**1. Introduction to relativity**

Most all measurements in the physical world are subject to relativity. Any object viewed from a distance appears smaller than its size seen at a closer distance. Its actual size however is the same, independent of the distance from which it is viewed. Likewise, time can feel very long when one is bored but very short when one is entertained, when the actual time is the same independent of such feelings. Relativity is this fact that perceptions for a particular object or event can differ for different observers and can depend on one's vantage point.

It is true that different observers watching a given event will describe that event differently. In this way relativity can be of particular value. The different disciples' accounts of Jesus reflect features differently that present a more complete picture for those reading the gospels. In other cases, relativity may be a hindrance that must be adjusted for, such as when determining the actual true value of a scientific measurement. Relativity can cause a measurement to be made incorrectly. Even though the absolute time for an event itself does not respond to physical changes of matter and is independent of whether matter exists or not, a long-held notion called time dilation is widely taught as fact in many Physics texts and must be explained. Time dilation stemmed from thoughts regarding the use of light and physical objects to attempt to measure time. Some examples use a lateral moving "light box" containing a light source that is represented to measure time, and other instances use a linear moving rod or train car that must be traversed by light. In all cases, observers

moving with the device perceive a different distance of travel than that for observers who are stationary who notice the motion of the device. In reality, light must travel farther to reach a receding target or less to reach an approaching target, whether a box, train, or rod that moves during the photon travel time, all while the time required to travel that distance is a single correct value. The true time for any event is not affected by one's position to observe the event. Umpires not in a position to observe well a play in a sports event often make incorrect decisions. Likewise measurement of time using fixed-speed light that interacts with matter depends on the relative motion of that matter. If it is observed easily, the correct time may be determined. If not, and not properly corrected, a meaningless time will result.

All scientific instruments must be calibrated for variables that affect readings, or the readings will be incorrect, and this includes the measurement of time using light. A watch with a lead weight placed on its hands ticks more slowly and reports a wrong time for an event. And this does not change the actual time required for the event to occur! Time cannot be measured correctly with a moving light box, or train or rod UNLESS the direction and magnitude of motion of the box or rod or train in relation to the propagating photon are known, and used to determine actual displacement of the light in the direction at which its velocity is known. Any light clock velocity unequal to zero, or moisture in the air that slows light speed, causes light clocks to report a time that is not the correct time. Real time for an event is not subject to motion of a device attempting to measure it. Real time is determined by the event itself, independent of whether an observer runs away, runs toward, or remains still with respect to the event. Twins are the same age, whether one runs differently than the other or travels in spacecraft.

#### **2. Light is massless and propagates at fixed speed c**

A photon of light is electromagnetic energy that can only exist while traveling at a fixed fast speed in a given medium and that propagates in perpetuity if uninterrupted by physical matter. James Clerk Maxwell (1865) successfully derived mathematically the speed with which light must propagate in a given medium from the point in space at which it is produced, where c = **E/B** = 1/(ευ) 1/2. **E** and **B** are the amplitudes of the electrical and magnetic field orthogonal components of light, and ε and υ are the electrical permittivity and magnetic permeability of the particular translucent medium in which light propagates. In vacuum, the speed of light is approximately c = 2.99792 × 108 m/s. The Nobel prize-winning American physicist from Poland, Albert Michelson, directly measured the speed of light experimentally in the San Gabriel mountains of California in 1926. The round-trip for light to travel from Mount Wilson near Pasadena to Lookout mountain at Mt. Baldy (Mt. San Antonio) near Alta Loma is a ground distance of 44 miles. Knowing the rotation speed of a rotating slotted set of mirrors and thus the time between successive slots through which light passed, the speed of light was computed to 6 digit accuracy at 2.99792 × 108 m/s, confirming experimentally the correctness of the Maxwell theoretic derivation. We now know that because the earth orbits the sun and light travels in fixed straight paths at a speed that does not add to that of the earth, that the true time to travel this 44 mile round-trip is slightly different because the total travel distance is larger due to the earth's motion during the photon travel time.

### **3. Time for light to traverse a moving object is relative: one-dimensional case**

The distance between two trees along the ground is **D** km (**Figure 1**). Because the speed of light in its propagation direction is c from the spatial coordinate at which

**41**

longer trip to be completed.

