∆ Galileo and Time.

Enter Galileo Galilee.

We can count the swings of a pendulum while another object moves. But this only prove that things can move, and we can compare their motion 'now'.

The first great thinkers of mankind, most probably the ancient Greeks, were perhaps unfortunately just that, ‘thinkers’. It was apparently first believed by early philosophers that everything in and about the universe could be understood by the use of pure thought alone. Some people can't see how one person sitting alone, ‘meditating’ motionless and silently on a mountaintop can learn anything about the world around them. Let alone about the deepest recesses of the universe. But this is because they don’t realise the person is in fact directly in possession of, and exploring in great detail one of the most amazing things we have found to exist so far. Namely a human brain. Incredibly useful, insightful, and productive as such ‘meditation’ can be, it also has its limitations because meditation doesn't involve empirical measurements and rigorous physical experimentation.

Luckily, at a certain point, people realised that careful physical experimentation, measurement and calculations, could be used to check and advance theories and ideas that had originated from thought alone. By ‘experimentation’ simple, repeatable and measurable, real world tests of what had been suggested by casual observations and thought alone helped feed back accurate real world results and corrections into the thought process, greatly advancing the accuracy and direction of our understanding in what was effectively the birth of ‘scientific process’.

One small step for Galileo.

This first leap into Science is often attributed to the Italian physicist and mathematician ‘Galileo Galilee’, who began experimenting with pendulums, projectiles, and ‘water clocks’. Therefore perhaps Galileo is the real father, not just of the scientific method, but of the serious and empirical notion of time. It is said that he began his work with time as a result of observing the swinging of ‘the bronze chandelier in the cathedral of pizza (Wikipedia) one day and comparing their periodic motion to the regular beat of his own pulse.

Galileo realised that, contrary to what we might expect, the number of heartbeats a lantern took to complete a swing did not decrease as the lanterns motion reduced. Instead the number of hearbeats per swing remained virtually the same until the lantern, or pendulum’s, oscillation was too small to accurately observe. He had therefore discovered one of the most fundamental, and easy to replicate, principles that was to govern the science of ‘time’ from that point on.

Now although comparing human heart beats to lantern swings might seem very inaccurate science to us these days, it is a fact of science that almost any discovery or invention can be refined, almost without limit, as it becomes better understood.

If for example one monitors the number of heart beats a small simple lantern takes to complete one swing the results would not be very accurate or useful, but if you replace the un-aerodynamic lantern with a heavier and more streamlined purpose built pendulum, and compare a greater number of complete swings or oscillations to your own heat beat, a simple water clock or even hour glass, you can see how it is logical that you would get more and more accurate, repeatable and therefore useful results.

Galileo’s observations and refinement of the construction and understanding of pendulums had incredible consequences for mankind, because while we are used to being surrounded in the modern world by hyper accurate technology wherever we look understanding the motion of a pendulum meant that even in in his day and without so much as (an hourglass) a spring or cog in sight Galileo simply by suspending a dense weight by a length of twine he could start experimenting with a reliable example of ‘regular periodic motion’, i.e ‘change’ or what some might call ‘time’, with remarkable accuracy.

By making the pendulum bob more aerodynamic, heavier and denser, suspending it over greater lengths, and setting it swinging in draught free environments, Galileo could have reduced the effects of random influences, and so refined his accuracy more and more

The beginning of comparing motion, one small, mathematical step for mankind.

And so Galileo conducted his own detailed experiments into the reliable motion of the pendulum and in doing so he made fundamental leaps in science. His work eventually leading to the invention of the world’s first accurate mechanical pendulum based clocks.

Figure 4‑1 Analysing a pendulum in 3 dimensions is not usually necessary, so we simplify it to just a simple count, 1,2,3 ... this can give us the idea that linear, one directional time has a genuine reality.

