[Mike Gale]

I'm lost. What happened to our free-falling traveller? We need to establish timey's prediction for dilation in that case to ensure that her theory is consistent with experiment. If that test fails, then all other debates (like this one about h) are moot.

I think we have the scenario boiled down to brass tacks. In order to ensure we are not pushing the boundaries of GR, we are analyzing a time slice in which a free falling traveller and a stationary bystander are at the same altitude and sufficiently removed from the event horizon that Newton's laws are valid. If the velocity vector is radial, GR says the bystander's clock runs slower by a factor of (1-2GM/c²r). This is consistent with SR if the traveller is falling at the escape velocity, which means v=0 at infinity. (Any other velocity invalidates the SC solution.) I think timey's theory predicts that the clocks run at the same rate because she attributes time dilation to altitude rather than velocity.

[timey (OP)]

The prediction for the 3rd time dilation 'is' the acceleration or deceleration of gravity in relation to M.
Observed in action experimentally, and in everyday life.  Everyone knows that gravity accelerates, but current physics doesn't have a physical cause for the phenomenon.
I'm just giving a physical cause to an observation that we already make, that has previously been given no physical cause.

[Mike Gale]

You're dodging the question. These observers are at the same altitude. Never mind what causes gravity to motivate things. What does your theory predict in terms of clock rates? Faster, slower or the same?

[Mike Gale]

BTW - I described the GR cause (of accelerated motion) in Reply #338.

[timey (OP)]

No - my model does add in SR time dilation.
You do make interesting point though, because I'm not sure what the answer is to your free faller versus bystander consideration, so having a look at it, but you'll have to realise this look of 'mine' won't involve the math.

However, if we place the bystander on the radial orbital velocity where SR time dilation equalises GR time dilation and the clock reads the same rate as a ground clock, the third time dilation would be inherent to the g-field at that radius and would be the equal but opposite value to GR time dilation, whatever that would be if SR time dilation at that velocity, at that radial orbit, hadn't cancelled GR effects out.
The craft+bystander them-self would not be registering this 3rd time dilation on the onboard clock, but the motion of the craft will be affected.

Now the question arises as to whom's clock the velocity of the craft is held relative to...
Is it the ground clock?
Is it the crafts clock?
Both are running at the same rate, but if we are holding the speed relative to the crafts clock, then we must appreciate that we are stating that both GR time dilation and SR time dilation are affecting the speed of that craft.
SR measurements can't affect the speed of the craft because if they did the speed of the craft would affect the time dilation, and the time dilation the speed of the craft, and we have a catch 22, so the question is, are we holding the speed of the craft relative to the ground clock, or to the GR time dilation portion of the crafts time?

On the basis that when time is held relative to the ground clock, the acceleration of 9.807m/^2 is a measurement held relative to the ground clock, when accelerating at 9.807m/s^2 on the ground in the unchanging gravity potential the distance covered per second squared is +9.807m...
The speed required to maintain an orbital at our bystanders radius, i.e. orbital velocity, held relative to the 3rd time dilation, which is the exact opposite of what GR time dilation would be at that radius relative to the ground clock, i.e. negative value, is causing the craft to cover 9.807m in a longer amount of time.
But both the ground clock and the bystander understand that that the bystander's clock is running faster, so  if both held the speed of the craft relative to the GR time dilation the craft's clock is experiencing, then both would think that the bystander was covering 9.807m in a quicker time.

Ok - so on the basis that near Earth approximation of gravitational acceleration is 9.807m/s^2, and at 2 radii from centre Earth it is around 4.25m/s^2, whatever the value is at the particular radial we are discussing, the radial where SR effects at that orbital velocity cancel out GR effects at h from M, this value of m/s^2 will be relevant to the orbital velocity required for that radial...
So the orbital velocity for each radius will be proportional to the m/s^2 value at that radius, for the reason that the crafts motion has been slowed by the longer seconds there, and it must increase its velocity in each increasing radius in order to counter these slower seconds, and this calculation must take into addition the extra distance involved in travelling the greater distance of that radius.

