VELOCITY OF LIGHT
Author: Dane Gacesa
Light source (macrosource) is a set of elementary sources which have different velocities in relation to inertial frame of the macrosource.
Elementary light which is emitted by an elementary source has a strictly fixed speed c in relation to that elementary source in the moment of emission.
Hereby follows that the macrosource is emitting lights that have different speeds in relation to its own inertial frame.
Elementary light detector can only detect the light that in relation to it has speed c. Just that kind of light is detectable in the inertial frame of the elementary detector.
The constancy of speed of light is only related to the detectable light and it is exclusivly the consequence of the strict detectors selectivity.
Change of relative velocity between the light source and the detector can`t effect the detectors selectivity therefore the light speed that we detect in the inertial detectors frame is always the same. But every time another light is detectable depending on that relative velocity.
In all of the experiments for determining the speed of light depending on the relative uniform motion between the source and the observer, the mandatory participants are:
- the light (electromagnetic waves) and,
- the light detector;
The results of these experiments could be the consequence of the property that belongs to the light, or the consequence of the property that belongs to the detector.
This other possibility was not ever analyzed in the domain of modern Science.
Without any doubt, it is a roughly overlooked matter, which must not be neglected in the strict scientific analysis of the experimental results.
The experimenters that were researching the dependence of the speed of light from the relative uniform motion between the source and the observer never asked themselves: how we could detect the light whose speed depends on such a motion; that is, a light that would not have a speed c in relation to the observer, that is, by which devices they could detect the light that would not be electromagnetic in nature?
Electromagnetic waves are spreading by the strictly determined speed c, in the relation to the source of these waves. The light is also spreading with that speed and it is the part of the electromagnetic spectrum. Thus, the speed c is an essential characteristic of the electromagnetic waves – which means that the waves spreading at the different speed than the speed c are not electromagnetic.
Thus, there is a chance that the lights with a different speed than the speed c were not detected not only because such lights do not exist, but because they could not have been detected. However, those lights could exist and could be detected when the relative speed c is achieved between any one of them and the detector.
If the light source emits even the lights that in relation to the source have different speeds than the speed c, being that the speeds are also mutually different, then the detector should be strictly selective, and more exactly it should interact with only one from them in order that the source information is clear and not blended.
The experimental fact is that the detector interacts with only such a light that in relation to it has the speed c, in other words when certain light in relation to it has a speed c. The detector could interact with any light emitted by the source with the condition of achievement of the speed c between that light and the detector. Then, such a light is electromagnetic in nature in the detector’s inertial frame, and more exactly, then – such light is detectable. Because the detector could move at any relative velocity (within determined borders) in relation to the source there follows that there is always certain light that in relation to the detector’s inertial system has the speed c with which the detector interacts.
“The Constancy of the speed of light” is the consequence of the strict detector’s selectivity. The speed of light is directly dependent on the relative speed between the source and the observer, but the light is detectable only when its speed is equal to c, in the relation to the detector.
Thus, it is obvious, that it was highly illusory to expect that by the help of any experiment it could be possible to detect the light that has a different speed from the value c.
If the light source, in fact, emits the lights with different speeds then it is necessary to single out certain interval of these lights with already known borderline speeds and then it should be experimented with this interval and not with the total emission of such a source. It is possible to achieve such a selection. The experiments with the lights from this interval are fundamentally different from the experiments already conducted. The suggested experiments, in this text, could unmistakably give an answer to the question why the speed of the (detectable!) light does not depend on the relative speed between the source and the observer.
The light velocity is a characteristic of light that has not been thoroughly researched. An error was made in the interpretation of experiments that had the following aim – establishing of the value of light velocity depending on the relative motion between a light source and an observer. The assumptions and expectations of an experimenter could be briefly described in a following way:
1. It was expected that the light would have lower velocity in its relation to observer, if the light source and the observer were moving away from each other and vice versa.
2. The attention was not given to the nature of such a light, in other words to the nature of light that would have lower or higher velocity than what the actual velocity of electromagnetic waves (c) was, in its relation to observer.
3. It was assumed that an eye or the other light detector would have the ability to detect even such light.
4. Because such light was not detected, it was determined that it does not exist!
Several natural phenomena are taking part in each experiment. The result of the interaction of characteristics of these phenomena is independent of the goal that the experimenter is trying to achieve, and hence - it is necessary to consider the principle of the research of characteristics distinctive to all phenomena taking part within the experiment. Let’s analyze in this sense, all of the four given conclusions:
Ad 1. This expectation is normal because it is in accordance with an experience.