*Clarifying Special Relativity*

**Figure 1.**

*DOI: http://dx.doi.org/10.5772/intechopen.86401*

it departs its source (that is, a stationary point in space) then the time required for a light photon to travel from the pine to the oak here would be t = **D**/c if the earth were stationary. However the earth orbits the sun at 30 km/s and, ignoring any contribution from any translational or rotational motion of the solar system, the more accurate distance the photon actually travels between the trees is directed distance **D** plus the distance the earth moves parallel to **D** (in the direction the photon travels) during the photon travel time between the trees, where t = (**D** + 30 t)/c so that t = **D**/(c − **v**) = **D**/(c − 30). Thus the true time for an event involving light interacting with material mass must be computed with proper vector algebra where the actual distance of travel must be known. Moreover, a stationary observer on earth easily computes an incorrect time as **D**/c because it is simple to assume the actual distance traveled is only **D** when it is not. The total distance is greater than **D** when the earth moves in the direction the photon travels and less than **D** when the earth moves opposite to the photon. Note that c in this case is the magnitude of the velocity of the photon in its travel direction and thus c and **D** are both vector quantities in this case. The original notion of time dilation derived from thoughts regarding a forward moving rod traversed by light. It was assumed that an observer on the rod would compute the time for light to traverse the rod forward and then backward again as 2 **L**/c where L is the length of the rod. A stationary observer watching the moving rod would notice the distance traveled by the rod while light was traversing it and would compute a different time than 2 **L**/c. On closer inspection it is clear that the actual time required for light to make such a round trip on a moving rod depends on the velocity of the rod (1, 3) and when computed properly by the moving observer matches the time computed by the stationary observer. If the rod were to move at very fast sub-light speeds, the light would not reach the end of the rod for a long time interval but using a clock instead of the length of the rod by the moving observer would report that prolonged time correctly. It was mistakenly assumed that the shorter time for light to return to the rod, where the relative velocity would be c + **v** when the rod approaches the light, would cancel the longer time the light requires to reach the end of the receding rod on the forward trip. This is not the case, where the total travel round-trip time is given by t = **D**/(c − **v**) + **D**/(c + **v**) = 2**D**/(c − **v**<sup>2</sup>

*The ground distance traveled by a photon from one tree to another tree differs from the actual distance the photon travels because the trees move along with the orbiting earth while the speed of light is nevertheless constant.*

Notice that if **v** = c, t would be infinite since the light would not catch the rod end. When **v** is zero then t = 2**D**/c, the time for a round-trip travel for light on a stationary rod. The faster the **v** of the rod, the longer is the time required to round-trip the rod. There is no dilation of absolute time, simply a longer time is required for a

/c).

**Figure 1.**

*Progress in Relativity*

moving with the device perceive a different distance of travel than that for observers who are stationary who notice the motion of the device. In reality, light must travel farther to reach a receding target or less to reach an approaching target, whether a box, train, or rod that moves during the photon travel time, all while the time required to travel that distance is a single correct value. The true time for any event is not affected by one's position to observe the event. Umpires not in a position to observe well a play in a sports event often make incorrect decisions. Likewise measurement of time using fixed-speed light that interacts with matter depends on the relative motion of that matter. If it is observed easily, the correct time may be determined. If not, and not properly corrected, a meaningless time will result. All scientific instruments must be calibrated for variables that affect readings, or the readings will be incorrect, and this includes the measurement of time using light. A watch with a lead weight placed on its hands ticks more slowly and reports a wrong time for an event. And this does not change the actual time required for the event to occur! Time cannot be measured correctly with a moving light box, or train or rod UNLESS the direction and magnitude of motion of the box or rod or train in relation to the propagating photon are known, and used to determine actual displacement of the light in the direction at which its velocity is known. Any light clock velocity unequal to zero, or moisture in the air that slows light speed, causes light clocks to report a time that is not the correct time. Real time for an event is not subject to motion of a device attempting to measure it. Real time is determined by the event itself, independent of whether an observer runs away, runs toward, or remains still with respect to the event. Twins are the same age, whether one runs differently than the other or travels in spacecraft.