So according to both the ground clock and the bystander the bystander's speed may have been affected as an increased rate, where the craft is covering 9.807m of the radial distance at a faster rate to the exact value that the craft is actually covering 9.807m of radial distance at a slower rate...
If holding the speed of the craft relative to the 3rd time dilation, this would be a slower speed.
If holding the speed relative to the GR time dilation, this would be a faster speed.
But in both cases, an equal amount of distance, i.e. 9.807m would be travelled at those speeds in both of those rates of time because we are talking about it taking a longer or shorter amount of time to travel a distance.
However... according to the ground clock the bystander and his craft would be covering 9.807m of radial distance at a speed held relative to the ground clock's rate of time, where 9.807m of radial distance covered in a faster time, or covered in an equal value slower time is being calculated as a distance covered by a speed as per the ground clock. i.e. orbital velocity.
So the difference between escape velocity for a particular radius and orbital velocity for that particular radius would be mathematically significant in relation to the 3rd time dilation.
For instance, if we were to say the bystander was orbiting the radius of 2 radii from centre of Earth, the acceleration of gravity at that radius is around 4.25m/s^2.  Where my model is saying that if we were to calculate this acceleration as per the second squared of that radius, this would be equal to an acceleration of 9.807m/s^2 at a near Earth radius at near Earth's rate of time.
In other words it just takes a longer amount of time to travel same distance, and it is only by calculating using an invariant time to measure an acceleration, that the distance travelled is reduced to being a 4.25m/s^2 acceleration.
Therefore by remit of the 3rd time dilation, the orbiting craft would only be covering 4.25m of radial distance for every second squared as per held relative to the ground clock and the speed of the craft as held relative to the ground clock would need to be increased in order to still be covering 9.807m of radial distance in the same amount of ground clock time.

It is also worth noting that where current physics holds the SR time dilation effects experienced by the craft as a speed measurement held relative to the ground clock, via the speed of the craft being a percentage of the speed of light held relative to the ground clock - my model holds the SR time dilation effects held relative to the 3rd time dilation, where the speed of the craft is a percentage of the speed of light held relative to the 3rd time dilation.
This will change the value of the SR effects being experienced by the bystander, but does not affect the rate of the speed that the bystander is covering distance at, not from an observer's point of view.  It will be the rate that the observer's own clock is ticking at that will influence his assessment of the crafts speed.
This also means that any spatial dilation that the free faller and bystander experience is a product of their own rate of time, and all actual distances remain constant.

So to sum up, the bystander at the 'current physics' radius where SR effects held relative to the ground clock are cancelling out GR effects, in my model - will this be at a radius that is closer to M?
This being for the reason that when holding the SR time dilation effects of that radius's orbital velocity as a percentage of the speed of light held relative to the 3rd time dilation at that velocity, the speed will be a higher percentage of the speed of light at that radius, and SR effects will be increased.
But... If we hold the speed the craft is moving at relative to the 3rd time dilation at that radius, the speed itself is reduced...
By calculating the reduced speed as a percentage of the speed of light held relative to the 3rd time dilation, we should end up with the same proportion of SR effects as when calculating the speed held relative to the ground clock as a percentage of the speed of light held relative to the ground clock, so the SR effects in my model would in fact be at the original radius, and synonymous to that which relativity predicts.

But enough of the bystander aye
The free falling observer would, in my model, have to start from somewhere tangible.  Let's say we dropped him at a radius where GR time dilation is twice what it is at the radius where orbital velocity SR effects cancel out the GR effects...
The free falling observer's clock is running 'that much' faster than the bystanders clock, and the bystanders clock is running at the same rate as the ground clock.

Now the question is, what speed will the free falling observer be travelling at by the time he reaches the bystanders radius?
The 3rd time dilation decrease in length of seconds at each decreasing radius in the g-field will have accelerated his speed...
Therefore whatever the value of m/s^2 acceleration existing at the radius we dropped him from in relation to what value m/s*2 acceleration exists at the bystander's radius is relevant.
However, we must recognise that when we say m/s^2, we are holding that measurement relative to the ground clock. 

