Light and Relativity – Sauerheber

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On the Nature of Light and Relativity

Richard D. Sauerheber
Department of Chemistry, University of California, San Diego, La Jolla, CA 92037 U.S.A.
Department of Tutorial Services, Palomar Community College, San Marcos, CA 92069 U.S.A.
October 24, 2012

A revised version of this article has been published in:
PHYSICS ESSAYS 27, 1 (2014)

Abstract. Although concepts from the special theory of relativity are widely believed, time dilation theory has not been proven with certainty in well-controlled, prospective experiments. Demonstrated here is that although relativity for light is special, in being an entity always traveling at fixed speed in the propagation direction from its source coordinate, the notion that time ‘dilates’ for objects in motion was an unfortunate extrapolation.1) An element is derived, missing from the original analysis, which demonstrates that for bodies in motion, the time required to be illuminated differs compared to that in the absence of motion, but absolute time itself does not ‘dilate’. The time required for a moving rod and for a stationary rod are identically calculated by both an observer in motion and one stationary. 2) Experiments with laser light sources, observed while the earth revolves and orbits and produces variable lateral source velocity, demonstrated that light pulses shift laterally along with the source and target while propagating at speed c to intercept the target. Pulses have a lateral velocity imparted by the orbiting earth, a necessary finding to understand special relativity. An example is provided in two dimensions to understand thought experiments commonly presented in Physics texts, and 3) intrinsic properties of light are discussed.

Key words: special relativity, intrinsic velocity, relative velocity, lateral momentum, time dilation

Introduction. Although evidence has been presented that the special theory of relativity for light has been confirmed and established (Giancoli 2009; Jennings in Halliday, 2001; Wolfson,1995; Hafele,1972), other evidence suggests the contrary (Otis,1960).  For example, Otis found that the velocity of light in the propagation direction indeed is c, but when observers are in motion toward (or away) from the light, the increased (or decreased) light frequency f detected proves that the velocity with which light and observer approach each other differs from c because of motion of the observer that cannot itself alter the wavelength l of the light produced by the source from which it speeds, where v (≠ c) =  lf. This suggests to us that the postulates of the special theory of relativity need to be clarified. Indeed, light velocity can have component magnitudes other than c, which are usually referred to as aberration of light.

Albert Michelson in the early 20th century (Livingston,1973) and Arthur Otis (1960) argued against time dilation theory, nevertheless most college and university physics textbooks around the world, many research manuscripts and special relativity articles and papers teach that time ‘dilates’ or slows for clocks or observers in relative motion compared to stationary (Giancoli, 2009; Haliday, 2001; Beiser, 1963).  To understand special relativity it is necessary to understand the intrinsic properties of light. Light pulses are here demonstrated to retain lateral momentum from lateral moving sources, and other aspects of the intrinsic nature of light are described. The original germinated idea of time dilation is reviewed, a missing element in the original theory is revealed, and here is delineated how objects in motion are illuminated by light wave rings to demonstrate why stationary and moving observers compute the same time for a specific event, regardless of their state of motion, as long as computations are proper.

I.Calculus Reveals Intrinsic Properties of Light.  It is generally accepted and borne out by experiment that physical objects with mass cannot exceed or achieve speed c.  Light having zero mass indeed propagates at this fast fixed speed that was determined with the aid of the Calculus to be c = 1/(em)1/2, from coordinate of origin, a universal constant in any frame of reference. The intrinsic speed with which light propagates in the direction it travels, from the location in space at which it leaves its source, is c. This is found for all light from any star independent of the frequency and energy of the light wave. Wavelength, amplitude, rotational speed, oscillation frequency, color and energy vary widely for starlight from various sources, while all must travel at fixed propagation speed c along the wavelength axis. Light produced from forward moving sources has higher frequency and energy, and shorter wavelength, than light from a corresponding stationary source, but in both cases speed remains fixed at c from the coordinate in space at which it departs the source. Increasing the velocity of the source cannot change the speed with which light emanates from it. Speed c is intrinsic to light and is constant for a given medium. We now know however that relative velocity with respect to moving detectors differs from c.

A photon of light is itself not a standing wave, or a waveform that propagates through space, but instead is a unit of electromagnetic energy comprised of orthogonal electric and magnetic fields that oscillate in amplitude over time perpendicular to the direction in which the photon speeds forward, tracing out a sinusoidal wave pattern.  A popular equation written as a function of time for the fluctuation in electric field amplitude of a photon of light, where x = 0 is placed at a wave node at t = 0, is E(t) = Emsin(2pft) (Bueche, 1988). Since f = c/l and if we choose a radiowave of 2p meters in length, then E(x) = Emsin(ct). At t = 0, p/c and 2p/c seconds, both the electric and magnetic field amplitudes, which induce and repress each other in synchrony, collapse to zero amplitude.

Sequential differentiation of the amplitude equation with respect to time reveals interesting features of light. The first derivative dE(t) = cEmcos(ct) provides an expression that computes the speed with which the field amplitude changes. The units of c are radians/second since in our simple example one meter equals one radian, so ct is in radian measure. The coefficient c ensures that the overall unit is Volts/meter per second. The second derivative -c2Emsin(ct) is the acceleration of the amplitude change. The third derivative is the velocity with which the acceleration changes in time, and the fourth derivative reproduces again the original sinusoidal functional form, d4[sin(u)]/dx4 = c4sin(ct). The fourth derivative is reflects the acceleration of the acceleration of change in field amplitude.

