PHYSICS OF OPTICS AND TIME
ABSTRACT: A brief proposition on the nature of light waves and how it affects the measurement of observers.
Imagine a stationary observer who is at a distance D, away from a stationary source of light that emits a light signal at a constant period t, and let's assume that both parties are provided with a clock. There is no relative motion between this two frames. If the source of light emits a light signal that travels towards the observer for a period of time t, both parties will agree that there is no change in the wavelength of the light wave emitted. More also, both parties will agree that their respective clocks records same time t, for the period of the light signal. In this instance, there is no relative motion between these two frames ( The stationary observer & the stationary source of light).
Now consider a similar instance where the source of light travels some meters during the same time t, as the period of the emitted light wave, the wavelength of the light wave recorded by a device attached to the source of the light will be different from the wavelength recorded by the stationary observer. Also, the clock attached to the moving source of light will disagree with the clock of the stationary observer over the period t, of motion of emitted light wave. This change in the wavelength of the light wave is as a result of the motion of the light source. In this instance, there is relative motion between these two frames (The stationary observer & the moving source of light).
The conclusion from the above instance is that:
1. There is "No change" in the measurement of the clocks of both parties when there is "No change" in the property of the light wave emitted.
2. There is "A change" in the measurement of the clocks of both parties when there is "A change" in the property of the light wave emitted.
To put this in orderly manner, "Change in the motion of the light source results to change in the wavelength of the emitted light waves; the change in the wavelength of the light waves results to the relative difference/change in the measurements of the clocks of the stationary observer & the moving source of light"
To put this in orderly manner, "Change in the motion of the light source results to change in the wavelength of the emitted light waves; the change in the wavelength of the light waves results to the relative difference/change in the measurements of the clocks of the stationary observer & the moving source of light"
It is clear that the motion of the light source creates a change in the physical property of the light wave. As I proceed in this article, I will show that the simple act of creating a change in the physical properties (wavelength) of the waves, automatically creates a difference in the measurements of observers of different frames. This change in the physical property of the light waves can make physical measurements of different frames to appear relative in nature depending on the magnitude of the disturbance produced in the waves of light.
In most experiments, the event, observer and the light signals are all bounded. The light signals act as a middle man between the event and the observer and therefore, any change in the physical structure of the light signals might have an unusual effect on the observation and measurements of the observer. In this proposition the light waves surrounding the event could be the same as the light signals.
Every light source which emits light waves, has a series of light waves spreading out from its vicinity and likewise a body in an illuminated region of space, has a series of light waves spreading out from its vicinity. Light waves act as a medium by which some information about an object, either at rest or in motion, propagate from one region of space to another. Observation of most events is possible because of the ability of light waves to transmit information about an event to an observer located at a distance in space.
According to Doppler's effect, during the motion of an object, the light waves reflected/emitted from the moving object either gets closer or further apart from each other and this results in changes, for example, the Blue or Red shift of a fast moving source of light. On the other hand, this change imposed on the physical properties of the surrounding light waves due to the motion of an object results in a phenomenon which I will summarize below.
"In a given system of an observable experiment, A change in the physical properties (E.g. Wavelength, Period etc) of the motion of the light waves (signals) emitted/reflected by an object due to motion, results in change in the Relative physical properties (E.g. Time, Distance etc) of the motion of the object as measured by observers of different frames."
Simply, change in the physical properties of the motion of the surrounding light waves, Results in the Relativistic Effects we observe in our measurements.
Imagine an isolated region of space with just one light source that emits uniform light waves strong enough to illuminate all regions of that space. let's have a stationary observer located somewhere on a plane surface in that region, and an object (car) of velocity V, located at a distance D, away from the stationary observer. Any observer located within this region of space who wishes to observe the motion of the car will depend on the light waves (either visible or non visible electromagnetic waves) emitted/reflected by the moving object for information about the motion of the object.
