the universal observation hypothesis

William Diffin

The Universal Observation Hypothesis

'An Object observed moving away from the Observer at a fixed velocity approaching or exceeding the speed of light, does not appear the same as an identical Object as seen by an Observer moving away from it at an identical fixed velocity.'

This hypothesis seems somewhat bizarre when one considers that, to either observer, it would seem irrelevant whether the object is moving away from the observer or the observer is moving away from the object; in both cases the distance between observer and object increases at the same rate and the visual effect should be the same. However, due to the nature of waves, and the wave nature of light, this may not prove to be the case at velocities approaching or exceeding the speed of light, as may be illustrated by the following experiments:

Consider two identical spaceships floating together in space, both with luminous clocks mounted on top of them, each occupied by a scientist, and both equipped with powerful telescopes with which the two scientists may observe each other's spaceships, at least well enough to be able to continuously read the time on each other's spaceship clocks, over distances of up to five light-seconds (about four times the distance from the Earth to the Moon). One spaceship plays the part of Observer, and the other spaceship plays the part of Object, as set out in the Universal Observation Hypothesis above. The spaceships float motionless together for five seconds as a countdown to the experiment. Then the Object spaceship moves away from the Observer spaceship at half of the speed of light for five seconds, and stops. What does the observer in the Observer spaceship see?

The only best way to answer this question is to actually carry out the experiment. However, at the time of writing, the fastest spaceships are only capable of achieving something like one four-thousandth of the speed of light, and only then by using the Sun's gravity. Although any optical effects visible at half of light-speed may be visible to a much lesser but still measurable extent at one four-thousandth of light-speed, in later experiments the two spaceships will need to be able to travel at or faster than light-speed. In any case spaceships are frightfully expensive, and I am relatively very poor. Therefore this experiment will have to be considerably scaled down before it may be executed, by assuming a more manageable value for the speed of light, and using a little imagination. The value of the speed of light, like the value of the speed of a spaceship, or of the speed of sound, or of the wind speed generated by the beating of a Chinese butterfly's wings, is just a number, and it is no more significant or meaningful than any other number just because it happens to be the value of the speed of our primary means of distance perception. And just as the sizes of the orbits of the planets may be scaled down for the purpose of illustrating their relative movements on a blackboard, just so the speed of light may be scaled down in order to work with it theoretically in a classroom or laboratory. For example:

Sol •~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~· Terra├────────93,000,000 miles───────┤

The above diagram roughly represents the relative size of the Sun and the distance of the Earth from the Sun. In reality the Sun is about 875,000 miles in diameter, the Earth is about 8,000 miles in diameter, and the distance between them is about 93,000,000 miles. The tilde signs (~) represent light waves of a particular wavelength, frozen in time as they

travel to Earth in a 93,000,000 miles-long stream. Let us say that the light is a blue component of sunlight, with a wavelength of 480 nanometres, or 0.00000048 metres. There are thirty-one tilde signs covering 93,000,000 miles, so each tilde covers 93,000,000 ÷ 31 = 3,000,000 miles of space, or 4,800,000 kilometres. 4,800,000 kilometres will contain 4,800,000 ÷ 0.00000048 = 10,000,000,000,000 individual peak and trough light waves, that's ten billion in British English, or ten trillion in American English or 1013 in scientific notation. So each tilde represents a stream of 1013

individual vibrations in the electromagnetic field between the Sun and the Earth, caused by Solar activity. Having scaled down these light waves, and the distance they travel from Sun to Earth, it is a simple matter to scale down their speed, which in reality is of course the speed of light, roughly 186,000 miles per second. In reality a single light wave will wiggle its way down the stream from Sun to Earth in 93,000,000 ÷ 186,000 = 500 seconds, or about 8½ minutes. On our scale diagram, the same journey is only 31 tilde signs across, or about 8½ centimetres. Hence the speed of light on this scale is about 1 cm per minute. That is going to be too slow to experiment with, but I can always choose another scale to experiment with that gives a more manageable value for the speed of light, and which makes it possible to experiment with speeds faster than the speed of light. So much for Relativity.

Let us then dispense with using spaceships for the purpose of this experiment, at least for the time being, and assume a speed of light of, say, twelve inches per second. This gives a scale of twelve inches to the light-second, roughly 1:980,000,000. The two spaceships may then be represented by two scientists each with stopwatches in, say, a church hall, with one scientist sat in a normal motionless chair such as are found in church halls, representing the Observer spaceship, and the other scientist sat in an electric wheelchair representing the Object spaceship, that may be set to move at either 6"/s, 12"/s, or 24"/s, representing half the speed of light, the speed of light, or twice the speed of light respectively, as representative speeds approaching or exceeding the speed of light as per the Universal Observation Hypothesis. There are a number of tables set together lengthways across the hall, with a ten-foot-long straight length of model railway track set across them, and the immobile chair with the Observer scientist sat in it is set at one end of the track. The model railway track will represent the vector of the Object spaceship moving away from the Observer spaceship in one direction, and also in the opposite direction it will represent the trajectory of the light emitted by the Object spaceship in the direction of the Observer spaceship. The scientist in the electric wheelchair carries a box full of numbered clockwork trains which all run at the identical speed of 12"/s, the representative speed of light. These trains will represent the individual light wave forms that are emitted by the Object spaceship clock on every second after it starts moving away from the Observer spaceship. In reality there would be at least another 450 million other light wave forms emitted by the Object spaceship over the course of each second, in between the wave forms represented by each train, but it is neither practical nor necessary to represent these too. From overhead then, the experiment set up appears thus:

┌────────────────────┐ ?│════════════════════│

└────────────────────┘ *

(? is the Observer, * is the Object, ═ is the train track)

With the experiment set up, variables may now be defined.

