∆ Light Clocks and a Hall of Mirrors

Light clocks, fish and a Hall of two mirrors.



Fig: We say things change 'locally' and  in 'location' - but these are the same thing.
In the pictures parts of a robot arm, or a rope ladder firing gun, can be said to just be "moving", or becasue of that same motion, the object as a whole can be said to be "changing". Therefore there really is only one thing "movement", that we also refer to by the word "change".

At first glance it seems that things in the universe change, and change in two seemingly different ways. In simple terms we appear to observe that things can change ‘locally’ as in within themselves, E.g. As in the hands apparently marking 'Time' in a 'clock'. And change ‘location’ as in an entire 'clock'  actually moving to a different place.
But careful examination shows there is only one type of motion, and not motion – and – the passing of time.

We might say that a complicated mechanism like a computerised robotic arm may change its shape or form as it carries out some task while essentially remaining in the same place on the factory floor, while a bullet, fired from a rifle may be said to change its location very dramatically in flight, while not significantly changing its form.

Although without giving it much thought these two forms of change, ‘shape’ and ‘location’ might seem to be different we can quickly see that they are essentially identical. The robot can be said to have changed shape, or the tip of its arm can be said to have moved location 2 metres to the left. The bullet can be said to have moved location, or the ‘rifle-bullet object’ can be said to have changed shape.

This concerns us here because in stating that ‘Time slows for moving clocks’ Einstein’s special relativity seems to both merge and differentiate between ‘local’ change, as in the position of hands in a ‘clock’, i.e. ‘the passage of time’, and ‘change in location’, as in how fast or far a ‘clock’ or any other object is moving and where it is moving in relation to other objects or the rest of the universe. If there is no such thing as time then this situation has to be fully explained in a timeless way.


If we consider the classic light-clock example we are first asked to imagine two synchronized light-clocks[1] standing side by side. By synchronized here we meant that the photons in each device are both set off in each clock such that as they both bounce up and down separately in each device they are both in the same place in each clock. To make this clearer we could set up a counter on top of each clock that is incremented by ‘one’ each time a photon completed a round trip between its mirrors. With the counters in place as we set the clocks off together we would see both displays very rapidly counting up ‘round trips’ or ‘clicks’ while also always both showing the same steadily increasing total. This shows us that the rate of ‘local change’ is constant.

If we then start moving one entire clock away from the other (at a significant fraction of the speed of light itself) we see that while the clock is moving the photon trapped within it will have to take a diagonal path if it is to keep reflecting off each mirror in turn. This means that the counter on that device will indeed increment more slowly compared to the stationary clock.

This shows us that if we moved the clock away from, and then back to, the stationary clock, its counter would be running more slowly throughout the entire round trip. The end result is that when the two clocks are again at rest together they again increment their counters at precisely the same rate, but the moved clocks display will be a fixed number of ‘clicks’ less that the stationary clock. 

It is important to realise here that the reason Einstein used the idea of a light clock is because it directly employs ‘the speed of light’ within its very simple mechanism, and while in these thought experiments we just concentrate on one or two photons interacting between mirrors in a box, in any and all objects – including our own bodies – all interactions including the interactions between atoms that result in us thinking, moving, growing, and changing, all happen because of  ‘electrochemical or electromagnetic’ processes. 

In other words all the interaction in all objects are similar to the workings of minute light-clocks. So in seeing how and why a light clock is said to run slow if in motion we are also seeing how and why every process in a human body or any machine will also run slow if in motion. It is this running slow that is seen as ‘time running slow’. We should note also that this is not just a thought experiment or proposed theory but something that has been experimentally proven in the 1971 Hafele and Keating experiment, and is feature of nature that is accounted for in every GPS system.

Hafele–Keating experiment - Wikipedia, the free encyclopedia


This difference in the displays between moving and stationary clocks is generally seen as being to do with, and indicating some, important details to do with ‘Time’ and ‘motion’. In particular this is interpreted as being something that shows us ‘Time dilation’, the ‘slowing of the passage of time for moving objects’.

In this work I am proposing that there is no such thing as time, therefore the idea of ‘time’, and ‘motion’ existing is just replaced by the existence of only ‘motion’ existing.

Although a light-clock seems to show us the passage of ‘time’, as its trapped photon counts up ticks, and the effects of ‘motion’, as the entire device is moved, slowing down the ‘ticks’, in fact we can see that such a device really just shows us a hidden bias we have in declaring that some particular examples or directions of motion are more important than, or mean something different to, other examples or directions when we set up experiments like this.

