914-18 war). He

recorder taken off the disc, and set up fixed in the laboratory (the set-up adopted by Harress).

carried out tests on the refraction of light. His

apparatus was similar to Sagnac's, consisting

of a rotating disc photographic recorder

(baoltihghftixeemdittienr athned

laboratory); light signals were sent around the

disc in 1920, showed

directions. that the Sagnac

effLecatuceo(u7l)d,bien

It should be noted that, in all these cases, the interference of the light signals occurs on board the spinning disc, i.e. the interferometer (fringe detector) is always fixed to the disc; the photographic recorder, which is either on ofrrinogffethsehdifist.c,Tthheen ceaxppteurriems ehnet imwahgeereof tthhee

detected in Harress's numerical results.

photographic equipment is off the disc is the

Pogany (1926-28) (8) repeated the Sagnac tests. By using more sturdy apparatus and higher speeds of rotation he obtained a fringe shift 25 times greater than that achieved by Sagnac (F = 1.8 versus F = 0.07 fringe), thus reducing the experimental error and allowing
the fringe shift to be measured with greater

more-complicated of the two. Two extra lenses are required to send the image out from the disc and on to the photographic plate fixed in the laboratory; consequently, the spread of the readings widens from &5% in the case where the record is made on board the disc to +15% when it is off the disc.

accuracy.

In 1939, Dufour and Prunier carried out their

To indicate the accuracy of more modern Sagnac-type tests, Macek and Davis (1963) (9) give the accuracy of the laser equipment
used as 1 in 1012. In 1913, when Sagnac carried out his tests, the accuracy was about 1
in 10 2.

final experiment. They did a test with both the beginning and end of the light path on the spinning disc, but with the middle portion of the path reflected off mirrors fixed in the laboratory (directly above the disc). In this test, they had both the light emitter and the photographic recorder fixed in the laboratory.

Langevin (lo), in 1921, commented on the
practical tests done by Sagnac, and claimed that the effect, i.e. the observed time difference dt, had to be in accord with the

[Note: by "on the spinning disc" is meant that: the light is confined to a path by a set of mirrors which are fixed to, and rotate with, the disc.]

Theory of Relativity. He said that because that Theory fitted the "whole of the known experimentalfacts" of physics in general, the tests had to be explicable by that theory. In 1935, however, Prunier (11) published a note questioning Langevin's reasoning, and argued

The fringe shifts resulting from all the above Dufour and Prunier tests were the same as in their original Sagnac-type tests. This fact is of critical significance in understanding what is occurring, as will be discussed later.

that the practical tests were not explained by relativity. There followed a series of papers, by Dufour (12) and Langevin (10) in which was debated the question whether or not the effect was in accord with the Theory of Special Relativity and whether an apparatus could be constructed to settle the question. This debate ended in stalemate.

In 1942 Dufour and Prunier published a
composite paper reviewing their total experimental work to date. At the end of this paper they state that "the relativity theory seems to be in complete disagreement with the
reexpsuerlitmewnht"i.ch was garnered from the
This was the end of the debate, and the matter

The Institution of Engineers of Ireland, Monograph No 1, Jan. 1995

- Time and the Speed of Light a New Interpretation

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was not resolved. This present paper takes up an observer stationary in the 1aboratory.The

the problem left unresolved in 1942, and a anticlockwise signal is going against the

solution is proposed that fits the test results. rotation of the equipment and will return to the

light source when the source and

The reader is referred to a paper by Post interferometer are now at S'. The signal

(1967) (14) for an historical review of the travelling clockwise, with the direction of

Sagnac effect.

rotation of the equipment, will return to the

interferometer at S".

TWO POSSIBILITIES
Consider now the following question:
At what speed is the light travelling relative to the rotating observer? There are two possibilities and only one can and must be correct.

Let ds' be the distance SS' and ds" the distance SS". Let t' be the time measured by an observer situated in the stationary laboratory for the light to go from S to S' in the anticlockwise direction.

(a) The light, viewed from aboard the disc, is observed to travel at a relative speed of c.

(b) The light, viewed from aboard the spinning disc, i.e. by an observer rotating with the disc, is observed to travel at a relative speed not equal to c.