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Let t be the time elapsed since the Object began moving, measured in seconds, from t = -5 at the start of the countdown, through t = 0 when the Object begins moving, then to t = 5 when it stops and the experiment ends.

Let c be the speed of light (roughly 186,000 miles/s, but assumed to be 12"/s for this experiment).

Let v be the velocity with which the Object moves away from the Observer, measured in multiples of the speed of light (c).

Let tO be the time that appears to the Observer spaceship to have elapsed at the Object spaceship, since the Object spaceship began moving, measured in seconds (in the original experiment this value would be read through the Observer spaceship's telescope from the luminous clock on the Object spaceship).

Let λ be the wavelength of the light emitted by the Object spaceship clock.

Let λO be the apparent wavelength of the light emitted by the Object spaceship clock as seen from the Observer spaceship.

Also, in the following explanation, ? represents the Observer, who sits in a chair at one end of the model railway track and does not move, whilst * represents the Object, who sits in an electric wheelchair and moves away from the Observer in it.

Experiment #1: Object moving away from Observer at a velocity of c /2 (6"/s)

At the start of the experiment, from t = -5 to t = 0, both Object and Observer are at the same location, counting down to 'launch'. For the purpose of the experiment, twelve inches represent a distance of one light-second (about two-thirds the distance of the Moon from the Earth) and so the speed of light is assumed to be 12"/s. Since the Object spaceship (*) is to move away from the Observer spaceship (?) at half of the speed of light in this experiment, the electric wheelchair representing * is set to travel at 6"/s, half of the representative speed of light of 12"/s. The scientists synchronize their stopwatches and count down from t = -5 to t = 0.

After t = 0 then, * moves away from ? at 6"/s in his electric wheelchair, and one second later at t = 1, he drops the first clockwork train on the track at the point 6" along the track which he has just reached, which then trundles merrily along the track towards ? at a constant speed of 12"/s. This little train, Train #1, represents the light wave that would have left the Object spaceship (*) after one second of travel, when the Object spaceship's clock would have first read t = 1, and the train's speed of 12"/s represents the speed of light.

Half a second later after t = 1½, Train #1, moving as it is at 12"/s in the opposite direction to *, covers the 6" that * had just travelled away from ? before dropping Train #1 on the track, in half the time that * took to cover the same distance in the opposite direction. Train #1 then reaches the end of the track, and tumbles off it into the lap of ?. Remember that Train #1 represents the light wave that was emitted by the Object spaceship (*) at t = 1, at the moment when the clock on the Object spaceship (*) would have changed to read t = 1. What with this train having reached the Observer spaceship (?) at t = 1½, it is apparent to ? that had the experiment been carried out with spaceships, the time on the Object spaceship (*) as observed from the Observer spaceship (?) through its on-

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board telescope, would have appeared to be tO = 1, when t = 1½. Of course, also during this half-second, * continues to move away from ? at the constant speed of 12"/s, and at t = 1½ is then 9" away from ?.

At t = 2, having travelled at 6"/s for 2s, * is now 12" away from ?, representing a distance of one light-second. At this point * drops Train #2 onto the track, which also trundles merrily away towards ? at 12"/s, representing the light wave that would have left the Object spaceship (*) after two seconds of travel, with the Object spaceship's clock reading t = 2.

At t = 3, Train #2 has been travelling for one second at 12"/s, and has just completed the 12" journey from the point on the track where it was dropped, to the end of the track at ?. Train #2, released when t = 2, then falls into the lap of ?, signalling that whilst t = 3, tO = 2. At this point * has travelled another 6" since dropping Train #2 and is 18" away from ?. Also at this point * drops Train #3 onto the track, which begins its run towards ? at 12"/s.

At t = 4, Train #3 has travelled 12" towards ? from the point where it was dropped 18" distant from ?, and is now only 6" from ?. Meanwhile * has travelled another 6" in the opposite direction and is 24" from ? when Train #4 is dropped onto the track.

At t = 4½, Train #3 falls off the end of the track and ? notes that whilst t = 4½, tO = 3. * is now 27" from ?, and Train #4 dropped onto the track half a second ago is running towards ? at 12"/s at a distance of 18", having just travelled 6" towards ? in the last half-second.

At t = 5, Train #4 has travelled another 6" towards ? and is now 12" from ?. Since dropping Train #4, * has travelled another 6" away from ? and is now 30" distant when Train #5 is dropped. At this point * stops still.

This experiment may be readily illustrated by means of the following simple diagram. In this diagram, ? represents the Observer, * represents the Object, and numbers 1 through 5 represent trains numbers 1-5 respectively.