To the stationary observer who is at a distance of D, behind the car, let us analyse his observation and measurement of the time of motion of the car through a distance d. Let us take that the speed of light in this thought experiment is C.
Light waves propagates information about an event from one region of space to another and it takes some time for light to propagate information about an event. During the measurement of the time of motion of the car by the stationary observer, the surrounding light waves also takes some little time to propagate information about the motion of the car to the stationary observer. This propagation of information by light waves matters most at the point when the car is just about to start its motion and at the point when the car immediately comes to rest.
MATHEMATICAL DERIVATION;
Let us assume that the car has a clock attached to it which will record the time of its motion through the distance d and let us use the time, t, as the time measured by the clock attached to the car, for the motion of the car through the distance d.
Let us assume that the stationary observer is also provided with a clock that will enable him to time the motion of the car through the distance d, and let the time he measures for the motion of the car through the distance d, be T.
At the start of motion of the car, when the stationary observer starts his clock, the stationary observer DELAYS in starting his timing on the motion of the car by a time delay of amount equal to D/C, which is the time for light signal to travel from the car to the stationary observer and inform him of the departure of the car, which means that the stationary observer starts his timing at the time t - D/C. Also, at the end of motion of the car, through the distance of d, the stationary observer will require another light signal to travel from the final point of motion of the car to the point of the stationary observer to inform him about the coming to rest of the car. The time for this last light signal to get to the observer is d/C + D/C . This means that the stationary observer EXCEEDED in his measurement by the amount of time d/C + D/C . The total time resulting from the light propagation effect is D/C + d/C + D/C.
Therefore the total time T, of motion of the car as recorded by the clock of the stationary observer is T = t - D/C + d/C + D/C. The propagation time of information by light can be removed in the above equation of time as below, -D/C + (+D/C) = 0.
Simplifying the equation gives:
T = t + d/C
d/C = T - t ……………….......................................................... 1
The factor d/C is not a light propagation time but a change in the physical property (Period/time) of the surrounding light waves. and I will prove further the origin of the factor d/C.
The above equation simply says that: "Change in the physical property of the motion of the surrounding light waves equals (=) Change in the measurements of observers of different frames, that's the Relativistic Effects we observe in our physical measurements"
Since d = vt, where v is the velocity of the car.
T = t + vt/C
Therefore;
T = t (1+v/C)…………................................................................... 2
To prove further that the factor d/C is a change in the physical property of light waves, precisely, a change in the period of the light waves, let's consider the below analysis using the Doppler's Effect.
Now, imagine a car that emits light of wavelength ƛ , when it is at rest but when it is in motion, it emits light pulse of wavelength ʎ . Let's take that the car is to travel away at a speed of v on a straight line from a stationary observer located at a distance of D behind the car and this car emits a pulse of light at a period of t when in motion. If at the beginning of the motion when the car is just about to move, it emits a pulse of light and after a time, t, it emits another pulse of light and comes to rest immediately, then it will be clear that the car travels a distance, d, during the t period of emission of the pulse of light.
Mathematically, the period t, of emission of the light pulse is the same as the time (t) of motion of the car through the distance, d. The distance, d, travelled by the car during the period of emission of the light pulse is:
d = vt
Also, the change in the wavelength of the light waves brought about by the motion of the car is expressed as:
ƛ - ʎ = d = vt ......................................................................................... 3
From equation 3,
ƛ - ʎ = d = Vt
d = ƛ - ʎ
substituting d in equation 1 gives:
T - t = d/c
T - t = ƛ - ʎ /C
Therefore:
ƛ - ʎ /C = T - t = d/C .......................................................................4
The above equation shows that "Change in the period of the light waves (as measured by an observer riding along with the source of the light waves (car) and a stationary observer standing at the distance D) results in Change in the relative time of motion of the car as measured by an observer riding in the car and a stationary observer standing at the distance D."
The equation 4 agrees with the earlier conclusion that says: There is "A change" in the measurement of the clocks of both parties when there is "A change" in the property of the light wave emitted.