By comparing motion of a pendulum to his own fairly regular pulse, Galileo was probably able to realise that in fact the pendulum (whose only variables would be it’s easily fixed dimensions and mass etc) should have the more reliable and consistent pattern of motion compared to a human pulse that can be affected by countless subtle factors. So really it would make more sense to compare the pulse to the pendulum.

(The first thing we would do (without thinking) is simplify the motion into just one plane)

At this stage Galileo was also comparing his observations against a form of water clock. Very ingeniously he would compare other examples of motion to the flow of water from one container to another. The water was controlled as he blocked or unblocked its flow with his thumb. So in allowing water to flow as a pendulum completed a known number of swings, Galileo could then weigh the collected water and use this value to compare to the swings completed. XXXtidy.

From here on Galileo and others went on to realise that one could mathematically, or theoretically, understand how and why a pendulum moved as it did. And go on to see that in theory a ‘perfect pendulum’ could exist. And then see how purely by working through some mathematical equations one could tell how the motion of two different pendulums would compare, without either of them ever actually being constructed or tested.

This small step from working with real pendulums, heart beats, regularly flowing water, to working with the mathematical ideas and equations of theoretical pendulums etc, represents a tremendous step in science. This because it led to us being able to ‘design’ objects or machines and calculate how they would perform with great accuracy, before a single component had actually been made. But this leap may also have been the first step in us jumping to the conclusion that a thing called ‘Time’ existed. Time, as something more than just a mental ‘notion’, or ‘mathematical tool’.

What is periodic motion, if not a measure of Time?

Another way of looking at the regular ‘periodic’ motion of a pendulum would be to realise that if we could see the patterns of light streaming out for millions of kilometres from a swinging lantern, and freeze their motion, the pattern of light produced would show, over a very great distance, a very regular, and evenly spaced ‘wave’ shape. The same kind of repeating curve you would expect to see if you set up an oscillating pendulum that was constantly trickling a thin stream of ink onto a conveyor belt of paper moving below.

Figure 4‑2 A one metre pendulum marks out 300,000 km long repeating patterns of light, but unless we can prove the past and the future exist, it may be wrong to say it mark out 'seconds of time'.

In both these cases, the lantern marking out a trail of light in its surroundings, and a pendulum showing its motion on a moving piece of paper, the distance between the ‘peaks’ of the waves marked out would always be very regular (assuming perfect conditions for the sake of simplicity).

From this observation, ‘that pendulums swing with a regular period’, we get another addition to the idea that not only does the ethereal ‘Time’ exist, but also that time is something that generally has a smooth and regular nature to it.

In reality all such light or ink trails would really show us would be a tangible, physical, regularity in the present moment. If for example we built a swinging lantern of just the right length (CHECK) we would find that the curving or wave like pattern of light it gave out would produce peaks that were always around 300,000 km from peak to peak.

We could say that we had built a lantern pendulum that swung with a period of one second, and that the patterns of light it produced repeated every 300,000 km because ‘light travels at 300,000 km per second’ – but all such a conversation, or description, would directly prove would be the fact that pendulums can exist and be moving in an interesting and restricted way, and location, move in a regular way. And given that light travels at a fixed rate, regular patterns of light can be created and would be streaming out from the ‘experiment’ if it was running.

What such an experiment would not prove is that time, or ‘seconds’, or ‘the future’, or ‘the past’, existed, other than as parts of the useful, mental, ‘notion’ of time.

The usefulness of the ‘notion’ of time.

None of this discussion on ‘pendulums’, effectively ‘clocks’, is meant to in anyway detract from their very real and practical usefulness. It is however meant to show that while pendulums, or clocks, give useful and controlled examples of regular motion and change – unless shown elsewhere - they do not track, or prove the existence of ‘Time’.

To put this another way, we can ask the question…

‘If ‘time’ did not exist, and objects could ‘just’ move in accordance with the laws of physics, would a pendulum still be able to do what it does ?’

At this stage the reader may want to say, ‘no’ a pendulum could not move without time. But this is only because we blindly say ‘objects need time in which to move’. As we will see this implication actually says nothing, and can be seen as a meaningless circular statement.

