[timey (OP)]

Colin - I read a lot of books about physics including information about where physics experiences problems and then applied logic.

I cannot write the logic in mathematical notation which is why I am here on the forum asking for help.
If I were able to describe the logic in mathematical notation I would not be here asking for help with it, I would have presented my model straight to peer review.

I can understand that it might seem impossible that I could derive a model of a universe without employing some type of recognisable methodology to purpose.   But for me I am merely thinking about a problem in the same sort of terms that I employ to understand anything.  And this just incorporates moving scenarios based on observation and given parameters around in my head (much like computer simulation) from every different perspective to see how they work under different remits...

Much like scales in music, there are only some scenarios that will work with each other harmonically, and this limits the physical possibilities by elimination.

I'm sorry Colin, but that is the best I can do.  I did not go to school.  My brain does not use the same methodology as yours.  I have arrived at my conclusions (after over 8 years of serious thinking btw) by means of a route you simply would not recognise.

[jeffreyH]

There are certain things that must be understood before any hypothesis can be developed. Firstly you need to understand how to model observable phenomena and how this model may predict the outcomes of those phenomena. If predictions do not match with the results of further experimentation then the model is incorrect. This all requires an understanding of how certain quantities are made up, what their constituent dimensions are. Also how to correctly manipulate those values mathematically. Even geometry is mathematically based. If you don't have the mathematics how can you have a model of the phenomena?

[timey (OP)]

I understand how the model fits together mathematically.  I do understand maths.  I just don't know how to write it out in notation that you may understand it is all...

Now do you wish me to describe my model in words that someone who does know how to write mathematical notation may calculate this model... or not?

[Colin2B]

I have arrived at my conclusions (after over 8 years of serious thinking btw) by means of a route you simply would not recognise.

The route doesn't matter - as long as you are not claiming, like some here, that your ideas were revealed to you by aliens - what does matter is that you make your ideas as understandable as possible.

Now do you wish me to describe my model in words that someone who does know how to write mathematical notation may calculate this model... or not?

Yes, BUT.
The but is that, as above, it need to be understandable.
When you say things like "I am simply ditching the notion attached to the 'length' of a wavelength being velocity related and attributing this 'length' as being time related." and "Calculation: e of wavelength is inversely proportional to length of second." you clearly have an idea in mind but the way you describe it makes no sense physically or mathematically so you need to find alternative ways of describing it. Otherwise none of us can turn it into mathematical notation. That's why I suggested examples.
Please continue, but bear in mind that our comments and questions reflect the fact that you are not getting your message across.

[timey (OP)]

Erm... Nope, aliens have not told me anything...
It has (chuckle)) crossed my mind that I might be an alien trying to tell you lot something.  I have indeed made a thorough check for scale, tail, or any peculiarities at-all to my seemingly humanoid veil.  And you know... the psychology books tell me that it is quite normal to find oneself feeling alienated...

Ok - you are not understanding how a length of distance (such as a wavelength) can remain the same length under the premiss of variable time, so:

Thought experiment;
Part 1:
We ask Janet and John to make some measuring tests.  We give them a car that runs at a constant of 10 metres per second and has a mechanism that makes a mark on the track for every metre that it travels.  We ask Janet and John to start driving when the green light shows on the dash board and stop when the red light shows.  Janet and John take off at exactly 10 metres per second maintaining this constant speed and stop 10 seconds later.  We can see 100 marks evenly marked out on the track in lane 1.  The space between each marker is 1 metre long.

Now, without telling Janet and John what we have done, we extend the length of a second by 10% via the timing between the green start light and red stoplight, and ask Janet and John to drive for 100 metres up lane 2 of the track.  After 10 of those lengthened seconds have passed, there are now 110 marks on the track and Janet and John's journey length in lane 2 appears extended.
Janet and John are scratch their heads.  They reel out a measuring tape, and check that the length of the metres marked out in lane 2 match the length of the metres marked out by their previous journey in lane 1.  There is no difference in metre length, just the number of them, and in understanding that a constant speed was maintained throughout, they conclude that a metre must be somehow stretched in lane 2 relative to lane 1.
We suggest that they try lane 3, where we again further extend the length of the second, this time by 20% more than it's original length in lane 1.
Janet and John immediately notice the correlation between the extra distance travelled in lane 3 relative to lane 2 and lane 1.
(Here we can see that the length of a journey can 'appear' to be longer in distance if it takes a longer amount of 'time' to travel at a constant speed.  The defining factor is the measuring device.  The car is set to make marks every metre at 10 metres per second, and the second it is set to mark out metres at is the original length that a second was in lane 1, and this length of second was not changed for the measuring of lane 2 and lane 3. *this is synonymous to calculating frequency per standard second*...
Clearly if the car was reset to make marks at 10 per elongated second, there would only be 100 marks, and the spaces between each marker would measure 1 metre)