THE CORRESPONDING DISTANCE EQUATION;
The corresponding distance can be derived through a more detailed form but let me use this short cut. From equation 1
T = t + d/C
since t = d/v
then:
T = do /v
Therefore: do /v = d/v + d/C
do = d (1+v/C) ........................................………………5
T and do is the respective time and distance travelled by the car, as measured by the stationary observer.
t and d is the respective time and distance travelled by the car as measured by the car or a clock attached to the car.
d/C is the change in the physical property of the light wave, which is also a change in the period of the light waves that were emitted when the car is at rest and when it is in motion..
This effect has been misinterpreted by other writers who claim that light travels a longer distance in a moving frame and thereby causing time to run differently in different frames. But it is very clear from the above derivation of time and distance that light travels through the same distance in all frames and time also runs the same in all frames. But what happens is that, when a disturbance is created in the waves of light due to the motion of an object, this disturbance does not just die out of existence. It goes on to affect the observation and measurements of all observers who depend on the light waves for their observation and measurement. This change in the physical property of the light waves can make physical measurements of different frames to appear relative depending on the magnitude of the disturbance produced in the waves of light..
The laws of physics are very absolute in the sense that in reality, light travels the same distance relative to every frame BUT the laws of physics could be relative in the sense that in measurement, observers of different frames might measure different values for the distance travelled by the light waves as a result of the behaviour of light waves which I explained above.
Also, the measurements of some frames are better/more valid than the measurement of other frames, depending on the resultant change in the physical property of the light waves from both the system of the observer and the event being observed. It seems from the derived mathematical equations that the measurements recorded by a person attached to the frame of the event are always more accurate, and this must be because of the fact that the person attached to the frame of event does not depend on the surrounding light waves for its measurement. Of course, no one needs light signals to walk from point A to point B but someone surely needs light signals to know that an object has moved from point A to point B.
It does follow that (The motion of the Car results in changes in the physical properties of the waves (Doppler's Effect); The changes in the physical properties of the light waves results in changes/Relativistic Effects in the measurements of observers of different frames). In the earlier version of this proposition, this, I was referring to as "Nwobu's Effect" ( T - t = ƛ - ʎ /C = d/C ).
TWO-BODY MOTION
During the motion of an object through space, the surrounding light waves experience change in its physical property E.g. the light waves get closer/further apart as a result of the motion of the object. It is worth noting that this change in the physical property of the light waves can be Positive (+) or Negative (-) depending on the direction of the light waves with respect to the moving object that emitted the light waves. This change in the physical property of the light waves is proportional to the speed of motion of the object that causes the change in the, E.g., the wavelength of the light waves. It can also be proportional to the speed of motion of the observer.
The change in the physical property of the light waves that are emitted/reflected in the direction which is opposite to the direction of motion of the object is Positive (+) in magnitude.
The change in the physical property of the light waves that are emitted/reflected in the same direction as the direction of motion of the object is Negative (-) in magnitude.
A look at a more complex experiment whereby both the observer and the event are in motion on a straight line travelling eastward. Lets label the observer's car as A while the event is labelled as B. Let the observer's car A, be at a distance of D behind the event B, such that the distance of separation between observer A and event B is D. Lets also take that both the observer and the event are just cars.
During the motion of the event B, away from the observer A, the light waves that propagate information about the motion of the event B to the observer A are the series of light waves that are emitted from the rear part of the event B. This light waves travel in a direction which is opposite the direction of motion of the event B and the changes in the physical property of this light waves due to the motion of the event B, are positive (+) in value. It is also this same light waves that travel towards the observer A, and inform him about the motion of the event B, through space.
