[jeffreyH]

It is not so simple as having the distant mass being the outer shell. You are talking about miniscule contributions from each source. If the universe contains infinite mass then you are talking about an infinite series whose limit would need to be determined. The limit cannot be infinity. Since then gravity would have infinite strength everywhere. This has a bearing on renormalisation and determinations of vacuum energy.

[timey (OP)]

I removed my last post and replaced it with the revised version.

And have now replaced the below text again with edit 2

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Maybe it might help if I give a quick breakdown of the video...

Page 1 through to 5 illustrate how the geometric curvature of spacetime can be attributed to an additional temporal phenomenon, and how by adding this temporal phenomenon, this constitutes a renormalisation term to the GR distortion of the metric, resulting in Euclidean geometry.
 
Page 1 introduces the diagram that I use.  This structure of diagram, that conforms to pythagaros, is a representation of the speed/distance/time formula.
Time is on the y axis, distance is on the x axis, and the line (which I call a vector) is the speed, where a straight line describes a constant speed, and a curved line can decribe an acceleration or a deceleration.
(that x is marked as equal to constant metres becomes relevant when x is not held equal to constant metres later on)

Page 2 demonstrates that by saying that seconds get longer proportional to distance, or that seconds get shorter proportional to distance, (clearly by a specific rate) that an acceleration or deceleration in the speed of an objects vector can be represented as a straight line.

Page 3 demonstrates that seconds getting longer or shorter proportional to distance are 2 sides (partial dirivitives) of the same consideration, this being changes in time dilation 3 (dt3), and that these changes in time can be held relative to a partial dirivitive of changes in acceleration. (partial b/c there are other changes in acceleration to be considered, dirivitive b/c all the considerations added together are then the 'changes' in acceleration (da) )

The diagram of a quarter sphere + equatorial bulge is quite simply ruminating the fact that the rate that clocks tick at here on Earth, and on other spinning masses, is a combination of both position in the gravity potential, and centripetal motion.
And the fact that clocks tick at the same rate at sea level at any elevation of the equatorial bulge where a lesser centripetal speed causes a speeding up of time, and a lesser altitude from centre of earth causes a slowing of time, means that the speeding up effects on time due to lesser motion directly cancel out the slowing down effects due to the lesser altitude, and visa versa for the inverse.
And that clocks that are raised in altitude from sea level earth will tick a fraction faster as a combination of both centripetal motion and postition in gravity potential that is not quite cancelled out.
Having introduced an additional time phenomenon and it's changes as (dt3) in pages 2 and 3, I now state that changes in time due to motion will be refered to as (dt1), and that changes in time due to position in the gravity potential will be referred to as (dt2).

Page 4a repeats the introduction of (dt3) from page 3, and then introduces (dt2) as an identical but inversed consideration, where the changes in rate of time are occuring for the clock that is on that vector travelling the distance on x.  This diagram is saying that an accelerated clock rate will cause an object's (the clock's in this case) vector in the 'up' direction to be decelerated , and that a decelerated clock rate will cause an object's vector in the 'down' direction to be decelerated.
(there is more on this distinction between a clock held in position to the earth and a clock in free motion 'up' and 'down' with respect to the earths motion, in detail, in pages 9 & 10.)

Page 4b inroduces the changes in time due to centripetal* motion as (dt1) where the changes in time are occurring inversely to the changes in time dilation 2 (dt2)
Now there are 3 partial dirivitives of acceleration.
Partial dirivitives of acceleration (b) being equal to (dt2) & (c) being equal to (dt1) are for where m doesn't equal zero.
Partial dirivitive of acceleration (a) being equal to (dt3) is for where m does equal zero.

Added together these partial dirivitives of acceleration becomes 'changes' in acceleration (da), where (da) are held proportional to changes in gravity potential.
(*other types of motion are considered in pages 9 & 10)

And the changes in time dilation 1 (dt1) + the changes in time dilation 2 (dt2) in the gravity potential are equal but inverse to the changes in time dilation 3 (dt3).
(edit question: Is that inversely proportional?)
Where the changes in time of a clock in the gravity potential are those observed by the observer who we presume to be making the calculations.

Page 4b then starts introducing the mechanics of what occurs when changes in x (dx) are implemented.

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I'll continue shortly in more detail about (dx) and what is going on in page 5.  I'm basically practicing for the paper, so if my use of the terminology 'vector', 'partial dirivitive', etc is at fault?