 The problem arises because in a light-clock we envisage a real, physical, object (a box containing two opposing mirrors), i.e. something that we could actually make or buy, and carry with us, while also envisaging a ‘photon’ trapped between the mirrors. A wooden box of mirrors might be quite an awkward heavy thing to lug around or try to accelerate to some great speed, while a photon is completely the opposite, you just can’t easily stop them rushing around at great speed and they aren’t exactly heavy. So when we set a light-clock off, and talk about moving it (say from left to right) we are comparing the super fast up and down motion of an inconceivably small and virtually massless photon, to the laboriously slow, ‘left to right’ motion, of a big heavy ‘box’. Both these things though are just examples of motion, in a direction, but we immediately set off with a bias towards thinking that the motion of the photon tells us more about ‘time’ and the motion of the box is more about ‘speed’ and changes in ‘location’.

If IT’S all just motion why does one clock lag behind ANOTHER?

If  there is no such thing as time, and instead just motion, then why when we move one clock away and then back beside another does its display show ‘less time has passed’?

The problem with this question is its hidden bias, the bias that declares, states, assumes, or claims that the display on the light-clock ‘shows the passage of time’. This bias starts as we initially call the device a ‘clock’ and claim that ‘clocks measure time’, and that ‘time’ is the stuff clocks measure.

So do these devices measure time or motion? If we set up our opposing mirrors so that each round trip a photon makes is exactly 3 metres, then we could set up our counter to rotate one tick on the dial for every billion round trips the photon makes. Because we say ‘light travels 300,000 km, or 300,000,000 metres per second, we could put a card under the counter display saying ‘Seconds’ and this would satisfy most people. However we could also put a card under the display saying ‘Billions of light-metres *3’, and this would be factually correct, it would simply be showing the actual distance the oscillating photon is travelling. The difference between the two ‘units’ is that ‘seconds’ are apparently units of a mysterious thing called time – whose existence hopefully the previous sections have at least brought into question, while ‘light’, and distances, e.g. metres, can be easily seen to exist[2].












Figure 351 -A basic light clock in motion. -One with a 'tick counter', and lastly with a tick, plus 'change of position' counter.

One way to address the different readings that would appear between the displays on a moving and a stationary light-clock would be to mount each device on wheels linked to an odometer. The ‘odometer’ doesn’t measure smells, but ‘distance travelled’ like the odometer or trip meter found in most cars.

By linking some cog or wheel to the wheels the light clock is resting on an odometer can measures the ‘change of location of the entire device’. While the trapped photon, and the counter it is linked to, show us the ‘change of location of the photon within the device’.

The trick is to see that both these examples of motion are absolutely identical, they are both just movement or ‘change’. They seem different because compared to the photon within it; the box of mirrors seems to be a phenomenally different thing, trillions of times larger, more massive, much, much harder to move than a photon and thus orders of magnitude slower than the restless photon it contains. Thus changes in location of the whole box, seem to be of a completely different nature or significance to changes in position of the photon within it.

However, with our trip meter connected to the counter via a computer or a couple of cogs to make sure the ratio is correct, we could set up a system to ‘add’ any change in the physical location of the whole clock to the ‘tick counter’ on top of the device. In simple terms (and using Time based terms for simplicity) we would have to gear the odometer down CHECK, such that for every 3 billion metres (300,000 kilometres) we moved the clock the system added ‘one unit’ to the tick counter.

In non time based terms, and with the card by the display saying ‘Billions of metres * 3’ we see this makes perfect sense.

With this set up we see that in the first experiment, (where we noticed that with one stationary, and one moved clock, the moved clocks display lagged behind the other) our error was that we thought of the photons movement, and the entire clocks movement as being significantly different things for some reason. And when we set up our tick, or movement counter, we completely failed to ensure it counted all movement. With the counter linked and correctly geared to the odometer we find the error is resolved. No matter how much we move one clock relative to the other our two ‘motion counters’ added together, always show the same steadily incrementing numbers, with no discrepancy[3].

So the error is thinking that time and motion both exist and are similar and related, and then seeing and considering or accounting for them in different ways, as opposed to seeing that just motion exists and making sure we add up all the motion we see in any experiment, if we are setting up an experiment to explore ‘motion’.