Part 2:
We then provide Janet and John with an exact same copy of the car they are driving in order that they may split up and compare journeys, and we make lane 1 of the track into a 100 metre circle.  Lane 2 and lane 3 are 110 and 120 metres respectively as the radius increases.
We decide that we are going to provide both Janet's car and Johns car with an onboard clock ticking relative to a stationary clock in their lane... but we are sneaky!  We have made the clock in lane 2 run faster relative to the clock in lane 1....

...John measures lane 1 and to give him a hint we tell him that his onboard clock is running slow relative to the stationary clock in his lane.
Janet measures lane 2 and to give her a hint we tell her that her onboard clock is running slow relative to the stationary clock in her lane.
Both Janet and John tell us that they are experiencing nothing slow about their clocks, so we ask them to check their clocks against each other and they report back that each finds the other out of sinc and running slow...
Janet and John are scratching their heads again...  They stop the cars and each studies the stationary clocks located in their lanes, and Janet notices that Johns clock in lane 1 is running slow comparatively to hers, and John notices that Janet's clock in lane 2 is running fast comparatively to his...
So here we can see that Janet and John a) now believe that a metre can be stretched in lane 2 relative to lane 1, b) that time is running faster in lane 2 than it is in lane 1, c) that if time is going faster in lane 2 relative to lane 1, then a moving body would travel further than 10 metres in a faster time, and d) that clocks in relative motion to each other will read each other as being both slow and length contracted.

We on the other hand have the benefit of knowing that a second is running 10% slower in lane 2, relative to lane 1 and 20% slower in lane 3 relative to lane 1.
We also have the benefit of observing all relative rates of time from the observation point of a standard second which we are holding all other rates of time relative to...

But please note that I have made a transgression.  One cannot have 2 rates of time happening in one reference frame, or can you?
If we equate Janet, John and their cars as being synonymous to light which has no rest mass, being unaffected by gravity potential, and that things with mass are affected by gravity potential, then we can say that lights wave length does not get longer or shorter in distance, it just takes a longer, or shorter amount of time to cover the same distance, as set out in part 1 of the thought experiment...   And we can say that light is travelling through this contra directional gravitational time dilation of the gravity field associated with the open space surrounding M.  (please note that a contra directional gravitational time dilation for empty space negates the necessity for relativistic mass, for both light and matter)

Then we can say that mass is affected by gravity potential,(although the value of m does not affect the value of gravity potential m experiences near M), and that time runs faster for mass at a higher gravity potential...

I have talked about adding e to m via temperature in the black body experiment, suggesting that it is the energy of m that is producing the frequency of the light emissions, adding energy increases frequency, and that the frequency of the light emissions can also be viewed as a contra directional time dilation related phenomenon...arising from (what my model suggests is) a GR 'mass in relation to energy' time dilation phenomenon here:

http://www.thenakedscientists.com/forum/index.php?topic=68849.0

[alancalverd]

Now, without telling Janet and John what we have done, we extend the length of a second by 10% via the timing between the green start light and red stoplight, and ask Janet and John to drive for 100 metres up lane 2 of the track.  After 10 of those lengthened seconds have passed, there are now 110 marks on the track and Janet and John's journey length in lane 2 appears extended.

No, there will be 90 marks. Or maybe not. You have given inexplicit instructions. The first time, they apparently gauged 100 meters by travelling at a known 10m/s for a known 10s. If you lengthen the second to a newsecond and tell them to drive for 10 news, they will make 100 marks each 1.1 m long. If you lengthen the second and tell them to drive 100m, they will make 90 marks in 9 news. But if you adopt the ISO definition of a meter, they will make 100 marks in 10 news.

"Sod this" says John. "Let's have a snog instead".  "I'm not sure" says Janet "our relationship is as inexplicit as Timey's instructions. Are we bro an sis, or just homies?" See John frown. John does not dig street slang.

Janet has a book. Janet opens the book. Janet reads to John. "L(v) = L(0)/sqrt(1-v^2/c^2)"   

John says "If c is a universal constant, Timey is talking nonsense".