**2. Light is massless and propagates at fixed speed c**

which it is produced, where c = **E/B** = 1/(ευ)

puted to 6 digit accuracy at 2.99792 × 108

**one-dimensional case**

A photon of light is electromagnetic energy that can only exist while traveling at a fixed fast speed in a given medium and that propagates in perpetuity if uninterrupted by physical matter. James Clerk Maxwell (1865) successfully derived mathematically the speed with which light must propagate in a given medium from the point in space at

trical and magnetic field orthogonal components of light, and ε and υ are the electrical permittivity and magnetic permeability of the particular translucent medium in which light propagates. In vacuum, the speed of light is approximately c = 2.99792 × 108

The Nobel prize-winning American physicist from Poland, Albert Michelson, directly measured the speed of light experimentally in the San Gabriel mountains of California in 1926. The round-trip for light to travel from Mount Wilson near Pasadena to Lookout mountain at Mt. Baldy (Mt. San Antonio) near Alta Loma is a ground distance of 44 miles. Knowing the rotation speed of a rotating slotted set of mirrors and thus the time between successive slots through which light passed, the speed of light was com-

ness of the Maxwell theoretic derivation. We now know that because the earth orbits the sun and light travels in fixed straight paths at a speed that does not add to that of the earth, that the true time to travel this 44 mile round-trip is slightly different because the total travel distance is larger due to the earth's motion during the photon travel time.

The distance between two trees along the ground is **D** km (**Figure 1**). Because the speed of light in its propagation direction is c from the spatial coordinate at which

**3. Time for light to traverse a moving object is relative:** 

1/2. **E** and **B** are the amplitudes of the elec-

m/s, confirming experimentally the correct-

m/s.

**40**

*The ground distance traveled by a photon from one tree to another tree differs from the actual distance the photon travels because the trees move along with the orbiting earth while the speed of light is nevertheless constant.*

it departs its source (that is, a stationary point in space) then the time required for a light photon to travel from the pine to the oak here would be t = **D**/c if the earth were stationary. However the earth orbits the sun at 30 km/s and, ignoring any contribution from any translational or rotational motion of the solar system, the more accurate distance the photon actually travels between the trees is directed distance **D** plus the distance the earth moves parallel to **D** (in the direction the photon travels) during the photon travel time between the trees, where t = (**D** + 30 t)/c so that t = **D**/(c − **v**) = **D**/(c − 30). Thus the true time for an event involving light interacting with material mass must be computed with proper vector algebra where the actual distance of travel must be known. Moreover, a stationary observer on earth easily computes an incorrect time as **D**/c because it is simple to assume the actual distance traveled is only **D** when it is not. The total distance is greater than **D** when the earth moves in the direction the photon travels and less than **D** when the earth moves opposite to the photon. Note that c in this case is the magnitude of the velocity of the photon in its travel direction and thus c and **D** are both vector quantities in this case.

The original notion of time dilation derived from thoughts regarding a forward moving rod traversed by light. It was assumed that an observer on the rod would compute the time for light to traverse the rod forward and then backward again as 2 **L**/c where L is the length of the rod. A stationary observer watching the moving rod would notice the distance traveled by the rod while light was traversing it and would compute a different time than 2 **L**/c. On closer inspection it is clear that the actual time required for light to make such a round trip on a moving rod depends on the velocity of the rod (1, 3) and when computed properly by the moving observer matches the time computed by the stationary observer. If the rod were to move at very fast sub-light speeds, the light would not reach the end of the rod for a long time interval but using a clock instead of the length of the rod by the moving observer would report that prolonged time correctly. It was mistakenly assumed that the shorter time for light to return to the rod, where the relative velocity would be c + **v** when the rod approaches the light, would cancel the longer time the light requires to reach the end of the receding rod on the forward trip. This is not the case, where the total travel round-trip time is given by t = **D**/(c − **v**) + **D**/(c + **v**) = 2**D**/(c − **v**<sup>2</sup> /c). Notice that if **v** = c, t would be infinite since the light would not catch the rod end. When **v** is zero then t = 2**D**/c, the time for a round-trip travel for light on a stationary rod. The faster the **v** of the rod, the longer is the time required to round-trip the rod. There is no dilation of absolute time, simply a longer time is required for a longer trip to be completed.

This system involves both classical and special relativity to understand. Classically distances traveled by any object moving at a particular speed toward a target that is also moving always depend on the relative motion of the target. The actual distance traveled may be greater or less than the original distance to the target at the time the light departs its source. The actual distance traveled by a photon to the target is relative to the distance moved by the target. One may perceive the photon only traveled the distance of separation between the source and target, when in actuality the photon travels a different path since the target moved during the time of travel for the light, while light speed is fixed.