However, to show how ‘clocks’ are still useful or essential even if it is not time that they are measuring, we can consider some of Galileo’s early experiments and see how he may have thought they proved the existence of time. While they can actually be interpreted ‘timelessly’ without losing any real meaning, usefullness or significance.

This might seem contradictory, but remember, what this book is trying to say is that the world around us is just as we ‘see’ it. Though we may make the error of over-interpreting what we see in some places, and so think that there is more to the world than ‘just’ what we observe.

Whether we make the error of thinking time is more than just a notion or not, everything we do, or make, apart from ‘time-machines’, will all work fine just as planned. And using the ‘idea’ of time to organise ourselves, our lives, our machines and so on, will also work. But, as I hope to show this ‘idea of time’ is a subtle misunderstanding of the observed fact that there is just matter and motion in existence, and so ‘time’, the past, and the future, are never actually seen because they simply do not exist.

Using pendulums to understand slightly more complex motion.

Given his construction of real and accurate pendulums and his understanding of theoretical or mathematically perfect pendulums, Galileo Galilee also went on to methodically explore and mathematically describe the motion of falling and rolling projectiles.

Seeing and accurately measuring the motion of a falling body or flying projectile with a modern day movie camera and accurate stopwatch is pretty easy. Galileo of course had none of these things. But in a stroke of genius he realised that by using gently sloped ramps or boards he could slow down the examples of motion he was trying to examine. Making the movement and trajectories much easier to observe and measure.

If for example we take a stone and throw it straight up into the air we can clearly see its particular motion but it is very hard to understand how it changes speed and height during its entire journey.

But if we make a marble as spherical as we can and then roll it away from us straight up a ramp inclined at say just 10 degrees, then we can see that while the marble’s motion mirrors that of one being thrown straight up in the air and returning to our hand, the rolling marble does so in a much slower and observable way.

Figure 4‑3. Galileo was essentially comparing the 3d motion of pendulums (X,Y,Z) to the 3d motion of objects moving on an inclined plane. Doing this in full X,Y,Z detail for both objects would work perfectly but produce unnecessarily complicated equations.

Figure 4‑4 For mathematical simplicity Galileo would have just counted each complete swing of the pendulum, ignoring its more complicated real direction and speed etc.

Just ‘counting’ a pendulum’s complete swings (or monitoring the amount of water flowing at a steady rate from a container) effectively produces the idea or ‘notion’ of a ‘non-physical entity - moving steadily in some way at a constant rate, in a direction not described by any combination of the dimensions X,Y or Z’.

None of these steps is a problem in itself. But if we assign the symbol ‘t’ to the ‘mathematical idea’ of some ethereal ‘count’ that moves or increments regularly and unstoppably in one direction, in a dimension that we cannot perceive - we may end up (wrongly) thinking that we have added to the evidence suggesting, or even proving, that the ‘idea’ of time really relates to a mysterious and intangible – yet genuinely separate and real ‘thing’. (While in fact ‘t’ just relates to the simple oscillation of energy in the pendulum).

Ramp and roll.

If we roll a marble not just up the ramp and away from us, but also give it a horizontal motion, its path mimics the parabola of an airborne projectile in a sedate and easily observable way. Not only this, but when using an inclined board we can write useful markings and grids directly on its surface, making the path covered by a moving object even easier to see and quantify.

So by observing the slower motion of these controlled objects and, critically, comparing their position at various points in their journey to the count of his own pulse or far more accurately to the count of the swings of a carefully constructed pendulum, or a controlled flow of water, Galileo was able to make very accurate and useful observations of motion.

At this stage Galileo would have been developing equations (XXXcheck) to explain and quantify his findings. ‘Equations’ are ‘mathematical tools used to liken, compare or equate’ different things. And specifically Galileo was equating one form of simple, steady, or regularly repeating, motion to the more varied and complex movements of hi projectiles as they travelled against the constant acceleration of gravity, in straight lines (up and down the board) or parabolic curves.