Janet is grumpy. See Janet smack John. John has no rest mass. v(Jo) -> c. Estimate Janet's recoil velocity if m(Ja)> 0. John has red shift. See John go red.

[timey (OP)]

Bottoms up Alan - Get back on it when you're sober aye

For anyone else, the mechanics of the car are set to make a mark every metre at 10 marks per second in lane 1.
In both part 1 and part 2 of the thought experiment, the second that the car is set to make marks at is not changed for measurements in lane 2 or 3.  Only the times between the start and stop light on the dashboard of the car are changed, (ie: extended.)

[guest39538]

I have a question regarding red-shift,

How can light become red-shifted a longer wave-length than 400nm , which is ''blue'' , when the light between bodies is apparently ''gin-clear'' and not blue like the sky above our heads?

red is ''faster'' than blue but ''slower'' than ''gin-clear''.

[alancalverd]

For anyone else, the mechanics of the car are set to make a mark every metre at 10 marks per second in lane 1.

And there's your problem. Every meter or 10 times per second? You can't have it both ways says Janet - but let's stick to physics. The meter is defined as the distance light travels in a fraction of a second, and a second is defined as whatever the clock reads in the car, which will be different from the second on the observer's clock.

[Colin2B]

Bottoms up Alan - Get back on it when you're sober aye ;

For anyone else, the mechanics of the car are set to make a mark every metre at 10 marks per second in lane 1.

Alan is right.

Now, without telling Janet and John what we have done, we extend the length of a second by 10% via the timing between the green start light and red stoplight, and ask Janet and John to drive for 100 metres up lane 2 of the track.  After 10 of those lengthened seconds have passed, there are now 110 marks on the track and Janet and John's journey length in lane 2 appears extended.

Fortunately, in the back of the car are their 2 children, Charlene and Darren, who are studying physics at school. Having stopped chanting "are we there yet" they look at the 110 marks on the track which they are told were made in the same time as the 1st journey. They therefore conclude that the frequency of the marks is greater than in the 1st journey and using c=fλ they work out that they were travelling faster than the 1st car and hence covered a greater distance.
They then sit their confused parents down and point out that if the speed of the cars - or light if that's what we are dealing with - is constant so that both cars completed the journey in the same time, then the measurement of distance must be wrong, they then recalculate the distance between marks which is indeed contracted if c is constant.

The problem is of course, as explained by Alan, that you have set up an experiment where you are mixing measurements and calling them the same when they are not.
If you want to do the experiment correctly you need to actually change the 'rate of time' for each car, but start and stop the cars after a fixed interval eg by a flashing light to synchronise the beginning and end events in each frame.

[jeffreyH]

Janet and John appear to require an intervention by social services.

[timey (OP)]

Nope - Alan is wrong.  But why he is wrong is what's interesting...

The experimenters are the people controlling the time here.  The experimenters have measured 1 metre.  They have said that at the constant speed the car is travelling that 10 metres will be marked out per second as their clock reads.  There is no clock in the car at this point.  The journey time is defined by a green start light and a red stop light on the dashboard of the car, and the experimenters allow ten seconds as their clock reads between start and stop light on dashboard of car for lane 1.

In lane 2 journey, nothing has changed with the car.  It is still marking out 10 marks per second as per the time on the experimenters clock.  What changes in lane 2 is that the experimenters add 10% to the length of a second, as read by their clock, to the duration of time between green start light and red stop light on dash board of car.
And the duration of the time between start and stop light is again extended in lane 3...

This part of the thought experiment is designed purely that it may be understood that a) by holding the second that these marks are being measured against constant, that distance will become stretched, and b) that if one then doesn't hold the second that these marks are being measured against as constant, but instead increases the length of a second that the car makes 10 marks at proportional to the increase in duration of time between start and stop light, then the distance remains constant.

Part 2 of the thought experiment is still slowing time down by 10% in lane 2, relative to lane 1 (and the experimenter's clock), and then adds clocks into 2 cars placed in lanes 1 and 2.  A pretend gravity potential difference is signified by placing additional stationary clocks in each lane, where the experimenters have made the clock in lane 2 run faster relative to lane 1, (the experimenters have slanted the clock in lane 2 to run at 90% of the length of a second as their clock reads and lane 1's stationary clock reads as the experimenters clock reads)  Please note that the time between start and stop light in lane 2 journey is still extended relative to the lane 1 duration of stop and start by 10%...(please remember that the duration between stop and start light on dashboard for car in lane 1 is 10 seconds as per the experimenters clock reads, and as per the stationary clock in lane 1 reads)

Part 2 of the thought experiment is designed to show exactly how, despite the addition of this slower running second, those children in back of car can still come to the conclusions that they have. (these conclusions being current model physics)

There has been some comment about how this addition of a contra directional gravitational time dilation will render the speed of light as variable, but the comment is wrong...
The speed of light REMAINS constant IN EVERY reference frame of the universe under the remit of my model and this contra directional gravitational time dilation that I propose...

