A revision of the principle of relativityJanusz DrożdżyńskiUniversity of Wrocław, ul. F. Joliot-Curie 14, 50-383 Wrocław, Poland.E-mail: janusz.drozdzynski@chem.uni.wroc.pl

Physics Essays  Vol. 26, Issue 2, pp. 321-325, June 2013 http://physicsessays.org/browse-journal-2/product/62-18-janusz-drozdzynski-a-revision-of-the-principle-of-relativity.html

Abstract: In this paper some question connected with the time dilation effect are discussed.

A thought experiment is presented in which it has been proven that, on the basis of the

trajectory of a laser pulse in a moving frame of reference (spaceship) with a constant

velocity, it is possible to determine the direction of movement and speed of the system with

respect to the velocity of light. It has also been shown how this statement could be

experimentally confirmed. We conclude from this that Einstein's principle of relativity

needs a revision.

Key words: Special theory of relativity; Principle of relativity; Thought experiments; Time

dilation effect; Inertial frames of reference; Detection of movement.

I. INTRODUCTION

The special principle of relativity states, that if an inertial system of coordinates K is

chosen such that, in relation to it, physical laws hold in their simplest form, the same laws

1

hold in relation to any other system of coordinates K' moving in uniform motion relatively

to K.1 This also means that a light pulse perpendicular to the x axis should always move

parallel to the y axis according to an observer in an inertial frame of reference. However,

when two observers in two different inertial frames of reference measure the observed path

length l(S-So-S) of the same light pulse at the same time interval (Δt), each observer should

notice a different trajectory and path length: l(S-So-S) and l(S-So-S’) ( Fig.1). Since the principle

requires the same relation l=Δt·c in both frames, in consequence a time dilation effect arise.

One may find all aspects of Einstein’s special theory of relativity, in numerous books,

particularly in a recent published book of David N. Mervin.2

In this paper a thought experiment is presented in which has been shown that a simple

analysis of the path of a light pulse in an inertial frame of reference should indicate the

motion of the frame with respect to the speed of light, despite of the special principle of

relativity.

II. THOUGHT EXPERIMENTS

In "Relativity, The special and General Theory" Albert Einstein has shown that the

vague word ”space” should be replaced by "motion relative to a practically rigid body of

reference" or more precisely - to a system of coordinates.1

In a visualization of this idea1 he describes a man who is standing at the window of a

railway carriage and drops a stone on the embankment, without throwing it. Since the

railway carriage is travelling uniformly then, if one is disregarding the resistance of the air,

he sees the stone descend in a straight line, with respect to the system of coordinates of the

railway-carriage. From the point of view of a pedestrian, who observes the event when

standing at he embankment, the stone falls to earth in a parabolic curve with respect to the

2

system of coordinates of the embankment. With the aid of this experiment, Einstein shows

that one may not register an independently existing trajectory, but only a trajectory relative

to a particular frame of reference.

This thought experiment has been commonly adopted in order to explain that time is

really not running in the same manner for everybody.2-5 In another thought experiment an

observer in an uniformly moving spaceship, directs a lightning flash from the ceiling to a

mirror placed on the floor of the spaceship. After reflecting from the mirror the light pulse

returns to the ceiling. According to the General Theory of Relativity, in the absence of

gravitational forces, the light pulse must than run along a straight line, a so-called null

geodesic. Hence, the observer in the spaceship sees that the light pulse is moving in both

directions along the same straight path S-So-S, down and up. However, according to an

observer who is watching the event outside the spaceship, in a relative state of rest, the light

pulse is moving along a trajectory in the form of a V letter (S-So-S’), whose path is much

longer than the simple path of down and up. Since the velocity of light is the same for both

observers and the path longer, then, according to the observer in the relative state of rest,

time is running much more slowly for the observer in the spaceship. This conclusion has

been called the time dilation effect and is graphically presented in Fig. 1a and 1b, respectively.

3

Figure 1.( a) The light pulse is emitted from the source S and is reflected back at So

along the same path, as observed in the frame of reference (R1) in the spaceship, which

moves with the velocity u relative to the frame of reference (R2) in the state of rest.

(b). The positions of the light source at the time of departure and return of the pulse are

given by S and S', respectively. It is assumed3-5 that as observed in R2, the same light pulse

is moving along a longer trajectory, in the form of a V letter. Since the speed of the light

pulse is constant and the path is seen to be longer in R2 it is assumed that when the rate of a

clock at rest in R1 is measured by an observer in R2, the rate measured in R2 is slower than

the rate observed in R1.4

Let R1 be the frame of reference of the spaceship and R2 the frame of reference of the

observer outside the ship. On this basis4 a quantitative relation between time intervals in the

R2 and R1 coordinate systems has been derived.

4

Δt =

Δt '

√1−u2 /c2 (1)

where Δt’ separates two events occurring at the same space point at a frame of reference

R1, Δt is the time interval between these two events as observed in R2 and u is the velocity

of the spaceship along the x axis relative to the outside observer. The Eq. (1) has been also

used to derive4 a similar relation

l =

l '√1−u2 /c2

(2)

between the lengths l and l' of a rod (which rests in R1) measured in R1 and R2,

respectively, which gives an effect called a contraction of length.

A fault in the interpretation of this and similar thought experiments arises from the

principle of relativity which assumes that an observer in an inertial frame ( spaceship) is

not able to determine its motion without an external frame of reference. Hence, the principle

assumes an equivalence of all inertial frames of reference also of that moving with a

constant speed equal to zero. In consequence, if the light source could be pointed parallel to

the y axis at absolute rest, the photon ( light pulse) should move down and up along the

same path, as well in a frame in motion and at absolute rest. However, as it is well known,

the velocity of the light pulse (or more precisely, the photon) cannot be influenced by the

motion of the source i.e. by the motion of the system of coordinates of the spaceship

because the mass of a photon at rest is equal to zero and therefore the photon cannot move

straight down like the stone in the Einstein's thought experiment. Thus, if the light or laser

5

source could be directed parallel to the y axis at rest than the laser pulse could not by any

means move down and up along the same path with respect to the system of coordinates in

motion i.e. that of the spaceship (Fig 1a), only because it has been assumed so.3,4 For

particles with a rest mass equal to zero (e.g. photons), one sometimes uses the notion

relativistic mass, as a quantity identical to their energy ( divided by c2 ), but any inertia of a

photon is out of the question in spite of its nonzero momentum.6,7 Hence the photons in the

light pulse cannot be influenced by the speed of the spaceship.