Note that we are not defining the two possibilities as being in Inertial Frames, nor is there any mention of Relativity Theory. A simple question is being posed, and the answer will be derived below.
/

DERIVATION of FORMULA

Whole apparatus turning at o clockwise

A derivation of equation (I), will now be given. Consider the theoretical circular model shown in Fig. 2. The light source and the interferometer are at S, and both are fixed on the rotating disc. Let to be the time taken for a light signal to traverse the circumference of the circle and to return to the source/interferometer,when both the disc and the observer are stationary. Thus, to is the path length 2 n r divided by the speed of light,

Fig. 2 Circular Sagnac Test
The time measured by that observer is
2 n r - ds' t' = --------------
C
But, t' is also the time taken for the disc to move a distance ds' in the clockwise direction. Therefore t' = ds' + v (v = r o ) , ds' = t' v and, from (4),

A light signal is emitted from the light source; a portion of the signal goes clockwise (denoted by the inner line on Fig. 2), and some goes anticlockwise.
Consider firstly the situation as observed by

ds' 2 n r

--- - -----------

7

v

C+ v

The Institution of Engineers of Ireland, Monograph No I , Jan. 1995

- Time and the Speed of Light a New Interpretation

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and (b) given in the previous section "Two

Possibilities".

Note that equations (4) and (5) both give the time recorded by a stationary observer; the equations simply state this time in different mathematical terms. We shall see the use of equation (5) below.
Following similar calculationsone gets for t", the time measured by a stationary observer for the light to go from S to S" in a clockwise direction,

Consider firstly option (a) where the light is assumed to travel at a speed of c relative to the observer regardless of the movement of that observer. Because a fringe shift F is detected it follows from the equation F = dt [cth] that it must be dt that is changing, (c and h are constants). This is clear from considering the position relative to the observer on board the disc; as far as this observer is concerned the path length is 2nr for one circumference of the disc, and that is the path that the light signal
appears to that observer to have travelled. If the light had travelled at a speed of c relative
to this observer then no fringe shift could be observed on board the disc. But a fringe shift is observed, and thus the light signal cannot travel at a speed of c relative to the observer on the disc.

Subtracting equation (5) from (6), the differencebetween the times for the light to go clockwise and anticlockwise is

2n r dt = ---------

-

---2--n--r--

-

---4--n-r--v---

C-v

C+V

c2 - v2

and, since v = r o , and nr2 is the area A of a circle, one has

Can there be a possibility that for some reason time must change aboard the spinning disc?
Abolghasem et al. (1989) (15)following this reasoning, say that one would have to "redefine time or rather 'correct' the local time interval of two adjacent events by an amount, so that the speed of light becomes the same in both directions. This corrected, or 'natural time' interval guarantees the clocks on the rotating disc to be Einstein-synchronised".

d t = 4 A o + (c2 - v2),

(7) Further Langevin (10) suggests "adopting a

local time that is not uniform, but changing by

The v2 term is negligible for practical tests and 2 2 o A a c2".

may be ignored, giving Equation (1).

However, this time difference has been derived for a stationary observer, fixed in the laboratory.
This time difference agrees with the fringe shift recorded on the interferometer.

It is not clear whether these authors are suggesting that the proposed "local timew changes are relativistic effects (in the relativistic sense of time altering at high velocities). In any case, it will be shown in a later section that, even were such a relativistic
time change to arise, it would be ten million times smaller than the time difference

(equation (1)) effect recorded in typical But the interferometer is rotating with the Sagnac-typetests. disc. How is is then that the interferometer

rotating with the disc records the same time difference?
This means that the time recorded in the fixed laboratory and on board the disc are identical.
To answer this question, consider options (a)

Therefore, assume that possibility (b), is the correct option, so that the speed of light is not confined to a relative speed of c.
Abolghasem et a1 describe this solution as that which "causes the velocity of light to be locally different in opposite directions"

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Langevin says that were this the case, "light explanation of the Sagnac effect.

speed would vary with the direction between c Because the interferometer on board
- w a n d c + or').Note that while both authors the moving disc records a fringe shift,
discuss the possibilities, neither realised that the relative speed of light to that spot,

Relativity Theory could not, as we will see, (which is being photographed from on

explain the dilemma.

or off the disc) is c f v , while the

.absolute speed of the light remains as
It should be stressed that, in all the tests, the c

interferometer on board the disc records the fringe shift correspondingto equation (1)) and Now consider a single light signal travelling that it is solely aboard the disc that the in one direction only, in this case the

inte$erence occurs, which causes the fringe anticlockwise direction. The difference in

shift. This fringe shift may be photographed times recorded for the stationary-disc case and

from on or off the disc.

for the single signal to travel from S to S' is, from equations (3) and ( 5 ) ,

We see above that equations (4) and (5) are

mathematically equivalent; they both give the same time interval.

to - t'

2nr = ------

-

2---n---r-

- 2---n---r--v---

Equation (4) may be restated as follows; the observer in the fixed laboratory observes that the disc moves a distance dSYwhile the light
completes a distance of 2nr - dSYaround the
other direction from S to S'. The equation describes the time interval as it would be discerned by the observer in the laboratory.
Equation (5) may be restated as follows; the moving observer thinks that the light has, relative to oneselj completed one revolution of the disc (2n r) at speeds of c+_vin the two opposing directions. This is the relative speed of the light; the absolute speed is always c.