  The return to the original sinusoidal form for the fourth derivative suggests that the resonant acceleration of the electromagnetic wave amplitude follows a pattern comparable in form to the original electric and magnetic field amplitudes themselves. This is similar to an oscillating spring weight system where the position of the weight is pre-determined by the initial stretch force on the spring. The variation in the amplitude position of the weight is determined by the pattern of acceleration of the acceleration of the weight as a function of time. If an accelerator pedal on a car is itself accelerated and decelerated rhythmically back and forth, the car’s changing position (amplitude) is determined directly by the rhythmic acceleration/deceleration pattern of the accelerator pedal.

For both the oscillating spring and a wave-generating photon, amplitude maxima and minima correspond precisely in time with sequential minima/maxima in their velocity and acceleration of change, and the acceleration of the acceleration. For the photon described, a miniscule time change dt beyond a time position of maximum field amplitude [E a sin(t), from say t1 = p/(2c) to t2 = p/(2c) + dt],  the field amplitude lessens, with a velocity [E’  a cos(t)] determined by the maximum negative acceleration [E’’ a -sin(t) at p/(2c)]. This negative acceleration immediately also begins to decline in magnitude, becoming slightly more positive, since the acceleration of the acceleration [E’’’’ a sin(t)] is maximum positive at p/(2c). Thus, intrinsic to a photon is the special ability for magnetic and electric fields by self-induction to rhythmically accelerate and decelerate their own field amplitudes, while propagating forward always at constant velocity (linear acceleration = 0), ever-transporting energy over great distances without change in mathematical, and actual, traced pattern. The intensity of a light beam, which is proportional to photon density, decreases as a function of distance from a source by the inverse square law due to dilution of photon density. It is thus profound that an individual photon, the indivisible fundamental unit of light, propagates itself in a linear manner in vacuum without intensity decline, in all perpetuity if uninterrupted. The empirical laws of classical thermodynamics prohibit perpetual motion without energy loss, so massless light is indeed special, and this information is necessary to understand special relativity.

II.Lateral Momentum of Light—key to understanding time dilation diagrams.  Many inferences have been made regarding time dilation theory and relativity that are often based on the notion that a pulse of light, after leaving its source, follows the source position while it moves lateral to the direction of light propagation (Beiser, 1963; Giancoli, 2009; Haliday, 2001). But pulses after exiting a source are not attached to it or subject to its subsequent motion.  We therefore here attempt to determine whether a securely positioned laser light source, emitting light perpendicular to the direction of travel of the earth in its orbit, reveals if light pulses travel in a directed manner after leaving a lateral moving source, or rather that pulses are displaced from the position targeted (the intended bearing). This information is necessary in order to evaluate the validity of the postulates of special relativity.

The precise position of a light beam’s reflection on a target was observed as the beam’s pulses traveled 30 meters from a laser light source, anchored to prevent relative motion between source and target.  Continuous monitoring of the illuminated target spot throughout the day as the earth revolved and orbited revealed that pulses of light exhibit a lateral momentum imparted from the moving source.  If the spot on the target had shifted right and left as the earth orbited over a 12 hour period (as the leading target edge switched from being on the right to being on the left as the earth revolved) this would have suggested that no lateral momentum was imparted to the pulses from the earth’s motion and that each traveled in a particular direction as the source laterally moved away from them.

Our results revealed that pulses have a lateral velocity imparted by the orbiting earth. The illuminated target spot did not wobble during continuous illumination for 12 hour periods. This demonstrates that light pulses, like bullets shot from a lateral shifting rifle, pick up the lateral motion of the laser. At noon (and midnight) the pulses thus shift along with the system 3 mm while traveling to the target. The horizontal shift and velocity for the pulses match that of the orbiting earth, 3 mm at 29,700 m/s at noon, -3 mm at -29,700 m/s at midnight and no horizontal shift at sunrise/sunset. Light pulses shift laterally along with the source and target, while propagating at speed c to intercept the target.

Computation of the time required for pulses to reach the target at noon is [(302 + .00032)1/2 meters]/c) for a stationary observer above the earth, viewing the horizontal shifting pulses, rather than simply 30/c. This information is crucial to interpreting tenets of the special theory of relativity and the interaction of sunlight with the orbiting earth.  It is now evident that lateral light sources produce lateral shifts when in lateral motion and do not do so when no lateral motion is present, much like a rifle bullet shot from lateral shifting rifles in classical relativity. Starlight aberration was discussed with a similar mechanism for stars in lateral motion with respect to theoretical stationary observers (Marmet, 1996), rather than Bradley aberration due to motion of observers relative to stationary stars.

In this experiment, both source and detector are in motion together with no relative velocity between them, which means the photons, being un-shifted at the detected location on the target, are continuously shifting laterally along with the lateral shifting source and target. As for the case for a moving source (Marmet, 1996), there is no directly observed shift because of the lateral travel of the pulse during its propagation to the target in its new location, shifted from its position when the pulse left the source.

The notion that light’s velocity (not its intrinsic speed in the propagation direction) is always magnitude c in any calculation, independent of relative motion of source or observer, is thus in error. The horizontal component of velocity for the pulses here is -29,700 m/s at noon, 0 at sunrise/sunset and +29,700 m/s at midnight.  The constancy of the speed of light derived by Maxwell (c = (1/eouo)1/2 = 2.997924 x 108 m/s with modern values for the permeability and permittivity of free space eo anduo), confirmed experimentally by Michelson (Livingston, 1973) with round-trip light paths on earth (2.99796 x 108 m/s) and with measurements of  frequency and wavelength by others (Jennings in Haliday, 2001) at 2.997924586 x 108 m/s) proves light speed is a fixed constant relative to the location it departs the source. These data do not indicate that relative velocity of light is constant in any frame of reference for an observer who may be in motion, but merely that the intrinsic velocity of light in free space relative to its source departure point is c. This, and our results, are consistent with the notion described by Otis in 1960 that the 2nd postulate of the special theory of relativity is invalid. Moreover, light can contain ‘momentum’ from the source at which it forms, so for an object seen because light penetrates the eye directly reflected from that object, the position the object was located at the time light reflected is sensed, not the position at which the object exists at the time it is sensed.