The motion of the observer A, towards the event B, also causes changes in the physical property of the light waves emitted/reflected by observer A. In this particular experiment, the light waves that has effect on the measurement of the observer A, are the light waves that are emitted from the observer A, which travels towards the event B. Since this light waves emitted by the observer A, travels in same direction as the motion of the observer A, the change in the physical property of the light waves resulting from the motion of the observer A, is Negative (+) in value.
In order to formulate the time of motion of event B as measured by the observer A; let us assume that the time of motion of the event B as recorded by a clock attached to the event B is t and its velocity is V. Also, let us assume that the time of motion of event B as measured by the observer A, is T. Let the velocity of observer A be U.
If the above described phenomenon and the below conclusion is correct:
"In any given system of an observable experiment, change in the physical information about the motion of light waves due to motion of an object, results in change in the relative physical measurement of the information about the motion of that object as measured by observers of different frames."
Then it simply means that the difference in the time (T) of motion of event B as measure by observer A and the time (t) of motion of the event B as recorded by a clock attached to the frame of event B is equal (=) to the sum total change in the physical property (Periods) of the light waves emitted by both the moving observer A and the event B.
that is:
T - t = +(y/C) + (-x/C) ......................................................... 6
where +y/C is the change in the period of the light waves emitted by the event B and it is positive in value.
Also +y/C is equal to tV/C
-x/C is the change in the period of the light waves emitted by the observer A and it is negative in value.
Also, -x/C is equal to -UT/C
Therefore:
T - t = tV/C + -UT/C
T + UT/C = t + tV/C
T (1 + U/C) = t (1 + V/C)
simplifying the equation gives
T = t ( C + V / C + U ).................................................................... 7
INDEPENDENCY OF VELOCITY OF ALL MATTERS
The velocity of motion of any object is independent of any frame whatsoever. If in a particular experiment, an object travels with a velocity of 10m/s as recorded by a speedometer attached to the object, then to every observers of its motion; it travels 10m/s despite the state of motion of the observer/frame. It doesn't matter what your perception tells you.
From this equation T = t (1+v/C)
It follows that d/t = v
and: D/T = v
then, D/T = d/t = v ……………………… A. independency of velocity of all matters.
It simply means that the velocity of motion of the car is independent of any frame observing its motion and likewise, the velocity of every matter is independent of any frame observing its motion.
Also from the equation of time T = t (1+v/C)
And from the equation of distance D = d (1+v/C)
It shows that there is no speed limit in nature. Provided that the energy needed to achieve whatsoever speed is available, an object can travel at any speed and I am very sure that there are matters that travel at much faster speed than light's speed.
CONSTANCY OF OBJECT’S TRUE MASS AND MATHEMATICAL DERIVATION;
The mass of an object is the same magnitude everywhere in the universe despite the gravitational difference between different locations of the universe. Let's consider an object that is set in motion and we invite about 3 observers of different frames due to their different velocities, to measure the mass of the object by using their respective clocks to measure the time of motion of the object, and afterwards, substitute their respective measured time in a suitable equation of physics and deduct the value of mass corresponding to their respective measured time. If at the end of the motion of the object, we check the magnitude of mass measured by each of the 3 different observers including the mass measured by a device attached to the object, we would find out that only the object, despite whatever value of its velocity of motion, will always record a magnitude of mass that is same as the mass of the object recorded by using a spring balance at anywhere in the universe while at rest. whereas any of the 3 different observers will always obtain a value of mass that will change as their velocities change .
This is very similar to this:
For example, a long straight stick dipped into water appears to bend when observed at some angles by an observer. we know that the stick is never bent at all and we know that the bending of the stick is the result of the refraction of light waves by the water body in which the stick is existing in. Also, imagine a fish in water, different observers can conclude differently about the length, color etc of the fish due to the action of refraction of light. yet, whatever conclusion arrived by the observers about the length of the fish, does not in any way affect the real length of the fish in the water. this variation in length of the fish as seen by different observers is actually as a result of refraction of light waves in water. The fish never experienced any shortage or elongation of its length at any point in time. It might be right to say that changes in the length, color etc of the fish as observed by an observer at different angles, did not actually take place in real life but it only existed in the measurements of the observers.