We should also note here that the odometer on the devices is set to only accumulate distance, i.e. whatever direction the device moves in a value is added to the counter, not added as the clock is pulled away, and decremented as it is returned.

(XXX note the effects of ‘acceleration’ general relativity are not covered here, + expand on the odometer always incrementing though changing direction – what of clock going backwards ?)

Something fishy.

While unintentionally creating the (invalid) idea that ‘time’ and ‘motion’ are two separate and existing things they also lead to some interesting conclusions about ‘time approaching a complete standstill’ as a light-clock object approaches the speed of light. This can be seen and re-explained ‘timelessly’ if we first consider a different, and hopefully more intuitive way to understand what is happening within a light clock.

To do this on a more human scale, imagine the path of a neurotic fish that constantly swims back and forth as fast as it can between the twin hulls of a catamaran moored in a large lake.


Figure 352: A fish swimming between the hulls of a catamaran has to use some of its forward motion to keep up with the boat if it is moving forwards through the water.

If the catamaran is not moving at all in the lake’s effectively still water then the fish can swim back and forth between the floats unhindered, clocking up round trips at a steady rate. If however the catamaran starts to move forwards through the water the fish has to compensate for this if it wants to keep swimming between the floats. So the fish now has to change direction a little so it too is partially heading in the direction the boat is now moving.

Because the fish is already always swimming at its maximum speed, and some of that speed is now being used up ‘chasing’ the boat as it also swims back and forth between the hulls, this means of course that the fish will have to swim further to reach each hull, and so complete each round trip less rapidly. In other words the ticking of this particularly unusual clock will in a sense now run slower than when the boat was stationary in the water.

This effect would be particularly noticeable to a passenger on the catamaran looking down and observing the fish’s bizarre behaviour. While moored up the observer might see that for every 100 of their own heart beats the fish makes 10 round trips between the hulls. But with the boat in motion through the water, at a significant fraction of the fishes maximum speed, the observer on the boat would first notice that instead of pointing directly at each hull as it headed for them the fish now had to point slightly towards the front of the boat as it swam. And then notice that the fish could now only complete say 5 round trips for every 100 of the observer’s heart beats.

If our observer was a little sadistic they could choose to speed up the catamaran a little more and watch the effect of the fish. What they would see is that the faster the boat moved through the water the more the fish would have to direct more of its motion through the water in the ‘forwards’ direction, instead of just at right angles between the floats. Thus of course the fish would actually be seen to be swimming ‘forwards’ faster, but ‘from side to side’ (between the floats) slower. Though the fish itself is always just moving through the water at its own fixed maximum speed[4].

If the water was murky or the fish was particularly ‘round’ or indistinct in appearance then the observer might not clearly see that the fish was having to point more ‘forwards’ to keep swimming between the two same, opposite, spots on each float. In this case, particularly if the observer also hadn’t noticed the boats motion through the water[5], it would seem as if the fish had actually just slowed down in its back and forth journeys.

What is interesting at this point is to imagine what would happen if the boat moved faster and faster through the water and approached the fishes own top speed. To the observer the fish would seem to ‘tick’ between the floats at a slower and slower speed, and at a certain point, as the boats speed through the water exactly matched the fishes top speed the fish would seem to stop swimming back and forth between the flats completely, and seem to just remain at one fixed spot between the floats, in a sense completing less and less ‘ticks’ per hundred human heartbeats until eventually the ‘fish clock’ seemed to stop entirely, completing ‘zero’ ticks per hundred, thousand, or any number of observer heartbeats. From the fishes point of view however it is always just swimming forwards through the water at it usual maximum speed.

A problem with the ‘fish’ and ‘photon’ analogy.

So this unusual and not entirely faithful analogy, between light-clock and ‘fish clocks’ gives us an idea as to how and why it can seem that ‘clocks’ slow down with motion.

I say not entirely faithful analogy because by aiming for simplicity this thought experiment bypasses a critical point which is that while an observer on a steadily moving catamaran might see the fish seem to slow down as it swims back and forth, an observer travelling at great speed in say a space ship, watching a photon bounce between mirrors instead of a fish between ship hulls, would not be able to see this slowing down effect. This is because in reality every atom ‘oscillating’ back and forth in the moving spaceship and the observers body etc become like a photon in a light clock, or the fish oscillating between the moving floats. In other words while a light-clock on a space ship will slow down its oscillation as the ship moves forwards – every atom in any observer on the spaceship will be subject to exactly the same slowing down or ‘dilation’ effect. So the observer, and the ‘clock’ will both be said to slow down, and both will do so at precisely the same rate, and thus to the observer it will seem as if the light-clock on the space ship has not slowed down.