Key to Diagrams:

distance to objective in light-seconds (or feet)

1 2 3 4 5 6 7 8 9 10?╞═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ * <— model railway track —>

? = Observer * = Object 1 2 3 4 5 = Trains 1-5

Diagram #1: Object moving away from Observer at a velocity of c /2 (6"/s)

At t = -5 to t = 0, tO = t:

?╞═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 1:

?╞═1═╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

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At t = 1½, tO = 1:

?1═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 2:

?╞═══2═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 3, tO = 2:

?2═══╪═3═╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 4:

?╞═3═╪═══4═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 4½, tO = 3:

?3═══╪═4═╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 5:

?╞═══4═══╪═5═╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

As can be seen from the diagram, whilst time naturally progresses at the same rate at both ? and *, to the Observer at ? the seconds tick by at * only once every one-and-a-half seconds, so that the time at * as seen from ? always reads only two-thirds of the actual time elapsed, whilst * is moving away from ? at half of the speed of light. Thus for an Object moving at velocity v = c/2 away from an Observer, where c is the speed of light, the apparent elapsed time tO at the Object as observed by the Observer may be described as follows:

When v = c/2, tO = 2t/3 [Equation #1]

(where v is velocity, c is the speed of light, tO is the apparent elapsed time of motion, and t is the actual elapsed time of motion)

Another thing to consider before moving on to the next experiment, is that the increased separation in space of the ends of each light wave forms emitted by * every second in the direction of ?, brought about by the motion of * away from ?, represents a decrease in the frequency of every wave form emitted by * and observed by ?. In other words, instead of receiving a train every second, ? receives a train only every one-and-a-half seconds. This decrease in frequency is perceived by ? as an apparent increase in wavelength i.e. the 450 million or so light wave forms emitted by * every second and covering every light-second between * and ?, are stretched by the motion of * over one-and-a-half light-seconds thus:

Over one second with * and ? at rest separated by one light-second:

◄─motion of light ?~ ~ ~ ~ ~ ~ ~ ~ ~ ~* ├──1 light-second─┤

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And over one second with * moving away from ? at c/2 from one light-second:

◄─motion of light ?~ ~ ~ ~ ~ ~ ~ ~ ~ ~*─►motion of *

├─────1½ light-seconds─────┤

The tildes (~) illustrate that the rate at which the light wave forms are emitted by *, like their velocity, c, and like the absolute passage of time, t, is always constant, no matter what velocity or direction * is travelling in relative to ?, at least for as long as the material nature of * remains constant and the batteries on *'s luminous clock do not run out. This means that the frequency with which the light wave forms are detected at ? is decreased when * moves away from ?, representing an apparent increase in their wavelength.

Thus it can be seen that for an Object moving at velocity v = c/2 away from an Observer, where c is the speed of light, the apparent wavelength λO of the light from the Object as seen by an Observer is one-and-a-half times its true wavelength λ. Hence:

When v = c/2, λO = 3λ/2 [Equation #2]

(where v is velocity, c is the speed of light, λO is the apparent wavelength observed at velocity v, and λ is the actual wavelength observed at rest)

This effect is best known as the Doppler effect, and is most famously illustrated by the drop in pitch of the siren of an ambulance that is moving away at speed, caused by the decreased frequency of the sound waves produced by the siren reaching the ear, owing to the ambulance's motion into the distance. The Doppler effect is also observable in astronomy, where stars and galaxies moving away from the Earth all appear redder than would be expected, on account of the decreased frequency of the light waves they emit reaching the Earth, on account of their motion away from Earth. The receding motion of objects apparently stretches the wavelengths of the light they emit and makes the wavelengths appear longer, which the eye sees as being redder. In fact this 'red shift' is used to measure the distance of galaxies, which appears to be proportional to their speed of recession.

Experiment #2: Object moving away from Observer at a velocity of c (12"/s)

This experiment is identical to the previous experiment, except that the velocity v of the Object spaceship is increased to 12"/s, representing c, the speed of light. Consider that the two spaceships in Experiment #1 have met up again. Again, the spaceships float motionless together for five seconds as a countdown to the experiment. Then the Object spaceship moves away from the Observer spaceship, this time at the speed of light for five seconds, and stops. Now what does the observer in the Observer spaceship see? In order to illustrate this, the scientists in the church hall replace the trains in the box carried by the scientist in the electric wheelchair, reoccupy their starting positions, and set the wheelchair to travel at 12"/s instead of 6"/s. They synchronize their stopwatches and count down from t = -5 to t = 0.

At t = 0, the electric wheelchair begins to whine and the scientist sat in it, looking a little silly with a shabby cardboard box full of toy trains on his lap, automatically begins to roll away from his colleague. In other words, the Object (*) begins to move away from the Observer (?) at the speed of 12"/s, representing the speed of light.

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After one second, at t = 1, * is 12" (representing a distance of one light-second) from ? and drops Train #1 on the track, which begins to run away from * towards ? at 12"/s (representing the speed of light).

At t = 2, * is 24" from ? and drops Train #2 onto the track. Meanwhile, in the previous second, Train #1 travelling at 12"/s has completed the journey of 12" from the point it was dropped by * to ?, and reached the end of the line. Train #1 tumbles off the end of the track into the lap of ?, who notes that whilst t = 2, according to Train #1 tO = 1.

At t = 3, * has moved another 12" from ? and is now 36" distant, and drops Train #3 onto the track. Meanwhile Train #2 has moved 12" in the opposite direction, and is now only 12" from ?.

At t = 4, Train #2 completes the remaining journey of 12" and drops off the end of the track at ?, and ? sees that whilst t = 4, tO = 2. Train #3 is 24" away from ?, whilst * is now 48" from ?, and drops Train #4 on the track there.

At t = 5, Train #3 still has 12" to go before reaching ?, whilst Train #4 has 36" to go. * has reached 60" distant and drops Train #5. Both scientists have seen enough now.