The free faller's clock will have been being decreased at each decreasing radius in its rate of time as per GR time dilation...  And at the bystander's radius the free faller's clock will be the GR time dilation at that radius, minus the SR effects due to the velocity he is travelling at.
The bystander and the free faller will be experiencing exactly the same GR time dilation effects, but the experience of their own time will differ due to travelling at differing velocities.*
However, the SR effects that the free faller will be subject to will be greater at the more distant radius.  This being because the SR effects related to his speed will be being held relative to his speed being a percentage of the speed of light held relative to the 3rd time dilation length of second at that radius.  But again - we can calculate the speed the free faller is falling at as held relative to the 3rd time dilation length of second  at each radius, and this will result in the same value as holding the speed of the craft relative to the ground clock, and the speed of the craft as being a percentage of the speed of light held relative to the ground clock.

*A scenario that would be apparent if we dropped the free faller from a radius that was only a few metres above the bystander's radius, where the sequential time involved in a shorter distance for the free faller to accelerate within would be in shorter supply, resulting in a lesser acceleration.

Here we come to the crux of the matter...
Who's time are we holding the sequential time relative to?
If we are not holding speeds and distance subsequently travelled relative to time dilated clock's, then we are not holding sequential time relative to time dilated clock's, and on this consideration we must remember that the ground clock is ideas itself a time dilated clock.  There is nothing special about the ground clock's time, other than the fact that a lot of measurements are held relative to it.
We did make it simple for ourselves because the bystanders clock is running at same rate as the ground clock, but it is doing so for different physical reasons.
So - if we slice the moment in time that the free faller happens to pass through the bystanders radius at the moment the bystander is passing the free faller's location at that radius, the bystander will see that the free faller's clock is likely running a tad faster, dependent on the value of the radius he was dropped from, and the free faller will see the bystanders clock running a little slower, again dependent on the radius he was dropped from.
As far as the bystander is concerned the free faller is falling at a speed that is increasing by m/s^2.
As far as the free faller is concerned, the distance that he has fallen is increasing by m/s^2...
Again we must note that this m/s^2 measurement is being held relative to the ground clock, and that the bystander's clock is running at same rate as the ground clock.
Both the ground and the bystander are in agreement with each other regarding speed, sequential time, and m/s^2, and therefore distance travelled, but they are doing so for differing reasons.

The case for the free faller on the other hand is that both the ground clock and the bystander's clock agree that the free faller's clock is running fast.  The free faller when at the bystander's radius on the other hand agrees that both the clock on the ground and the bystander's clock are running at same rate, this being a bit slower than his own.
Now the question here is raised in how one interprets the speed the free faller is covering distance at...?
Are we saying that the free faller is covering distance by the remit of a second as held relative to the ground clock?
Or are we saying that the free faller is covering distance by his speed held relative to his own clock?
My model is saying that the free faller is covering distance by his speed held relative to the 3rd time dilation.
The free faller covering distance as per his speed held relative to the 3rd time dilation, would be travelling distance at a constant speed, in variable times that cause the speed to appear accelerated when measured via an invariant time, such as the ground clock's time, and also in this case the bystanders time when at that radius, at that orbital velocity.  When holding both speed and SR effects relative to the 3rd time dilation, we arrive at a constant speed to deduce the SR effects from*, (this being the same result as calculating an increased speed with the speed being held relative to a percentage of the speed of light held relative to ground clock), and we may now deduct these SR effects from the GR time dilation effects at that radius for a clock time for the free faller.
(*the free faller's acceleration from a starting point of 0 speed will be 0, and this can't be correct because he will be going nowhere, but his clock's rate will be decreasing, so by holding the speed of 0 relative to his decreasing clock rate, this negative approach to motion will result in a distance travelled, and therefore a speed)

So to sum up - a slice of the free faller's time may be, dependent on the distance between the radius that he was dropped from, slightly slower, or slightly faster than the bystander's clock, where in that instant of sequential time both the free faller and the bystander observe each other.
My model states that it is of no significance that each observes the other as having a differing rate of time because they both share a universally common present moment, where the observation of 1 rate of time from the other is proportional to the difference in rate and will appear quantised, or discrete.
For instance, if we dropped our free faller into free fall at 0.806c as per held relative to the ground clock, the ground clock would observe that speed to be accelerating as the radius decreased, the bystander would observe that speed to be accelerated as per the ground clock does due to the clock's running at same rate, but the free faller would not experience any acceleration of his speed, his speed would remain constant as far as his accelerometer is concerned* but his rate of time will be decreasing as per GR time dilation, and as his speed becomes a lesser percentage of the speed of light held relative to the increasing length of seconds at decreasing radius where the SR effects affecting the free faller will then be reducing.  GR time dilation is elf will be reducing into longer seconds, and SR time dilation effects that cause longer seconds will be reducing...