But where distance and length are variable under the remit of the current physics model, both distance (lengths of empty space between masses), and lengths (distances comprised of mass between empty spaces) are maintained as constant, and the curvature of space between masses, (ie: not as the crow flies), that 'adds distance' to space, is time dilation related.

[alancalverd]

say that lights wave length does not get longer or shorter in distance, it just takes a longer, or shorter amount of time to cover the same distance,

Lots of physics words here, but no physics. The only thing we know as absolutely true in physics is that the speed of light is constant.

[timey (OP)]

...and the speed of light 'is' kept constant under the remit of my model!

Yes, agreed, this is not current physics model, but... divide extra distance by constant speed for extra length of second.  What's not physically possible about that?

In looking for a means to ditch Hubble's red shift velocities for a contracting universe of the type I describe, it is a simply solution to state length of wave as a constant, and length of second as variable, for a direct description of the red shift observation to distance correlation.

In fact there just isn't any other possible means of describing the red shift distance correlation for a contracting universe of the type I propose, in much the same way as there isn't any other means for GR to describe the universe without dark energy and dark matter!

[Colin2B]

The experimenters are the people controlling the time here.

No, you are controlling this experiment and the reasoning of Janet and John.

This part of the thought experiment is designed purely that it may be understood that a) by holding the second that these marks are being measured against constant, that distance will become stretched

No, this is not understood. It is you who suggests this conclusion.
If Janet and John are given no information about the travel time, then based on the number of marks and the distance between them the only logical conclusion is that they have traveled further than lane 1 and the distance is not stretched.
If you inform them that the time was the same for each journey then their children can soon work out that is untrue as previously demonstrated - even though they might reach the wrong conclusion.

The problem is that the thought experiment is not a true representation of what happens when journeys are made in lanes with differing rates of time. In your experiment only the clocks are set to run faster, no one ages faster. Let's try a different experiment where the lanes are at different GP and time passes more quickly.
Consider 3 cars in 3 lanes (frames) where time passes at different rates 1x, 1.1x and 1.2x - not just clock ticking faster, but time actually passing faster. Start the cars together and stop them together on the same signal.

Lane 1 rate= 1x.    Car travels for 10s, leaves 100 marks and travels 100m.
Lane 2 rate= 1.1x. Car travels for 11s, leaves 110 marks and travels 110m.
Lane 3 rate= 1.2x Car travels for 12s, leaves 120 marks and travels 120m.
All the cars have, in their own lane, the same speed, same frequency of mark making, and same (wave)length between marks - however, all the cars started and and stopped on the same signals. This really isn't a problem for any of the car drivers until one of them wants to measure the length between marks in another lane using the elapsed time in their own lane, then they discover that the frequency and wavelength in the other lane are different to their own.

[timey (OP)]

Thought experiments are known for not being true representations. The whole point is to set a scenario with the idea that one thinks in the terms set out to the purpose of an understanding that the deviser of the thought experiment wishes to portray.. (admittedly I could be more adept, but I am trying)

Ok Colin - You have worked out that if time is going faster for Janet and her car in lane 2 then the car will travel further at the same speed.  You do recall that a gravity potential difference between lanes 1, 2 and 3 was outlined in part 2 of the thought experiment.

In part 1 of the thought experiment no such GP was added.  The experimenters did not tell Janet and John that the time period between start and stop light on dashboard was extended for lane 2, and extended again for lane 3.
All Janet and John were told was that the car makes a mark on the track every metre at 10 metres per second.   
On the basis of this information and the premise of their first journey in lane 1, Janet and John can only arrive at 1 of 3 conclusions...
That a metre is becoming longer in lane 2 relative to lane 1. and longer again in lane 3 relative to lane 2 and lane 1.
Or that a second has become longer in lane 2 relative to lane 1, and longer again in lane 3 relative to lane 2 and lane 1.
Or that a second has become shorter in lane 2 relative to lane 1, and shorter again in lane 3 relative to lane 2 and lane 1.