Also in the light trees example here, since light speed is fixed at c with respect to a stationary coordinate in space, this special behavior of light requires one only use this speed or its proper component in relation to the travel directions of the light and the moving target. The speed of light is fixed in a given medium, unlike physical objects which pick up additional speed and energy 1/2 mv2 from moving sources. Both sound waves and light waves also travel at a fixed speed even from moving sources. The frequency and wavelength of the sound or light are changed, but not the speed which is the product of frequency *f* times wavelength λ and for light we write c = *f*λ. Although the frequency of light and its intrinsic energy E = h*f* where h is Planck's constant are increased by a source moving in its propagation direction, it is not possible to increase its speed which is fixed at c. A rifle bullet travels between the two trees on the moving earth at a combined speed of muzzle velocity plus earth orbit velocity, so the time to reach the target tree is simply **D** divided by the muzzle velocity because the extra distance moved by the trees during the bullet travel time is matched and overcome by the extra velocity the bullet has from the moving earth. This is not the case for light which must travel at fixed speed c independent of motion of its source or the target toward which it speeds. This is the key aspect of special relativity. Light, but not true for physical objects, emanating from moving sources requires different times to travel to a target in motion than when stationary.

Another special property of light is that it is massless and its propagation speed c is not exceeded by any object having mass. However before proceeding to the two dimensional light box case, it must be emphasized that light velocity is simple to exceed, because light is only velocity c specifically in its travel direction [1]. Velocity components for a light ray are less than c and may be easily exceeded by physical objects. Merely point a laser light North and you walk East and you will reach an Eastern target that the light does not, because you exceeded the Eastward component velocity of the light ray.

From the above relativity considerations, to compute time for an event that involves using light interacting with physical objects, it is necessary to match distance and velocity vectors, or the computed time will simply be incorrect. The original concept of time dilation unfortunately did not consider vector algebra when computing time for theoretic light timing devices in either the linear or lateral motion cases and these have now been corrected. The concept of dilation of time, presumed to occur when light is used as a time piece, has been disproven, theoretically, mathematically, and experimentally (1–3).

#### **3.1 Two-dimensional case: a light box**

A light photon in a *stationary* light box travels the height of the box **d** in time **d/c** (**Figure 2**).

However, in a *lateral moving* light box, a photon must have a horizontal component velocity equal to that of the box **v** in order to hit the moving box top spot. A stationary observer sees the true path **r** of the photon (**Figure 3**) and calculates the correct time **r**/c.

**43**

observer.

motion (or not) of an observer.

*Clarifying Special Relativity*

**Figure 2.**

**Figure 3.**

*imagined to be stationary.*

*DOI: http://dx.doi.org/10.5772/intechopen.86401*

The vector **r** does not represent a beam of light, but rather the path traced by a single photon. This is because the photon that arrives at the top of the box left the source when it was at its leftward position earlier as shown. The source at the time of arrival is vertically directly under the arriving photon in the box, and photons leaving the source at that time begin their angled path from this new source location and will arrive at the target after it shifts to another location. So photons all angle travel with this bearing and arrive at the target later at another shifted position. Several photons produced in succession cause the illusion that all traveled vertically to the target, when actually all angle travel distance **r** to arrive. An observer inside the box who only notices the vertical component of the photons could falsely compute time as if it were **d**/c. But light photons in the moving box did not follow the path along vector **d**. Each actually follows a vector parallel to **r** to reach the moving spot on the box top. **d**/c is false because it is a vector mismatch. Correct displacements for light must be determined not by appearance, but by truth, before time can be calculated correctly. Just like a virtual image is not a real image, the appearance that light followed **d** for the moving box is a mirage, not the real displacement path **r**. Notice that a stationary observer far to the right might also assume the photons only moved upward distance **d** and could compute time incorrectly, so the incorrect computation has nothing to do with

*The arrow represents the path of a photon emitted from its source to the top of the box of height d when the box is imagined to be moving rapidly laterally. The path distance to reach the to of the box is now length r.*

*The arrow represents the path a photon could take from its source to the top of a box with height d that is* 

It is improper to claim that time "slows down" for some event simply because an observer moves during that event. Light cannot sense that an observer is in motion, to adjust its time required to travel a particular distance. Stated simply, a longer distance requires a longer travel time for light at a fixed velocity than a shorter distance, regardless of the state of motion of any

To avoid a vector algebra blunder, it is always mathematically necessary to couple the correct light velocity component with the vector component actually traveled with that velocity. In this way, time calculated for any particular event is the same for any observer, regardless of their state of motion. Note that in time **d**/c, the photon above travels distance **d** (since velocity c times time t equals distance: **d** = c(**d**/c) = **d**). This means that the photon traveling along vector **r** travels

Experiments conducted at Palomar Community College with a laser light [1–3] demonstrate that light photons that propagate at speed c pick up lateral velocity when produced by a lateral moving source and thus have a component velocity

a distance **d** in time **d**/c but of course has not yet reached the box top at **r**.