Therefore, the difference in time dt' is
For small values of v the difference is to v + c. As v approaches c, d t' approaches to t 2, and the speed of light relative to the observer is then 2c.
Similarly, for the clockwise direction, letting t" be the time for the signal to arrive back at point S", one has

Eauation (5) describes the same time interval as>t is measured by the interferometer aboard the spinning disc (also t ' '). Note that equation (4) does not apply to the observer on the disc because the numerator is the distance that the light signal travels as observed by an observer in the fixed laboratory. The observer on the disc could, by marking the disc against a spot in the laboratory, deduce that the disc had moved a distance ds' (relative to the laboratory), while the light was travelling a complete circuit relative to the observer on the disc:
It is to be noted that t' [the time defined earlier as the time recorded in the stationary laboratory in deriving equation (4)] is the same as the time recorded aboard the spinning disc, as shown above.
It is important to appreciate the above distinctions, because it is at the core of the

In this case, as the speed approaches c, the result becomes infinite because the light and
the Point S are travelling in the same direction, and the time for the light signal to gain one complete circuit on the Point S is infinite. At low velocities, the result is again to v + c.

fForrotmheetqwuoatdioirnesct(i3ontos a9r)e, athlseoteimxperedsifsfiebrleenacses

v

v

dl' = t' ----- and dl" = t" ----- (10)

C

C

Because, d s ' c v = t ' and d s " c v = t", equations (10) may be written as

dt) = s, + and dt,,=

,) c. +

(1 1)

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Time and the Speed ofL.ight- a New Interpretation

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By subtracting equation (4) from equation (3) affected in any way by the movement of an we also get the first of the two equations (11). object in a straight line, which is the limit of
an infinitely large circle.

From the above discussion we conclude that::

Therefore it follows that an observet. aboard

The Sagnac effect is thus seen to be a an object which is travelling oflin a straight

measure of the difference in the times line, at constant speed relative to the

taken by the two light signals, while laboratory, will record the speed of light

they are away on their travels in the relative to oneself as c rt v. Thus, this

two opposing directions.

observer will record the same time as the

observer in the laboratory. Defining both

Another way of stating this is to say that the these Frames as Inertial i.e. ones in which

light is behaving as if the rotating disc did not Newton's first Law applies, we derive that the

exist.

speed of light measured in the moving Frame

is not the constant c relative to the moving

The Sagnac effect shows that the light observer. This conclusion is in direct

is operating independently of the contradiction of the requirements of the

spinning apparatus.

Theory of Special Relativity on the behaviour

of light.

It was stated earlier that it would be shown

that the fact the spinning disc was not an If light were sent in two opposite directions

Inertial Frame would be irrelevant. This is from aboard an object which was travelling in

now clear.

a straight line, the two signals of the light

would not ever again meet to be compared.

Many authors contend that, because the The literature refers to the Sagnac effect as

spinning disc is not an Inertial Frame, the arising from the rotation of the spinning disc

Theory of Special Relativity does not apply. simply because it is only upon such an

This problem does not arise because the light apparatus that an interference pattern can be

is simply travelling in the Frame of the examined.

Stationary Laboratory, and not in the Frame

of the spinning disc.

COMPARISON of the SAGNAC

The Sagnaceffect is not so much an "eflect", EFFECT with SPECIAL RELATIVITY

but rather it is a confirmation of this fact.

Because the light ignores the movement of the While the following discussion is not relevant

disc, the Theory of Special Relativity is not to the conclusions drawn in the previous

relevant to any "behaviour of the light on a section, it is included for completeness. It

rotating Frame". The light has no activity should be remembered, in reading this

aboard the disc.

section, that none of the arguments therein are

in any way a defence of the conclusions of

this paper.