In his equations he will have at some point used a symbol to represent the simple steady reference motion of a pendulum or water flow, and other symbols to represent the speed, direction and position of whatever ‘projectile’ he was comparing this motion to.

Galileo may or may not have used his own word and symbol for ‘Time’ in his writings and equations (CHECK) just as we use ‘t’ today. The precise symbols or words used are not the point, but it is probable that here in its appearance as a symbol in his equations the idea of time being something more than just an idea or notion really became firmly established. REP?

Many great names followed Galileo building on his brilliant work, Johannes Kepler observed the motion of the planets in the heavens and worked out that the line from a planet to its sun always marks out ‘equal areas in equal times’[1].

Following on from Kepler’s work, Sir Isaac Newton using his discovery or invention of calculus, was able to show mathematically why Kepler’s observations made such sense. And then to produce extremely accurate equations explaining the motion of the planets in space, the workings of the law of gravity, his three laws of motion and countless other very significant discoveries.

Newton carried out all his work on the backbone of the idea that time was some universally perfect and constant clockwork mechanism creating a totally reliable yet completely invisible framework of perfectly regular and universal ‘time’ that ‘ticked at a constant rate throughout all of God’s creation’.

And this idea of the existence and reliably ridged nature of time was completely accepted, and functioned perfectly well enough for our needs, until Albert Einstein revealed that time could not possibly be the separate and rigid thing is first seemed. Einstein suggested that to explain our more subtle observations of the universe - in particular some very slight but still significant inconsistencies in the orbit of mercury - ‘time’ could not be a rigid and separate part of the universe. Instead, he demonstrated that not only did it seem to make sense to merge space and time together to create ‘Spacetime’, but also tht this Spacetime should be stretchable and warpable !

How and why this is scientifically logical Einstein explained in great detail in his works on special and general relativity, theories that have been tested and shown to be fundamentally correct in a myriad of different ways, not least of which in the workings of every single Global Positioning Satellite device we use today.

As I hope to show, while it is evidently clear (e.g. from the fact that GPS clearly works) that relativity is mathematically correct, it can also be shown that what relativity explains need not be explained in terms of time existing and being distorted, but instead, just in terms of matter, forces, and ‘rates of change’ being distorted as described, but simply ‘in the present’.

Reviewing the history with and without time.

So here in an extremely brief history of the idea, and our work with, Time we seem to have shown how man’s passive observations of the sun’s natural path through the sky may have led us to make water clocks; How we may have then moved on to hour-glasses and pendulums; and how we may have introduced symbols (such as ‘t’) to represent time when we started to create highly useful, intricate and accurate ‘equations’.

From there how we began mathematically comparing regular and complex motion, and how all of this work combined with brilliant minds and careful astronomical observations led us to understand with great clarity the perfect motion of the planets in the heavens.

But remembering, that with an open mind, we have to consider equally both possibilities; that time may exist in its own right - and that time may exist only as a notion. We have to look at this history in two ways.

Is it the history of our discovery and understanding of a real thing, or is it the history of our creation and development of a very useful tool or idea?

Reviewing the story with time.

If we review this rough history from the starting point of believing that time is real then the answer is obvious; the observations, experiments, mathematics and subsequent inventions all make sense. The discoveries and ideas all progress logically, they describe and use time with more and more refined and reliable accuracy and ultimately, all our machines and calculations work, so time exists, case closed.

Reviewing the story without time.

However, if we review the same history more carefully and without the default assumption that ‘time’ exists and can be used to explain what we observe, and instead see if it can be explained from a viewpoint that only ‘matter and motion’ exist, then things become rather interesting.

First we note that our early ancestors only really observed constant motion. The sun constantly shines and the earth constantly spins on its axis.

Figure 4‑5 The Sun constantly shines and the Earth steadily spins, 'days' and 'nights' don’t begin and end, or 'happen' one after the other.