#### **Figure 2.**

*Progress in Relativity*

when stationary.

This system involves both classical and special relativity to understand. Classically distances traveled by any object moving at a particular speed toward a target that is also moving always depend on the relative motion of the target. The actual distance traveled may be greater or less than the original distance to the target at the time the light departs its source. The actual distance traveled by a photon to the target is relative to the distance moved by the target. One may perceive the photon only traveled the distance of separation between the source and target, when in actuality the photon travels a different path since the target moved during

Also in the light trees example here, since light speed is fixed at c with respect to a stationary coordinate in space, this special behavior of light requires one only use this speed or its proper component in relation to the travel directions of the light and the moving target. The speed of light is fixed in a given medium, unlike

sources. Both sound waves and light waves also travel at a fixed speed even from moving sources. The frequency and wavelength of the sound or light are changed, but not the speed which is the product of frequency *f* times wavelength λ and for light we write c = *f*λ. Although the frequency of light and its intrinsic energy E = h*f* where h is Planck's constant are increased by a source moving in its propagation direction, it is not possible to increase its speed which is fixed at c. A rifle bullet travels between the two trees on the moving earth at a combined speed of muzzle velocity plus earth orbit velocity, so the time to reach the target tree is simply **D** divided by the muzzle velocity because the extra distance moved by the trees during the bullet travel time is matched and overcome by the extra velocity the bullet has from the moving earth. This is not the case for light which must travel at fixed speed c independent of motion of its source or the target toward which it speeds. This is the key aspect of special relativity. Light, but not true for physical objects, emanating from moving sources requires different times to travel to a target in motion than

Another special property of light is that it is massless and its propagation speed c is not exceeded by any object having mass. However before proceeding to the two dimensional light box case, it must be emphasized that light velocity is simple to exceed, because light is only velocity c specifically in its travel direction [1]. Velocity components for a light ray are less than c and may be easily exceeded by physical objects. Merely point a laser light North and you walk East and you will reach an Eastern target that the light does not, because you exceeded the Eastward component velocity of the light ray. From the above relativity considerations, to compute time for an event that involves using light interacting with physical objects, it is necessary to match distance and velocity vectors, or the computed time will simply be incorrect. The original concept of time dilation unfortunately did not consider vector algebra when computing time for theoretic light timing devices in either the linear or lateral motion cases and these have now been corrected. The concept of dilation of time, presumed to occur when light is used as a time piece, has been disproven, theoreti-

A light photon in a *stationary* light box travels the height of the box **d** in time

However, in a *lateral moving* light box, a photon must have a horizontal component velocity equal to that of the box **v** in order to hit the moving box top spot. A stationary observer sees the true path **r** of the photon (**Figure 3**) and calculates the

from moving

the time of travel for the light, while light speed is fixed.

cally, mathematically, and experimentally (1–3).

**3.1 Two-dimensional case: a light box**

physical objects which pick up additional speed and energy 1/2 mv2

**42**

**d/c** (**Figure 2**).

correct time **r**/c.

*The arrow represents the path a photon could take from its source to the top of a box with height d that is imagined to be stationary.*

#### **Figure 3.**

*The arrow represents the path of a photon emitted from its source to the top of the box of height d when the box is imagined to be moving rapidly laterally. The path distance to reach the to of the box is now length r.*