Likewise, if 3 different observers measure 3 different values for the mass of an object, the object did not at any time during its motion, assume simultaneously the 3 different values of masses measured by the 3 different observer. The object assumed only one magnitude of mass throughout its motion. It is worth noting that “The relative values have no physical existence but it exists only in measured magnitude” and that is why different observers of the motion of a particular object can measure different values for the motion of the object .
The relative masses measured by different frames are also related to one another mathematically. The mass of the car as measured by a device attached to the car and the mass measured by the stationary observer is related as below.
MASS EQUATION
Let the capital alphabets (P, M, E) represent the value of mass, momentum and energy measured by any other frame measuring and observing the motion of the car while small letters represent the values of mass, energy and momentum measured by a clock or a measuring device attached to the car (m, p, e).
Since the momentum of a body is related to the mass by velocity, then p = mv
v = p/m, but v is also equal to T/D = d/t = v according to the equation for the independency of
velocity.
Then p/m = D/T = d/t = v.
Therefore P/M = p/m = v………………..C
Therefore the respective mass measured by the car , which is also the value of mass , m, of the car everywhere in the universe, when it is measured with a spring balance and the mass M, measured by the stationary observer E, is related by the below equation.
M = m (1 + v/C) ………………………………….8
The mass that we measure which increases with increase in velocity is the mass M. The value of the mass, m, is absolute and does not change relative to any frame or location in the universe. The true mass, m, of a body does not increase with increase in speed of motion or change in state of motion. What increases with increase in speed of motion, or change in frame of reference is the mass, M, because it can be topped up or down as a result of changes in the physical property of the surrounding light waves.
MOMENTUM EQUATION
Since the momentum of a body is related to the mass by velocity, then p = mv
Therefore v = p/m. but v is also equal to T/D = d/t = v according to the equation for the independence of velocity. Then p/m = D/T = d/t = v.
P/M = p/m = v………………..D
Therefore the respect momentum measured by the car and the stationary observer E, is related by the below equation.
P = p + pv/C where the factor pv/C is the change in the physical property of the light waves.
Simplifying the equation gives;
P = p (1 + v/C) …………………………….9
ENERGY EQUATION
The energy of a body is related to the momentum of the body by the below equation,
Since energy is equal to momentum times velocity, then energy (e) = pv.
Then : P/M = p/m = e/p = v………………………..E
And: E = Pv and e = pv.
Therefore E = e (1 + v/C) …………………………………10
This states that as the velocity of a body increases, the energy of the body increases in a correspondent quantity and not the mass because the true mass of a body is constant despite the state of motion.
WAVE EQUATION FOR ATOMIC PARTICLE
From one of the predictions above, I concluded that "Only a body/frame performing motion has the privilege of measuring 100% accurate its motional properties e.g. Time, wavelength, distance etc.
WAVELENGTH EQUATION
Let us consider the motion of an Electron through a distance of d, away from a stationary observer. Given that a stationary observer is given a clock and also, a clock is attached to the electron, with aim to measure the period of motion of the electron (wave). The period as measured by the stationary observer is related to period as measured by the clock attached to the electron as below:
Let ƛ, T = stationary observer's measured data
Let λ, t = Electron’s data (absolute motional factors)
From the wave equation λ = h/mv, we can deduce the relationship between the respective wavelengths measured by both the stationary observer and a measuring device attached to the moving electron.
Since from the equation 8 of mass, M = m (1 +v/C) we know that mass measured by different frames vary in magnitude and as a result, the equation of wave λ = h/ mv, should refer to different quantities of masses as in the below.
ƛ = h/ Mv ……………………..F
λ = h/ mv……………………….G
Therefore ƛ / λ= m/ M …………..H
The Plank’s constant, h, and the velocity of the electron which does not change irrespective of state of motion or frame, cancels out of the equation.