In the following analysis of the thought experiment (Fig. 2) it has been proven that an

observer in an object in motion with a constant speed may by oneself determine as well the

speed and direction of the system with respect to the constant velocity of light. For clarity

reasons the frame R1 on Fig.2 has not been repeated in the subsequent six positions of the

spaceship. If the laser source in motion could be aimed parallel to the y axis at rest, the

observer in the spaceship should notice that the laser pulse is moving down and up along a

V-shaped trajectory with reference to the y’ axis of the coordinates of the spaceship in

motion (dotted lines, Fig. 2) and is not returning to the starting point. Whereas the observer

in the state of rest should notice that the laser pulse (photon) is moving along the path of the

straight line parallel to the y axis (solid line, in Fig.2) and is not returning to the starting

point either. The path of the photon (laser pulse) as seen in the frame of reference R1 (Fig.

2, dotted line) results from a superposition of the motion of the spaceship and the motion of

the photon. In other words, the longer path of the photon (dotted line) is dependent on the

motion of the y’ axis (spaceship) and not the activity of the photon.

6

Fig. 2. The laser source is directed parallel to the y axis. The pulse, as observed in the frame

of reference at rest R2, is emitted from the source S and reflected back by the mirror along

the same path of a straight line (solid line). In the frame of reference of the spaceship (R1)

which moves with the speed u relative to the frame of reference at rest (R2), the observed

trajectory of the path is in the form of a V letter and is marked by a dotted line. The

positions of the light source at the times of departure and return of the pulse are given by S

and S'’, respectively and are different with those in Fig 1. For clarity, the reference frame

R1 for the subsequent six figures of the spaceship has not been repeated.

7

The observer in the spaceship may establish there the speed and direction of the system

by measuring the distance d between the positions of the laser (or photon) source ( S ) and

return laser pulse ( S’’) at the time of the round trip (Fig. 2). Consequently, by using the

simple relation u = dc/2h ( where c is velocity of light) the observer can determine the

speed of the spaceship, too. An experimental confirmation of this thought experiment would

already be possible in an object 20 m high, moving at a rate of 30 km per sec. The distance

d should then amount to around 4 mm. However, for that purpose the observer in the

moving object (spaceship) should know how to direct the laser source parallel to the y axis

at absolute rest or should themselves be able to set up the direction of the movement. At this

point it should be emphasized that the R2 frame of reference at absolute rest is

indispensable only in the process of extrapolation of R1 to u=0.

Let us assume that in the spaceship at absolute rest the observer may send a laser pulse

parallel to the y axis, along the straight S1-S2-S1 trajectory and mark the reflection point on

the mirror as S2 (Fig.3a). If the observer will repeat this action without a change in the

pointing of the laser source in the spaceship at motion with the speed u, the pulse will not

return to the starting point but terminate at a S1”, similarly to the motion along the S- S’-S’’

trajectory shown on Fig.2 (dotted line). In order to send the laser pulse from S1 to S2 and

back to S1 in the moving spaceship (Fig.3a, frame R1) the observer must turn the laser

source by the α1 angle with respect to the former position. Otherwise the laser pulse will

reach the mirror at the S2” point due to the motion of the spaceship and the y’ axis with

respect to the x axis. The relationship between the points is expressed by d=d(S2’’+S2) +d(S2+S2’)

= u× t , where t is the time of the roundtrip of the laser pulse, u is the speed of the

spaceship and d is the distance passed by the spaceship during the time t with respect to the

reference frame R2 (Fig.3a).

8

Fig.3. (a). In order to reach the point S2 on the mirror at the bottom (seen at rest of the

frame R1), the laser pulse must be directed from the source S1 to the point S2’ at the front of

the spaceship. The position of S2’ depends on the speed of the spaceship. The observer in

R1 will note that the photon is moving along the straight trajectory S1-S2-S1 (dotted line)

whereas that one at rest will detect that the trajectory traces out a longer, angled path ( solid

line). For clarity reasons the reference frame R1 for the subsequent five figures of the

spaceship has not been repeated. (3b). After a counter-clockwise rotation of the spaceship

by 90o (a ‖ x’), the observer in motion may detect also the trajectory S1 -S2’-S1’, seen at

rest.

9

Thus, in the frame R2 at absolute rest, the trajectory of the laser pulse will be seen to

move along the longer V-shaped trajectory (Fig.3a, frame R2, solid lines). Since in the frame

R1 the photons of the laser pulse cannot be influenced by the motion of the spaceship the

trajectory cannot be influenced, also (Fig.3a, solid lines). As it follows from the subsequent

positions of the spaceship, the V-shaped trajectory will be seen in R1 as the shorter, straight

S1–S2–S1 line (Fig.3a, frame R1, dotted lines) due to the motion of the y’ axis and the a (y’)

coordinate of the spaceship. For clarity reasons the frame R1 has not been repeated for the

subsequent figures of the spaceship..

This means that the observers in R1 and R2 ( Fig. 3a) will detect the same trajectories as

those postulated in Fig.1a and 1b by the Special Theory of Relativity. However, depending

on whether the laser source is pointed on S2 or S2’, the observer in the spaceship will see

the trajectory of the laser pulse in the form of a V letter or a straight line, respectively. In

the latter case the observer in motion ( R1 ) may detect also the angled V shaped trajectory

of the pulse by a rotation of the spaceship by 90o (a ‖ x’, Fig. 3b), where a and b are

arbitrary coordinates of the spaceship, with b initially directed along the x’ axis. This is due

to the fact that the laser source is now inclined at the α1 angle in the direction of the motion.