I, the thought experiment divisor, have decided that Janet and John choose to view their part 1 of the thought experiments journey's in lane 2 and lane 3 as stretched.
I, the thought experiment divisor, then decide that the experimenters should introduce the concept of time dilation to Janet and John by making a clock run 10% faster and 20% faster in lane 2 and 3 respectively relative to lane 1...
...But I, the thought experiment divisor, decide that the experimenters should continue not to tell Janet and John that there is a 10% slower and 20% slower rate of time inherent to lane 2 and lane 3 respectively relative to lane 1.
(Please note: there is a distinct difference being drawn between the increased rate of time (ie: faster time = shorter second) for a clock in the lane, and the decreased rate of time (ie: slower time = longer second) for the lane itself.  Do I here you ask yourself 'well surely one would cancel the other, right?' ...?

Well now, this is where things start getting interesting, and this is why:

Janet and John are split up into 2 exact same cars and given on board clocks.  To bring this into the realm of visualisation... I, the thought experiment devisor, am now going to introduce relativistic speeds to the thought experiment.  The cars are still marking metres per second as per the experimenters clock reads, but the speed of the car is now set to exactly the percentage of the speed of light that causes a length contraction of 50%.

Ok - so John is measuring lane 1 which is pretty straightforward.  John starts his journey at the green start light on his dashboard and stops at the red stop light on his dashboard 10 seconds later.  There will be x amount of marks on the track at the constant speed of y, this being the percentage of the speed of light that causes 50% length contraction.

Janet is measuring lane 2.  The clock in Janet's lane is reading normal to her, as is the onboard clock in her car, both of which are ticking at the same rate.  She knows that her clock is reading normally because there is no evidence of events occurring faster, or slower in her car, or in her lane.  But the experimenters have told her that her clocks in lane 2 are running faster by 10% relative to Johns clocks in lane 1...
I, the thought experiment devisor, have told the experimenters not to tell Janet and John about the 10% and 20% extended time between start light and stop light in lane 2 and lane 3 respectively relative to lane 1...

...Now according to your analysis Colin, the fact that Janet's clocks are experiencing a rate of time that is faster than John's clocks are experiencing, means that Janet's car in lane 2 will mark out more metres than John's will in lane 1.
But when the experimenters extended the duration of time between start and stop light on dashboard of Janet's car, the car also marks out more metres than John car does in lane 1.
So under the premise of this thought experiment a question arises as to what the outcome of these 2 effects working oppositely to each other will do....
...Will the distance covered be 20% longer?  Or will the distance covered still be 10% longer?  Or will the opposite effects cancel each other out and the distance remain the same as in lane 1.

Before we can really make a definitive answer to the questions I've posed above, we must consider that both Janet's and John's onboard clocks will be slowed by their speed accordingly relative to the stationary clock in their lane.
But hang on a mo, didn't Colin say that if Janet's clock in lane 2 is running at a 10% faster rate than John's clock in lane 1, that Janet's car would travel 10% further than John's car will in lane 1?
...So does this mean that when Janet's and John's onboard clocks are slowed by their speed, that the distance the cars travel is reduced?

"NO!!!" shouts the whole physics community, "You don't understand relativity." ...they chant in unison. "The clock in motion is ticking normally and only appears to be ticking slow to an observer from another frame of reference."...
"Yes, I know..." she said... "But when calculating time dilation for a satellite, doesn't this include the fact that the satellite is experiencing a difference in time dilation due to both the effects of gravity potential difference and relative motion with respect to the comparison clock on earth?"
"Nope" says the physics community. "We still view it as being relative"
"Even when NASA states astronauts on satellites as ageing in keeping with their time dilated clocks?" she asks.
"Hmmm" says the physics community.
"Does the clock in motion appear to be travelling slower as well?"... She adds.
"NO!!!"... they all chant, "But it is length contracted!"

I, the thought experiment devisor, now re-introduce the fact that the speed that Janet and John are travelling at is a percentage of the speed of light that causes 50% length contraction...