Time Computations for Earth-bound Sunlight Photons. A concrete example in nature is the path of sunlight photons that strike the earth. Sun light photons that travel toward an earth location along its elliptic orbit never actually reach the earth. The earth shifts 2.5 earth radii while the photons travel, and the photons instead pass that location and propagate into deep space.  Only photons that angle-travel to a position in front of the orbiting earth actually strike the earth to be seen. The time required for a light pulse to angle-travel from the sun, at the time the earth is at perihelion, to earth at its later shifted position, may be computed, knowing that all radii for an ellipse are not equal, exhibiting a minimum magnitude at perihelion and a maximum at aphelion. The earth-sun distance at perihelion rp is approximately 147.1 x 106 km, where earth orbit speed is 30.20 km/s. The actual ellipse radius length r that a photon must follow from sun to strike the earth is approximated for simplicity by r = [rp2 + (vet)2]1/2 where r is the actual travel length, ve is earth lateral travel velocity and t is the time required for the pulse to travel path r. Since t = r/c, after substitution r = rp/[1 – (ve/c)2]1/2 (ignoring that the true orbital path radius length has a lesser increase than this as a function of position from perihelion minimum, and that earth orbit velocity changes smoothly over time from its maximum at perihelion).  The earth orbits here 14,500 km, over 2.5 earth radii, while a light pulse travels over 8 minutes from the sun to join it, and the path length of light travel r is roughly 0.7 km longer than the earth-sun distance rp at the time the pulse departs.

So the time for a pulse to travel from the sun to the perihelion position is rp/c = 8 minutes 12 seconds, but about 33 milliseconds more time is required for a pulse following the true path r that photons follow to strike earth at its shifted position during travel of the photon (ignoring the galaxy rotation smaller contribution). On earth, one who does not consider the earth orbit shift, and instead uses the stationary earth-orbit distance at perihelion in the computation of time, performs an error. This erred time, rp/c, would be that for a photon to reach the position at which the earth was located earlier at perihelion, but not the true time, r/c, required for the pulse to reach the earth at its shifted location. The difference between these two calculated times, ∆t = r/c – rp/c, reflects the magnitude of error on the part of observers, but not the ‘dilation’ of real time, which is expected because this is a single event for a linear traveling photon to achieve, at that particular exact distance of travel, which is not affected by motion of observers.  This is a principle in Physics, that measurements when conducted properly from two frames in relative motion must always produce the same result for a specific event.

Please understand that if an opposite traveling photon were to depart the earth at the instant of perihelion, the time to reach the sun would be different than that for the sun photon to strike earth, because the forward and reverse trips by the separate photons are distinct events. The lateral momentum. or aberration, of light from the orbiting earth means that only photons with a bearing toward one side of the sun would land at sun’s center. So the time for this to occur would be rp/c, not r/c, because here the perihelion radius is the path the sun-bound photon actually follows. This event is different than r/c because this is a different path and length than for the sun-to-earth photon that travels along a radius greater than at perihelion to reach the shifted earth later. If the path had been circular there would be no difference in the times for the two photons. Diagrams that demonstrate ‘dilation’ of real time either compute time for a single event incorrectly, or present different events requiring different times as though they are the same event. Care must be taken to analyze them.

Intrinsic vs. Relative Properties. Intrinsic velocity for light is distinct from intrinsic speed, since velocity is the rate of distance accumulation along any particular direction (rather than simply the  total distance traveled during a time interval in any direction, for intrinsic speed). Light reflected that returns to its origin has a velocity of zero. It is a simple matter to exceed the velocity (but not the speed) of light. Simply do not make a u-turn, or point the light in a direction other than the travel direction desired. Component velocities are not c, even though intrinsic propagation velocity is c.

While intrinsic velocity remains c in the particular single propagating direction, the intrinsic velocity for a light component depends on the bearing one uses in a computation, where component velocity may vary from +c through 0 to –c.  Light beams emanate from a lit candle at speed c only in their specific direction of travel. All technically have different velocities, some velocity +c (East), others –c (West) and any traveling North have velocity to the East of 0.

Maxwell’s equations for EM radiation demonstrate that intrinsic translational propagation speed (or velocity if no direction change occurs) for light is fixed at c in a given medium, which is a factual tenet of special relativity.  The relative speed and velocity however between a moving detector and a light wave are NOT described by Maxwell’s equations. And Otis (1960) found that detectors on earth when moving toward starlight detect increased light frequency, compared to that when detectors are receding. Since intrinsic velocity v = fl, it is the relative total velocity (between light front and the detector) that increased the observed frequency, from f to f*, of the waves detected with a Doppler effect, since c is fixed and the wavelength likewise is not altered by motion of a detector. The total relative velocity is v = f*l = c + s, if the detector approaches at velocity s. So, two light beams propagating in opposite directions illuminate twice the distance in unit time than can a single beam. Relative velocity of illumination is then magnitude 2c while intrinsic speed is still c.