So we have a GR phenomenon that speeds a clock's time up observed as reducing, and an SR phenomenon that when held relative to the 3rd time dilation, results in slowing a clock down, that is reducing.  One can see a balance in that scenario where it is possible that the speed of the free faller may be held relative to the rate of time of the free faller's clock for a constant speed.
Lastly, when the bystander observes the free faller who is now travelling 0.806c as per held relative to the ground clock, in the slice of the moment of time that they observe each other, the bystander will observe that the free faller has become length contracted, because the bystander can only view a proportion of the free faller's rate of time.  And the free faller will observe that the bystander has become length contracted because the free faller can only view a proportion of the bystander's time.  What they are actually viewing of each other is just portions of each other's time, but the motion will blur these discrete packages of the image.  If neither were actually moving in relation to each other, which would of course change the remit of the time dilation difference, but let's say that this impossible situation of an observation of 2 very differing rates of time could be observed at close proximity to each other, then the slower time would observe gaps between action of the faster time, and the faster time would observe action missing of the slower time.
The important bit being that we can consider that sequential time is like a light cone scenario, where different rates of time can share the same present moment.
This is not so different a perspective than that of calculating quantum states...

Continued in next post...

[timey (OP)]

And this is already far too long a post despite my edits, but to go the whole hog:

We can now examine what one observer would observe of the other if we were to send a light signal from each observer to the other, but the free faller being dropped into free fall at 0.806c is unrealistic, I only used that to illustrate an exaggerated proportional observation, but again we can use this exaggeration as an illustration of such.

According to my model both the free faller's and the bystander's light emitters will be emitting a photon as per the electron transitions caused by the sum of SR and GR time dilation effects that are affecting each of them.
At the point in sequential time, (which we have established is the same for both free faller and bystander because both agree that the same amount of distance is being travelled by the free faller, no matter if they cannot agree on the speed, or a time unless referring back to the ground clock(current physics), or 3rd time dilation (my model), where we now have the bystander and the free faller both emit a single photon.
The distance between the free faller and the bystander is 1000 metres, they share the same gravity potential at their locations at this radius, their GR time dilation is equal but they have a vast difference in SR effects going on, due to travelling at differing speeds.
In my model the 2 respective photon's will travel the 1000 metre distance between the bystander and the free faller, and the free faller and the bystander, at a speed of light held relative to the 3rd time dilation of that radius.
This doesn't really matter very much over a distance of 1000 metres within  an unchanged gravity potential, the light will just take that much longer to travel the distance...
But the ground clock, the bystander and the free faller will deduce that the distance between the bystander and the free faller is greater than 1000 metres if they are holding the speed of light relative to the ground clock.
If the bystander holds the speed of light relative to his own clock he will agree with that the distance is greater than 1000 metres to the same proportion that the ground clock is, but this is taking into account both the GR and SR effects on his clock.  If he were at a differing radius he would have a perspective differing from the ground clock...
The free faller is experiencing a lot more SR time dilation on his clock than the bystander, so according to his clock, the bystander is a much greater distance away than the distance that both the bystander and the ground clock agree upon, but only if he measures the speed of light as held relative to the ground clock with respect to distance.  If he holds the speed of light relative to his own clock with respect to distance, the bystander will be much closer.  Perhaps closer than the 1000 metres of actual distance between them in fact...
If we hold the speed of light relative to the GR time dilation only, then both the bystander and the free faller will agree on the distance between them, but they will as a result have to hold their own speeds relative to their GR time dilation.  The ground clock will disagree on the distance travelled, unless the ground clock also holds the speed of light relative to the GR time dilation, in which case the ground clock would also have to hold the speeds travelled relative to the GR time dilation.  When applying SR to achieve curvature of space, as per current physics remit, under the remit of holding the speed of light and speed of craft/free faller relative to GR time dilation, SR must also hold its measurements to the speed of light relative to the GR time dilation, and the GR time dilation coordinate becomes a catch 22 under the remit of spatial dilation.