Again, the experiment is illustrated by means of a diagram:

Diagram #2: Object moving away from Observer at a velocity of c (12"/s)

At t = -5 to t = 0, tO = t:

?╞═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 1:

?╞═══1═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 2, tO = 1:

?1═══╪═══2═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 3:

?╞═══2═══╪═══3═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 4, tO = 2:

?2═══╪═══3═══╪═══4═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 5:

?╞═══3═══╪═══4═══╪═══5═══╪═══╪═══╪═══╪═══╡ *

Again, as can be seen from the diagram, whilst * is moving away at the speed of light, to the Observer at ?, the seconds tick by at * only once every two seconds, so that the time at * as seen from ? always reads half

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of the actual time elapsed. Thus for an Object moving at velocity v = c away from an Observer, where c is the speed of light, the apparent elapsed time tO at the Object as observed by the Observer may be described as follows:

When v = c, tO = t/2 [Equation #3]


Similarly, due to the Doppler effect, the frequency of the trains arriving at ? has also halved from one every second, to one every two seconds, doubling the apparent wavelength of the light represented by the trains. Thus it can be seen that for an Object moving at velocity v = c away from an Observer, where c is the speed of light, the apparent wavelength λO of the light from the Object as seen by an Observer is twice its true wavelength λ. Hence:

When v = c, λO = 2λ [Equation #4]


Experiment #3: Object moving away from Observer at a velocity of 2 c (24"/s)

And so to the final experiment in this series studying objects moving away from observers. This time, the electric wheelchair is set to travel at the dizzy speed of 24"/s, representing twice the speed of light. The question now is what would an observer see when watching a spaceship moving away from him at twice the speed of light? Einstein himself never imagined anything so fantastic. Again, there is a five-second countdown after the scientists synchronize stopwatches and before the experiment begins. And then:

At t = 0, the Object (*) begins to move away at 24"/s, equivalent on the scale of the experiment to a velocity of twice the speed of light.

At t = 1, * is 24" away from ?, representing a distance of two light-seconds, and drops Train #1 onto the track, which moves towards ? at 12"/s, equivalent on this scale to the speed of light.

At t = 2, * is 48" away from ?, and drops Train #2. Train #1 is 12" from ? at this time.

At t = 3, * is 72" from ?, and drops Train #3. Train #1 reaches ? at this time, and ? notes that whilst t = 3, tO = 1. Meanwhile Train #2 has travelled 12" in the direction of ? and is now 36" away from ?.

At t = 4, * is 96" from ?, and drops Train #4. Train #2 is now at 24" from ?, and Train #3 is at 60" distant from ?.

At t = 5, * is 120" from ? at the other end of the track, and drops Train #5 before stopping. Train #2 is now 12" from ? and would reach ? in another second if the experiment continued, so that when t = 6, tO = 2. The other trains are spaced 36" apart further away from ?, with Train #3 at 48" from ?, Train #4 at 84" from ?, and Train #5 at 120" from ?.

The diagram illustrating this experiment now follows:

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Diagram #3: Object moving away from Observer at a velocity of 2 c (24"/s)

At t = -5 to t = 0, tO = t:

?╞═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 1:

?╞═══╪═══1═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 2:

?╞═══1═══╪═══╪═══2═══╪═══╪═══╪═══╪═══╪═══╡ *

At t = 3, tO = 1:

?1═══╪═══╪═══2═══╪═══╪═══3═══╪═══╪═══╪═══╡ *

At t = 4:

?╞═══╪═══2═══╪═══╪═══3═══╪═══╪═══4═══╪═══╡ *

At t = 5:

?╞═══2═══╪═══╪═══3═══╪═══╪═══4═══╪═══╪═══5 *

As can be seen from the diagrams, whilst * is moving away at twice the speed of light, to the Observer at ?, the seconds tick by at * only once every three seconds, so that the time at * as seen from ? always reads one third of the actual time elapsed since * began moving away at twice the speed of light, or 2c. Thus for an Object moving at velocity v = 2c away from an Observer, where c is the speed of light, the apparent elapsed time tO at the Object as observed by the Observer may be described as follows:

When v = 2c, tO = t/3 [Equation #5]


Similarly, due to the Doppler effect, the frequency of the trains arriving at ? has also decreased from one every second, to one every three seconds, trebling the apparent wavelength of the light represented by the trains. Thus it can be seen that for an Object moving at velocity v = 2c away from an Observer, where c is the speed of light, the apparent wavelength λO of the light from the Object as seen by an Observer is thrice its true wavelength λ. Hence:

When v = 2c, λO = 3λ [Equation #6]


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Having completed this first round of experiments then, we have six equations:

1. When v = c/2, tO = 2t/3 2. When v = c/2, λO = 3λ/23. When v = c, tO = t/24. When v = c, λO = 2λ 5. When v = 2c, tO = t/36. When v = 2c, λO = 3λ

Taking Equations #1, #3, and #5 then, dealing with time:

1. When v = c/2, tO = 2t/3 3. When v = c, tO = t/25. When v = 2c, tO = t/3

It can at once be seen that a relationship exists between v, tO, and t. This relationship is:

ttO = —————— (v/c)+1

This relationship can be demonstrated by substituting the values of v found in Equations #1, #3, and #5. First with Equation #1 with v = c/2:

t t ttO = —————————— = —————— = ——— = 2t/3 ({c/2}/c)+1 (1/2)+1 (3/2)

Then Equation #3 with v = c:

ttO = —————— = t/2 (c/c)+1

Finally Equation #5 with v = 2c:

ttO = ——————— = t/3 (2c/c)+1

Hence as the object's velocity away from the observer increases towards the speed of light, time appears to the observer to slow down at the object. Nothing special apparently happens after the object passes the speed of light, the observer merely sees time continue to slow down at the object, slowing to a stop as the object's velocity approaches infinity.