After the round trip the laser pulse will be then seen to terminate at the d distance at the

right side from the starting point (Fig. 3b). If the laser source will be next directed parallel

to the x’ axis (α1= 0o) and the spaceship rotated clockwise by 90o (b ‖ x’‘) then one will

receive the status shown in Fig.2. After the roundtrip the laser pulse will now terminate at

the distance d = d(S1’’- S1) on the left side of the laser source.

Hence, an experimental approach for determination of the S2, S2’ and S2” positions at

absolute rest of the spaceship has been achieved. That also means that the determination of

the speed of the spaceship with respect the constant velocity of light as well as of the

10

direction of the movement ( the x’ axis) is possible. Since at the time of the S1-S2-S1

roundtrip, each of the observer in R1 and R2 will note a different trajectory of the laser

pulse, the equation (1) for the time dilation effect should formally be valid. However, the

observer in R1 may easily find that the motion of the y’ axis is for this effect exclusively

responsible.

For determination of the direction of motion let the b coordinate of spaceship be

inclined at an arbitrary µ angle to the x’ axis (Fig. 4a). Let us now perform the same

analysis as presented above. Since the results are similar they have been summarized on

figures 4a and 4b. In order to send the laser pulse from S1 to S2 and back to S1 the laser

source must be now inclined at the α2 angle with respect to the a coordinate because during

the roundtrip the spaceship is moving parallel to the b coordinate with the component speed

u’ (Fig.4a, dotted lines). The observer in the spaceship will then be able to see the pulse

moving along the straight S1-S2-S1 trajectory (Fig.4a, dashed line). From the analysis it

clearly follows that the d’ value is directly proportional to the speed of the spaceship in

perpendicular directions to the straight S1-S2 line. Consequently it is also dependent from

the µ angle. It follows that the largest d’ value, equal to d, should be detected by turning

the spaceship parallel to the x’ direction ( b ‖ x’, µ=0o). In general when the µ values come

close to 90o (b ┴ x’, a ‖ x ’) the d’ interval will tends to zero because the component speed

of u in the y’ direction will amount to zero (u’ =0). If then the spaceship with the fixed

laser source parallel to the a coordinate is rotated by 90o in the x’ direction (b ‖ x’ ) the

pulse will be seen to terminate at the distance d= d(S1-S1’) but on the left side of laser source

S1 (not shown on Fig.4b). It follows that we are again dealing here with a similar case to that

shown in Fig.2 because the laser source may be now considered as directed parallel to y axis

at absolute rest.

11

Fig. 4. The spaceship in Fig.4a and 4b is moving with the speed u along the x’ axis. The

optional coordinates of the spaceship are marked by a, b and c (Fig. 4a and 4b ). The

spaceship shown in fig. 4b has been in Fig.4a rotated by the μ angle. The laser pulse as

seen in the spaceship at motion is moving along the straight, dashed line S1–S2–S1 (Fig.

4a and 4b ) whereas the observer at rest will see that the pulse is moving along the longer

trajectory S1-S2’-S1’, in the form of a V letter (Fig. 4a and 4b ). After a counter-clockwise

rotation by 90o of the spaceship shown in Fig.4a (a ‖ u’) and in Fig.4b (a ‖ x’) the observer

in motion may detect the d2’ and d2 values, respectively. The distance between the starting

point S1 and terminating point S1’ of the laser pulse depends on the speed of the spaceship

along the b coordinate of the spaceship and is smaller in Fig 4a.

12

The experimental procedure for the detection of the direction of movement may be

carry out in several steps. Firstly, a device consisting of a target screen with a laser source

and a mirror should be put together. The target screen should be rigidly connected with the

mirror at a sufficient large distance; as precise as possible parallel to each other. Besides,

these two parallel surfaces should posses the ability to rotate at any angle with respect to

their central point marked as on Fig.4b or to the origin of the coordinate system a, b and

c of the spaceship. On Fig. 4a the whole spaceship is rotated by µ and plays the part of the

device. The laser source should also have the ability to be directed at any angle toward the

parallel located mirror. For clarity of the experiment, all other possible sites of the spaceship

(or mobile device) which may be achieved by rotation in the z’ direction, have been omitted

from this discussion, but they should not have a noticeable influence for the understanding

of the analysis.

Since at the beginning the optional b coordinate of the spaceship with respect to the x’

direction is unknown, the coordinate may be positioned somewhere between b‖x’ and b┴x’

i.e. in the 0 to 90o range of μ (Fig. 4a). On the figure the spaceship is shown in motion with

the speed u along the x’ axis with the b coordinate inclined at the optional μ angle with

respect that axis. Next the laser source should be directed on to mirror under such an angle

e.g. α2, that the return laser pulse should terminate as close as possible to the starting point

and subsequently fixed at that position (dashed line S1-S2, Fig. 4a). The laser source is now

pointed at the α2 angle with respect to the a coordinate at absolute rest of the spaceship

shown on Fig.4a. Thus, the observer in the spaceship at motion will note that the laser

pulse will always move along the straight S1-S2-S1 dashed line (only once marked on Fig.

4a). However any change of the µ angle will cause that laser pulse will not move along that

line but will reach the target screen at a distance d’’ from the starting point (not shown on

13

the Fig. 4a). The difference arises from the fact that a change in the direction of

measurements will change the component speed in that direction which in turn is not

adjusted by a change of the fixed α2 angle. The procedure should be repeated for all

positions of the spaceship (device) in the 0 to 90o range of μ. The largest determined

distance between the starting and terminating point of the laser pulse, observed on the left

side of the source only (including the zero value), will indicate the direction of motion ( the

x’ axis). From the analysis follows that an experimental procedure for determination of the

d value by means of the approach shown on Fig.3 is possible.