The vector **r** does not represent a beam of light, but rather the path traced by a single photon. This is because the photon that arrives at the top of the box left the source when it was at its leftward position earlier as shown. The source at the time of arrival is vertically directly under the arriving photon in the box, and photons leaving the source at that time begin their angled path from this new source location and will arrive at the target after it shifts to another location. So photons all angle travel with this bearing and arrive at the target later at another shifted position. Several photons produced in succession cause the illusion that all traveled vertically to the target, when actually all angle travel distance **r** to arrive. An observer inside the box who only notices the vertical component of the photons could falsely compute time as if it were **d**/c. But light photons in the moving box did not follow the path along vector **d**. Each actually follows a vector parallel to **r** to reach the moving spot on the box top. **d**/c is false because it is a vector mismatch. Correct displacements for light must be determined not by appearance, but by truth, before time can be calculated correctly. Just like a virtual image is not a real image, the appearance that light followed **d** for the moving box is a mirage, not the real displacement path **r**. Notice that a stationary observer far to the right might also assume the photons only moved upward distance **d** and could compute time incorrectly, so the incorrect computation has nothing to do with motion (or not) of an observer.

It is improper to claim that time "slows down" for some event simply because an observer moves during that event. Light cannot sense that an observer is in motion, to adjust its time required to travel a particular distance. Stated simply, a longer distance requires a longer travel time for light at a fixed velocity than a shorter distance, regardless of the state of motion of any observer.

To avoid a vector algebra blunder, it is always mathematically necessary to couple the correct light velocity component with the vector component actually traveled with that velocity. In this way, time calculated for any particular event is the same for any observer, regardless of their state of motion. Note that in time **d**/c, the photon above travels distance **d** (since velocity c times time t equals distance: **d** = c(**d**/c) = **d**). This means that the photon traveling along vector **r** travels a distance **d** in time **d**/c but of course has not yet reached the box top at **r**.

Experiments conducted at Palomar Community College with a laser light [1–3] demonstrate that light photons that propagate at speed c pick up lateral velocity when produced by a lateral moving source and thus have a component velocity

#### **Figure 4.**

*Diagram depicting the experiment conducted with a laser light continuously illuminating a target 30 m distant while on the rotating and orbiting earth. Light photons travel north to the target, while earth and target orbit 65,000 mph laterally around the Sun. This experiment proves that light photons angle-travel in a straight line and catch the target on earth which shifts laterally 1.3 mm during the time it takes for the photon to arrive. The photons do not simply travel 30 m north and miss the center of the target. Because the earth spins like a twirling figure skater also circling a rink, the 3 mm shift is east of its original position when the photon left the source at midnight but 3 mm west of its original position when a photon leaves at noon. The light continuously on for 24 h periods nevertheless always lands on the center of the target. The photon travel path is thus always larger than the 30 m distance along the ground to the target, because the earth never stops orbiting. Thus photons take longer to reach the target because the earth target is always shifting away from the light. This extension of travel time is not a "dilation" of absolute time due to the motion, but is simply due to the longer distance traveled compared to the time to travel 30 m if the earth were not moving. Anyone who computes time as 30/c rather than (30 + d)/c is sincere, but wrong. Time does not slow down or dilate when objects move. Motion has nothing to do with the fact that absolute time marches on. The special theory of relativity is here modified to indicate that time dilation does not exist, while light remains special in propagating at fixed forward speed independent of motion of the source.*

equal to that of the source (**Figure 4**). While a photon travels at speed c 30 m to a target, an observer on earth, orbiting with the source and target, would be incorrect to computer time as 30/c because the photon actually travels farther than the ground distance to the target. Since the earth orbits at 30 km/s, the target and source move laterally 3 mm West at noon (or 3 mm East at midnight) during the time required for a photon to propagate 30 m North. Thus the true travel time to arrive at the new target position is slightly longer than if the earth were stationary. A stationary observer in outer space could see such an angled travel path, while a moving observer on earth would not and the photon travel distance would then

**45**

velocity **v**x and **v**y is t = [2**v**y ± (4**v**<sup>y</sup>

*Clarifying Special Relativity*

textbooks as: t = **d**/(c2 − **v**<sup>2</sup>

registers a tick.