Ad 2. The light with lower, or higher velocity of actual velocity c, would not be electromagnetic in nature in its relation
Ad 3. Here, without doubt, an error was made in principle. Ad hoc characteristic was given to an eye, or to the electromagnetic waves’ detectors.
The detector does not have and could not have this characteristic because in such case, the detector would stand for a device able to achieve interaction even with non-electromagnetic waves, in other words – detector would be able to interact with two phenomenally different types of waves. In such case, the information would be unclear, mixed up or even impossible. And, that by itself is the case why we have to have strictly selective light detector. The light detection device detects only specific light that in relation to it (light detector) has the speed c.
Ad 4. In the meantime, a strict selectivity of the detector does not exclude possibility of existence of the waves that have different velocity and not the velocity c.
Therefore, the light source could emit other lights with velocities different from the velocity c, but those lights cannot be detected until relative velocity c is reached between any one of them and the detector. (If for example, the source of light emits the light which in its relation to the source has the velocity: c + 5 km/sec., then the detector (an observer) should be moving away from the source at a velocity v = 5km/sec in order to achieve the relative velocity c between that light and the detector; in other words: in order to achieve interaction between that light (now electromagnetic in nature) and the detector. This is, of course, true for the light velocities lower than the value c – when a detector should be moving to the source at the appropriate velocity).
From these conclusions results the following
1. The light source emits limited set of light spectra spreading at various velocities in the relation to the source’s inertial system.*
2. Any light spectrum could be detected only in the particular inertial system and it has to have velocity c in its relation to it. At that time, that spectrum is the electromagnetic spectrum in that inertial system.
3. Relative velocity of the light spectrum in its relation to the observer is equal to the vector related difference of the velocities of both, light spectrum and the observer in their relation to the referential system.*
A term “light spectrum” is used because the Hypothesis supports the following: the spectrum (as a part of the whole spectrum) could be electromagnetic and non-electromagnetic. Under the term “light”, we usually mean detectable light spectrum (electromagnetic). The velocity of the entire spectrum (that could also be electromagnetic and non-electromagnetic) is the same as the velocity of its part (light spectrum).This Hypothesis is not opposed to the Maxwell electro-dynamics because it does not treat spectra of non-electromagnetic nature, but it is opposed to the Special Theory of Relativity for it does not accept light speed constancy. The Second Postulate of the Special Theory of Relativity according to this Hypothesis, should be formulated in the following way:
* inertial system = inertial frame
* referential system = reference frame
Light source (macro source) is the final set of elementary sources that are intensively moving at various speeds in their relation to the inertial system of the macro source and this is due to the incoming energy. Those speeds ve form a speed set limited by the extreme speed values of the elementary sources:
ve min < ve < ve max 1
At a certain moment, at any elementary source speed ve, elementary source could emit the elementary light. In the moment of emission, elementary light has the speed c in its relation to the instantaneous inertial system of elementary source, and speed c + ve in its relation to the inertial system of the macro source. Thus, the lights emitted by the macro source have various speeds vs in the set of speeds defined by the maximal and minimal elementary source velocity. If we adopt the direction of light in its relation to the source as a positive one, then we have:
c + ve min < vs < c + ve max 2
where, ve min and ve max are the extreme speed values of elementary sources, and vs are the velocities of light spectra in their relation to the inertial system of macro source (pic. 1).
The set (1) is a final one, and it has as many members as there are different active elementary sources’ speeds in a specific moment. Elementary sources with same speeds at the time of emitting elementary light, represent a sub-set emitting light spectrum of speed :
vs = c + ve 3
Every set member is the sub-set of the particular speed in its relation to the inertial system of the macro source whose speed differs from the speeds of other sub-sets. In the next moment, new set is «formed» in the macro source with its sub-sets that are different than the previous ones, but are within the same borders. Sets' shifting is highly intensive and thus is created the impression of a macro source emitting light in every moment with all possible speeds from the interval (2).
If we could imagine a fictitious macro source emitting complete electromagnetic spectrum in its inertial system altogether with other complete non-electromagnetic spectra, then all conclusions about light spectra are related to such source (complete spectra) as well.