Slipping behind the times?

An interesting detail that seems never to be mentioned when Einstein’s light-clocks are discussed is highlighted by the fish analogy, and it is the fact that the fish, swimming between two hulls on a catamaran, would have to start changing direction more and more towards the direction the boat is heading in if it wants to keep oscillating between fixed points marked on each hull.

In light-clock terms, if we imagine our first two, perfectly aligned, or synchronized devices side by side we see no problem. If however we were to actually make such devices, set a photon oscillating in each, and then at some point send ‘clock B’ off to the right we would not in fact see the ‘diagonal’ path of the photon in the moving clock and all the effects this leads to but we would instead run into some ‘practical’ problems.

If we could create two perfectly parallel, perfect mirrors, and set a single photon bouncing between them then all would be fine if nothing was moved. But if we sent the mirrors off to the right at ½ C, while the photon is somewhere between them, then that photon won’t actually end up meeting a mirror as expected at some point because that mirror will actually be a few metres off to the right and moving away at speed instead of staying patiently in place to keep its appointment. So the mirrors would effectively just slip away to one side leaving the photon to fly off in a straight line in whatever direction it happened to be heading as the mirrors were removed from its path. This is what would happen if our fish was not aiming for marked points on the hulls of the catamaran, but just swimming back and forth through the water and happening to be blocked by the hulls, and thus deciding to just turn around, as the boat is pulled away the fish would then find its obstruction removed and keep swimming in a straight line in whatever direction it happened to be going.

The light ‘slipping out’ of a moved light clock isn’t much of a problem because if we are sending a light-clock off to the right at say ½ the speed of light we could set the device in motion and launch a photon into it tilted by just the right angle also to the right, for things to work out perfectly. Or we could set the clock off in motion, and then launch the internal photon in the ‘moving’ clock. In this way the photon would be launched with the right amount of momentum in the ‘sideways’ direction to effectively end up just bouncing between the mirrors as if nothing unusual was happening[6].

This is basically the same as saying ‘if you started a light-clock running, while you were on a space ship moving at a steady, but significant speed, the clock would function perfectly. However even then, in (perfect) reality, if the space ship started to accelerate we would see the oscillating photon drift towards the back of the opposing mirrors because while the ships engines accelerated the body of the ship, and the clocks mirrors, the photon in transit between them would not ‘know about’, or be adjusted in angle, for this extra forwards motion.

All of this might seem a bit confusing and aimless but luckily the circumstances surrounding all these moving light-clocks, photons and space ships can be greatly simplified with a ‘hall of mirrors’. 

A hall of mirrors.

 

Figure 353: there is no particular difference between a stationary light clock and a photon bouncing at right angles in a 'hall' of two opposing mirrors.

Our hall of mirrors is nowhere near as complicated as the unflattering set up you might find at a fairground, all we need imagine is two extremely long, perfectly flat, and perfectly parallel opposing mirrors. In other words just the same set up as a single light-clock but stretched out a few million Km in one direction.

With this set up we can simplify and observe some interesting points. Just going to one end of the hall of (two) mirrors, or ‘stretched light-clock’, we can set up a photon to bounce between them at a perfect right-angle and thus mimic everything we observe with a simple stationary light-clock.  More interestingly we could also send a photon between, and also down along the hall of mirrors, at say ‘45 degrees’. By doing this we are effectively mimicking a separate, independent light-clock that happens to be moving off to the right at some fraction of the speed of light. Now because we are using the idea of a photon just bouncing down a long fixed hall of two opposing mirrors, we can imagine the zigzag path created by the angled photon, and imagine it travelling at the speed of light as it is in transit between the mirrors, while also progressing more ’slowly’ along the hall.


Figure 354: A Photon bouncing 'along' a hall of mirrors is similar to a moving light clock as far as the photon is concerned.

The greater we make the angle we send the photon the more the situation becomes like a faster moving light-clock, (or like our neurotic fish trying to keep up with the catamarans faster moving floats), in that more and more of the photons motion is used, or directed to be along the hall. So we seem to observe more of a change in the ‘location’ of the photon – as opposed to just observing a lot of ‘local’ (back and forth, returning to the same place) change.