One may take advantage also of the directly proportional dependence between the

components of the speed u in perpendicular directions to the straight S1-S2 line and the d’

distance. The d’ values may be obtained as previously described, by first pointing the laser

source in such a way that the return laser pulse should terminate as close as possible to the

starting point and a subsequent counter-clockwise rotation of the spaceship ( or the screen

and mirror device ) by 90o, similarly as shown in Fig.3b. With this in mind, the largest

distance between the starting and terminating point of the laser impulse for a given speed u

may be obtained, when the spaceship (or device) is finally turned at µ = 0 (b ‖ x’)

followed by a counterclockwise rotation by 90o. For that purpose such measurements should

be performed for all µ angles in the 0 – 90o range. The largest obtained d’ interval (in our

case equal to d ), seen on the right side from the source, will indicate that the b coordinate

is positioned perpendicular to the direction of the movement x’. After a successive,

clockwise rotation of the spaceship by 90o (b‖x’) the circumstances presented in Fig 3a may

be possible to obtain. The b coordinate is now parallel to x’ and the source is inclined at the

α1 angle with respect to that axis (Fig. 4b).

14

On the basis of the known values for the velocity of light (c), the height of the spaceship

(h), the distance (d) and application of the Pythagorean theorem the observer in motion

may establish the speed of the spaceship with respect to the constant velocity of light. Since

the observer in motion at this point knows how to turn the laser source first parallel and next

perpendicular to the x’ axis, he may also determine the d distance similarly as earlier shown

(Fig.2) and use the somewhat simpler relation u = d c/2h.

From the performed analysis it follows that an observer in an object moving with a

constant speed, may themselves determine the trajectory of a laser pulse seen in motion as

well as at absolute rest. Since for the roundtrip S1-S2–S1 the pointing of the laser source

must be different in the frame at absolute rest (R2) and at motion (R1), the time of the

roundtrip and trajectory of the laser pulse must obviously also differ. One may conclude

that Einstein's principle of relativity needs a revision.

III. CONCLUSIONS

From the analysis of the thought experiment follows that depending on whether the laser

source is directed parallel to the y axis at absolute rest or seen at motion, the observer in an

object moving with a constant speed along the x’ axis will detect the trajectory of the laser

pulse in the form of a V letter or a straight line, respectively. In the latter case the observer

may receive experimental evidence for motion of the object by pointing the laser source

with the mirror first perpendicular to the direction of the movement and next turning it

counter-clockwise by 90o. It has been also shown, that contrary to the Special Theory of

Relativity the observer in motion may independently detect the direction (x’) and speed (u)

of the object with respect to the constant velocity of light. He may also themselves analyze

the trajectory of the laser pulse in the whole 0 ≤ u < c range. In addition it has been shown

15

how one may perform such measurements in experimentally achievable ranges. The basic

relations stated by the Special Theory of Relativity may formally remain unchanged

however their understanding needs a revision, in particular the time dilation and length

contraction paradoxes.

ACKNOWLEDGEMENTS

The Author wishes to thank Dr. Krzysztof Zawisza from the University of Warsaw, for

many stimulating discussions.

1A. Einstein, Relativity, The special and General Theory, (Tess Press, an imprint of Black

Dog & Leventhal Publishers, Inc., 151 West 19th Street New York, 1952, New York

10011)

2N. D. Mermin, It's About Time: Understanding Einstein's Relativity,

(Princeton University Press, 2005).3I. Novikov, The River of Time, (UK: Cambridge University Press, 2001).

4F. W. Sears, M. W. Zemansky, H. D. Young, University Physics (Addison-

Wesley Publishing Company, 1982) Chap.43, pp. 822-839)

5R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures of Physics, vol. 1,

(Second Edition, Addison Wesley, 2005, California Institute of Technology).

6W. A. Ugarow, Special Theory of Relativity, ((Moscow, Mir Publishers, 1979 , translated

from Russian)

7L. B. Okun, Am. J. Phys., 77, 460 (2009)

16

A revision of the time dilation effect in the Special Theory of Relativity.

Janusz Drożdżyńskia)

University of Wrocław, ul. F. Joliot-Curie 14, 50-383 Wrocław, Poland

Abstract: In this paper it has been shown that some experimental confirmations for the

so-called “time dilation effect” may be in a rational way explained on the basis of a thought

experiment presented in a previous paper1. The performed analysis has proven, that in order

to carry out a round trip of a laser pulse from the source to a perpendicular located mirror

and back to the starting point, the laser source in motion of the spaceship with a constant

speed must be pointed at an angle in the direction of movement; whereas at rest it should be

directed perpendicular to that axis. This means, that we have not to deal with a “time

dilation effect” but with two separate measurements of two separate laser signals, moving at

two different distances. The ratio of the two time intervals is expressed by a somewhat

different equation as stated by the Special Theory Relativity and possess also a dissimilar

meaning. It has been shown also that it can be evaluated by the observer in motion by

himself as well as that the phenomenon of a relativistic length contraction does not exist.

On this basis, a quantitative relation between time intervals of such oscillations in two

reference frames, which are in motion with a different speed with respect to the frame at

absolute rest, has been received. The relation may be of some significance for the Global

Positioning System (GPS). A rational explanation of the “moving clocks” experiments as

well as the “time dilation effect” of muons is presented. The existence of “paradoxes”,

resulting from Special Relativity has been excluded. A new elucidation of the null result in

the Michelson-Morley experiment is presented. The analysis was based on classical

physics and is giving additional evidence for the erroneous of the principle of relativity.

17

Key words: Special theory of relativity; Falsity of the principle of relativity; Thought

experiments; Revision of time dilation effects; explanation of moving clocks experiments;

“Time dilation effect” of muons; Paradoxes.

______________________________________a) janusz.drozdzynski@chem.uni.wroc.pl

Résumé : Dans cet article il a été montré que « l’effet de dilatation du temps » peut être

clairement expliqué sur la base d’expériences réfléchies présentées dans un article

antérieur1.