GRAPHIC VIEW OF THE LIGHT EMISSION
VS = C + Ve
Spectrum (3) could be detected in such inertial system in which such spectrum has the velocity c, in other words speed vr of such inertial system in its relation to the inertial system of macro source must satisfy condition
vs - vr = c 4
This is the requirement for a detection achievement. Because vs = c + ve, it follows that
vr = ve 5
If the observer's (detector's) velocity in relation to the macro source is outside of such set, interaction between any spectrum emitted by the source and the detector is not going to be possible because such source does not emit spectrum which is possible to detect in such case in the observer's inertial system. Thus, the extreme velocities of the spectra yet possible to be detected are vs min = c + ve min, and vs max = c + ve max.
The light could be detected from any inertial system in the set (6), but the group (6) contains an infinite number of inertials systems, so it appears as macro source should emit an infinite number of spectra, so to speak, one spectrum of appropriate
speed for each inertial system, or otherwise macro source ought to radiate with infitely great energy, or with final amount of energy necessary to be divided over infinite number of inertial systems. Naturally, neither one, nor the other is possible. However, it comes out that it is not even necessary !
The macrodetector is also a set of elementary detectors that are moving (vibrating) at various speeds vd in their relation to the macrodetectors inertial system. Those speeds are of much lower intensity than those speeds of the elementary sources. The assemblage of these speeds is limited by the extreme speeds, and so we have got
vd min < vd < vd max 7
No matter how small the difference between the extreme speeds of such set, it contains an infinite number of various speeds taken over by the elementary detector during only one vibration. If macrodetector (an observer) is positioned within the inertial system which in relation to the macro source’s inertial system has a velocity vp, then the elementary detector is within certain moment positioned in the inertial system with velocity vr = vp + vd in relation to the macro source’s inertial system.
By exchanging the signs in the expression (4) we get
vs - vp - vd = c 8
Elementary detector takes over all speeds vd between the speeds vd min and vd max in the very short period of time, so it is sufficient that macro source emits any one and only one spectrum from the interval of speeds
c + vp + vd min < vs < c + vp + vd max 9
at least for that much time that is needed for one elementary detector's vibration to last (pic. 2), so thus will that spectrum be detected in the moment when the elementary detector reaches such velocity vd so that the requirement (8) is met. Thus, the entire set (9) containing infinite number of speeds could be « covered » only with one spectrum and any one spectrum whose speed meets the requirement (8). Hence, the observer (macrodetector) could detect any spectrum from an interval (9) not violating in any way the detection requirement (4), because it is strictly valid at the elementary level (8).
The set (2) contains final number of sets (9) and out of that fact there follows the conclusion : macro source should not emit infinite number of spectra, and more exactly, infinitely great energy although we can detect light from infinite number of inertial systems whose speeds are within the set defined by the expression (1).
The extreme interval values (7) must be very close in order to preserve detector’s selectivity.
Consequently, this hypothesis asserts – light is multilateral. The observer could be moving with any speed (from the interval (1)) in the relation to the source, but every time in relation to him there will exist some light that has the speed c.
Because of that, there we get the impression that it is the same light and that its speed does not depend on the relative speed between the source and the observer.
Naturally, any time it is another light, in other words it is another spectrum having a different speed in relation to the source.
If the observer is « measuring » the speed of light at any given relative speed between him and the source, then the observer is always « measuring » a speed of detectable light in his inertial system and he always gets the same value which is natural.
The constancy of light velocity is only illusion since the light spectra are detectable only when they have the speed c in their relation to the observer.
GRAPHIC VIEW - REQUIREMENT OF THE DETECTION
VS – Vr = C
The Interpretation of the Michelson’s Experiment
according to this Hypothesis
The light paths in the legs of the Michelson interferometer for the moving observer with a speed v, in the relation to the interferometer, in principle, look like those in the picture 3.
v v l pi G1 G2 ki v v O3 O4 b
O1 O1 O2 b Pic. 4
The beginning of the light impulse pi travels over the path O1G1O3 and the end of the light impulse travels over the path O2G2O4. This, of course, by analogy is valid for any elementary part of an impulse. Thus, the reflected light impulse is normal to the direction of the incoming light and it has translative speed v in the relation to the observer. Hence, it follows that the orientation of the light impulse does not coincide with the path direction of its elementary parts for the observer who is not in the inertial system of an interferometer.
The light paths are looking differently in the relation to different inertial systems, but as it is going to be seen, the light paths in their relation to interferometer look equal when observed from any inertial system.
a) Interferometer is moving with a speed v in relation to the referential system
oPr source o Op v Pd l o v
sn c c’ v Ok b
l o v
The interferometer and the observer Pd are moving with the speed v in the relation to the referential system. The observer Pr and the source are located in the referential system.