But we know from equation 8 that M/ m = (1 +v/C)
Therefore, since ƛ / λ= m/ M and M/ m = (1 +v/C),
Then ƛ / λ = (1 +v/C)
ƛ = λ (1 +v/C) .............................................................…………….. 11
The wavelength ƛ is same as what Doppler’s theory refer to as wavelength of a wave at a rest frame while the wavelength λ is same as the wavelength Doppler’s effect refers to as wavelength while in a moving frame.
The above wavelength formula is responsible for red shift and blue shift we observe in a light wave in motion. the direction of the wave with respect to the observer, will determine whether the wavelength formula will have a positive (+) or negative (-) sign for equation 11. just as it will determine the color of a light wave an observer will observe.
FREQUENCY OF A WAVE
The frequency corresponding to the above wavelength of the electron (wave) can be formulated as below.
Since the frequency of the wave is related to the wavelength by the equation
f = v/λ. let the frequency corresponding to the wavelength λ be f and let the frequency corresponding to the wavelength ƛ be F.
Then v = F ƛ and v = f λ
Therefore, f λ = F ƛ that is to say ƛ / λ = f/F
Since ƛ / λ = (1 +v/C) = f/F
Then f/F = (1 +v/C )
f = F (1 +v/C) .................................…………………….12
RELATIVE AND ABSOLUTE NATURE OF PHYSICAL MEASUREMENTS
In one of the predictions I noted above, I concluded that “some frames are better than others in measurement of physical quantities” and I also concluded that “ only the body performing motion has the privilege to measure 100% accurate its motion properties like, time, distance, energy etc. some other observers of different frames may also obtain same value of data, just like a measuring device attached to the event but it depends on the resultant changes in the physical properties of the light waves from both systems.
I also concluded that “Relative and Absoluteness co-exists because, during measurement, we might obtain values that show the relative nature of physical quantity but in reality, physical quantities are very absolute.
Physical quantities are only relative in measured values (i.e. in magnitude) but absolute in reality. “an observer may measure the time of travel of a car whose clock attached to it records 20 mins, to travels 25 mins but that applies only in magnitude measured by his device. It does not apply to the real magnitude of time of motion of the event. The value of physical quantities any observer measures is always “the Real value + or - Change in the physical property of the surrounding light waves”. The relative values have no physical existence but it exists only in magnitude and that is why different observers of a particular event can measure different values for the motion of the event. Each observers measurement depend on the resultant change in the physical property of the light waves emitted by both the observer and the event.
The relative nature of physical quantities is correct in the senses that if we send forth many observers to make record of time of motion of an even with their clocks, they will all come back with values showing a relative nature of physical quantities.
The relative nature of physical quantities is correct in the sense that it is an inherent property of the natural world because we cannot deny our daily dependency on light for measurement and light wave is also part of the natural world.
The relative nature of physical quantities is WRONG in the sense that it exists only in measured numerical magnitude that has NO real existence/correspondence.
Inasmuch as our physical measurements are relative in nature, absolute value do exist because whatever relative value that is known to us, has its root from an absolute value unknown to us.
Inasmuch as all motions may seem relative, as always confirmed by our physical measurements, absolute motion does exist and it can be calculated; for behind the relatives dwell the absoluteness.
Conclusions From The Above Equations
1. The velocity of any matter travelling through space is independent of any frame observing and measuring its motion.
2. Some matters can travel faster than the speed of light.
3. Some frames are better than others in the measurement of physical quantities.
4. Time runs the same in all frames even though our measuring devices may record otherwise.
5. Relative and absoluteness co-exist.
6. Between two or more inertial reference frames, an event which is present tense to one frame may not be present tense to other frames but may be past or future tense to other frames
7. Optical observation of our past time/world and its mathematical estimation is perfectly possible.
8. The future is not optically visible but is mathematically solvable.
"To fall is human; to rise is intelligence"