CIRCULAR PATH VERSUS

STRAIGHT LINE

Einstein (1) accepted that movement on a

closed polygonal circuit (and indeed in a

In this section it will be shown that the closed curved path) has the same consequence

conclusions derived from the Sagnac effect, in as movement in a straight line, when

relation to a spinning disc, apply equally to considering the question of measurement of

motion in a straight line.

distance or time (1905 paper, p.49, last

paragraph). Having derived his formula for

We saw in the previous section that the light straight line movements, he said "it is at once

was behaving independently of the spinning apparent that this result still holds good i f the

disc. If, as has been demonstrated, it has been clock moves from A to B in any polygonal

oblivious to the movement of small discs of line", and that "if we assume that the result

varying radii such as used in the tests, then it proved for a polygonal line is also valid for a

will also ignore a disc of immense radius; this continuously curved line, we arrive at this
leads to the conclusion that it will not be result: If one of two synchronous clocks at A

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is moved in a closed curve with constant The derivation of the corresponding Sagnac
velocity until it returns to A, the journey ratio dt s is as follows:

lasting t seconds, then by the clock which has

remained at rest the travelled clock on its k t to be the time for a light signal to traverse

arrival at A will be ID t V 2 /c2 second slow. the circumference of a stationary disc, and t'

Thence we conclude that a balance-clockat the be the time for a light signal to traverse the

equator must go more

a

circumference of a spinning disc, as recorded

amount, than a precisely similar clock situated by the observer on the disc. ~

i from ~

~

at one of the poles under otherwise identical equation (8)

conditions"

Because Einstein accepted that the Theory of Special Relativity applied equally to motion in a straight line, to motion in a polygonal path and in a closed circuit, it can thus be taken that that Theory can be assessed against the Sagnac test results. The problem caused by the non-conformity of the Sagnac test results with the Theory cannot be avoided, since Einstein himself had no difficulty in applying his Theory to rotating Frames e.g. the spinning Earth, compared with a stationary Frame (an observer at a Pole).
Because many investigators claim that the Sagnac effect is made explicable by using the Theory of Special Relativity, a comparison of that theory with the actual test results is given below. It will be shown that the effects calculated under these two theories are of very different orders of magnitude, and that therefore the Special Theory is of no value in trying to explain the effect.

Note that, for a circular path, t 0 is the same in
both cases, namely 2 n r + c.
The ratio of dt s to dt R is therefore
When v is small as compared to c, as is the case in all practical experiments, this ratio reduces to 2c s v.
Some authors imply that the Sagnac effect could be explained by the Theory of General Relativity. Apart from the fact that any acceleration is radial, the effect would be minuscule, as is the effect calculated under the Theory of Special Relativity.

The Theory of Special Relativity stipulates that the time t' recorded by an observer moving at velocity v is slower than the time to recorded by a stationary observer, according to
where y = (1 - v2 + c2 )-0.5 and t o and t' are
the times recorded by the respective observers. Using the Binomial Theorem to
expand y,(1 - vz+c2)-0.5= 1 + ( v Z r 2 c 2 )
+ terms involving v4 rc4 or less, so that from
equation (13). t0=t'[1+(v2+2c2)] Thus dtRtthe Relativity time ratio, is given by

Thus the Sagnac effect is far larger than any purely Relativistic effect. For example, considering the data in the Pogany test (8), where the rim of the disc was moving with a
velocity of 25 m/s, the ratio d t s r dtR is about 1.5 x 107. Any attempt to explain the Sagnac
as a Relativistic effect is thus useless, as it is smaller by a factor of 107.
Referring back to equation (I), consider a disc of radius one kilometre. In this case a fringe shift of one fringe is achieved with a velocity at the perimeter of the disc of 0.013m/s. This is an extremely low velocity, being less than l m per minute. In this case the Sagnac effect would be 50 billion times larger than the calculated effect under the Relativity Theory. This example is given to illustrate that there is no question of any relativity effect explaining the fringe shift at these velocities, since relativistic effects could only arise at great velocities. For a disc the size of the equatorial

The Institution of Engineers of Ireland, Monograph No 1, Jan. 1995

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section of the Earth, the velocity required for laboratory. The tests show that this is not so.

one fringe is only 2x10-6m/s. This figure is

given for comparison with the equatorial clock However, as we have seen, this debate is

rotating with the Earth.

unnecessary, because the light is not affected

by the rotating disc.