Similarly with Equations #2, #4, and #6, regarding wavelength:

2. When v = c/2, λO = 3λ/24. When v = c, λO = 2λ 6. When v = 2c, λO = 3λ

The relationship between v, λO, and λ is plainly:

λO = [(v/c)+1]×λ

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And demonstrating the relationship by substituting the values of v in Equations #2, #4 and #6, firstly with v = c/2 in Equation 2:

λO = [(v/c)+1]×λ = [({c/2}/c)+1]×λ = [(1/2)+1]×λ = 3λ/2

Then with v = c in Equation #4:

λO = [(c/c)+1]×λ = [1+1]×λ = 2λ

And finally with v = 2c in Equation #6:

λO = [(2c/c)+1]×λ = [2+1]×λ = 3λ

As the object's velocity away from the observer increases towards the speed of light, the wavelength of light from the object appears to the observer to lengthen, and the object appears redder. Again, nothing special apparently happens after the object passes the speed of light, the observer merely sees the wavelength continue to lengthen through the infra-red into the radio wavelengths, lengthening to infinity as the object's velocity approaches infinity.

Having established these simple relationships between the appearance of an object over time as it moves away from the observer at velocities approaching or exceeding the speed of light (in terms of how time appears to elapse and of how the wavelength of emitted light appears to lengthen) it is now time to test the Universal Observation Hypothesis, by considering the appearance of stationary objects which the observer moves away from, and thereby discover if the simple mathematical relationships between appearance and velocity for observers moving away from stationary objects, are any different to those mathematical relationships already discovered for objects moving away from stationary observers.

Of course, if these experiments were being carried out by spaceships, two experiments could be carried out at the same time, with the Observer in one experiment doubling as the Object in another experiment simultaneously, and vice versa. However this is not practical in the miniaturized version of the experiment; the Object scientist is too busy dropping trains onto the track himself to watch what the trains dropped on a second parallel track by his colleague are doing. Hence the following three experiments are identical to the previous experiments, except that the Object spaceship and Observer spaceship swap chairs, or the scientists swap roles, so that the Object (*)sits on the motionless chair dropping trains onto the end of the track in front of him every second, whilst the Observer (?) moves away in the electric wheelchair and times the arrival of each train as before from the point on the track he has reached as each train passes him.

Experiment #4: Observer moving away from Object at a velocity of c /2 (6"/s)

The two scientists have reversed their roles, or swapped places. Now we consider the problem of the two spaceships, floating motionless together for five seconds as a countdown to an experiment. The Observer spaceship moves away from the stationary Object spaceship at half of the speed of light for five seconds, the scientist inside looking back through his telescope at the luminous clock mounted on top of the motionless Object spaceship, and then stops. What does the observer in the Observer spaceship see? The scientists in the church hall agree to use their model railway set and electric wheelchair to simulate the experiment using the scaled-down value for the speed of light of 12"/s. They synchronize stopwatches, and after a count of five the wheelchair-bound Observer (?) moves off at 6"/s, representing half of the speed of light, holding onto his stopwatch,

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leaving the Object (*) behind sitting in his immobile chair and ready with his box of clockwork trains.

At t = 1, ? is 6" from the stationary *, who drops the first train onto the track at 0" from * and 6" from ?. This ridiculously innocuous little toy train, Train #1, trundles ominously towards ? at 12"/s, representing a light wave moving at the speed of light, ineluctably catching up with ?, as if with something of tremendous importance to prove.

At t = 2, ? is 12" from *, and Train #1 has already caught up with him and passes him. ? notes that, although his stopwatch says t = 2, Train #1 says that tO = 1. ? also feels a little nervous, as he tries not to remember that in Experiment #1 when he was sat still, and the Object * was moving away at 6"/s, tO was 1 when t was only 1½. But he pulls himself together and continues with the experiment, telling himself that this is important. Meanwhile * blissfully sets Train #2 running at the start of the track.

At t = 3, ? is 18" from *, and Train #1 continues on its way, forgotten for the time being. If anybody was looking they would see that Train #1 is 24" away from * and 6" behind ?. Meanwhile Train #2, moving as all the trains do at 12"/s, is now 12" from *, and catching up with ? at only 6" distant from him. * casually places Train #3 at the start of the track.

At t = 4, in the previous second ? has travelled another 6" away from * at 6"/s and is now 24" from *. Train #2, having been travelling for 2s at 12"/s in the same direction, is also at 24" along the track from *, and now passes ? whilst ? notes that whilst t = 4, tO = 2. He is concentrating hard and doesn't remember that in Experiment #1, t was 3 when tO was 2. Meanwhile Train #3 is bearing down on ? too, 12" from and directly between * and ?. At this point * drops Train #4 at the start of the track, with what appears to ? almost to be manic glee. 'What's really going on here?' thinks ?.