To someone hovering inspace over the north pole with clear view of everything the simple constatnt rotation of the Earth would be obvious. But to anyone stuck at a fixed location on the Earth, the Earth seems flat, and the sun seems to repeatedly appear and disappear. So it seems not that one constant thing is happening (the Earth spinning) but that repeatedly, a new though always similar event, ‘sun rise’, keeps happening over and over. This would seem to be especially true, or ‘obvious’, to people who didn’t know that the Earth was a sphere spinning in space[2].

The creation of dripping water clocks was really the creation of our first constant and smoothly or regularly ‘changing’ machines. Machines made to do no job other than to show some example of such smooth and regular change, which we then checked against and compared to other motion around us; and the first motion we compared our clocks to would be the apparently repetitive motion of the sun.

The origin of the symbol ‘t’.

So far this doesn’t reveal much but If we look carefully at the point where time seems to start getting credibility as being something real and measurable, at the point where Galileo started to mathematically compare heart beats or pendulum swings to the motion of projectiles we can see how some small and seemingly irrelevant mathematical factors may have been overlooked in a way that did not affect the accuracy of his results at all by may have led to falsely strengthening the idea that time is something other than a notion.

These factors are mathematically considerations that in a strange way should have appeared in his early equations and then been removed leaving the final results unchanged, so how can they be important?

Imagine Galileo setting up an experiment to observe and understand the motion of a projectile through the air or across an inclined plane. The projectile being studied can have its actual position described in equations by the symbols X,Y and Z, and its speed and direction given by other appropriate symbols, while for ‘time’ Galileo just needs a single number or symbol representing the ‘ticks’ of his pendulum, hours, minutes or seconds all just being arbitrary units of the same ethereal thing.

And so Galileo joins and equates the real motion of the projectile with the ethereal time, or ‘t’ in his equations, and this works perfectly.

But hold on, what is the real source of the numbers we put into thus symbol ‘t’?

Galileo would get his values for ‘t’ from the very real physical motion of his pulse or a pendulum, each of which are real three dimensional things that exist and beat, pulse, oscillate, swing, back and forth i.e. move.

The motion of a pendulum is both simple and complex, we can see and use its outward simplicity by just counting ‘entire swings’.

But a pendulum bob’s real motion is more complicated. As the bob swings back and forth it naturally arcs up at each extreme of the swing, and could also be swinging side to side. So the bob’s real motion is usually a ‘curved up’ ellipse. Galileo could have overcome this problem by just releasing the pendulum carefully so as not to put any sideways swing on it.

But even then the actual bob itself is always travelling at a different speed, and with a different acceleration, at every point in its swing. It even has a speed of zero at each and of its swing, and throughout its motion its left to right position constantly changes along with its height at every point.

So nothing about the pendulum bobs motion is really linear, its speed, its direction, its rate of change of speed, its height or ‘Z’ location, along with its X and Y positions are all constantly changing in cyclical but still slightly complicated ways.

In comparing a pendulum to the motion of a projectile Galileo may have been able to write rather complex equations taking all of these aspects of the pendulums motion also into account. In this way he would have ended up with equations that would show you precisely where a pendulum bob would be relative to say the corner of his workshop, perhaps +5 cm X, 2 cm Y and + 3cm Z, as a projectile being studied was at say 3 metres away X, 2 metres away Y and .5 metres high Z.

But describing his findings this way would have been unnecessary, extremely confusing and very counterproductive because precisely what real world mechanism we use for ‘t’ doesn’t really matter as long as we use something that results in a steady rate or reliable ‘tick’.

So while Galileo may have been able to write equations merging the position of a projectile to precisely where and how fast in the X and Z directions his pendulum bob was he would have very sensibly for simplicity just kept adding up complete swings of the pendulum and assumed the existence of some constantly flowing or accumulating number, and so the same actual results are for convenience expressed in much simpler terms, and with no real loss of information, for example as ‘at 3 ½ swings the projectile is 5 metres high (Z) and 10 metres away (X)[3].