However we can also consider that this is a very simple experiment, all we are really imagining, or even actually doing, is sending a photon on a journey somewhere. In this case it just happens to be between some perfectly stationary mirrors – as opposed to us having to consider a seemingly more complicated journey inside a ‘moving light-clock’.

Experimentally we can adjust the angle at which we send the photon between the mirrors from being ‘straight across the hall’ such that it just bounces back and forth at one end of the hall to closer and closer to ‘straight down the hall’ so the photon uses more and more of its motion moving down along the hall than it does across it.

Ultimately we can send the photon straight down the hall; in this way it becomes similar to the fish trying to swim between catamaran floats that are moving at the fishes maximum swim speed. In this situation, (we would say that) the photon, like the fish, thus uses none of its motion to ‘complete ticks’ between the mirrors/floats. In the basic ‘light-clock’ experiments this is the same as saying ‘as a light-clock approaches the speed of light time within it slows down – and ultimately, for a light-clock moving at the speed of light time will effectively stop!’

The significance here being that if we are saying ‘a clock is something that shows or measures time’, then by saying a moving light-clock slows, and theoretically stops, as it approaches ‘C’, we are also effectively saying that ‘Time slows for moving objects, and effectively stops at the speed of light’.

Over extrapolating the observations.

Here, hopefully I have both clarified and (temporarily) confused things, perhaps a little like the effect we get when pulling apart the threads of a tangled piece of string, it seems to make things harder to see but it is sometimes the best way to actually make things easier to understand.

 What I am trying to show is that in the fish analogy it is easy for us to see that as the boat moves at speed nothing particularly mysterious happens (especially time wise),  the fish just ends up ‘swimming in a different direction’. As observers we may like to label these directions ‘float to float’, or ‘in the direction of the catamaran’, or we may call them direction ‘Y’ or direction ‘X’. But the laws of nature, the fish, the boat, and the water don’t know or care[7] how we choose to label and compare the motion we see.

And in particular the laws of nature don’t know or care that we choose think of travel in the ‘Y’ direction (oscillating between the floats or mirrors) as being to do with ‘time’ or like the ticking of a clock– while we also choose to see direction ‘X’ as being to do with ‘actually physically changing location’.


Figure 355: A photon bouncing along a hall of mirrors at a slight angle is similar to a fast moving light clock, travelling straight down the hall it is similar to a light clock moving at the speed of light.

Make no mistake, I am not suggesting that the effect that is generally seen as and called ‘time dilation’ does not occur or is insignificant[8]. Ultimately the idea of the ‘twins paradox’ experiment for example says that if you stay on earth while your twin travels a great distance and returns you could literally end up with grey hair and ‘laughter lines’ while on return your twin may have ‘aged’ only a few days, and although it hasn’t been proven with actual twins, there is a proven phenomena at play, and it does result in ‘moving things’ being made to change locally ‘within themselves’ more slowly, but I am suggesting that this is not to do with the ‘dilation’ or slowing down of a thing called time e.g. on board a space ship moving at great speed – it is just to do with the dilation or slowing down of ‘change’ on board a ship moving at great speed. The difference being that ‘time’ is apparently a thing that in some way exists (i.e. perhaps merged with space to as in space-time) and has a ‘past’ and a ‘future’ as part of its existence – though time and all of its properties are never tangible, while change can be directly seen to just constantly happen wherever energy is released, and creates physical evidence of its happening in any matter existing around something that is changing. XXX tidy

Therefore what I am saying is that while they seem to be phenomenally and fundamentally very different things to us ‘local change’ is the same as ‘change in location’.

Time and motion do not exist... only motion does.

To merge these two things, ‘local change’ (that which we see as the passing of time) and change in location (that which we see as movement over distance) consider the following chain reasoning that hopefully combines all of the ideas explored above…

 


1 -A stationary light-clock holds a photon oscillating back and forth within in the same defined area, and seems to show that time exists and flows at a constant rate for static objects.

 


2 -A moving light-clock seems to show that time slows down… because (from an outside point of view) the trapped photon now has to travel diagonally, and move sideways with the box over some significant distance to keep its meetings with the mirrors – and because all change can happen only at up to the speed of light every interaction (in any object or person etc) moving with the device will be similarly slowed.