Les analyses réalisées ont prouvé que sur l’aller et retour d’une impulsion laser de la

source à un miroir localisé perpendiculairement au faisceau, la source laser, étant en

mouvement dans l’espace avec une vitesse constante, doit être orientée selon un angle

par rapport à la direction du mouvement ; alors qu’au repos elle doit être dirigée

perpendiculairement à cet axe.

Cela signifie que nous n’avons pas à considérer un effet de dilatation du temps mais plutôt

de deux mesures séparées de deux signaux lasers séparés, se déplaçant sur deux distances

différentes. Sur cette base, une relation entre l'intervalle du temps de telles oscillations,

dans deux cadres de réference lesquels sont en mouvement avec vitesses différentes par

rapport au cadre en état absolument immobile, a été démontrée. Cette relation doit avoir

une signification certaine pour Global positioning System (GPS)

Le rapport des deux longueurs parcourues s’exprime par une équation légèrement

différente conformément à la théorie de la relativité spéciale (special theory of

relativity ou STR) et ce rapport appelle une signification différente. Il a été montré aussi

que cette relation peut être évaluée par l’observateur, lui-même en mouvement.

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Sur cette base, on peut expliquer les expériences des « horloges en mouvement » aussi

bien que « l’effet de dilatation du temps » des muons. Il a été montré également que le

phénomène de la longueur réelle d'une contraction relativiste n'existe pas. L’existence de

paradoxes lesquels résultent de Relativité Spécialle a été exclue. Une nouvelle explication

du résultat nul dans l'expérience de Michelson-Morley est présenté. L'analyse se base sur

la physique classique et donne une preuve additionelle de fausseté de principe de

relativité.

I. INTRODUCTION

The Special Theory of Relativity states that all experiments performed inside of a

moving system drifting along with a constant speed will appear the same as if the system

were standing still2-4. This means that if a spaceship is moving at an uniform speed (Fig.1,

reference system R1) and a laser source is directed perpendicular to the direction of motion

on a mirror placed on the floor ( as seen by the internal observer ), the pulse should move

down and up along the same straight line S-So-S ( Fig.1, solid line ). The theory states also

that an external observer in the state of rest (the R2 frame of reference) will see a longer

path of the same pulse, moving in the form of a “V” letter (Fig.1, dotted line). It follows,

that if a time interval Δt1 separates the departure and arrival of the laser pulse at R1 at the

same space point S (Fig.1) then the time interval Δt2 between the same two events as

observed in R2 is larger than Δt1.2 Hence, when the rate of a clock at rest in R1 is measured

by an observer in R2, the rate measured in R2 is faster than that one observed in R1, despite

of the fact that the departure and arrival of the pulse in R1 and R2 must start and end

simultaneously. It is concluded that time itself appears to be slower in the spaceship.3 On

this basis a well known quantitative relation between Δt1 and Δt2 has been derived 2-4.

19

Δt2 /Δt1 =

1√1−u2 /c2

(1)

where c is the velocity of light and u is the speed of the spaceship along the x axis, relative

to the outside observer. An experimental confirmation of the slowing of time with motion is

among others reported to be furnished by mu-mesons (muons)3 and the moving clocks

experiments.3,5,6 In our previous paper1 it has been proven that the principle of relativity of

the Special Theory of Relativity is erroneous as well as how this statement could be

confirmed experimentally. However so far it was not understandable how to explain the

agreement of the reported3,5,6 experimental results with those calculated on the basis of the

incorrect equation [1]. In this paper has been shown that this inconsistency may be

explained in a much more rational manner by a new relation, derived on the basis of

classical physics.

20

Figure 1.

In a spaceship, which moves with a constant speed u (reference frame R1 ) relatively to

that at the state of rest (R2 ), a laser pulse is emitted from the source S parallel to the Y axis

and is reflected back on a mirror at So. Since, according to the Special Theory of Relativity

such a frame of reference (R1) is not distinguishable from that at absolute rest, it is

erroneously assumed that the internal observer will see the pulse moving along the same

straight solid line S-So. It is also incorrect assumed that as observed in R2, the same laser

pulse is moving along a longer trajectory, in the form of a “V” letter.

II. A REVISION OF THE TIME DILATION EFECT

The fault in the interpretation of the thought experiment which lead to equation [1] arises

from the principle of relativity, which assumes that an observer in an inertial frame of

reference (spaceship) is not able to determine its motion without the presence of an observer

in an external frame of reference. In consequence, the principle assumes an equivalence of

all inertial frames of reference, including that frame which is ”moving” with a speed equal

to zero, and leads to numerous odd paradoxes

Since particles with a rest mass equal to zero ( e.g a laser pulse) cannot be influenced

by the motion of the source i.e. by the motion of the system of coordinates of the

spaceship6,7, the trajectory of a laser pulse must be one and the same as well at absolute rest

and in motion of the frame with a constant speed. This means that contrary to the Special

Theory Relativity the path length of the same pulse must be identical in any inertial frame

of reference. Hence, if the laser source is pointed perpendicular to the X axis, the photons

should move down and up always along the same path (solid straight line on Fig.2).

21

Naturally, it must be pointed perpendicular to the ceiling by using non-optical methods.

However, due to the motion of the R1 reference frame, it will be seen by the inside observer

to move along the path in the form of a letter “V” (Fig.2, dotted line S-S’-S’’). The longer

path length results from overlapping of the two independent perpendicular motions.

In contrary to the Special Theory of Relativity (Fig.1), the observer in motion (R1) will

notice also that the pulse is not returning to the starting point S (Fig.2) what takes place at

absolute rest of the spaceship. (Fig.2, point S). Furthermore, it has been shown that an

observer in an object in motion with a constant speed, may himself determine the speed of

the system with respect to the velocity of light, according to the equation1 u = cd/2h = c ×

tgβ (based on Fig.2).