Comparing complex to straight-line motion.

Now consider that it is a logical fact that Galileo’s experiments and equations comparing the ‘ethereal’ time to the X,Y and Z motion of real objects would work in essentially the same way, if instead of comparing the complex motion of a flying projectile, or a marble rolling in an arc on an inclined board, to the simplified motion of a pendulum, he had compared the projectiles complex motion to the even simpler motion of some other real and physical reference object.

An object whose motion had been made as simple as practical so that it was just moving in a straight line, at a constant rate, along a track evenly marked with the numbers 1, 2, 3, 4, 5 and so on.

In realistic terms, particularly with the technology available to Galileo, it is not only hard to set up an object to move in a straight line at a constant speed but if you do so you run into many practical problems. First you need a lot of carefully made track, then the ‘longer’ you run any experiment the object gets further and further away, it gets harder to see accurately where the reference object is, it needs its own source of power, and lastly at the end of any run you have to chase after the reference object and bring it back![4]

So a human pulse, a water clock, a pendulum, an hour glass, or as we have now clocks with rotating hands that never move away from the clock face or even have numerical readouts generally make far more practical sense than any ‘linear’ device.

Using a ‘straight line’ reference object instead of a pendulum.

If Galileo had made a simple ‘reference object, moving steadily along a straight track’, instead of using the more complicated motion of an oscillating pendulum when first exploring the 3dimensional motion of ‘projectiles’ the mathematics would have been simpler and more transparent.

With a linear ‘clock’ he would have been comparing the X, Y and Z speed, direction, and distance covered by the projectile, with the speed, distance and direction of the smoothly moving reference object.

However because of the way the track would be constructed the reference object would, by design have the following properties...

• The reference object would only be moving in one direction, e.g. ‘X’,

• The rate this direction was changing would be zero.

• The object’s speed would be constant in this direction.

• And ‘the rate of change of speed’ of the object in this direction would be zero.

Also, because the object was only moving in the X direction it would also be true that ...

• The rate the reference object’s direction was changing in the Y axis, would be zero.

• The objects speed in the Y axis would zero.

• And the rate of change of speed of the object in Y direction would be zero.

And also true that...

• The rate the reference object’s direction was changing in the Z axis would be zero.

• The objects speed in the Z axis would zero.

• And the rate of change of speed of the object in Z direction would be zero.

Most of the above details have a value of ‘zero’, and seem mostly redundant, because all they are effectively saying is ‘that the reference object moves at an unchanging rate, in some arbitrary but fixed direction’. This is because when looking for a good sample of steady motion to compare other motion to, all that matters is that the amount of distance the moving object covers when in use constantly increases, at an unchanging rate.

This breakdown might seem a bit unnecessary, but it is very important for us to consciously highlight all the factors that Galileo would have ignored here, because this is effectively what we do when we just count entire pendulum swings, (or clock ticks) without thinking about their real origin. Because it is this tiny detail of ignoring a couple of sets of seemingly irrelevant, zero value, and unchanging numbers, that leads us ending up with a bizarre ‘one dimensional, steadily progressing’ entity, which seems to always be there or to have come out of nowhere, as we shall see.

DIAGRAM – showing what is ignored?

Mathematically comparing the Reference object and the projectile.

Mathematically comparing the X,Y and Z motion of the ‘straight line’ reference object with the X,Y and Z motion of the projectile in full detail would result in a long equation with lots of zero values for the reference object’s Y and Z speed, position and rate of change of both, and unchanging values for the objects actual direction, speed, rate of change of speed, and rate at which the distance it was covering increased.

Not only would it turn out that all of the six separate ‘zero’ values concerning the Y and Z motion can be ignored but the actual X direction of motion becomes insignificant, any direction will do. And the actual speed in the chosen direction is also irrelevant as long as it is constant! (though as we will see in practical terms the fastest speed, and the most sensible speed to use as a reference will be the fastest speed possible according to the laws of nature).

