A revision of the principle of relativity
Janusz Drożdżyński
University of Wrocław, ul. F. Joliot-Curie 14, 50-383 Wrocław, Poland.
E-mail: [email protected]
Physics Essays Vol. 26, Issue 2, pp. 321-325, June 2013
http://physicsessays.org/browse-journal-2/product/62-18-janusz-drozdzynski-a-revision-ofthe-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
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
1
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-SoS)
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 railwaycarriage. 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 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.
2
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
t 
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  u 2 / 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 source could be directed
5
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 direction
10
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 S1S2’-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 the Fig. 4a).
13
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 counterclockwise 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 how one may
15
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.
1
A. 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)
2
N. D. Mermin, It's About Time: Understanding Einstein's Relativity, (Princeton University
Press, 2005).
3
I. Novikov, The River of Time, (UK: Cambridge University Press, 2001).
4
F. W. Sears, M. W. Zemansky, H. D. Young, University Physics (AddisonWesley Publishing Company, 1982) Chap.43, pp. 822-839)
5
R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures of Physics, vol. 1,
(Second Edition, Addison Wesley, 2005, California Institute of Technology).
6
W. A. Ugarow, Special Theory of Relativity, (Moscow, Mir Publishers, 1979 , translated
(
from Russian)
7
L. 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 socalled “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)
[email protected]
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.
18
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
t2 / t1 =
1
1  u 2 / 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.
Figure 1.
20
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 spaceship 6,7,
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). Naturally, it must be pointed
perpendicular to the ceiling by using non-optical methods. However, due to the motion of the
21
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 lasermirror 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 nonoptical 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 same straight line as seen
23
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.
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
24
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/ c 2  u 2 . Thus, we have received a different relationship
∆t1/∆t2 = 1/ 1  u 2 / c 2
(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).
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
25
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 ∆t12/4 , then h2= e12- u2 e12/c2 =e12( 1 - u2/c2) and finally
∆t1/∆t2 = e1 / h = 1 / 1  u 2 / c 2 . 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 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  u 2 / c 2
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:
27
𝑢′2
∆t1/∆t1’ =
c2  u ' 2 / c2  u2 = √
1− 2
𝑐
𝑢2
(3)
1− 2
𝑐
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.
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  u 2 / c 2 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
28
The mechanism of the disintegration is unknown, however if one agree that it is
𝑢′2
proportional to the factors √
1− 2
𝑐
𝑢2
1− 2
𝑐
or 1/ 1  u 2 / c 2 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 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
29
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..
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.
30
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.
31
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 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
32
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 0.05 o - 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.
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
33
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 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
2
J. Drożdżyński, Physics Essays 26, 321 (2013)
F. W. Sears, M. W. Zemansky, H. D. Young, University Physics (Addison - Wesley
Publishing
Company, 1982) Chap.43, pp. 822-839)
3
R.P. Feynman, R.B. Leighton and B. Sands, The Feynman Lectures on Physics, Addison
Wesley Publishing Company (2003)
34
4
N.D. Mermin, It’s About Time: Understanding of Einsteins Relativity, (Princetown
University Press, 2005)
5
J.C. Hafele and R.E. Keating, Science 177, 168-170 (1972)
6
J.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)
9
A.A. Michelson and E.W. Morley, Am. J. Science 34, 333 (1887)
35