At t = 5, ? is now 30" from *. Train #3 is 6" away from him and 24" away from *. Train #4 is 12" further away from ? than Train #3, 18" from ? and 12" from *. Train #5 is placed at the start of the track 30" from ?, but ? stops the experiment now and gets out of the wheelchair to collect Train #1, now 48" from *, and indeed the other trains following after it, before they run off the other end of the track and fall onto the floor.

The diagram for this experiment now follows:

Diagram #4: Observer moving away from Object at a velocity of c /2 (6"/s)

At t = -5 to t = 0, tO = t:

*╞═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 1:

*1═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 2, tO = 1:

*2═══1═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 3:

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*3═══2═══1═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 4, tO = 2:

*4═══3═══2═══1═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 5:

*5═══4═══3═══2═══1═══╪═══╪═══╪═══╪═══╪═══╡ ?

Without having to bother to make any calculations, it is already apparent that the Universal Observation Hypothesis has more than an element of truth in it. Plainly, objects observed moving away at velocities approaching the speed of light, do not look the same as identical objects being moved away from at identical velocities approaching the speed of light.

As can be seen from the diagram, to the Observer at ?, the seconds tick by at * only once every two seconds, so that the time at * as seen from ? always reads half of the actual time elapsed, whilst ? is moving away from * at half of the speed of light. And as has already been seen from Experiment #1, when * is moving away from ? at half of the speed of light, the time at * as seen from ? always reads two-thirds of the actual time elapsed. Therefore objects moving away from observers really do appear differently to identical objects being observed by observers moving away from them at the same speed, at least in terms of the way time appears to pass. Thus for an Observer moving at velocity v = c/2 away from an Object, where c is the speed of light, the apparent elapsed time tO at the Object as observed by the Observer may be described as follows:

When v = c/2, tO = t/2 [Equation #7]


As regards apparent wavelength, since trains arrive at ? every two seconds instead of every second as they would normally do when both * and ? are at rest, the frequency has halved and therefore the apparent wavelength must has doubled. Thus it can be seen that for an Observer moving at velocity v = c/2 away from an Object, where c is the speed of light, the apparent wavelength λO of the light from the Object as seen by an Observer is twice its true wavelength λ. Hence:

When v = c/2, λO = 2λ [Equation #8]


As was already seen in Experiment #1, when the Object moves away from the Observer at the identical velocity of half of the speed of light, the apparent wavelength only increases by a factor of 3/2. Hence an Object moving away from an Observer at a velocity approaching the speed of light, does not appear as red-shifted as an identical Object being moved away from by an Observer at an identical velocity.

Experiment #5: Observer moving away from Object at a velocity of c (12"/s)

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Experiment #4 is now repeated with the wheelchair-bound Observer ? moving away at 12"/s, again equivalent to the speed of light at a scale of 12" : 1 light-second. At t = 0, ? begins to move away at this speed, again representing a spaceship moving away from another spaceship at the speed of light.

At t = 1, ? is 12" from *, and * drops Train #1 at the start of the track, moving at 12"/s.

At t = 2, ? is 24" from *, Train #1 is at 12" from *, and * drops Train #2 at the start of the track. All are moving at 12"/s.

By t = 5, it is plain to see that none of the trains are ever going to reach ? unless he slows down or stops. ? is 60" from *, and the numbered trains pursue him in vain 12" apart from each other. Train #1 is 48" from * and 12" from ?, Train #2 is 36" from * and 24" from ?, Train #3 is 24" from * and 36" from ?, Train #4 is 12" from * and 48" from ?, and Train #5 is at *, 60" from ?.

If * had begun dropping trains on the track during the countdown, at t = -5 ? would have seen Train #-5 go past at the same time as *, so both t and tO

would be -5. Similarly Trains #-4, #-3, #-2, and #-1 all go past ? at the same time that they leave *, and t = tO for t = -4, t = -3, t = -2, t = -1, and t = 0. Finally after t = 0, Train #0 (if there had been one) would have accompanied ? all the way along the track, so that tO = 0 no matter what the value of t once t > 0.

This experiment is illustrated here:

Diagram #5: Observer moving away from Object at a velocity of c (12"/s)

At t = -5 to t = 0, tO = t:

*╞═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 1, tO = 0:

*1═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 2, tO = 0:

*2═══1═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 3, tO = 0:

*3═══2═══1═══╪═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 4, tO = 0:

*4═══3═══2═══1═══╪═══╪═══╪═══╪═══╪═══╪═══╡ ?

At t = 5, tO = 0:

*5═══4═══3═══2═══1═══╪═══╪═══╪═══╪═══╪═══╡

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?

It can be seen from the diagram that, to the Observer at ?, the seconds do not apparently tick by at * at all. If ? even sees anything of * at all (the light waves are entirely motionless relative to him, unless he moves his head) time for * has apparently frozen at t = 0. Therefore, for an Observer moving at velocity v = c away from an Object, where c is the speed of light, the apparent elapsed time of motion tO at the Object as observed by the Observer is always equal to zero:

When v = c, tO = 0 [Equation #9]

(where v is velocity, c is the speed of light, and tO is the apparent elapsed time of motion)

As regards apparent wavelength, since no trains ever arrive at ?, the frequency is zero, and the apparent wavelength is the reciprocal of zero i.e. infinity. The implications of a light wave of apparently infinite wavelength are a headache which somebody else, a theologian perhaps, may meditate upon. I assume that it is invisible. In any case, it can be deduced if not seen that for an Observer moving at velocity v = c away from an Object, where c is the speed of light, the apparent wavelength λO of the light from the Object as seen by the Observer is always infinite. Hence:

When v = c, λO = ∞ [Equation #10]

(where v is velocity, c is the speed of light, and λO is the apparent wavelength observed at velocity v)

This result is radically different to the result of Experiment #2, with Object moving away from Observer at the speed of light; the most obvious implication of the result of Experiment #5 being that anything that an observer moves away from at the speed of light appears to be frozen in time. However, it was seen in Experiment #2 that when an object moves away from an observer at the speed of light, time only appears to slow down by one half. Therefore it should be possible for an observer to discern whether an object is receding from him, or whether he is receding from an object, by the effect of the motion upon the apparent passage of time at the object.