*DOI: http://dx.doi.org/10.5772/intechopen.86401*

rotating earth are always in motion.

need to be calculated. This distance must be used by either stationary or moving observers in order to compute a correct time interval when using light to measure time. Light boxes are inferior timepieces because physical objects on the orbiting

Light speed in fog is slower than in dry air. So the number of light box ticks (photon round-trips) in fog is always less than for dry air, for any specific event being timed by a 'light clock". Twins 1 year from now will not be different in age simply because one lives in fog and measures time with a foggy light box. This foggy clock reports a different time for an event compared to what a dry clock reports, not because the actual time is different, but because the clock is affected. Light "clocks"

As for any scientific instrument, all variables affecting its operation must be calibrated. Light boxes are affected by lateral velocity from the point at which the light leaves its source. The equation for this dependence is correctly derived in Physics

stationary point. At **v** = 0, the box is stationary, and the time reported by the clock is **d**/c for the event where light travels **d**. But the clock in motion reports a smaller number of ticks (or round-trips for a light photon inside the box) for that same given event being timed. The observer inside the box who uses t = **d**/c for the moving box has wrongly placed 0 for **v** into the formula. The formula must be followed to obtain a correct time, and **v** is not 0 for the moving box. **d**/c is a nonsensical computation for a moving box because more time is required for a tick at the longer distance required by light to travel.

Only when velocity of the box (and humidity of the air inside) is calibrated can a correct time interval be reported. Humidity is needed to know the value of c, and **v** is needed to know the displacement distance that photons travel before the clock

The typical Physics textbook conclusion, that since a moving light box ticks more slowly then absolute time itself "slows" [4] does not appreciate that the clock operation is altered by its own motion, similar to being slowed when operating in fog. The explanations of the Hafele-Keating experiment with atomic clocks in airplanes, environmental muon lifespans, the perihelion progression of the planet Mercury, or the actual meaning of the Michelson-Morley split light beam interferometer data have all been presented earlier without need to invent the notion of time dilation [2]. An additional proper way to calculate t for the moving observer inside a light box, moving lateral with velocity **v**x, is to match the vertical net displacement **d** with the velocity component for the photon in that vertical direction, which is **v**y = csinθ (where θ is the angle made by the vector **r** from the horizontal). Here sinθ is **d/r**. Time then becomes t = **d**/csinθ = **d**/(c**d/r**) = r/c, the same time as properly computed by the stationary observer. Although there are several other possible incorrect ways to compute time for this event, these are not further discussed here. Note that if the light box moves in the direction of the long axis of the box, the box top recedes from the propagating photon, and the equation for time is t = **d**/(c − **v**) (from Einstein, 1905) [5]. This is because the relative, net velocity of the photon toward the top of the box, c − **v**, depends directly on the receding velocity **v** of the box. The equation becomes very complicated if the box velocity is neither perpendicular nor parallel to the orientation of the box. If the box were to remain aligned with the Y axis, then the time for a photon to traverse the moving box with horizontal

1/2, where **v** is the lateral velocity of the box with respect to a

must be calibrated for humidity, or else the reported time is incorrect.

Time doesn't slow, it is simply that it takes longer for light to arrive.

2 + 4**d**<sup>2</sup>

 + c2 = **v**<sup>x</sup> 2 = **v**<sup>y</sup> 2

involves three dimensions, the equation becomes even more complex, which proves that a light box is an improper device for measuring the time for an event. (A light box is however a good motion detector since light arrives at a position other than a target spot when only slight motion of the source with respect to the detector occurs).

))1/2]/c. If the box velocity

)

#### *Clarifying Special Relativity DOI: http://dx.doi.org/10.5772/intechopen.86401*

*Progress in Relativity*

**44**

**Figure 4.**

equal to that of the source (**Figure 4**). While a photon travels at speed c 30 m to a target, an observer on earth, orbiting with the source and target, would be incorrect to computer time as 30/c because the photon actually travels farther than the ground distance to the target. Since the earth orbits at 30 km/s, the target and source move laterally 3 mm West at noon (or 3 mm East at midnight) during the time required for a photon to propagate 30 m North. Thus the true travel time to arrive at the new target position is slightly longer than if the earth were stationary. A stationary observer in outer space could see such an angled travel path, while a moving observer on earth would not and the photon travel distance would then