Light is special in requiring a different time to illuminate a moving object than when that object is at rest (Einstein, 1905), because light intrinsic velocity c is pre-determined and cannot add to source velocity. The difference in time is due to the fact that a moving object shifts while light travels across it, requiring extra time for light to accumulate the entire span. The effect would be detectable of course only at very large object speeds, where the total relative velocity is significantly different than c between target and light pulse, c – s if the target recedes from the pulse. References to time dilation involve differences in distances perceived to be spanned by light beams, rather than shortening of absolute time, because light must travel through space at c independently from the moving object being illuminated.

The proposal that the total relative velocity between a light wave and a moving detector somehow ‘warps’ to a fixed value c anyway, an extrapolated part of special relativity theory, has been the source of much contention, disputed frequently by Maxwell, Dirac, Dingle, Albert Michelson and his understudy Dorian Miller, Petr Beckmann, and Arthur Otis, whose findings above confirmed that Maxwell fixed intrinsic light velocity is not influenced by relative motion of source or detector. Relative speed between light front and a moving detector ranges from c + s to c – s, an important feature of Einstein’s analysis of relativity in 1905 (Einstein, 1905), where s is the velocity of the detector (see below). We now know that Doppler motional effects caused by source motion produce corresponding changes in frequency and wavelength (higher frequencies of solar radiation occur on the side of the sun spinning toward earth compared to frequencies on the side spinning away from earth) while their product, intrinsic velocity c = fl, remains constant.  Doppler effects due to detector motion though are different and alter the relative velocity and the relative frequency with which waves are detected, without of course affecting either intrinsic frequency, wavelength or speed of the light produced at the source. The velocity of light directly measured for a 44 mile round trip with a calibrated rotating mirror chopper by Michelson in 1926 in the San Gabriel Mountains, CA were successful because the earth recedes away from the beam front for one leg of the trip and approaches toward the beam for the other leg. The overall time for the trip was as if the earth had been nearly stationary (see full explanation below). These facts are necessary to understand the truth regarding time dilation theory.

III. Time Dilation Original Construct. The following paragraph is the crucial portion of the original 1905 manuscript On the Electrodynamics of Bodies in Motion (Einstein, 1905) that first described time dilation theory. Einstein proposed that the duration of time for an event was not the same for observers who are in relative motion with respect to one other. Here are his original words:

We imagine that at the two ends A and B of a moving rod, clocks are placed which synchronize with the clocks of a stationary system; that is to say that their indications correspond at any instant to the “time of the stationary system” at the places where they happen to be. These clocks are therefore “synchronous in the stationary system.” We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established for the synchronization of two clocks. Let a ray of light depart from A at the time tA, let it be reflected at B at the time tB, and reach A again at the time t’A. Taking into consideration the principle of the constancy of the velocity of light we find that:


               t1 = tB – tA = rAB/(c – v) and t2 = t’A – tB = rAB/(c + v)


where rAB denotes the length of the moving rod–measured in the stationary system. Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous. So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.  

In the remaining discussion, vector quantities are listed in boldface, and we recognize that light indeed travels in a linear path in a given medium at fixed constant velocity.  Here, the observer on the rod uses the length of the rod rAB for the distances he sees the light pulses travel. To compute the correct times of travel, he divides this distance by the relative velocity between the pulse and his position, that is, the velocity with which the light pulses are catching up with him because he is not traveling away as fast as the light travels toward him. For the trip from A to B, the magnitude of the velocity of light in the forward direction with respect to its point of origin is c. The magnitude of the total relative velocity between the pulse and point B is c – v, as shown, because of motion of the rod in the pulse direction. As quickly as light travels toward B, the effective speed toward B is reduced because point B moves away from it.

In the reverse direction, the velocity of light from its origin from B is -c. From B back to A, the magnitude of total relative velocity is -c – v, with an absolute value of magnitude c + v. The light reversed direction, but the rod continued forward.  In this reverse direction, the magnitude of the total relative velocity is greater than c because, as light speeds toward A, A approaches the returning pulse, causing the relative velocity between the pulse and point A to exceed the intrinsic speed of light on its own. This phenomenon was confirmed (Otis, 1960) with spectroscopes in motion on earth measuring starlight frequencies. The wavelength of starlight is obviously unaffected by motion of an unattached, distant detector, but the detected frequencies depend (from v = fl) on the relative velocity between the pulse and spectroscope. The frequency blue shifts if the relative velocity is greater than c when approaching the light and red shifts when less than c while retreating.

In the above example then, the two calculated times, for the forward and reverse trips, are not equal. But it is not that ‘the clocks are no longer synchronized because they are in motion’, compared to being initially synchronized at rest. It is simply that the time forward is different than the time back, because the two events are different. The forward and reverse trips represent different distances of travel for the light.  This also refutes the claim that two velocities acting in concert “cannot exceed c,” since c + v clearly does, as Einstein listed. The intrinsic velocity of light is magnitude c, while the relative velocity here is different than magnitude c due to motion of the arrival location with respect to the beam front.  This example compares to the real example in nature presented above, where sun-to-earth photon travel time differs for that from earth-to- sun because the two travel paths are not the same for photons departing from opposite positions.

Missing Mathematical Element Revealed.  Although no equation was presented for the stationary earth observer of the moving rod, this is necessary to understand the theory. The stationary observer also sees two different times for light to travel the two paths. The clocks are synchronous in the stationary system, as was initially defined, but the stationary observer sees the relative motion of the rod with respect to the earth. He calculates time from A to B as t1 = (rAB + vt1)/c, which rearranges to t1(c – v) = rAB and to t1 = rAB/(c – v), the same expression as originally above. Here vt1 is the distance (velocity times time) to the right the rod moves during the observation. Similarly for the reverse trip, time t2 = (rABvt2)/c, which rearranges to t2 = rAB/(c + v), again the same corresponding expression for the moving observer as well. Therefore, both observers, as expected, agree on the time for the forward direction (t1 for both observers) and on the time for the reverse direction (t2 for both observers).