Under the 2nd regulation of the Hypothesis, the spectrum that could be detected in the inertial system of the interferometer has a speed vs = c + v in the relation to the source, and under the 3rd regulation of the Hypothesis, in the relation to the interferometer the speed is declared as vps= vs – v = c + v – v = c.
With that speed, the spectrum comes to the semi-permeable mirror and it is reflected at the angle of 90 o toward the direction of that spectrum also with the speed c (pic. 5). Because the mirror is moving with the speed v, then a reflected spectrum also moves translatively with that speed, and thus any elementary part of that spectrum is moving with the total speed c’ = c + v. However, here we should highlight that the spectrum orientation is normal to the direction vs of the incoming spectrum after it had been reflected off of the mirror. The orientation of the reflected spectrum and the direction of movement of elementary parts of such spectrum are not coinciding for the observer Pr.
The total path of the elementary parts of spectrum is 2sn = 2 (l2 + b2)1/2 and their speed is c’ = (c2 + v2)1/2 in relation to the referential system. The time needed for travel of such path is
2× sn v×l
T = ¾¾ , and because b = ¾¾ then
T = 2 [(l2 + v2l2/c2)/(c2 + v2)]1/2 = 2l/c
It should be taken into the consideration that the observer Pr is considering the spectrum that is not electromagnetic for him but for the observer Pd who is moving along with interferometer.
Obviously, the relative spectrum speed is not c’ = (c2 + v2)1/2 in relation to the leg of interferometer but c, because normal leg of the interferometer also has spectrum’s translative speed v, and thus this component of the spectrum speed in the relation to the interferometer is equal to zero.This is of course valid for the path which is not 2sn = 2(l2 + b2)1/2 but 2l, for the component of the path b is the consequence of the speed v, and this speed in the relation to the interferometer does not exist, for b = v×l/c = 0.
Thus, light ray’s speed in the relation to the interferometer equals c, and the path equals 2l for both of the observers. The time needed for such travel is 2l/c.
Here we should highlight that it is necessary to observe only what is happening in the relation to the interferometer and not what is going on in the relation to the whole referential system, so that the true about this happening will be identical and absolutely independent from the aspect of the viewing position.
First of all, let’s determine first spectrum’s path part in the leg of interferometer which is positioned in the direction of an incoming spectrum. This path part is the path that spectrum travels from the passage through the semi-permeable mirror to the non-permeable mirror (pic. 6).
sp’ sp’ – l l sp’ l
After ratio ¾¾¾ = ¾¾¾ it follows that sp’ = ¾ (c + v) and T1 = ¾¾¾ = ¾
c + v v c c + v c
The second part of the path that the spectrum travels when reflected from non-permeable towards semi-permeable mirror is accomplished from the ratio (Pic. 7)
sp’’ l – sp’’ l sp’’ l
¾¾¾¾ = ¾¾¾¾. Hence, sp’’ = ¾ (c – v) and T2 = ¾¾¾ = ¾
c – v v c c – v c
so the total travel is
sp = sp’ + sp’’ = l×(c + v) / c + l×(c – v) / c = 2l
and the total time is
T = T1 + T2 = l / c + l / c = 2×l / c
It could be seen that the spectrum with speed c + v in relation to the source has both the speeds : c + v, and c – v in relation to the referential system, but in relation to the interferometer that velocity is always c.
By accepting this hypothesis, there is no difficulties with interpretation of the Michelson’s experiment – there is no difference in path lengths within interferometer, neither there is a time differences, and thus there could be no interference.
b) Interferometer is within the referential system
If the source is moving in relation to the referential system at any speed v, such light spectrum could be detected in the interferometer that in relation to the source has the speed c + v, for such spectrum would, according to this hypothesis, have speed c in relation to the referential system, which is identical to the case when the source was in the same inertial system as was interferometer. For an observer in referential system, it is not at all important to know the speed of source movement –
for him the only important fact is that light’s spectrum (with speed c), the observer could detect is incoming into the interferometer. Thus, all happening in the interferometer will be identical and independent from speed of the source.
Because the light paths in the interferometer legs are also equal, there could be no interference.
Experiment with the source and device located on the Earth
The first part of the experimental task is to single one spectrum out of the spectral order which is emitted by the source (that is practically impossible) ; more exactly the goal is to single out one interval of spectra as narrow as possible, so we can determine its borders.
In the second part of the task we are testing interaction possibilities of an already singled out interval of spectra with a light detection device in various inertial systems.