I have 'again' replaced the text with an editied version.

(main edit insert being that (dt1) + (dt2) are equal and oposite to (dt3)
(edit question: Is that inversely proportional?)

(edit 2 insert being a reference to the relativistic nature of the observation of clocks ticking at differring rates in relation to the addition of (dt3), and that all considerations are formed from the observers reference frame.

[Colin2B]

@timey  “Maybe it might help if I give a quick breakdown of the video...”
Devil is always in the detail. From your summary I wouldn’t have noticed the terminology issues.
I need to go through in detail and ill keep a list of items worth changing.

[timey (OP)]

Ok - this is the 3rd edit of the captions for pages up to 4b.  I think I have finally included all of the relevant points in order to go on and describe the rest of page 4b and move onto page 5.  I think that some of these descriptions can be condensed a little, but I am worried that in cutting explanation in order to be less long and potentially tedious, that this is at the risk of under-explaining and being potentially misunderstood.
--------------------------------------------------------------------------------------------------
Page 1 through to 5 illustrate how the geometric curvature of spacetime can be attributed to an additional temporal phenomenon, and how by adding this temporal phenomenon, this constitutes a renormalisation term to the GR distortion of the metric, resulting in Euclidean geometry.
 
Page 1 introduces the diagram that I use.  This structure of diagram, that conforms to pythagaros, is a representation of the speed/distance/time formula.
Time is on the y axis, distance is on the x axis, and the line (which I call a vector) is the speed, where a straight line describes a constant speed, and a curved line can decribe an acceleration or a deceleration.
(that x is marked as equal to constant metres becomes relevant when x is not held equal to constant metres later on)

Page 2 demonstrates that by saying that seconds get longer proportional to distance, or that seconds get shorter proportional to distance, (clearly by a specific rate) that an acceleration or deceleration in the speed of an objects vector can be represented as a straight line.

Page 3 demonstrates that seconds getting longer or shorter proportional to distance are 2 sides (partial dirivitives) of the same consideration, this being changes in time dilation 3 (dt3), and that these changes in time can be held relative to a partial dirivitive of changes in acceleration. (partial b/c there are other changes in acceleration to be considered, dirivitive b/c all the considerations added together are then the 'changes' in acceleration (da) )

The diagram of a quarter sphere + equatorial bulge is quite simply ruminating the fact that the rate that clocks tick at here on Earth, and on other spinning masses, is a combination of both position in the gravity potential, and centripetal motion.
And the fact that clocks tick at the same rate at sea level at any elevation of the equatorial bulge where a lesser centripetal speed causes a speeding up of time, and a lesser altitude from centre of earth causes a slowing of time, means that the speeding up effects on time due to lesser motion directly cancel out the slowing down effects on time due to the lesser altitude, and visa versa for the inverse.
And that clocks that are raised in altitude from sea level earth will tick a fraction faster as a combination of both centripetal motion and postition in gravity potential that is not quite cancelled out.
Having introduced an additional time phenomenon and it's changes as (dt3) in pages 2 and 3, I now state that changes in time due to motion will be refered to as (dt1), and that changes in time due to position in the gravity potential will be referred to as (dt2).

Page 4a repeats the introduction of (dt3) from page 3, and then introduces (dt2) as an identical but inversed consideration, where the changes in rate of time are occuring for the clock that is on that vector travelling the distance on x.  This diagram is saying that an accelerated clock rate will cause an object's (the clock's in this case) vector in the 'up' direction to be decelerated , and that a decelerated clock rate will cause an object's vector in the 'down' direction to be decelerated.
(there is more on this distinction between a clock held in position to the earth and a clock in free motion 'up' and 'down' with respect to the earths motion, in detail, in pages 9 & 10.)

Page 4b introduces the changes in time due to centripetal* motion in the gravity potential as (dt1), where the changes in time dilation 1(dt1) are occurring inversely to the changes in time dilation 2 (dt2)
(*other types of motion are considered in pages 9 & 10)

Now there are 3 partial dirivitives of acceleration.
Partial dirivitives of acceleration (b), (being equal to (dt2)), and (c), (being equal to (dt1)), are for where m doesn't equal zero.
Partial dirivitive of acceleration (a), (being equal to (dt3)), is for where m does equal zero.
(Note that none of these demonstrations of curve manipultation are representing any true values yet)

Added together, these partial dirivitives of acceleration become 'changes' in acceleration (da), where (da) are held proportional to changes in gravity potential.