 


3 -Ultimately, if the light-clock moves at the speed of light, the photon trapped within it will have to be travelling at a completely slanted or elongated way and thus will be using all of its motion just to keep up with the device, thus the photon will have no motion left to use in moving ‘up and down’ between the mirrors. Any attached ‘tick counter’ will never be triggered by a photon hitting a mirror, and thus the counter will be seen to ‘stop’.

 – seeming to show ‘time has stopped’[9]. As shown in the previous section the same situation can be replicated by sending a photon down a hall of two fixed mirrors at an appropriate angle. If the angle is not completely ‘left to right’ the photon will keep bouncing between the mirrors, if it is completely left to right – parallel to the mirrors, it will mimic the ‘stopped clock’



4 - But now consider what happens if, while the photon continues on, without affecting its path, we take away the original mirrors...

 

 Now we are left with just a lonely photon travelling in a straight line...


 5- But then, again, without affecting the photon as we do it, we put in place two other mirrors, in front of and behind the photon.

  

 

As we do this, the very same unhindered photon suddenly seems to be part of a stationary light-clock with a photon all set to bounce back and forth at perfect right angles to its mirrors, thus apparently showing ‘time’ ticking by at its normal, or maximum rate.


Is the ‘clock’ ticking or not – has time stopped ?

This situation, where we seem to have either a completely stopped clock, or a normally ticking one depending on how we arrange our mirrors around it, can look very confusing if we try to understand it with the instance that ‘time’ exists , and that photons bouncing around near mirrors have something to do with also showing us something to do with ‘the passage of time’.

Analysing the situation is easier if we consider that the photon itself is always just travelling at the speed of light ‘C’. In most discussions about relativity it is generally accepted that time does stop for particles travelling at C. In a timeless view however we just accept that something in the process of using up all its possible ‘change’ to change location then has  no change left to ‘change itself locally’. Similarly anything doing all of its change in location in say the ‘x’ direction cannot be changing its location in the ‘y’ direction at all. Timelessly we also do not assume that the photons motion tells us anything about a thing called ‘time’ or about the rate of passage of objects through ‘time’ – or the flow of time from a thing called the future through the present and into a thing called the past. So the point of this analysis is to show how looking at the above situations in a time based way simply does not work or make sense – which should indicate that there may be errors with the assumption that a thing called time exists. While looking at the situation timelessly is easier, makes sense, and does not conjure up extra (superfluous), hard to explain, problems, and therefore perhaps the timeless analysis of the situation should be seen as correct.

XXXComplete the conclusion here.

Odometer tidies things up.

One of the problems that arises when looking at ‘time dilation’ and relative motion is that it always seems questionable as to who is stationary and who is moving. The classic example of this is what happens when we are sitting on a smooth comfortable train and become distracted inside the train while glancing at a magazine etc. sometimes when this happens, particularly near a station, we may see some motion out of the corner of our eye and identify it as another train on another set of tracks. For a moment we can be completely confused as to whether our train, the other train or both are stationary or moving.

If we imagine two spacecraft ‘A’ and ‘B’ each travelling without acceleration and passing each other in outer space who is or is not moving becomes unanswerable. For an observer on one ship it will be their own craft that ‘feels’ as if it is not moving, and the other ship will seem to whizz past it.

The problem is that this will seem to be exactly the same for an observer on that other ship. Even if there is some nearby planet to use as a third reference this wouldn’t help. If you on your ship seemed not to move at all relative to the reference planet then you might insist that you were stationary and the other ship whizzed past you. But as far as the other ship is concerned it still feels as if it is not moving, while you and the planet whiz past it together.

 This doesn’t seem that important, it’s not surprising that its hard, or even impossible, to tell who’s moving and who’s stationary in space but what is significant is that on spaceship ‘A’ plants, people and machines (clocks if you wish) will all seem to function normally, while looking through the window of ship B as it whizzes by (at a significant fraction of ‘C’) things within the ship will actually be seen to be happening much more slowly than normal.

Theory and experiment prove that if you could do this any ‘clocks’ you might observe on the other ship will seem to display time passing more slowly (say 1/10th normal speed for example) than your own ‘local’ (stationary) clock.