The experiment consists of the following elements : light source (i), moving obstacle (Z) with openings (A and B), immobilized mirror (Os), movable mirrors (Od) and light detection device (P) . The distance between moving obstacle and immobilized mirror is marked with l, moving obstacle speed with w, movable mirrors speed with u, speed of any one spectrum with vs. The openings’ dimensions A and B are equal, and the meaning of marks h1 and h2 is visible in Picture 8. The moving obstacle with openings represents a spectra group (interval) separating device. By a way of moving mirrors, various inertial systems are being accomplished.
It is obvious, from a picture, that spectra with all speeds in the interval marked borders could go through the spectra separating device
2 l 2 l
vmin = ¾ w and vmax = ¾ w
and more exactly, particular spectrum with speed vs can go through the spectra separation device only if the following requirement is met
2 l 2 l
¾ w < vs < ¾ w
That separated interval comes to the movable mirrors where it is reflected and then reaches light detection device. According to the Hypothesis, the interaction between particular spectrum from that interval and light detection device could be achieved if
vs – 2 u = c
but more exactly, while the movable mirrors’ speeds are within the interval,
l c l c
¾ w - ¾ < u < ¾ w - ¾
h1 2 h2 2
If we give the speeds outside of such interval to the movable mirrors by not changing the speed of movable obstacle, then the interaction of light detection device is not going to be possible with neither one spectrum from the group that is going through the movable obstacle’s openings, and more exactly the light belonging to one inertial system could not be detected from the another
The Experiment Utilizing the Space Light Source
The source must be such that something is happening at it (for exam. Supernova). The information about event at the source is reflected by any spectrum from the order which such source emits, thus, the information about the same event travels at various speeds in the relation to the source and in the relation to the observer on the Earth. The observer has the option of detecting both the light coming from the source and the reflected light from the movable mirror which is moving at uniform velocity u, in the relation to the observer (Pic. 9.).
Among the spectra coming from the source, there is a such with the following speed in the relation to the observer
vs= c + 2 u
Such spectrum has been slowed down by the movable mirror so the observer could detect it, and it brings the information from the source earlier than the spectrum with the speed c that is observed directly.
If we mark the distance between the event location at the source and the observer at the Earth with l, then the arriving information’s time difference will be
l l 2 l b
Dt = ¾ - ¾¾¾ = ¾ × ¾¾¾
c c + 2 u c 1 + 2 b
where b = u / c. In such a way, it is possible to detect the event at the source earlier than when the source is observed directly, if a mirror is moving in the direction away from the source. By changing the direction of a mirror movement it is possible to register reprisal of the events after the time
2 l b
Dt = ¾ × ¾¾¾
c 1 – 2 b
in relation to the time when the event was detected and when source was directly observed.
By knowing the difference Dt and the movable mirror’s speed, the distance of the observed space source could be calculated with
c× Dt 1 + 2 b
l = ¾¾ × ¾¾¾¾
depending on the direction of mirror movement.
If for a long period of time we follow these changes, observing the source directly (for example, the change of shine of the γ Cassiopeiae star) and by means of movable mirrors, only to show them as a separate diagrams, then the same diagram configuration will be shown in the various times depending on the speed and the direction of moveable mirrors (Pic. 10.).
If we would have three devices drawing shine diagrams at the same time, the device detecting light directly from the source would at some point draw the diagram spot b.The device detecting light reflected off of the rotating mirror moving away from the source would already draw the spot c, while the device detecting light reflected off of the mirror rotating towards the source would only begin drawing a spot a. The time, device needs to draw the diagram from the spot a to the spot b, is ∆t1; and time from the spot b to the spot c we mark with ∆t2 depending on the mirror’s speed.
This is most likely the cheapest and the easiest experiment that should be conducted in order to prove the correctness of this Hypothesis.
According to this hypothesis, it is possible to explain the phenomenon of the speed of light’s constancy, as it was shown, in a very simple way. This manner differs from the one suggested by the Special Theory of Relativity. The experiments offered herewith, could prove beyond the shadow of a doubt, or they could unmistakably refute the correctness of the one of these two solutions. The dilemma about the correct solution must not exist, and the only way to eliminate it is by conducting fundamentally different experiments from those that had already been conducted. Some of them are suggested herewith.
The results of these experiments will certainly be against one or the other solution, but that in fact is not the most important thing – they won’t be against the Science.
I appreciate any and all suggestions, questions, comments, and notes that have a logical and experimental basis.
Author Address :
Sestara Bukumirovic 108 a
This paper and its parts are authorized by:
Biro za zaštitu autorskih prava; Belgrade, No 59/78 – 29. May 1978.
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