If the rate that Janet's stationary clock runs at in lane 2 has a bearing on how much distance Janet travels in lane 2, then the percentage of the speed of light that Janet will be travelling at will no longer be the same percentage that causes 50% length contraction.***
Then we can look at the fact that in simulating a longer second for lane 2 we are stating the speed of light as being 299 792 458 metres per second that is 10% longer than a second in lane 1.
The speed that the car is travelling at is the percentage of the speed of light per second that causes 50% length contraction and this second is as per the length of a second in lane 1.  A longer second will result in that speed being a higher percentage of the speed of light per the longer second of the lane 2 reference frame.
You may now tell me that by introducing this contra time dilation that I have compromised the speed of light.  But I now refer you back to the paragraph above marked at the end with 3 stars, and tell you that you also have compromised the speed of light...
...In saying that Janet will travel further in lane 2 because her clock is running faster, the percentage of the speed of light that she is travelling at is lower than that which would cause 50% length contraction.

*

Next we can move on to looking at how these differences, when viewed under the premise of the thought experiment, compare when totting up between lane 1 and lane 2, and try to answer some of the questions posed earlier.

But I'll check to make sure we are all good so far...

[alancalverd]

"Yes, I know..." she said... "But when calculating time dilation for a satellite, doesn't this include the fact that the satellite is experiencing a difference in time dilation due to both the effects of gravity potential difference and relative motion with respect to the comparison clock on earth?"
"Nope" says the physics community. "We still view it as being relative"

On the contrary, both effects are always taken into account. Interestingly, the orbital speed at 9550 km altitude exactly compensates for the gravitational shift at that altitude, but for all other clocks we need to apply both corrections to align with Zulu time. 

[timey (OP)]

Hence the latter comment:

"Even when NASA states astronauts on satellites as ageing in keeping with their time dilated clocks?" she asks.

So the question arises, under the premise of this thought experiment - does the slowing of time experienced by Janet and John, when travelling at the percentage of the speed of light that causes 50% length contraction, cause the distance Janet and John's cars travelled to be extended in the same way that Colin suggests that an increase in the rate of time caused by gravity potential will?

(...and yes, that is an interesting correlation Alan.  Further out than this radius, the slowing of time caused by velocity of motion should be greater than the increase in the rate of time caused by difference in gravity potential.  The polarities are swapped.)

[alancalverd]

A reasonable conclusion. For any observer in a finite gravitational potential, the maximum gravitational blueshift will be from where g = 0, i.e. "deep space", but there's no limit on velocity redshift.

[Colin2B]

But I'll check to make sure we are all good so far...

Not yet, some points to address before moving to rest of your post

Ok Colin - You have worked out that if time is going faster for Janet and her car in lane 2 then the car will travel further at the same speed.

Didn't have to work it out, it is what we've been saying in the other threads. It is inherent in the simplified examples I gave. Probably my fault for assuming you would understand the implications.
However, one point of clarification, it is travelling further at the same speed only because there is more time in which to do so - look carfully at the example. It may seem a subtle point but it is important.

The experimenters did not tell Janet and John that the time period between start and stop light on dashboard was extended for lane 2, and extended again for lane 3.
All Janet and John were told was that the car makes a mark on the track every metre at 10 metres per second.   
On the basis of this information and the premise of their first journey in lane 1, Janet and John can only arrive at 1 of 3 conclusions...
That a metre is becoming longer in lane 2 relative to lane 1. and longer again in lane 3 relative to lane 2 and lane 1.
Or that a second has become longer in lane 2 relative to lane 1, and longer again in lane 3 relative to lane 2 and lane 1.
Or that a second has become shorter in lane 2 relative to lane 1, and shorter again in lane 3 relative to lane 2 and lane 1.

Napoleon once said that when your enemy has only 2 courses of action available to him, and you have decided which one he will take, then you can be certain of only one thing – he will decide to take the third option. Or in this case, the 4th.
Based on the information in bold, Janet and John can only make one conclusion, that they travelled 110m and it took 11s.
We need to clear this up before moving to the rest of your post.
In the example I gave, Janet and John in lane 2 cannot do this measurement, their distance is extended when measured by someone in lane 1, but not as measured by themselves.

So the question arises, under the premise of this thought experiment - does the slowing of time experienced by Janet and John, when travelling at the percentage of the speed of light that causes 50% length contraction, cause the distance Janet and John's cars travelled to be extended in the same way that Colin suggests that an increase in the rate of time caused by gravity potential will?

It depends. They will see the distance between themselves and their destination as contracted, so taking less time. Someone who is at rest relative to them will see them travelling the full 'extended' distance.

(...and yes, that is an interesting correlation Alan.  Further out than this radius, the slowing of time caused by velocity of motion should be greater than the increase in the rate of time caused by difference in gravity potential.  The polarities are swapped.)

Excellent. We are starting to get into common understanding. Without this you can never properly analyse your proposal.