Given all this mathematical dead wood it would make great sense to factor out all of these (9 or 10) zero value, irrelevant or completely unchanging factors.

XXX POSS SHOW SOME EQUATIONS and ‘zeros’ here.

More realistically in fact any good, let alone excellent mathematician would probably write out his or her first equations without ever including these values in the first place knowing they would and still get perfect mathematical results![5] So if the job is simplified and the results are still perfect what, you may ask, is the problem?

The error of ignoring seemingly insignificant zeros.

The problem is that all the unnecessary baggage described above can be mathematically factored out of any equation and safely ignored – safely apart from the fact that it is by ignoring these seemingly irrelevant details that we end up thinking ‘time’ really exists.

This can happen because it is in the very process of doing our calculations with just the few numbers relating to the reference object that do change time seems to ‘appear’ and appear as if it was always there.

In this way time seems to legitimately get the status of being something apparently universally very real, and functional, while also being uniquely invisible, one-directional and mysterious.

And it is here that time appears to be something real, that we have discovered and clarified in our equations. As opposed to the truth, which is that by using the idea of a set of steadily incrementing numbers we have created the notion of time. And then by ignoring the true origin of the idea, we think we have solidified what was at first just a ‘notion’, giving it the status of apparently relating to some scientifically discovered, real yet mysterious and intangible, continuous, and fourth dimensional, phenomena or ‘thing’.

The ideal nature of a reference object.

Figure - It seems to me that in all equations, (including what I understand about relativistic mathematics), 't' as 'time said to pass in seconds', could be replaced by reference to the position of a pulse of light moving a long a measured and numbed track as above.

The point here is that in using the symbol 't' and saying it refers to 'time', we are suggesting that any mathematics that uses 't' and works, also counts as some evidence towards proving the existence and passing of 'time'.

Whereas if the above substitution does work, it show that all that is necessary for for such maths to work is 'matter and motion' happening now.

The sudden and unnoticed jump from studying and comparing some examples of motion, to assuming we have proved the existence of one or more real and existing features of a thing called ‘time’ happens because when we use a ‘reference object’ ideally we are looking for, imagining or physically making[6] an object such that...

• The reference object only moves in one direction,

• The direction the reference object moves in is irrelevant.

• Whatever direction the reference object moves we will insist on calling it ‘forwards’.

• It always moves at a constant and unchanging rate.

• It doesn’t matter what that rate is.

• The distance the reference object is from its real or imaginary start point always ‘theoretically’ or ‘ideally’, increases constantly and unceasingly.

In the moment that we ‘paper over’ the real and simple fact that all we are actually doing is comparing the motion of two objects, and instead simplify the numbers for one of the objects for mathematical ease, we imply that the number whose true origin we papered over is ‘time’. And while we end up with the mathematics working perfectly, we absolutely critically, and wrongly, also leave ourselves with a ‘new’ idea or notion. A notion that we end up thinking relates to ‘real time’ existing. i.e.

Time – being; ‘The idea, or notion, of the existence of some extra, invisible, and all permeating, ‘ethereal’ thing. A thing that is constantly moving (or we are moving through) at a fixed rate, in a direction that ‘doesn’t matter’. Some 4^th Dimensional thing, that can be said to be containing or driving the 3Dimensional objects and motion we actually see around us.

And something that can be equally well thought of as either coming towards us, or heading away from us or just flowing in its own dimension. Or taking us along with it as it moves along at a steady rate. Powered by something that is unknown, as it moves in an unstoppable way, never meeting an end point, at a rate that matches the speed of light.

Time, passing in a way that both constantly increments or accumulates some ‘past’ numbers or ‘record’ of its passing, while also pulling into existence ‘the future’ from whatever is ‘ahead’ of it’ .