Dilation Theory Analyzed. ‘Dilation’ of real, or true, time never actually occurs simply because someone is in motion. If the rod were stationary, then the time to traverse the rod forward or backward is rAB/c for both observers, on the ground and on the rod. When in motion however, different times for the forward and the reverse trips occur because these then are different events.

Relativity for light is special. Unlike classical relativity, for objects with mass and finite speed, when light is involved in computing time for an event, different results occur for objects in motion rather than at rest because light’s velocity in the propagation direction remains c even when produced from moving sources. When light is used to measure time, stationary and moving reference frames produce different results because the events are indeed different. Although absolute time does not dilate or slow for clocks in motion, instead, light can distinguish events taking place in stationary, verses moving, reference frames (see below). Objects with mass, and velocities that depend on the motion of the source, cannot be used for this purpose because velocities are additive for physical objects.  

  For a real example, return to the Michelson direct measurements of the speed of light conducted 2 decades after time dilation theory was invented. While the earth orbits at velocity v, the time for a light pulse to travel along that direction, from Mt. Wilson 22 miles to Mt. Baldy, is 22/(c – v). This is longer than the time 22/(c + v) required for the pulse to return opposite the direction of the orbiting earth. Roughly the total roundtrip time used to measure light speed is nearly the same as if the earth were stationary, because earth speed is only 0.01% of light speed. The total time is, as for the roundtrip of travel for the moving rod, ttotal = D/(c + v) + D/(c – v) = 2Dc/[(c + v)(c – v)] = 2D/(c – v2/c) where D is 22 miles in place of rab and v is the earth orbit velocity. This expression is useful, where indeed at v = 0 (or v << c) the roundtrip distance travel time reduces to that of the stationary earth, 2D/c.  If orbital velocity v = c, then the time required to travel becomes 2D/0, infinite, because the light would never catch the target!

The observed relative speed Michelson reported, cobs, was 2.99796 x 108 m/s (Michelson, 1927), to the precision obtained.  The difference between cobs and the true speed (1/eouo)1/2, estimated with current values that are independent of earth velocity to be 2.99792458 x 108 m/s, is 3.4 km/s. The distance shifted by the earth in the direction of the traveling pulse is 3.8 meters plus 12.2 mm, which is larger than the distance shifted by the earth during the pulse return trip to the detector of 3.8 meters plus 11.5 mm (using an earth velocity of 30.2 km/s).  But the time for the forward trip (t1 = D/(c – v) = 0.126233 ms) is also longer, and for the reverse trip (t2 = D/(c + v) = 0.126208 ms) is shorter, than the time if the earth were stationary (tstat = 0.126221 ms each direction). So, calculation of cobs for the roundtrip using 44 linear earth miles differs from true c (if other errors are ignored) by only 30 m/s, where ∆c = [(2D + vt1vt2)/ttotal – 2D/tstat]. The distance between mountains was measured to within 76 mm (3 inches), but other errors in the measurement were due to variable moisture content and atmospherics and technical precision of the instrumentation, and depending on the time of day, the earth either orbits along the Eastward direction the light pulse travels, or lateral to it depending on the earth’s rotational position. That cobs ≠ c is partly because the true distance of travel was larger (by 0.7 mm) than if the earth had been stationary. This specific difference is not due to motional dilation of real time, length contraction of the earth, or intrinsic light speed being somehow other than c. This difference is merely computational when linear ground distance, rather than total distance due to earth motion, is divided by the time. Note that this good agreement to 6 digits also suggests that little motion of the universe exists that would otherwise cause more significant deviations from the Maxwell value.

Faster orbital velocities produce greater time and distance shifts during the measurement of c with the Michelson apparatus (Figure 2). This direct observation method is subject to the calculation error, but in reality cobs will always equal true c, for any v < c, as long as the calculation is conducted properly. This is revealed by substituting for t1 and t2 in the expression: cobs = (D + vt1 + Dvt2)/(ttotal) = {[2D(c2v2) + Dv(2v)]/(c2v2)}{(c2v2)/[D(c + v) + D(c – v)]} = (c2v2 + v2)/c = c (which is independent of D or v, as long as v ≠ c).  So (if other sources of error could be eliminated), this method would yield true speed c = (1/eouo)1/2. Multiplying measured wavelength and frequency also produces accurate results because the light source motion affects frequency equally to the change in observed relative frequency of a moving detector, and indeed such measurements agree with the Maxwell value to nine digit precision (Haliday, 2001).

Light Travel Time in Two Dimensions. Often two dimensional diagrams with light rays are presented to introduce the theory of time dilation. An optics diagram in Figure 3 is used to demonstrate that light wave rings consist of rays traveling in straight paths at intrinsic speed c from the coordinate at which each departs from the source. All rays have velocity components in space forming a spherical pattern. The diagram illustrates why illumination of objects that are in relative motion require different time intervals than for objects at rest. This is due to relative velocity being different than that for the intrinsic velocity of light. The idea that time dilates for clocks or observers in motion compared to when at rest is easily demonstrated to be an error. Special relativity for light explains this time difference without requiring dilation of absolute time.