My model, by attaching the speed of light to the 3rd time dilation, and the speed of the craft to the 3rd time dilation, ensures that distance remains constant where perceived spatial dilation is a temporal perception due to the rate of time on one's clock.  The g-field remains unchanged in relation to M and the 3rd time dilation also remains unchanged with relation to M, so it doesn't really matter what anybody's clock is doing really, the important thing is that no matter who's time one is measuring from, the distance covered always remains the same.

Finally - while noting that the gravity potential between bystander and free faller is equal at the moment in time we ask each to emit photons, the photon's emitted by the emitter in the faster rate of time of the bystander will be of higher energy and frequency than the photon's emitted by the emitter in the free faller's slower rate of time.
What one observes of the others photon's will be a proportional observation, where missing action, or gaps between action will cause each to observe a frequency of the others photon's that is not the frequency the photon's were emitted at, but in reality, there would be no such case as a free faller free falling from a start speed of 0.806c, and the difference in frequency between the photon's emitted in locations of differing rates of time between bystander and free faller would be minimal and barely tangible.

Crikes Mike... (chuckle) you got me right at it there let me tell you...

[timey (OP)]

In addition to my 2 posts above outlining my model's remit of the bystander and the free faller...

BTW - I described the GR cause (of accelerated motion) in Reply #338.

Here is post 338:

Zero velocity is a perfectly valid initial state. That's how Newton's apple got started for example. Newton makes no hypothesis about how the force of gravity gets things moving. The GR view is that a stationary object moves through time at light speed and acceleration simply rotates the velocity vector into the spatial domain. It's a change of heading in the spacetime continuum.

In my simplified scenario, the traveller is in free fall and the bystander is accelerating. That change eliminates the need for variable thrust, which is a significant complication.

Variable light speed is one possible interpretation of GR. Some people prefer to think of it as spacetime dilation, akin to SR. In either case, we have eliminated the effect by placing the observers at the same altitude at some instant of time.

If mass, space and light speed are invariant then higher energy (potential or kinetic) equates to shorter seconds.

Anyway, that's the picture painted by GR. The question is, what does it look like in your theory?

I don't see that you have given a physical cause for the acceleration of gravity here... What is the physical cause of the acceleration?
...and if higher kinetic energy leads to shorter seconds then a) why is light of higher kinetic energy near M than further away, and b) why does a clock at rest with respect to the g-field tick faster at h from M?

[timey (OP)]

On the basis that this conversation wasn't continued where you have said this in response to my post:

and where the value of p changes for already emitted light (in the gravitational field*) in relation to the h constant, this extra or lesser length in the wavelength isn't distance related anymore,

Your obsession with h is worrying. p doesn't change "in relation to h". p changes because the photon's kinetic energy changes as it travels through a gravitational field gradient. The value of h is irrelevant to the fractional change in p, E, L or f, which are all related through c and  given by the same equation (or its inverse, obviously).     

...and I have replied:

Yes - that's right, p doesn't change in relation to h, but wavelength changes in relation to p in relation to h.

p is changing in relation to v, and v is changing in relation to a, where a is either increasing or decreasing due to a potential energy to kinetic energy conversion, (where relativistic mass in relation to kinetic energy for light in current physics remit ensures 0 acceleration/deceleration), but it is indeed p in relation to h that denotes the change in the wavelength...

And you replied:

v doesn't change. We're talking about photons.

Where I then said:

Which is why I said:

where a is either increasing or decreasing due to a potential energy to kinetic energy conversion

...for mass accelerated or decelerated in the gravity potential.

... And added this:

(where relativistic mass in relation to kinetic energy for light in current physics remit ensures 0 acceleration/deceleration)

For light in the gravity potential..