Experiment #6: Observer moving away from Object at a velocity of 2 c (24"/s)

This final experiment is going to be really strange, thinks ? as the two scientists set up again. This time ? will move away from * at 24"/s, equivalent to twice the speed of light. The question the scientists are trying to answer is this: what does the Object spaceship look like from an Observer spaceship that is moving away from it at twice the speed of light? The scientists count down 5... 4... 3... 2... 1... and at t = 0, ? begins rolling away from * at 24"/s like Davros in reverse.

At t = 1, * drops Train #1 at the start of the track, running as always at 12"/s. ? is now already at 24" away from * and sees straight away that the little train has no hope of catching him this time.

At t = 2, Train #1 is 12" from *, with Train #2 at the start 12" behind him. ? is all of 48" away from *.

By t = 5, ? has reached the end of the track 120" away from *. He's out of there. Trains #1, #2, #3, #4, #5, all follow in his wake like the last tired marathon finishers, despite still moving at the equivalent of the

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speed of light. They are all 12" apart from each other, at distances from * of 48", 36", 24", 12", and 0" respectively.

Again, if * had begun dropping trains on the track during the countdown, at t = -5 ? would have seen Train #-5 go past at the same time as *, so both t and tO would be the same. Similarly t and tO would be identical for Trains #-4, #-3, #-2, and #-1. Finally at t = 0, ? would have immediately left Train #0 behind, and by t = 1 would have caught up with Train #-1 that he saw leaving * two seconds previously. At t = 2 ? would catch up with Train #-2, and by t = 5 would have overtaken Trains #-3 and #-4, and caught up with Train #-5. This is somewhat clearer in the following diagram:

Diagram #6: Observer moving away from Object at a velocity of 2 c (24"/s)

At t = -5 to t = 0, tO = t:

*0══-1══-2══-3══-4══-5═══╪═══╪═══╪═══╪═══╡ ?

At t = 1, tO = -1:

*1═══0══-1══-2══-3══-4══-5═══╪═══╪═══╪═══╡ ?

At t = 2, tO = -2:

*2═══1═══0══-1══-2══-3══-4══-5═══╪═══╪═══╡ ?

At t = 3, tO = -3:

*3═══2═══1═══0══-1══-2══-3══-4══-5═══╪═══╡ ?

At t = 4, tO = -4:

*4═══3═══2═══1═══0══-1══-2══-3══-4══-5═══╡ ?

At t = 5, tO = -5:

*5═══4═══3═══2═══1═══0══-1══-2══-3══-4══-5 ?

The interesting point to note here is that, whilst the Observer spaceship (?) is looking at the Object spaceship (*) and moving at a velocity of twice the speed of light, he sees nothing of *. Nothing. In fact, at twice the speed of light ? will not see anything at all looking in the direction of the Object spaceship (*) in the opposite direction to his direction of motion, since at any speed faster than light no light from behind his direction of motion can ever catch up with him and is always falling behind him, and is therefore invisible. All ? sees behind him is a horrible infinitely black void, although like blindness this is of course an optical illusion. However, if ? takes the trouble to look ahead of himself, in the direction of his motion at twice the speed of light, what he sees there may possibly send him bonkers mad, because in that direction he will see a far more interesting optical illusion. Travelling at twice the speed of light, and looking in front of him in the direction of his motion, ? sees a mirror image of his own spaceship together with the Object spaceship *, which he already knows to be falling far behind him at twice the speed of light,

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somehow directly in front of him, and apparently moving far ahead of him in the opposite direction at twice the speed of light again! This is because ? is moving at twice the speed of light and is overtaking from behind the light that already left his starting point at *, light that is itself moving in the same direction as ? but at only once the speed of light. This light is therefore entering ?'s eye backwards at the speed of light (-2c + c) as he overtakes it, the effect being somewhat like watching a film from behind the screen and facing the projectionist. What is more, ? sees that * and himself are apparently moving backwards in time as well, since he is overtaking light that left * further and further in the past, the further away from * he travels faster than light. So ? sees in front of him the mirror image of the two spaceships reversing their preparations for the experiment, whilst racing ahead in exactly the wrong direction at twice the speed of light again, and hears himself talking backwards with his colleague on the radio. 'Passengers are advised not to look out of the windows whilst travelling to their destinations. This is the 0915 Coordinated Universal Time service to Epsilon Indi. Calling at Tau Ceti, YZ Ceti, EZ Aquarii, Lacaille 9352, Ross 154, and Epsilon Indi. Next stop will be Tau Ceti. The bar is now open. Thank you for flying with Qantas.'