Only light rays having a proper horizontal component strike the mirror. The light ray traveling in the vertical y direction on the left has velocity in that direction of ||vy1|| = c, while the horizontal component of its velocity is ||vx1|| = 0 (i.e., v1(x, y) = 0i, cj). The ray on the right travels at c in its propagation direction, with horizontal and vertical components given by ||vx2||= c(cosq) and ||vy2|| = c(sinq), where q is the angle made by this ray from the horizontal (i.e., v2(x, y) = c(cosq)i, c(sinq)j). Let H be the magnitude of length of the propagation vector H (||H|| = H) for the ray that traveled between the coordinate of the source on the left to the coordinate of the mirror upon arrival on the right. Then, the time required to strike the mirror is simply this distance divided by its velocity in that direction, t = ||H||/||c|| = H/c. This correct time for the event is easily observed by stationary observers, compared to an observer in the moving system.

An observer riding on the mirror might compute time for this event in three different ways. Let D be the vertical directed distance vector between the y coordinates of source and mirror. Knowing the ray striking the mirror traveled this far in the vertical y direction, the moving observer might be tempted to compute time as t = ||D||/||c|| = D/c.  Since he doesn’t notice the horizontal distance the mirror traveled, calculating the time as D/c is based on an illusion, because the ray that actually travels in the y direction with velocity c never strikes the mirror. He could also correctly compute time as D/[c(sinq)], knowing that only light rays with a horizontal component could join the mirror after it shifted to its rightward location, and these rays from the source when at the leftward location would have had a vertical component velocity vy = c(sinq)). Then t = D/[c(sinq)] = D/[c(D/H)] = H/c. Or he could compute time as t = [(vt)2 + D2]1/2/c = H/c, where v is the horizontal velocity of the mirror, shifting distance vt. In these cases the time is the same as that also computed correctly by the stationary observer, H/c, but these require use of this additional information that is known to the observer by calculation.

The component velocity in the y direction for the ray that does indeed angle-travel to the mirror is not c, but is vy = c(sinq). It must be emphasized that the vertical ray already passed the y coordinate of the mirror at the time the angled ray strikes the mirror, as shown by the vertical ray on the left at time H/c, when the rightward ray arrives at the mirror new location. D/c is an incorrect computation for time required for light to strike the moving mirror because it represents a mismatch of vector components, in spite of this technique being widely published and taught. D is a vertical direction distance, but the particular ray that actually strikes the mirror has velocity magnitude c only in a direction that is not in the vertical. The true time for this event, to strike the mirror, is unaffected by whether an observer moves laterally with the light, or rather remains stationary. Notice that velocity addition does not occur with light from moving sources, so always vy2 = c2 – vx2, while objects with mass thrown from sources in motion, velocities are additive, and (vx2 + vy2)1/2 is not a pre-determined constant, but is a greater velocity.

Discussion. Studies of the intrinsic nature of light reveal, by calculation and by experiment, that light photons when formed exhibit a pre-determined property, where the acceleration of the acceleration of the field amplitudes, and the variation in amplitudes themselves, are sinusoidal in form and must travel, when uninterrupted, in straight paths with constant velocity c from coordinate of origin. In a thought experiment  in which the illumination of a moving rod by light suggested ‘dilation’ of absolute time for observers in relative motion (Einstein, 1905), a missing element was the expression for the time to traverse a moving rod computed for the stationary observer. When this term is considered properly, the expression rearranges to that for the moving observer. The original foundation for the ideas of time dilation, and that simultaneity is somehow ‘relative’, are thus overturned. Whether an observer or clock is in motion or not, when time is computed correctly, both observers arrive at the same value for any single illumination event.

Notice in our diagram that it takes longer for the ray to strike the moving mirror than required if the system were stationary. Without any shift, the mirror would be struck by the vertical light ray in time t = D/c. In the moving system, D/c is the time for a vertical light ray to travel from the source origin to the coordinate where the mirror was at the time this ray first formed. It is not the time for reaching the receding mirror’s rightward position. Likewise, the time for the ray to reach the moving mirror, H/c, corresponds to the time for the vertical-traveling ray to travel distance H, not D but beyond it.

It takes less time to illuminate an object that is stationary than when in motion in the direction of the light travel path, and this is the conclusion also reached by Einstein in 1905 for moving rods. This is because the relative velocity between the light ring and the mirror is less than c when the mirror recedes from the light beam, requiring more time, while the velocity of light, from any source, is intrinsically fixed at c. Detectors receding from sunlight indeed record lower frequencies than when approaching sunlight because of the relation v = fl (Otis, 1960). Here, the intrinsic wavelength and speed of the light is unaffected by any action of a detector on earth, being characteristics of the light produced from the sun. The reason the frequency increases while approaching (and decreases while receding) is because the relative velocity between the light ring front and the detector is c + v on approach (or c – v while receding), as Einstein also presented for the total relative velocity between a light ray and the moving rod. The oversight was that observers in relative motion would somehow calculate different times for the same event and thus would have nonsynchronous clock times.

IV. Conclusion: Newtonian mechanics explains the motion of objects with physical mass subjected to finite forces at finite velocities, but is recognized as not applicable to many of the features of light, which is massless energy not subject to gravitational force. Moreover, the special theory of relativity as currently devised is also an inaccurate description of the nature of light. Although relativity for light is special, where a longer time is required to illuminate an object if it is receding from a light beam than when stationary (or a lesser time when approaching), this is due to the fixity of the intrinsic velocity of light in its propagation direction and is not due to ‘dilation’ of absolute time.  The data taken together suggest the special theory of relativity should include four concepts.

1. The intrinsic speed of light in its propagation direction (its velocity from the location at which it departed from the source) is a fixed constant in a given medium. This is similar to the classical theory of relativity for light proposed by Otis and also by J.J. Thompson that the velocity of light is to be regarded as constant only in the system in which its source is at rest. We here clarify this to mean that it is a constant with respect to the location from which the light pulse departed from the source.

