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. 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 & 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 value of 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 change in the motion of the light source. In this instance, There is relative motion between these two frames (The stationary observer & 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 the change in the wavelength of the light wave; the change in the wavelength of the light wave results to the relative difference/change in the measurements of clock of the stationary observer & 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.
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.
INTRODUCTION: 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."
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"
total bs
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