With any luck by now you can see that the above description, which seems to match all that we expect of or imagine the mysterious invisible fourth dimensional entity of ‘time’ to be, is in fact only a description of what we need from a real or imagined reference object moving in a straight line at a constant rate, be it a ball on a specially made ramp, or child’s model train set up to move at a fixed speed along a straight piece of track, so we can use it as a simple reference object to compare to some other ongoing motion.[7]

And while it seems that like an explorer panning for gold we have washed away the worthless stuff and been left with or discovered something valuable this is not quite the case because what we are left with when we wash away our unnecessary X,Ys and Zs, the symbol ‘t’ that we use to represent the swinging pendulum is not something that exists and is discovered but something we have created for our convenience.

You may also see here, how simply comparing some regular straight line motion, (be it a ball moving along a fixed path, or a toy train running steadily along a straight piece of track), to some other more complicated motion and claiming some sensible results - is a far cry from comparing the motion of two objects, declaring some sensible results, and also declaring that you have proved the existence of some other ethereal thing called Time as well.

‘Time’ not just being a real ball or toy train whose position we are monitoring, as it simply moves along a track until it reaches the end of the line. But a mysterious thing that moves unstoppably in a fixed direction, through an invisible fourth dimension, while controlling and recording the motion of all objects in the universe as it does so!

The first regular clock.

And from there you can see that given the usefulness of a reference object moving at a fixed rate in a straight line, but seeing the impracticalities of this, it is small step to curve the reference objects groove or ‘track’ into a continuous circle.

Doing immediately this solves both the problem of running out of track, and of the reference object constantly getting further and further away as we let it move.

From there of course it is another small step do away with a rolling ball, or chuffing train, completely and just have a source of energy, say a weight hanging from a cord wrapped around a drive shaft, or if your engineering is up to it, just a wound up coil spring, and release that energy in an orderly way. Say at a rate governed by a swinging pendulum, and then use that energy to drive a rotating hand at a steady rate. Then you have a much more manageable, compact and convenient constantly moving reference object... something we might misleadingly call a ‘clock’ if we insist that just calling a motorised hand a clock proves the existence of Time.

But also you can hopefully see that, all of these logical practical steps to produce a convenient reference object to simplify the way we compare motion make sense, but each of them only actually proves that we can make machines that efficiently release some supply of energy in a controlled manner. And none of these steps either points to, or proves the existence of, some other constantly flowing, invisible, fourth dimensional entity.

>> SEE ∆ Common assumed, but invalid, 'proofs' of Time.

[1] POSS ADD Kepler diag. In fact this expression of kelpers law is just another way of saying that ‘an orbiting planet always holds the same amount of energy’ – in other-words, while a planet has a varying distance from its star (in a sense a ‘height it can fall from’ – or an amount of potential energy) it also has a varying speed (or amount of potential energy). Adding these two amounts of energy always must give the same figure (where could the planet gain or lose energy?). thus an orbiting planet in its elliptical orbit is very similar to a pendulum – holding the same total energy but swapping it between potential and kinetic smoothly and reciprocally.

[2] The idea that something else repeatedly starts and stops is a misunderstanding similar to thinking that a light-house actually produces flashes of light instead of just a constant stream of light from source that happens to be constantly rotating.

[3] There is no real loss of information here because if we know the details of the pendulum used we could if we wished work out where such a pendulum would be in and X,Y,Z sense at 3 ½ swings.

[4] Note, it would have been hard for Galileo with his resources to actually create a simple straight line reference motion because if he had set up a single long gently sloping track to roll a reference marble the ball would not have moved smoothly and regularly but would have accelerated faster and faster along the track, he could instead of used the motion of a strolling donkey or friend along a straight path, etc but the practicalities of the idea are not the point here.

[5] Which we can assume Galileo or his followers probably did without thinking much about them.

[6] When we create a device and call it a ’clock’.

[7] It may seem at first that the speed of the reference object would be irrelevant as long as it was constant but in fact we can't just pick any speed in reality because we couldn’t make a device that exceeded the speed of light.