*Diagram depicting the experiment conducted with a laser light continuously illuminating a target 30 m distant while on the rotating and orbiting earth. Light photons travel north to the target, while earth and target orbit 65,000 mph laterally around the Sun. This experiment proves that light photons angle-travel in a straight line and catch the target on earth which shifts laterally 1.3 mm during the time it takes for the photon to arrive. The photons do not simply travel 30 m north and miss the center of the target. Because the earth spins like a twirling figure skater also circling a rink, the 3 mm shift is east of its original position when the photon left the source at midnight but 3 mm west of its original position when a photon leaves at noon. The light continuously on for 24 h periods nevertheless always lands on the center of the target. The photon travel path is thus always larger than the 30 m distance along the ground to the target, because the earth never stops orbiting. Thus photons take longer to reach the target because the earth target is always shifting away from the light. This extension of travel time is not a "dilation" of absolute time due to the motion, but is simply due to the longer distance traveled compared to the time to travel 30 m if the earth were not moving. Anyone who computes time as 30/c rather than (30 + d)/c is sincere, but wrong. Time does not slow down or dilate when objects move. Motion has nothing to do with the fact that absolute time marches on. The special theory of relativity is here modified to indicate that time dilation does not exist, while light remains special in propagating at fixed forward speed independent of motion of the source.*

need to be calculated. This distance must be used by either stationary or moving observers in order to compute a correct time interval when using light to measure time. Light boxes are inferior timepieces because physical objects on the orbiting rotating earth are always in motion.

Light speed in fog is slower than in dry air. So the number of light box ticks (photon round-trips) in fog is always less than for dry air, for any specific event being timed by a 'light clock". Twins 1 year from now will not be different in age simply because one lives in fog and measures time with a foggy light box. This foggy clock reports a different time for an event compared to what a dry clock reports, not because the actual time is different, but because the clock is affected. Light "clocks" must be calibrated for humidity, or else the reported time is incorrect.

As for any scientific instrument, all variables affecting its operation must be calibrated. Light boxes are affected by lateral velocity from the point at which the light leaves its source. The equation for this dependence is correctly derived in Physics textbooks as: t = **d**/(c2 − **v**<sup>2</sup> ) 1/2, where **v** is the lateral velocity of the box with respect to a stationary point. At **v** = 0, the box is stationary, and the time reported by the clock is **d**/c for the event where light travels **d**. But the clock in motion reports a smaller number of ticks (or round-trips for a light photon inside the box) for that same given event being timed. The observer inside the box who uses t = **d**/c for the moving box has wrongly placed 0 for **v** into the formula. The formula must be followed to obtain a correct time, and **v** is not 0 for the moving box. **d**/c is a nonsensical computation for a moving box because more time is required for a tick at the longer distance required by light to travel. Time doesn't slow, it is simply that it takes longer for light to arrive.

Only when velocity of the box (and humidity of the air inside) is calibrated can a correct time interval be reported. Humidity is needed to know the value of c, and **v** is needed to know the displacement distance that photons travel before the clock registers a tick.

The typical Physics textbook conclusion, that since a moving light box ticks more slowly then absolute time itself "slows" [4] does not appreciate that the clock operation is altered by its own motion, similar to being slowed when operating in fog. The explanations of the Hafele-Keating experiment with atomic clocks in airplanes, environmental muon lifespans, the perihelion progression of the planet Mercury, or the actual meaning of the Michelson-Morley split light beam interferometer data have all been presented earlier without need to invent the notion of time dilation [2].

An additional proper way to calculate t for the moving observer inside a light box, moving lateral with velocity **v**x, is to match the vertical net displacement **d** with the velocity component for the photon in that vertical direction, which is **v**y = csinθ (where θ is the angle made by the vector **r** from the horizontal). Here sinθ is **d/r**. Time then becomes t = **d**/csinθ = **d**/(c**d/r**) = r/c, the same time as properly computed by the stationary observer. Although there are several other possible incorrect ways to compute time for this event, these are not further discussed here.

Note that if the light box moves in the direction of the long axis of the box, the box top recedes from the propagating photon, and the equation for time is t = **d**/(c − **v**) (from Einstein, 1905) [5]. This is because the relative, net velocity of the photon toward the top of the box, c − **v**, depends directly on the receding velocity **v** of the box. The equation becomes very complicated if the box velocity is neither perpendicular nor parallel to the orientation of the box. If the box were to remain aligned with the Y axis, then the time for a photon to traverse the moving box with horizontal velocity **v**x and **v**y is t = [2**v**y ± (4**v**<sup>y</sup> 2 + 4**d**<sup>2</sup> + c2 = **v**<sup>x</sup> 2 = **v**<sup>y</sup> 2 ))1/2]/c. If the box velocity involves three dimensions, the equation becomes even more complex, which proves that a light box is an improper device for measuring the time for an event. (A light box is however a good motion detector since light arrives at a position other than a target spot when only slight motion of the source with respect to the detector occurs).