Apart from the difference in magnitude, there

are other conceptual differences. In the actual We thus see that the Sagnac effect is

Sagnac test, the difference between the not to be confused with an effect

moving and stationary cases was a time gain, calculated under the Theory of Special

or time loss, depending on the direction of Relativity.

travel. Relativity predicts that there should

always be a time loss, regardless of the The results of the Sagnac test indicate that the

direction of travel.

two requirements of the Theory of Special

Relativity quoted above are mutually

Can it be, however, that both a Sagnac effect exclusive, at least in Sagnac-type tests. They

and an effect calculated under the Theory of show that, if the light velocity is independent

Special Relativity can co-exist? This was of the motion of the source, then it is not at

assumed by Langevin (10) and Post (14); the same time measured as identical, by

they showed that applying Relativity Theory observers who are travelling relative to each

had an infinitesimal effect on the result, which other.

stood unaltered as the basic Sagnac effect. In

other words, in a Sagnac-type experiment, is

it possible that there is a Relativity effect, even DISTANCE and TIME UNCHANGED

though it is too small, in comparison with the

Sagnac effect, to be detected? That this cannot Let us accept that the analysis in the previous

be so is seen from the fact that, as mentioned sections is correct, and that light is not

before, a fringe shift is detected and that thus confined to travel at a speed of c relative to all

the behaviour of the light on the spinning disc observers in Inertial Frames. In this, and the

does not evince a speed of c relative to the following section, some consequences of this

observer on board the disc.

are discussed.

In setting out the two requirements for the The Theory of Special Relativity requires that

behaviour of light under the Theory of Special the measuring instruments in one Inertial

Relativity Einstein (1) stated "light is always Frame must record different results from

propagated in empty space with a definite those in another Inertial Reference Frame,

velocity c which is independent of the motion when these frames are moving relative to each

of the emitting body" and "any ray of light other. [For an observer to measure velocity, a

measured in the moving system, is propagated ruler (rigid rod) and a clock can be used.] It

with the velocity c, f as we have assumed, follows from this that rulers shorten and that

this is the case in the stationary system".

the ti.merecorded on clocks would run slow at

higher speeds.

The speed of the light is confirmed in the

Sagnac test to be independent of the speed of However, such a conclusion is not necessary

the source of the light. This is in conformity because, in reality, it is the relative speed of

with the former requirement. The latter the light, and not the time, that is changing.

requirement is that the speed of light is

constant, as measured by observers in all It can be concluded that, referring to

Inertial Reference Frames. Accepting Inertial Frames, motion in a straight

Einstein's logic for application of the theory line at constant speed will not affect

to both a polygonal shape, and to a clock on the measurement of time or distance

the rotating Earth at the equator, would aboard a moving object, as compared

require option (b), in the "Two Possibilities" with the time or distance measured by

section above to be true. It would require that a stationary observer.

the light be measured as travelling at a speed

of c relative to both the observer aboard the The factor y, to be applied in all relativistic

spinning disc and the observer in the fixed calculations on distance or time, is a direct

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10

consequenceof the second requirement of the could go off on a circuit as defined by

Theory of Special Relativity. The derivation Einstein and quoted earlier. Thus, on

of this is seen on p.46 of Einstein's first 1905 reuniting both twins would observe the other

paper (I), in which he put forward the theory. to be younger at the same instant. This

apparent contradiction is the paradox. Most

It is solely to distance and time that texts deny the second half of the comparison,

the amendment has to be made to the by claiming that only one of the twins ages

Theory of Special Relativity. The less and there are many and varied supposed

application of that Theory to other solutions to justify this one-sided relativity.

aspects of physics is not being Some say the one-sided aging occurs solely

questioned in this paper.

during the reversal of direction at the far end

of the journey for the twin who goes away.

It is suggested that space and time are Rindler, in 1982, (17), on the other hand,

absolute, not relative; and that absolute space says that the aging occurs at the initial

is a basic coordinate frame for all acceleration phase of the departing twin. Such

measurements in the Universe. This means attempts at justification are presumably to

that the speed of light has an absolute limit of avoid the difficulty of explaining how each of

c, but may have a speed relative to an the two twins will, on reuniting, observe the

observer that is less or greater than c.

other to be younger, at the same instant.

This explains the behaviour of superluminal
objects that are observed in outer space. Such objects are observed from Earth as separating
from each other at speeds of up to ten times the speed of light. Four such objects (three quasars and one radio galaxy) had been
identified by 1977 - see Cohen et a1.(16) This
is now explicable by a calculation of the relative speeds of the objects as viewed by an
observer on Earth, where the objects are separating at high speed, while also
approaching our galaxy, with a small angle of separation subtended to Earth.