In order to carry out a round trip, in which the laser pulse will return to the starting point

in a spaceship in motion with a constant speed, the laser source must be turned at an α angle

in the direction of motion (Fig.3a) and has to be determined experimentally by the trial and

error method, appropriately to the speed of the spaceship.

The angle may be observed also after a counter-clockwise rotation by 90o of the laser-

mirror device (the S1-S2 axis) with the fixed at the α angle laser source in the direction of

movement. For clarity reasons in Fig. 3a the whole spaceship with the fixed at that angle

laser source has been rotated. From the relations shown in the figure it follows also that in

order to perform such oscillations (round trips) the speed of the object (u) cannot exceed

the velocity of photons, according to the relation u = c × sin α (see the relations on the basis

of Fig.3a).

22

Fig. 2. In the moving spaceship with a constant speed u, a laser source (S) is directed

parallel to the Y axis, as seen at absolute rest. This position of the laser source may be

determined by the observer in R1 by pointing the laser source perpendicular to the ceiling

by using non-optical methods. It may be obtained also by pointing the source first parallel

to the direction of motion (X) and next turning it counter clockwise by 90o. From the

source a pulse is emitted and is subsequently reflected back from the mirror S’. Since the

laser pulse cannot be influenced by the motion of the source i.e. by the motion of the

system of coordinates of the spaceship, the laser pulse must move down and up along the

23

same straight line as seen in the frame at rest but not seen by the observer in R1 (solid

straight line). Due to the motion of the reference frame R1, it will be seen by the internal

observer to move along the path in the form of a letter “V” (Fig.2, dotted line S-S’-S’’).

Contrary to the statement of the Special Theory of Relativity (Fig.1), the observer in the

spaceship will notice that the pulse is not returning to the starting point (S, Fig.2). The

positions of the light source at the times of departure and return of the pulse are given by

S and S'’, respectively, and are different with those shown in Fig1. To clarify, the reference

frame R1 for the subsequent six figures of the spaceship has not been repeated. The

relations between the components of the trajectory of the laser pulse in R1 are given at

the base of Fig.2, where c is the velocity of light and v2 is the component speed of c as seen

in R1.

Thus, for a comparison of the time intervals in a round trip as well in motion and at rest,

one has to carry out two separate experiments. In the first one, the laser source must be

pointed at such an angle (α) in the direction of movement, which will make possible the

termination of the laser pulse at the starting point; whereas at rest, it should be directed

perpendicular to that axis. Consequently, the path S1 - S2’- S1’ in the form of a letter “V”

of the pulse in R1 (Fig. 3a,b, solid line) is longer than that of a straight line seen at rest in

R2 (Fig.2, solid line). However, due to the motion of the spaceship, the first one will be seen

by the inside observer as moving down and up along a straight line (Fig. 3a, dotted line).

One should realize also, that in motion the calculated speed in this direction represents a

component value of the velocity of light (v1 in Fig.3a). It follows that we are not witnessing

a time dilation effect but two separate laser signals, covering two different distances in two

time intervals, Δt1 and Δt2.

24

The value of ∆t2= 2h/c expresses the relation in the frame R2 and may be obtained also

from the determined in R1, values of g2 and e2 as shown on the base of Fig.2 . The relation

for ∆t1= 2h/v1 is presented in Fig. 3a and 3b, where v1 is the component speed of c in the

perpendicular direction do X. From the relations follows also that v12 = c2 – u2 and

consequently ∆t1/∆t2 = c/v1 = c/√c2−u2. Thus, we have received a different relationship

∆t1/∆t2 = 1/√1−u2 /c2 (2)

as postulated by Special Relativity; (1). The meaning of the ratio is also dissimilar and may

be expressed as follows: if a time interval (∆t1) separates the departure and arrival of a laser

signal at the same space point S1 of a reference frame in motion (R1, Fig.3) with the speed

u, expressed by the equation u = cd/2h = c × tgβ (R1, Fig.2), then the determined time

interval (∆t2) of such an laser signal in a frame at absolute rest (R2) is smaller than in R1.

On this basis a derivation of a quantitative relation (3) between the rate of such two “light

clocks” (laser – mirror devices), moving with different speeds with respect to the frame at

absolute rest, is also possible. Henceforth, the understanding of the so-called time dilation

effects should be explicitly clear and does not require such an odd explanation as that in

the spaceship “time itself appears to be slower.”

The ∆t1/∆t2 ratio may be established in the moving spaceship (R1) by the internal

observer himself by measuring also the ratio e1/h or d’/d (e1 and d’ on the basis of Fig. 3b;

h and d on the basis of Fig.2). For that purpose, the internal observer in the moving system

should point the laser source first perpendicular to the direction of the movement as seen

in R1 i.e. along thy Y axis but with the α angle of the source along S1-S2’ (Fig.3a) and next

turn it with the mirror mechanically counter-clockwise by 90o (Fig.3b, to clarify, the whole

spaceship is turned by 90o).

25

In this way, the he will detect the path of the pulse as seen in the stationary reference

system R2 (Fig. 3a) as well. The observer in motion may then independently detect the

trajectory of the laser pulse in the whole 0 ≤ u < c range as could be seen by an observer at

absolute rest. On the other hand by pointing the laser source in the moving system, first

parallel to the direction of motion and then by turning it mechanically clockwise by 90o, the

observer in motion will be able point the source parallel to the Y axis as seen at absolute rest

(Fig.2) and may determine the distance d.

Subsequently, the observer in motion can determine the equation (2) on the basis of the

relationships e1= c × ∆t1/2 (Fig. 3b, R1) and from a separate measurement, h = c × ∆t2/2

( Fig.2, R1). By applying the Pythagorean theorem for the relations given in R1 on Fig.3b,

one obtains first that h2= e12- u2 ∆t1

2/4 , then h2= e12- u2 e1

2/c2 =e12( 1 - u2/c2) and finally

∆t1/∆t2 = e1 / h = 1 / √1−u2 /c2. As it will be shown later the analysis is not in

contradiction with the Michelson-Morley Experiment.