... So it can be said, for an Observer moving at velocity v = 2c away from an Object, where c is the speed of light, that the apparent elapsed time of motion tO at the Object as observed by the Observer in the direction of the Observer's motion, is always equal to the negative value of the actual time elapsed since the Observer began moving i.e. the apparent time of motion tO

away from a stationary Object at twice the speed of light, is equal to the time of motion before the Observer began moving. Hence:

When v = 2c, tO = -t [Equation #11]


As regards apparent wavelength, trains arrive at ? every second moving backwards relative to ?, from the opposite direction to which the Object (*) is situated. This may be described mathematically by saying that for an Observer moving at velocity v = 2c away from an Object, where c is the speed of light, the apparent wavelength λO of the light from the Object as seen by an Observer is always the negative value of the true wavelength λ. Hence:

When v = 2c, λO = -λ [Equation #12]


Again, this result is drastically different to the result of Experiment #2, with the Object moving away from the Observer at twice the speed of light.

Thus, from our three further experiments we have obtained six further equations:

7. When v = c/2, tO = t/2 8. When v = c/2, λO = 2λ 9. When v = c, tO = 010. When v = c, λO = ∞11. When v = 2c, tO = -t12. When v = 2c, λO = -λ

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Taking Equations #7, #9, and #11 then, dealing with time:

7. When v = c/2, tO = t/2 9. When v = c, tO = 011. When v = 2c, tO = -t

It can at once be seen that a relationship exists between v, tO, and t. This relationship is:

tO = t - [(v/c) × t]

As can be demonstrated by substituting the value of v = c/2 from Equation #7 into the deduced relationship:

tO = t - [({c/2}/c) × t] = t - [(1/2) × t] = t/2

And v = c from Equation #8:

tO = t - [(c/c) × t] = t - t = 0

And v = 2c from Equation #9:

tO = t - [(2c/c) × t] = t - 2t = -t

Hence time at the object appears to slow down to a stop as the observer approaches the speed of light, and at the speed of light, time at the object appears to stop. Having passed the speed of light, time at the object appears to accelerate backwards as the observer's velocity increases further beyond the speed of light.

Again with Equations #8, #10, and #12, regarding wavelength:

8. When v = c/2, λO = 2λ10. When v = c, λO = ∞12. When v = 2c, λO = -λ

This one was a little trickier to spot, but the relationship between v, λO, and λ is clearly:

λλO = —————— 1-(v/c)

Substituting the values of v used in Equations #8, #10 and #12 into the deduced relationship by way of demonstration, beginning with v = c/2 from Equation #8:

λ λλO = ——————————— = ————— = 2λ 1-({c/2}/c) (1/2)

And now v = c from Equation #10:

λ λλO = ——————— = — = ∞ 1-(c/c) 0

And then v = 2c from Equation #12:

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λ λλO = ———————— = —— = -λ 1-(2c/c) -1

Hence, the apparent wavelength of an object observed by an observer moving away from it lengthens towards infinity as the observer approaches the speed of light. Having passed the speed of light, the wavelength then shrinks from negative infinity towards zero as the observer's velocity increases to infinity, and having passed the light barrier the observer can only observe the object from the opposite direction of the object, in the same direction as the observer's motion.

Plainly, in theory at least, the Universal Observation Hypothesis is correct. Now might be a good time to postulate some Universal Laws of Observation.

Law Number One: 'As an object's velocity away from an observer increases, time at the object's location appears to the observer to slow to a stop as the object's velocity approaches infinity, according to the formula:

ttO = —————— (v/c)+1

where tO is observed time, t is actual time, v is the velocity of the object away from the observer, and c is the speed of light.'

Law Number Two: 'As an object's velocity away from an observer increases, any wavelength of light from the object appears to the observer to lengthen to infinity as the object's velocity approaches infinity, according to the formula:

λO = [(v/c)+1]×λ

where λO is the observed wavelength, v is the velocity of the object away from the observer, c is the speed of light, and λ is the actual wavelength.'

Law Number Three: 'As an observer's velocity away from an object increases, time at the object's location appears to the observer to slow down to a stop as the observer's velocity passes the speed of light, then accelerate backwards as the observer's velocity increases further beyond the speed of light, according to the formula:

tO = t-[(v/c)×t]

where tO is observed time, t is actual time, v is the velocity of the observer away from the object, and c is the speed of light.'

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Law Number Four: 'As an observer's velocity away from an object increases, any wavelength of light from the object appears to the observer to lengthen to infinity as the observer approaches the speed of light, then completely change direction by 180° as the observer passes the speed of light, then shrink from negative infinity towards zero as the observer's velocity increases beyond the speed of light to infinity, according to the formula:

λλO = —————— 1-(v/c)

where λO is the observed wavelength, λ is the actual wavelength, v is the velocity of the observer away from the object, and c is the speed of light.'

It is apparent from these experiments that whether or not an observer is present at either a stationary point or another point moving away from it at 'Relativistic' velocities, the way that incident light waves originating from each point behave upon arrival at the other point is always different at each point in a manner that is mathematically predictable. This contradicts Relativity Theory insofar that Relativity would have it that relative to the moving point, the moving point is stationary and the stationary point is in motion. However the light distortion effect observed at the moving point reveals the truth that it is in fact in motion, and the stationary point is in fact stationary. This implies an absolute frame of reference in the Universe, a stationary backdrop of void against which all matter and energy may measure motion, whose motionlessness is dictated by the speed of light relative to it.

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the universal observation hypothesis

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