2. c in vacuum is empirically regarded as the maximum intrinsic velocity of propagation for a single entity. It is generally accepted that the motion of a light source in the direction of light propagation does not change the speed but rather the energy and thus the intrinsic frequency f and wavelength l since fl is constant c. (It is not surprising that electrons energized in linear accelerators produce, at speeds approaching c, EM radiation, which travels at c).  Light velocity is a directed, vector quantity. Relative velocity vc can be written as c + s when detectors have velocity s in relation to the coordinate at which the photon departs its source. Two light beams traveling in opposite directions illuminate a combined distance in half the time as a single beam, thus at a total relative velocity of 2c. Two beams that approach each other illuminate space at a combined relative velocity of 2c. And component velocities for light in directions other than the true travel or propagation direction are always less than c in magnitude (||c|| < c).

3. The second postulate of special relativity theory needs greater revision. The speed of light remaining an invariant constant with respect to all frames of reference certainly applies to the speed calculated for light with respect to the source that produced it. But this statement is not profound for light, as it can apply for sound or physical objects, since the speed of any entity (measured with its own speedometer) always matches the speed reported by a sidelined detector who knows his own intrinsic speed or lack thereof to correct the value measured. That both the stationary observer and the moving observer would detect light’s speed to somehow be the same value c without correction is not established and is challenged by our findings. Otis (1960) concluded that light’s speed is classically relative, particularly with respect to a moving detector, where the detector cannot change the wavelength of the light produced while the frequency by which photons are detected by approaching detectors increases, so that the relative speed of light (but not its intrinsic value) is unequal to c. For masses picking up lateral momentum from moving sources, velocity vector addition may be applied to describe the total velocity; for light however, velocity subtraction is necessary to determine perpendicular components since the speed in the propagation direction must remain maximum c.  The components of velocity have a domain from –c to 0 to +c.

4.  That light requires another unique postulate stems from the fact that its intrinsic maximum speed c is fixed even when produced from sources having varying energies. Longitudinal momentum (rather than lateral) may not be imparted, because the speed in this direction is already maximal, leaving only energy to change. This is unlike masses that exhibit variable velocities from forces imparting differing energies. This is a corollary of the well-known photoelectric effect where a work function minimum frequency, rather than a minimum power, is necessary for photons to dislodge electrons.  Energetic light sources produce merely a higher beam density per cross section and higher frequency radiation, while its intrinsic speed remains c from the location where it was produced and from which it speeds.  Light photon energy, given by hf or hc/l, are not vector quantities, but as long as the propagation direction is considered, ||v|| = c = fl.  Component velocities in directions other than the actual photon propagation direction of course have a domain from –c to +c. These postulates more accurately summarize the nature of the special relativity of light.

Acknowledgments. Thanks always to the excellent students of Palomar College. We can all be grateful that God said “Let there be light”, and that Isaac Newton separated light into its component colors, Thomas Young re-blended them, James Maxwell calculated light intrinsic speed, and Albert Michelson experimentally verified that speed for roundtrip light travel on earth. This author was raised at the foot of Mt. Baldy in California where Albert Abraham Michelson, the first American to receive the Nobel Prize (Physics, 1907), performed these important measurements.


Beiser, A. (1963) Concepts of Modern Physics, MacGraw Hill Book Co., N.Y.

Bueche, F., (1988) Principles of Physics, MacGraw Hill, Inc., N.Y., 5th edition, p. 495.

Einstein, A., (1905) On the Electrodynamics of Bodies in Motion, in: The Principle of Relativity, Methuen and Co., Ltd., London, 1923.

Giancoli, D. (2009) Physics for Scientists and Engineers, Prentice Hall, N.J.

Hafele, J. and Keating, R. (1972) Science, vol. 124, July, p. 166.

Haliday, D., Resnick, R. and Walker, J. (2001) Fundamentals of Physics, John Wiley and Sons, Inc., N.Y., 6th ed.

Livingston, D, (1973) The Master of Light, University of Chicago Press, Chicago, ILL; The Albert Michelson Museum, China Lake, CA houses his equipment and the Nimitz Library, Annapolis, MD contains his textbooks, scientific publications and correspondence (see

Marmet, P., (1996) Stellar Aberration and Einstein’s Relativity, Physics Essays 9(1), pp. 96-99.

Michelson, A. A., (1927) Measurement of the Velocity of Light Between Mt. Wilson and Mt. San Antonio, Astrophysical Journal, Volume 45, pp. 1- 22.

Otis, A. (1960) Light Velocity and Relativity, Burckel and Associates, Yonkers-on-Hudson, N.Y.

Wolfson, R., Pasachoff, J., (1995) Physics, Harper Collins College Publishers, N.Y., 2nd ed.

 time   tA:                          




                                         time  tB:




                                                                               time t’A:


                                                                              A            B


Figure 1. Sequential depiction of a rightward moving rod A___B, while a light beam (~) travels past it, from the left end of the rod labeled A (at time tA) to the right end of the rod labeled B (at time tB) at forward speed c that is reflected back to A (at time t’A) with velocity = -c as the rod continues forward. Observers described in the text are either stationary (on the ground) or in motion (on the rod), but share the fact that the rod is a single fixed length for either frame of reference.

Figure 2A. Actual time t (ms) for a light pulse to travel a 44 mile roundtrip distance along the ground in a Michelson speed of light measurement, plotted as a function of ground velocity v (x 10-8 m/s) parallel to the roundtrip direction of travel. The function varies with the inverse square of the reflector/detector velocity, given by t= 2D/(c – v2/c) where D = 22 miles. At v = 0, t = 0.25 ms. At v = c, t = ∞.