And the changes in time dilation 1 (dt1) + the changes in time dilation 2 (dt2) in the gravity potential are equal but inverse to the changes in time dilation 3 (dt3).
(edit question: Is that inversely proportional?)
Where the changes in time of a clock in the gravity potential are those observed by the observer who we presume to be making the calculations.
(Note that no actual value has been attributed to the magnitude of: a 'change' in time, a 'change' in acceleration, or a description of within what distance in the gravity potential a 'change' occurs, as of yet)

Page 4b then starts introducing the mechanics of what occurs when changes in x (dx) are implemented.

[jeffreyH]

Just a note on the spherical shell cavity. If we place a detector at the Lagrange point then any photon fired from the interior surface will be red shifted by the time it reaches the detector. If the system were large enough then the central mass could be a celestial object such as a planet. Then the field of the central body would be applying blue shift to the incoming photon. There would be two opposite time dilation effects.

[timey (OP)]

Yes - a photon is particle m=0, moving through space m=0.  And it is possible to say that a change in the length of wavelength for both gravitational redshifted light, and gravitational blueshifted light, can be attributed to a change in the rate of time in the gravity field of space, rather than being attributed to any actual spacial change in the wavelength, and that these two opposites 'could' be regarded as partial dirivitives, or 'up'/'down' dirivitives of an additional time dilation phenomenon for where m=0.

Things to consider:

The detector (in your post) measuring the magnitude of the redshift, will be measuring that redshift phenomenon with a clock that is ticking faster than the clock on the mass that the photon was measured with when it was released from that position on that mass.
There is a school of thought that will say that the light has not changed frequency at-all, and that it is just the fact that the detector's time is running faster at that position than it would on the ground, that is the cause of the measurement of a longer wavelength.
(For anyone wishing to refer to the rules of relativistic observation, the 'far away' clock will agree that the ground clock is ticking slower than the elevated clock)

However, the possibiity exists that we can attibute half of the detector's measurement of a longer wavelength to the fact that the detector's clock is running faster, and we can attribute the other half of the detector's measurement of the longer wavelength to this additional time dilation for where m=0, where it is taking light moving into the weaker gravity fields longer amounts of time to travel the same unit distance, 'causing' a lower frequency.
(A blue shift towards gravitational M can be the above consideration inversed)

Is it then interesting that Einstein's GR states twice the curvature than Newtonian Mechanics?

[Colin2B]

Then the field of the central body would be applying blue shift to the incoming photon. There would be two opposite time dilation effects.

I did wonder if this might be similar to what @timey  might be thinking. Obviously current physics treats this as the difference in GP between the 2 points, but i dont see why it shouldn’t be modelled this way. Not sure i would call it an inverse function, more a contra-directional one.
I will be interested to see how it produces the anomaly close to higher density.

@timey   Ive been through the video, but skipped the repetitive bits. In the paper you can start with the principle of longer/shorter seconds with distance and then not need to go over it each time.
Just to explain what i said earlier:
A vector has both direction and magnitude, so although on the graph of t vs x the line can be thought of as being in the x direction it doesnt have a specific magnitude. So i would refer to the line as a graph or plot.
Are you absolutely sure you know what partial derivative is, how it is used and what it implies? If so then do use it, but it gave me real problems understanding what you are trying to show. I think of the time axis more as varying with x, so it isnt a linear scale eg you will be familiar with frequency in a frequency response curve being shown log scale to match how we hear it.
Overall it is up to you to decide how best to present your ideas.
I will be interested to see next stage, the meat.

[timey (OP)]

I think perhaps the shorter descriptions that I will give as captions to the worksheets will be more accessable.  I'll definately be working to that end anyway.

With regards to giving these considerations magnitude, the whole exercise of this spacetime structure is to describe a formula of proportionality in the same way that the left side of the GR equation does, where both sides of that GR equation are background independent, meaning that the proportionality expressed by that equation is valid for any magnitude, and any reference frame.
Page 8 gives a description of how this proportionality is established, thus giving magnitude to the graphs or plots, (bearing in mind that a more experienced mathematician could and would describe these graphs and plots as vectors in a far more eloquently expressed equation), and pages 9 & 10 describe the physical mechanics of this proportionality.
However GR breaks down at high density, ie: black holes.  My suggested spacetime structure won't.