Dingle (1972) (18) gives a blow by blow description of the paradox controversy, which raged between him and Prof. W.H. McCrea, and others. This controversy continues, among other protagonists, to the present day. While some authors argue that the paradox does not make sense, none offer a solution which "explains" it away. Dingle forecast dire consequences for mankind were the Theory not amended in such a way that the paradox was dispelled. However, the "paradox" does not in reality arise, because there is no alteration in time with speed, as proved by the Sagnac-type tests.

PARADOXES
The so-called "clock paradox" or "twins paradox", is a consequence of Relativity which has generated much controversy over the past ninety years. The Theory of Special Relativity predicts that one twin who travels away from Earth at very high speed and returns after a long number of years will appear to the twin who has remained on Earth to have aged less.
It can be claimed that, strictly in accord with Relativity, the reverse should also hold, namely that the twin who remained stationary on Earth should also appear to be younger, to the traveller on the return of the latter to Earth. That this is so can be seen by considering twins in outer space who pass each other at high speed; neither twin can determine which is "receding" from the other. These twins

Consider now the conundrum quoted by Zukav (1991) (19) (in a Chapter aptly titled "General Nonsense") where he considers two concentric circles of different radii revolving with the same angular velocity, so that two points, one on each circle, joined by a line passing through the centre of the circles are
moving at different velocities (v=ro). He applies the Theory of Special Relativity, and states "the ratio of the radius to the circumference of the small revolving circle is not the same as the ratio of the radius 20 the circumference of the large revolving circle". This is because, according to the Theory of Special Relativity, distance contracts with increasing velocity, when measured along the direction of motion. Thus, distance to an observer on the larger circle contracts relative to that measured by an observer on the smaller circle. This situation leads to a changing value
of n, or to different measuring standards for

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- Timeand the Speed of 1.ight a New Interpretation

11

measuring the radii, from those used to days were of the order of one-tenth of that.

measure the circumferences.This deduction is

contradicted by the Sagnac tests, because The behaviour of the clocks during the ten

there is no diminution of the distance along days prior to the tests, and during the five

the perimeter of a circle with increased speed. days after the tests, showed that the results

were highly dependent on the period in which

Another strange consequence of the Theory of the tests were actually performed. The

Special Relativity is that, under uniform changes during the flight periods were radical

motion, it is only the dimensions in the for three of the clocks. A clock that had been

direction of travel which contract, dimensions gaining time prior to flight was seen to be

perpendicular to the direction of motion being losing time after the flight. Other clocks

unaffected. This leads to the conclusion that a suffered changes in their rate of drift during

sphere travelling away at high speed would be the flight period, by a factor of two or three. It

observed to contract to a disc. An oft-quoted is not known at what stage of any flight such

amusing result of the Theory is that a fast changes in behaviour occurred, because no

moving long ladder can be fitted into a short clock could be compared with the ground
stationary garage - see Rindler 1982 (16). reference station during flight.

These situations do not arise.

Despite the fact that one of the four clocks on

each of the Eastward and Westward journeys

FLYING CLOCKS

showed time changes of opposite sign to

those predicted by the Theory, Haffle and

Haffle and Keating (20), in 1972, conducted Keating still took the average of all four

tests with four cesium clocks, where the clocks; the average turned out to be of

clocks were flown Eastward and Westward in the same order, but of opposite sign, aeroplanes around the Earth. The results of to the time changes of the

these investigations are often quoted as proof aforementioned aberrant clocks. Taking

that time changes with speed, as predicted by the average of the time changes recorded by

the Theory of Special Relativity. It will be the four clocks does not provide evidence, on

shown here that the tests were of insufficient which a conclusion may be based.

accuracy to draw the conclusion that time is

altered. They used the Theory of Special Realising the somewhat disparate behaviour

Relativity to forecast a difference in time of the four clocks, the authors proceeded to

between that recorded by flying clocks, and make corrections to these results. Whenever,

the time recorded by a standard station at during flight, one clock displayed a sudden

Washington, USA.

change in drift rate relative to the other three,

its rate change was ignored. Had but one such

All four clocks were predicted to lose time correction been made, there could have been

flying Eastward; two of the four did so, one some credibility in this procedure; but

gained time, and one showed no significant fourteen such sudden rate changes were

change. On the Westward journey, the clocks ignored, with seven of these on one clock.