Figure 2B. Total distance (km) traveled by a light pulse to illuminate a 22 mile length roundtrip, when the ground is in motion with velocity v (x 10-8 m/s, or 100 Mm/s) parallel to the pulse travel bearing. The function is given by dtotal = 2D + 2Dv/(c2v2). At v = 0, dtotal = 2D. At v = c, dtotal = ∞. The curves in 2A and 2B vary in synchrony, so the velocity of light, when computed properly, is always c, independent of v, where dtotal/t = c for any matched distance and time for any particular value of v. The proof is as follows, where t1 = D/(c – v) and t2 = D/(c + v):

cobs = dtotal/t = (D + vt1 + Dvt2)/(t1 + t2)

= [2D + v(t1 – t2)]/(t1 + t2)

= [2D + Dv/(c – v) – Dv/(c + v)]/(t1 + t2)

= [2D(c2v2) + 2Dv2)]/(c2v2)[(c2v2)/(D(c + v) + D(c – v)]

= 2D(c2v2) + 2Dv2)/2Dc

= (c2v2 + v2)/c

= c.

Figure 3. A flat mirror M that moved horizontally at a fast speed, while light rays emitted from the lower left source S travel along paths indicated by arrows. A light wave ring, produced by the source while at its leftward position, traveled to strike the mirror in its later position shown to the right. All rays travel at fixed speed c = 1/eouo1/2. The diagram helps explain why light forms spheres of illumination around a source coordinate at which it is first produced. The equation for the ring in a plane is given by r2 = x2 + y2, where x is the component of distance traveled along the horizon and y is the component accumulated vertically for any given ray, and r is the length of all rays, being identical at any time since intrinsic speed in all directions of travel is fixed. (Since photons pick up lateral momentum from moving sources, the rings are distorted from spherical). The ray with an original bearing toward the mirror at its initial location does not strike the mirror, but travels past the location at the instant in time a ray with the angled bearing strikes the mirror. The time required to strike the mirror is easily computed correctly by a stationary observer as r/c (where r is the distance all rays, including the ray striking the mirror, travel in any direction during that time). An observer riding on the mirror could incorrectly compute time as D/c, assuming the distance the pulse traveled was that to the location the mirror originally was (at the time the pulse departed). The time required to strike the moving mirror is longer than the time required to strike the mirror if it were stationary with respect to the light front. However, the correct time, when computed properly, is identical for both stationary and moving observers because it is a single event which cannot be controlled or determined by mere motion of an observer.



More from Dr. Sauerheber:

Another thing in the article is the description of the fact that light has no mass.  It is not a “small”particle. It is an electromagnetic field set that propagates through space in perpetuity if uninterrupted. So the Einstein idea, that E = mc2 means that m = E/c2 and that somehow this computes the tiny mass that light would have, is false. He was given a ticker tape parade down 5th Avenue in New York City after photographs taken in Mexico during a solar eclipse suggested that the sun bends starlight as the light passes by because it was felt this “confirmed” light has mass. But light has no mass and is not moved by gravity.  Any bending around an object like the sun can easily be explained by other factors. But the light was not bent anyway–an observatory in England photographed the same eclipse and found no shift in starlight at all. Sadly, few people discuss that good data and instead most want to believe the crude pictures taken in the field.



More from Drl Sauerheber:

The non technical explanation perhaps could be obtained in the section on sunlight that travels to the earth vs sunlight that travels from the earth to the sun when in both cases the light leaves at the same instant. The times of travel required are different, and this is not because of “time dilation” and “special relativity”, but rather is due to the fact that the path lengths for the two events are different in length.   This is true because the earth orbits in an elliptical path where the distance from perihelion to the sun is r, but the distance from the sun to the earth is less than r because the earth moves 2.5 diameters while the light is traveling for approximately 8 minutes.
Currently satellites operate under the theory of “time dilation” to explain why more time is required for a signal to travel to the earth from a moving satellite than for a signal from the earth to the satellite.  But it is not that “time slows down” because an object moves. The difference in time is due to the fact that the travel path toward the satellite is longer than if the satellite were stationary, while light emitted from lateral moving sources picks up lateral speed. Only those photons that were directed rearward would actually travel straight to the target. And only signals sent in front of the satellite would catch it, so again the travel paths are different distances.
The people who will be mad are Einstein relativists.  These people have corrupted Physics textbooks used worldwide in colleges and universities for over 50 years and have dominated thought and ridicule those who oppose Einstein’s theory. They argue the theory has somehow become “fact.”  I hired my daughter to send an earlier version of the article to every University Physics department in the U.S. and Canada several years ago. I got zero responses. Also the author of the main best-selling most-used College Physics text told me that he would not read the article because it seemed to go “against Einstein” and that if there were any problems with relativity theory then today’s modern expert theorists would have found them already.

When I got the article from the printer I realized that this was the end of a 48 year saga. My high school physics teacher took our class to Harvey Mudd College in CA to visit their Math/Physics department. We were given a tour and an exam.  The entire class got a zero (except i was given 1 point) and my teacher was extremely disappointed. But I knew then that one of their questions they had graded wrong, on relativity.  If one ship approached you at speed c and you yourself were approaching it at speed c, what is your combined relative velocity? Our answer was 2c which is correct (except that objects with mass cannot travel at speed c). The “correct” answer according to Einstein was c because c “cannot be exceeded.” This nonsense is now disproven, but it took 48 years to get the experiment finished, to write it up in a way that could not be challenged or misunderstood by reviewers, and to get it published. So this was a huge load off my back.


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