What is really significant about this is that because the exact same thing would seem to be true for observers on space ship B looking at you on A as the ships pass each other, then for you on A, everything on B seems to be happening at 1/10th normal speed and simultaneously for those on B, you seem to be moving at 1/10th normal speed! This seems to be physically and logically impossible, but it can be explained... timelessly.

(XXX add notes on the distinction between what might actually be observed say through windows on a passing spaceships, and what is calculated to be happening on distant fast moving objects)

 In some of the previous discussions on ‘Time travel’ it was suggested that a lot of mysteries could be dispelled by imagining a ‘glass box time machine’. If we had a machine that sat in the corner of a room such that anything put in it would change more slowly there, then some confusion or even apparent paradoxes can be clarified.

So a subject might be in the box for ‘2 weeks’ of ‘outside time’ – which would seem to be only 1 week of ‘inside time’. In this case on leaving the box the subject might explain this as them having ‘travelled one week into the future’, while to the people in the room the subject will seem to have ‘come from one week in the past’. But throughout the whole experiment everyone could constantly sit and directly observe and agree that the person in the box just constantly existed, and just moved and changed more slowly than the people outside of it. Conversely the person in the box would say those outside just moved faster so accounts would still logically tally – the point being that no signs of the ‘past’ or ‘future’ existing, and no examples of anyone whizzing ‘from the past into the future’ are actually seen, though someone insisting that time exists, and that it must be forced into an explanation of the experiment may use these intangible notions.

For the ‘relative motion’ experiment though this would be like placing two glass box machines in one room and trying to make it so that for the people in machine ‘A’, those in Machine ‘B’ could be directly seen to be moving and changing unusually slowly - while simultaneously those in machine ‘B’ also directly observed those in machine ‘A’ to be moving SLOWLY!


This seems logically impossible, for one to see the other as moving more slowly or quickly is fine, but for both parties to see the same effect ? How would things appear to both parties if they stepped out of the boxes together, who would be in whose past or future, or more simply who would have been able to get more done than the other while both were in identical machines.

This situation is easily resolved however of we consider again the idea that only change exists, and consider again the idea of light-clocks (XXX poss rename all light clocks to light boxes to clarify) with built in odometers, or ‘trip meters’. With trip meters measuring the ‘distance covered’ by any light clock, (i.e. the distance between the space ships) and adding this to the light clock ‘tick counter’ (which really just adds up the distance the trapped photon has covered within the box) in the correct way we have seen that given two such clocks at rest relative to each other their counters stay in sync. And even if one clock is moved away, although its photon seems to slow down the trip meter adds on the fact that other motion has occurred, and so both device’s counters still always show identical values.


Now we can imagine being with one clock in outer space, with no sensation of motion, and seeing another clock whizz past us. In this case we do see what we may call the ‘clock’ part of the other device running slow, but if we consider ourselves to be stationary, and then constantly add on the ever growing ‘change in distance’ created as the other clock moves away from us, to the ‘slow change’ this other ‘slow’ clock seems to show us,  then we would agree that the total change the other system is going through (by ticking and moving) is exactly the same as the amount of change we are experiencing by just sitting at rest and ticking.

Likewise, on the other ship, they feel stationary, and their clock seems to them to be running normally while ours looks to be (is calculated to be?) running slow as we whiz past at speed. On this other ship however they locally add on the change in distance we seem to be creating between the ships as we rush away to our ‘slow running clock’, and in this way they agree that we are going through the same amount of change as they are.


Figure 356 the counters on a stationary light clock - and a moving one - will both always remain in perfect alignment or synchronization ( for want of a better term) if the counters display the combined change in location and internal action.

So the reason we could not simulate this effect with two stationary glass box machines, such that we could see what was going on (and both each sit side by side while watching the other apparently moving more slowly than ourselves), is that the two parties must be moving relative to each other, because it is not just the ‘speed’ that causes the effect, it is the actual  physical motion, the accumulating ‘distance’ or ‘change’ (in location) that is also essential.

In relativity we often ignore the fact that party A will have to end up billions of KM away from A in an actual light clock experiment event because it seems trivial, but it is in this detail that what we see as ‘time dilation’ can be re-explained without the need for time- which is of course the point of this book.

When this important factor (that A and B end up physically a significant distance apart[10]) is taken into consideration then we can consider how things must seem if the two clocks are brought back close together and compared. What we would find is that no matter what location or object we chose to bring them to as an agreed ‘stationary meeting place’, as long as the devices on board counted up all change, and did not take the incomplete and illogically biased view that one type of motion ( e.g. of a photon between mirrors) was more important than another (the motion and change in position of the entire device) then we would see that the ‘clocks’ would again tally, while in motion, and wherever we brought them to meet at rest side by side.