In either case:
Wavelength = h/p
where
p = mv
or
p = h*vbar
where
vbar = v/a

And I am looking at acceleration in the gravity potential being 3rd time dilation related, where I am also looking at GR time dilation being potential energy related, and considering that temperature energy added to the blackbody is increasing the rate that an atom of the blackbody emits a photon at, i.e. an increase in rate of electron transitions, and consequently the quantum energy level of the atom that then emits a higher energy, higher rate/frequency of photon.

Planck calculated the energy increases via an invariant second.  Calculate the temperature energy added via the rate (second) of the emitted frequency and the quantum nature is negated.

Do you have anything to say?

[Mike Gale]

I haven't nodded off. Well, technically I did, but I haven't abandoned this thread. I think we are in a different time zone or there was a delay in the forum engine.

[timey (OP)]

Hey no problem - I am on UK time, but sometimes I stay up to talk to you.  My reply to your 'dodging an answer' post is somewhat long winded, I'll admit...

P.S.  The site isn't refreshing New Theiries threads to the recent topic's page properly, so if you are looking there to see if anyone has posted... it may be that they have but it isn't showing on that page.

[Mike Gale]

The reason I'm trying to change your scenario is that GR gives ambiguous results when the observer is using a rocket engine to overcome (or augment) gravity and SR can't cope with orbital motion. You may have a clear picture of how your theory deals with those cases, but mainstream physics does not. It is therefore impossible to make comparisons unless you concede the simplifications I propose.

[timey (OP)]

I am not sure what the simplifications you wish to make are...
Is it setting speed at 0 on the outbound?

[Mike Gale]

As to the cause of spooky action at a distance, GR and SR interpret acceleration as a change of heading in the spacetime continuum. How a force like gravity changes one's heading is not known. QM postulates an exchange of particles called gravitons, which are essentially photons going backwards in time. However, that explanation only leads to more questions. You ask, what causes 'A'? The answer is 'B'. Then you ask, what causes 'B'? The answer is 'C'. Ad infinitum. At the end of the day, it all boils down to observables and causal relationships. We can observe that your clock is running slower than mine for example. We propose a relationship that explains that observable in terms of another, such as our relative velocity. Then we do experiments to see if there are cases where the relationship doesn't hold. That's the best we can do. You can imagine a cause for the 2nd observable (e.g. goblins and fairies), but there is no way to determine if it is true. That's the dilemma of string theory for example. It seems plausible, but there's no way to test it.

[timey (OP)]

GR is the best theory we have of gravity, but all it does is give a mathematical representation that is the best fit to observation.
This is why my model sets out to use the same mathematics remixed into a differing arrangement that also describes observation.

In very simple terms all my model is doing is trading the spatial dilation that an observer observes to being a temporal dilation that is caused by the attributing the force of the acceleration of gravity to being 3rd time dilation related, where the 3rd time dilation is caused by the strength of the g-field in relation to M, and the curvature of space is a temporal dilation of flat space.
The result of this change knocks on to GR time dilation which becomes a phenomenon that is only affecting m in relation to M, and this is gravity potential energy related.
We then take this change to GR time dilation back to the blackbody and note that temperature energy is causing emissions of photon's that get higher in frequency as more energy is added.  Frequency is held relative to an invariant time.  Hold frequency relative to variable time, as the frequency escalates, seconds get shorter, and if you calculate the energy added per second held relative to the shorter seconds, the quantum nature deduced via the ultra violet catastrophe is negated.

[Mike Gale]

I am not sure what the simplifications you wish to make are...
Is it setting speed at 0 on the outbound?

As I described in Reply #360, a free falling traveller and a stationary bystander (the latter supported by a planetary crust) are at the same altitude and sufficiently removed from the event horizon that Newton's laws are valid. The velocity vector points radially inwards and is equal to zero if the world line (i.e. flight path) is extrapolated back to an infinite distance, in which case traveller speed at the altitude in question is the so-called escape velocity: sqrt(2GM/r). As a further clarification, traveller velocity is nowhere near light speed.

GR and SR predict that the traveller perceives the bystander clock to run slower by a factor of (1-2GM/c²r) or, more accurately (if you buy into my relativistic correction to the SC solution), sqrt(1-v²/c²). I think your theory predicts that the clocks run at the same rate because it attributes time dilation to altitude rather than velocity.