were required by the theory to gain time; two These corrections changed the results derived

did so, one lost time, and one showed no by the average method from -66ns to -59ns

significant change (the same clock that going Eastward, and from +205ns to +273ns

showed no difference on the Eastward going Westward. It was not possible for the

journey)

authors to make corrections to offset possible

gradual changes in drift pattern. The results

It is normal for a particular cesium clock to predicted by their theory were -40ns and

show a drift rate relative to a standard clock +275ns, which were very close to the

station, which records the average of several published experimental results.

very accurate clocks. Indeed, individual

clocks can display inexplicable gradual, or It is of interest to note that a previous test, sudden, changes in drift rate. Sudden drift carried out over some weeks in 1970, and

changes can be, in extreme instances, as large referred to in the Haffle and Keating paper,

as 1 ps per day; the differences forecast by resulted in no discernible gain or loss during the authors over the total flight time of six the flights. It is evident that tests of a far more

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Time and the Speed of L.ight - a New Interpretation

12

accurate nature are required to discern the atmosphere; this is analogous to the case

effect, if any, of transportation on cesium where light escapes from water (where it

clocks.

travels at 0.7%) to air, whereupon it assumes

the speed of light in air.

COMPATIBLE SOLUTION

The synchronisation of clocks on Earth, using

signals reflected off satellites, would require a

The Sagnac results do not contradict the slight amendment, to take into account the

results of the Michelson and Morley change in the speed of the light as it leaves

experiment (1887) (21). In that test, the speed and reenters the atmosphere.

of light was measured to be the same, whether

measured in the direction of the motion of the

Earth on its orbit around the Sun, or at right ELECTROMAGNETISM

angles to that direction.

In a test done in 1917 Pegram (23) showed

A solution is now needed, which fits both the that, using a solenoid carrying a steady D.C.

Sagnac and Michelson-Morley experiments, current:

and which also agrees with the requirement of

the Theory of Special Relativity quoted 1. A stationary short straight isolated radial

earlier, and which is confirmed by the Sagnac conductor, inside a stationary solenoid, is not

tests, namely that the speed of light is charged (as would be expected).

independent of the speed of the source.

2. The stationary radial conductor, inside the

One possibility is that light, on Earth, travels rotating solenoid, is not charged. This is

with respect to a coordinate frame fixed certainly not as would be expected.

relative to the Earth. Katz (22) says (when

commenting on the Fizeau experiment on the 3. When both the solenoid and the conductor

behaviour of light in moving water) that "the are rotating there is a charge. Again this is

speed of light in a medium must clearly be not as would be expected.

with respect to a coordinateframe fixed in the

medium,for the very structure of the medium, These tests accord with the conclusions in this

the position of its atoms and molecules, paper in relation to the behaviour of light,

provides a preferred reference frame". In which is also an electromagnetic

water, the speed of light is 0 . 7 5 ~bu~t this phenomenon.

speed is increased (decreased) when the water

is moving with (against) the direction of the If the current in the solenoid is flowing,

light signal.

relative to the laboratory, and is not moving

with the moving solenoid, then the tests make

As is the case for all media, light travels in air sense. Altrnatively, if the magnetic field was

at a speed less than c (which is the speed in a relative to the laboratory and not to the

vacuum). The speed is c divided by the index spinning magnet, the results would also make

of refraction of the medium; for air the index sense. Pegram stated that Faraday was of the

is 1.0003. No distinction has yet been made latter opinion, but this seems to have been

in this paper between the speed of light in a overlooked in the meantime.

vacuum and in air, because the difference is

so small.

Pegram said "the generation of an

electromotive force is not simply a questiion

It is proposed that light travels in all of the relative motion of the conductor and the

directions in the atmosphere at a solenoid whichfurnishes the magneticfield".

speed of 0.9997c, and is unaffected

by the motions of the Earth, or by the In a 1990 leader in Nature (24) John

motion of any observer.

Maddox, the editor, posed a problem similar

to No. 2 above and stated that if there were no

Under this proposal, when light escapes from charge in such a case "relativity has vanished

the Earth, it travels at c in free space, relative out the window". In the leader he was

to the point where it escapes from the discussing a theoretical claim by a Bulgarian

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- Time and the Speed of L.ight a New Interpretation

13

exile (Marinov) that in such a test there would 1. A Michelson-Morley test on the moon,

be no charge.

where there is no atmosphere. It would be

interesting to determine whether the result is

different from that on Earth.