26

Fig.3. (a). In order to reach the point S2 on the mirror at the bottom (seen at rest of the

frame R1), the laser pulse must be directed from the source S1 to the point S2’ at the front

of the spaceship. The position of S2’ depends on the speed of the spaceship. The observer in

R1 is may not aware that he is pointing the laser source at the α angle and will note that the

photon is moving along the straight trajectory S1-S2-S1 (dotted line); whereas the one at

rest will detect that the trajectory traces out a longer, angled path (solid line). To clarify, the

reference frame R1 for the subsequent five figures of the spaceship has not been repeated.

(b). After a counter-clockwise rotation of the spaceship by 90o (a ‖ x’), the observer in

motion may detect also the trajectory S1 -S2’-S1’, seen at rest in R2. The relations

between the components of the trajectory of the laser pulse are given at the base of

27

Fig.3b, where c is the velocity of light and v1 is the component speed of c in the S1-S2

direction, as seen in R1. of Fig.2a.

In reality we are dealing with reference frames in motion, only. A comparison of two

time intervals (Δt1 and Δt’1) in a round trip of a laser pulse in two reference frames, which

are in motion with relatively different speeds u and u’, should refer in each of them to the

same starting and terminating point (Fig.3). This means that the laser source at motion

cannot be not pointed parallel to the Y axis as seen at rest or on Fig.2 ( i.e. pointed

perpendicular to the ceiling by non-optical methods) but as seen in motion i.e. with the α

angle of the source along S1-S2’ (Fig.3a). The time intervals should be first evaluated with

respect to such a round trip (oscillation) at absolute rest (R2), according to equation (2).

From this follows that: ∆t1/∆t2 = 1/√1−u2 /c2 and ∆t1’/∆t2 = 1/√1−u '2 /c2

.

Afterward, one may perform a comparison of observed time intervals in the two frames in

motion, which leads to the following general formula:

∆t1/∆t1’ = √c2−u ' 2 /c2−u2 = √ 1−u '2

c2

1−u2

c2

(3)

If u’≪ c then equation (3) converts into the formula (2) and one may assume that ∆t1’ can

represent the interval (∆t2) of the laser signal in a frame at absolute rest (R2). A correct

application of equation (3) for the performance of the measurements requires that the b axis

of such “light clocks” (Fig.3, the laser-mirror device) was turned parallel to the direction of

motion (X’) or to the resultant direction of a number of motions. For that purpose the

procedure presented in the previous paper [1] may by employed.

28

One of the most often cited examples for the confirmation of time slowing with motion

is the observed difference in lifetimes of mu-mesons (muons), produced artificially in

laboratory and created by cosmic rays at the top of atmosphere3,4. In the first case, they

disintegrate spontaneously after an average time of 2.2 ×10-6 sec and may pass in

atmosphere less than 600 m. In the latter case, they live much longer, may move almost

with the speed of light, pass through about 10 km and can be found down on Earth. The

average life time for muons of different velocities is reported3 to agree closely with the

criticized in this paper formula (1). According to Special Relativity the factor by which the

time is increased in a moving system is given as 1/√1−u2 /c2 which is in agreement also

with equation (2), but the origin and meaning of equations (1) and (2) are totally different.

In addition, from the presented analysis follows, that the difference in lifetimes of muons

may be explained in a rational manner by equation (3). Moreover, for the elucidation of this

phenomena one does not need to use such an odd explanation as: While from their own

point of view they live only 2 µsec, from our point of view they live considerable longer.3

The mechanism of the disintegration is unknown, however if one agree that it is

proportional to the factors √ 1−u '2

c2

1−u2

c2

or 1/√1−u2 /c2 one should assume also an

oscillation character of the disintegration. Hence, if one assume e.g. that the particles

disintegrate after a definite number of some kind of its own oscillations, than they should

“live” in motion longer because each oscillation is accomplished at a longer path in

comparison to that at relative rest. In consequence for each one also a longer time interval is

required. Since the average speed (u) of muons created by cosmic rays is very large and that

of the moving Earth u’≪ c, the application of equations (2) is giving as well a good

29

agreement with the experimental data. One should be aware however that we may be

dealing here with very complex relations.

An experimental confirmation of the slowing of time with motion is reported also to be

furnished in the reported “moving clocks” experiments.3,5,6 In that experiments four cesium

beam atomic clocks were flown on jet flights around the world in order to test Einstein’s

theory of relativity. According to the authors the results are giving an unambiguous

empirical resolution of the ”clock paradoxes” with macroscopic clocks.

From the presented in this paper analysis follows, that for a correct comparison of the

time intervals of a “moving clock” on the plane and a “stationary clock” on the moving

Earth, the equation (3) should be applied. The results should agree with the reported data

but the predicted time differences may be somewhat larger. However, in the moving clocks

experiment of Hafele and Keating5,6 one has not received a confirmation of the ”clock

paradoxes” as well as that “… not time itself appears to be slower”3 but the clock in

movement must run somewhat slower, due to the longer path of the oscillations. On this

basis one should also better understand why atomic clocks on satellites fall behind clocks on

Earth The application of equation (3) may be of some significance for the Global

Positioning System (GPS).

Nevertheless, to this point one may be certain only on “time dilation effects” connected

with particles with a rest mass equal to zero. Thus, one should be very careful with an

extension of the obtained results on other events. It is difficult also to predict the influence

of these effects on biological systems at extremely high speeds. However, there is nothing

to be said for the existence of such paradoxes as e.g. the famous twin brother paradox or a

relativistic length contraction2-4..

30

Furthermore, due the fact that a laser pulse must move down and up along the same

straight line as well at absolute rest and at motion of the spaceship (Fig. 2, solid straight

line), one may obtain a possible explanation why the Michelson-Morley experiment2,3,9 is

giving a null result. For that purpose a well known schematic diagram of that experiment is

shown on Fig.4. The apparatus is essentially comprised of a of light source (s), a beam

splitting mirror (p) (partially silvered glass plate), a detector (d) and two reflecting mirrors

(m1) and (m2) placed at equal distances ( l ) from (a), all mounted on a rigid base moving

with the velocity of Earth (v) in the x direction.