Note that many GR theorists (I dare say most) make that mistake, too. They usually compensate for their error by invoking SR again and then adding that dilation to the (null) GR result. (I say "again" because GR already incorporates SR if it is interpreted correctly.) You'll see shenanigans like that in the GPS literature for example. It's hard to talk them down because they do get the right answer. It's a case of two wrongs making a right.

[timey (OP)]

I was talking about this on 'my model of a cyclic universe continued', where I had been studying this:

https://en.m.wikipedia.org/wiki/Parabolic_trajectory

If
v = square root 2* v orbital
and
d = v*0.4142
where
d/v = 3rd time dilation

Where d is the distance that 'hasn't' been travelled due to the 3rd time dilation, i.e. flat space, temporal curvature...
I'm not so strong on maths though Mike...
The idea is that the speed is constant, it's just the time dilation that accelerates, or decelerates the speed.

If the craft started out at 0 speed, then any acceleration it experiences is 3rd time dilation related.

According to a diagram I made on the square to diagonal, if we hold distance and time constant on the square, and run time dilation up the diagonal, I worked out via dividing the geometry of my diagram into constants, that a temporal dilation can be placed into a Newtonian geometry, and that the time dilation is the value of 0.4142.

So the equation you post where you say

in which case traveller speed at the altitude in question is sqrt(2GM/r).

This speed at each radius can be treated to the maths above (I think, scratches head)

In reply to your edit:
No - you keep on overlooking the fact that my model, despite describing the curvature of space as a temporal dilation of a flat space, this temporal dilation rendering space coordinates as infinitely more definable, still retains the SR effects as a phenomenon that the traveler travelling at that velocity experiences himself.
SR effects are held relative to the 3rd time dilation where the velocity is a percentage of the speed of light held relative to the 3rd time dilation length of second at that radius.
SR time dilation effects will cancel out GR time dilation effects, and SR spatial dilation will be experienced by the traveler due to his slower rate of time, but the velocity he is travelling at, and the speed of light his SR time dilation is held relative to, are both being held relative to the 3rd time dilation length of second at that coordinate.

[Mike Gale]

OK, if I understand correctly, your theory predicts no time dilation for these observers until you invoke SR. I can't fault you for that because, as I said, GR theorists make the same mistake and I am probably in the minority when I express the opinion that they're wrong. It would be nice to have a 2nd opinion from a scholar on this subject (where's Alan Guth when you need him?), but I guess it's off the table for now. I'll have to do some more noodling.

[timey (OP)]

No - I'm saying that GR time dilation and the 3rd time dilation are separate phenomenon that occur simultaneously.
That GR time dilation affects mass only at h from M, and at that h from M the 3rd time dilation will be the exact and equal negative of GR time dilation, where the 3rd time dilation has no effect on the time dilation for mass, but it will affect how that mass moves through space.
SR is then added in for mass only, where SR effects will cancel out GR effects and vice versus.

[Mike Gale]

Understood, but the test mass 'm' does not factor into the GR equations so I'm still at a loss to explain your distinction between dilation for m at h from M and dilation for nothing at h from M. That's the missing recipe I was talking about earlier. As I said, I need to do some more noodling.

[timey (OP)]

Near Earth the acceleration of gravity is 9.807m/s^2.
At 2 radii from centre of Earth, at this radius the acceleration of gravity is 4.25m/s^2.
If you held the measurement of this acceleration relative to the length of a 3rd time dilation second at that radius, then the acceleration would be 9.807m/s^2.
(roughly speaking)

The current GR time dilation perception is that this GR time dilation is inherent to open space where the rate of time gets faster at the higher gravity potential, and that mass in that open space at a particular gravity potential will be affected by that time.
My model changes this and states that GR time dilation only affects the mass via gravity potential energy, and that it is the addition of this potential energy that increases the rate of the electron transitions. i.e. frequency.
Then it states that the g-field of open space itself is inherent with the 3rd time dilation that affects how this mass moves through open space.

I'll leave you to it though, and happy noodlings...