E = rnc2 MAINTAINED

2. A Sagnac test on the moon would show if

In many texts (e.g. Young (S)), the derivation the light travelled relative to fixed space, and of E = mc2 begins with time dilation and ignored the movement of the moon.

distance contraction. To sustain the theory put forward in this paper, an alternative 3. Both of those tests repeated in space off a explanation is required, because that famous satellite or rocket.

formula is not being questioned. In this respect, it is interesting to note that Lorentz 4. A repeat of the Pegram tests would (25, p.24) had published the relationship confirm the conclusion concerning between energy, mass and the square of the electromagnetism.

speed of light in 1904, a year before Einstein

published his first paper (in which he stated that time and distance differed aboard moving CONCLUSIONS

objects). Also, in 1906, Einstein in a "thought experiment", by considering solely the momentum of photons as they moved from one end of a closed box to the other, came to the E = mc2 equivalence - see French (25, p.16).

1 Light, which is sent around the circumference of a rotating disc, in opposite directions, does not travel at the same speed c, relative to an observer aboard that disc. This was first demonstrated by Sagnac in 1913, and repeated, with ever greater accuracy by

The rest of the results concerning mass and many investigators over the intervening years.

energy follow directly from E = mc2 and the relationship E=pc where p is the "virtual"
momentum of a photon. French (p.20), using these relationships, derives other mass and energy relationships such as E = Eoy and m = moy. The theory put forward in this paper
does not question these equivalences.

2 . The explanation put forward for the Sagnac effect in this paper is that light travels in the co-ordinate frame of the laboratory, even when it is generated aboard a spinning apparatus. and that the behaviour of light is unaffected by the motion of the apparatus.

The matters disproven in this paper will not cause any dire consequences. The result should give a better insight into the behaviour
of electromagnetic phenomena. There may be phenomena that do not appear to fit with the theory proposed here, but the basic, simple and incontrovertible experimental practical tests described in this paper must be explained

.3 This leads to the deduction that distances
and time as measured by an observer aboard a spinning disc are the same as those measured by an observer in the stationary laboratory;
they are also the same aboard any object that is moving with uniform speed relative to the stationary laboratory. This does not agree with the Theory of Special Relativity.

by any proposed theory.

.4 Tests done, which purport to prove that

The General Theory of Relativity is not the timekeeping of clocks varies with speed, addressed in this paper: The effect of the are of insufficient accuracy to support such a conclusions of this paper on the wider realm theory.

of physics will require separate publication. 5 . It is suggested that light travels at a

constant speed of 0.9997~with respect to a

TESTS TO BE DONE

coordinate frame fixed relative to the Earth. This proposal fits with the Michelson-Morley

It would give confirmation of the theory in and Sagnac tests, and with the first

this paper were the following tests to be requirement of the Theory of Special

carried out.

Relativity, (that the speed of light is not

affected by the speed of its source).

The Institution of Engineers of Ireland, Monograph No I , Jan. 1995

Time and the Speed of Light - a New Interpretation

6 . The relative motion of a conductor and a

Haffle, J.C. and Keating, R.E. Science,

current carrying solenoid is not the

1972, 177, 166 and 168.

determining factor in whether there is a charge 2 1 Michelson, A. and Morley, E. Phil.Mag,

across the conductor.

1887, S5, 24, No 151, 449.

2 2 Katz, R. An Introduction to the Special

7. Time and space are absolute. A relative, but not an absolute, speed of light in excess of c is possible. This explains the appearance of objects in outer space, that are observed to travel at relative speeds greater than the speed of light.

Theory of Relativity, 1964 (Van Nostrand). 2 3 Pegram,G.B. Phys. Rev. 1917, 10, No.6,
591. 2 4 Maddox, J, Nature, 1990, 346,103. 2 5 Lorentz, H. 1904 paper in The Principle of
Relativity, (Metheun) 1923.

2 6 French, A.P. Special Relativity, 1991,

8. Some experiments could be performed to

(Chapman & Hall).

test the conclusions of this paper.

REFERENCES

1 Einstein, A. The Principle of Relativity, (Metheun),1923.
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3 Hasselbach, F. and Nicklaus, M. Phys. Rev. A, 1993, 48, No 1, 143.
4 Einstein, A. The Meaning of Relativity, (Metheun), 1922.
5 Young, H.D. University Physics, (Addison -
Wesley), 1992. 6 Harress, F. 1911, Thesis, Jena University. 7 von Laue, M. Ann. der Phys. 1920, 62, 448. 8 Pogany, B. Ann. der Phys, 1926, 80,217;
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The Institution of Engineers of Ireland, Monograph No 1, Jan. 1995