31

Fig.4. d- detector, s - light source, p - beam splitting plate, m1, m2 - reflecting mirrors at

the distance l , ab + bc - transverse beam path length, ab’+ b’a’ -longitudinal wave path

length. The numbers indicate the location of the plate p and the mirror m2 during the

motion of the interferometer in the x direction. In the figures are not shown the real

relations between the dimensions.

From the source (s) a light beam is directed to the plate ( p ) at the site 1, where it splits

into two mutually perpendicular wave beams: a longitudinal (ab) and a transverse one

(ab’). The beams are reflected back by the mirrors m1 and m2. The numbers indicate the

location of the plate p and the mirror m2 at the starting time (site 1) of the longitudinal

light beam, after the time taken for the flight from the plate p (site 1) to the mirror m2

(site 2) and after the return time to the plate p (site 3). The transfer of the plate p to site 4

follows during the time taken for the light to go from a to c.

Since the motion of the apparatus cannot influence the direction of the transverse

beam (ab + bc), it must be always perpendicular to the x axis i.e. to the base of the

apparatus. Hence, the path length (ab + ba ) after the time (t) must be equal to that of the

32

longitudinal (ab’+ b’a’). However, after that time only the latter one will arrive on the plate

p at the a’ point (Fig.4, site 3). The transverse beam in order to appear at the plate p has to

pass an additional distance ac’ + c’c and is afterward reflected parallel to w1 in the

direction of the detector d. The distance aa’ = vt is due to the motion of the apparatus

with respect to starting point a, as seen at rest. Since the plate p must be inclined at 45o in

the X direction, the length of the aa’ and ac’ distances with a change of v (the vt distance)

ought to be as well equal. The additional distance c’c is caused by the motion of the

apparatus from site 3 to 4, for the time taken for the light to go from a to c. Hence, at the

points a and c the beams w1 and w2 have passed nearly the same distances ab’+b’a’+a’a

and ab+ba+ac, with the exception of c’c. A change of the velocity v should have a small

influence only on the length of the c’c distance and should not noticeable contribute to the

times taken for the flights of the two beams. However, as one may easily find out, for the

speed of Earth of v ≈ 30 km/s the ac distance amounts to ca. 2×103 µm and is too large to

result an interference between the W1 and W2 beams.

On the other hand the requirement of a mutual termination of the two reflected beams

ba’ and b’a’ at the same point on the plate p (point a’, site 3) demands a small rotation of

the mirror 2 by an α angle in the x direction, as shown on Fig. 4b. For l = 11 m and v

between 30 to 5000 km/s the angle should be comprised in the 0.05o - 0.5o.range.

Consequently the “transverse” beam ba’ will be not reflected parallel to W1 but also at an

angle in the direction of W2 (Fig.4b). That's why no changes in the interference pattern,

generated by the longitudinal light beam, could be observed. It follows that Special

Relativity is not necessary for the explanation of the Michelson and Morley experiment.

However, as this is a general idea only, more detailed investigations are required.

33

In view of the fact, that it has been given evidence that the principle of relativity is

erroneous as well as that the discussed in this paper experimental confirmations for

Special Relativity may be explained based on classical physics, one may assume that also

other aspects of the theory need a revision.

III. CONCLUSIONS

It has been shown1 that if in a reference frame (spaceship) in motion with a constant

speed, a laser source is fixed on the top of the spaceship and directed perpendicular to the x

axis, then in a round trip of a laser pulse from the source to a mirror placed on the floor and

back to the ceiling, the laser pulse will return at a distance d from the starting point. In

order to carry out in the moving frame (spaceship), a similar round trip to that at rest, in

which the laser pulse is returning to the starting point, the laser source must be

experimentally pointed at an α angle in the direction of the motion, appropriately to the

speed of the spaceship. Hence, the trajectory in the round trip of the laser pulse is in motion

longer then in a similar one at rest. The ratio of the two different distances is expressed by a

different relation (2) as presented in equation (1) by Special Relativity and possess a

dissimilar meaning. Henceforth, we have not to do with a “time dilation effect” but with

two separate laser signals moving at two different distances in two separate experiments. A

quantitative relation (3) between the rates of oscillations in two frames of reference, moving

with different speeds with respect to that at absolute rest, has been derived. The application

of equation (3) should be of some significance for the Global Positioning System (GPS).

On that basis an rational explanation for the the “moving clocks” experiments5,6 as well as

the “time dilation effect” of muons is reported. Besides, it has been shown why the

34

Michelson-Morley experiment must give a null result. The analysis was based on classical

physics and is giving additional evidence for the erroneous of the principle of relativity. The

existence of “paradoxes”, resulting from Special Relativity has been excluded.

;1 J. Drożdżyński, Physics Essays 26, 321 (2013)

2 F. W. Sears, M. W. Zemansky, H. D. Young, University Physics (Addison - Wesley

Publishing

Company, 1982) Chap.43, pp. 822-839)

3R.P. Feynman, R.B. Leighton and B. Sands, The Feynman Lectures on Physics, Addison

Wesley Publishing Company (2003)

4N.D. Mermin, It’s About Time: Understanding of Einsteins Relativity, (Princetown

University Press, 2005)

5J.C. Hafele and R.E. Keating, Science 177, 168-170 (1972)

6J.C. Hafele and R.E. Keating, Science 177, 168-170 (1972)

7 W. A. Ugarow, Special Theory of Relativity, ((Moscow, Mir Publishers, 1979 , translated

from Russian)

8 L. B. Okun, Am. J. Phys. 77(5), 430 (2009)

9A.A. Michelson and E.W. Morley, Am. J. Science 34, 333 (1887)

35