So the apparently impossible or at least deeply mysterious problem of A seeing B as being slow while B sees A as slow really boils down to a great deal of change (local and positional) happening between two parties, but this change being interpreted in different ways.

(A sees B changing position a lot, and this change in position ‘eating into’ B’s change locally – but seeing the two types of change add up to an agreed total, while B sees A changing position a lot, and this eating into A’s local rate of change. – while what they are really both agreeing on is that a photon can only go ‘up and down’ so much while also covering some agreed ‘left to right’ distance between them.

That A sees B as changing slowly while B sees A as running slowly seems impossible – but for A to feel they are stationary and to see things as if ‘B is moving away’, while ‘B feels they are stationary while ‘A is moving away’ is pretty easy to understand.

If we then see that ‘change’, be it change in the position of the tip of second hand around a numbered dial, or the change in position of the tip of a second hand from some geographical location as being the same thing – just ‘change in location’, we see that there is not ‘change in position’ – and the passage of time’ – but just internal and/or positional ‘change’.



Fig 7 B: In this second version of the diagram we can consider that as the 'clock' moves 'location', and the tip of the hand rotates, all things are of course just moving 'location'.
in the case of the hand 'tip' it thus has to move further. if the whole device is moving (and it cannot exceed 'c'). 

The key is to see the 'clock' as just a (possibly misleadingly named) 'machine' that displays 'motion'.
And to be very wary of seeing it as a thing that proves the existence of a thing called 'time' - which flows from an 'invisible future' into an 'invisible past'. So whether just the rotating tip of a hand on teh machine moves, or whether the whole machine also moves, things are just moving. 


Figure 357: whether the hand on a dial changes location by rotating around the dial - or because the entire 'clock' has moved makes no difference. and in changing location all the hand does is prove that things can change location - not that a thing called ‘time’ also exists’.

XXadd here – digram – distance is the same as ‘stored changed’ a-b = 300000km etc distance IS change – there is only change  - only distance and motion- 1km of change – fix diagram arrow above

 



[1] A ‘light-clock’ being a box in which two parallel mirrors face each other a fixed distance apart such that a single photon released between them will repeatedly reflect back and forth giving a simple and accurate example of the ‘ticking’ of a clock

[2] Although we can agree that ‘units’ such as ‘metres’ are an odd mixture of a real thing ‘distance’ and a useful notion (metres) we should not confuse this with the idea that ‘seconds’ are ‘units’ of ‘time’ in a similar way, and critically it is not scientific to try and shoehorn this incorrect comparison into being some kind of proof that ‘time exists, because distances exist’, and ‘seconds’ kind of exist - because metres kind of exist.

[3] Note also this counter is steadily incrementing not because ‘time is passing’ but because the photon is moving. That ‘things can move’ proves ‘that things can move’, bluntly adding to this observation - ‘things can move’ but they ‘need Time’ to move: therefore ‘time’ also exists’ is not scientific.

[4] We are of course pretending in this analogy that the fish is like a photon travelling in free space and that it does not get exhausted and actually slow down its speed though the water. And also ignoring the fact that a fish needs a medium to push against to move (water) while light does not.

[5] Just as you and I don’t tend to notice that we, and the entire Earth can be said to be constantly moving through space at some significant fraction of the speed of light.

[6] This is another way of showing that if something is coasting steadily in one direction, this is basically identical to that thing not moving at all – i.e. the principal of equivalence Xxcheck term.

[7] I.e. it is not significant to the universe that ‘we’ know or care about something, or choose to see one motion or direction as being more important than any other etc

[8] Note also we are not addressing other effects of special relativity here such as ‘length contraction’ and ‘mass increase’ – real as these effects may be just because a particle or object gets shorter or more dense under certain conditions this does not also point to or prove or the existence of ‘time’ and/or a ‘temporal’ past or future which is the matter of discussion here.

[9] Though if the ‘trip meter’ set up is added as described in earlier sections showing the total change in location all will be fine.

[10] In other words! A static distance, say 1 billion km, is an amount of change. And even if A and B are stationary relative to each other we should always consider that there is an amount of ‘distance/change’ between them. 

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