Partial dirivitive definition: "A partial derivative of a function of several variables is its derivative with respect to one of those variables."
Partial dirivitives of a time dilation being directional 'up', 'down' variables of a singular function,  of 1 of any 3 time phenomenon.
Partial dirivitives of changes in acceleration (a), (b), & (c) being variables of a singular function of observed changes in acceleration.
Am I wrong in my assessment of the terminology?

But going back to page 6, this being my main concern, if you can find the time at some point Colin to help me properly formalise that R scale consideration with the appropriate mathematical notation, that would be really great.  In the meantime I'm just going to get my head down and re-write the paper, so will be missing for a bit.
Thanks for the advice so far.

Edit: diriv'a'tive

[timey (OP)]

Chuckle...

[pasala]

Mr. timey
Well, here i am sharing mine ideas on gravitational time dilation.  Right from the starting we are looking at the one side of the coin only.  At present we are of the view that outside area is empty and in case if that is true then why don't we measure speed of light in open area.  It is true that certainly there is a influence.  Each photon released from the clock is not free from outside influence.  Unless a new photon is released and makes a way there is no pressure or force and this pressure causes movement of particles.  In a constant gravitational field, your watch, needles, photons and EMF everything is undergoing constant pressure.  When velocity is gained, everything is relaxed from gravity and the release of photons slows down.  Unless a new photon is released your watch fails to gain KE. 

"Time dilation is only a simple instrument to measure gravitation variations at two different places and nothing else and in fact it cannot tell you what exactly a gravity is". 

First of all we have to set our mind that open area is not free and there is strong EMF is present and it is influencing each and everything including functioning of atomic clocks.

Yours
Psreddy

[timey (OP)]

Mr. timey
Well, here i am sharing mine ideas on gravitational time dilation.  Right from the starting we are looking at the one side of the coin only.  At present we are of the view that outside area is empty and in case if that is true then why don't we measure speed of light in open area.  It is true that certainly there is a influence.  Each photon released from the clock is not free from outside influence.  Unless a new photon is released and makes a way there is no pressure or force and this pressure causes movement of particles.  In a constant gravitational field, your watch, needles, photons and EMF everything is undergoing constant pressure.  When velocity is gained, everything is relaxed from gravity and the release of photons slows down.  Unless a new photon is released your watch fails to gain KE. 

"Time dilation is only a simple instrument to measure gravitation variations at two different places and nothing else and in fact it cannot tell you what exactly a gravity is". 

First of all we have to set our mind that open area is not free and there is strong EMF is present and it is influencing each and everything including functioning of atomic clocks.

Yours
Psreddy

Please excuse me that I do not engage with you in discussion regarding time dilation.  I am entirely focused on expressing my own ideas on this thread, bar the string theory v quantum loop gravity comedy interlude.
I simply do not have the time for a debate, and to be frank, unless you are telling me that your ideas result in a falsifiable prediction for a doable experiment, then I'm afraid my interest will not be much piqued...
If your ideas do result in a falsifiable predicition then please do feel free to post a link to 'your' thread, and the posts that describe your prediction, and I shall read with interest.  If not, then good luck to you all the same, and sorry again that I'm too busy to be conversational.

[timey (OP)]

Well the good news is that I have discovered that I can describe that which is on page 5 far more clearly. (fun, fun)
The bad news is that I will have to put pen to paper and draw it out again. (sigh)

[Colin2B]

bearing in mind that a more experienced mathematician could and would describe these graphs and plots as vectors in a far more eloquently expressed equation

My point is that they wouldn’t, and it’s nothing to do with ‘eloquently expressed equations’, just with the definition and usage of the term vector. They would reserve vectors for describing a specific magnitude and direction (eg of speed or acceleration) rather than using the term on a graph which shows all possible magnitudes.
At the end of the day you are responsible for final edit and how you say it. Most people will reinterpret what you've said and move on, so it’s not a show stopper.

The next one you really need to be clear on

Partial dirivitive definition: "A partial derivative of a function of several variables is its derivative with respect to one of those variables."

Correct, but it depends on a thorough understanding of derivatives.

Partial dirivitives of a time dilation being directional 'up', 'down' variables of a singular function,  of 1 of any 3 time phenomenon.

Partial dirivitives of changes in acceleration (a), (b), & (c) being variables of a singular function of observed changes in acceleration.

I don’t understand what you are saying in those 2 statements.

You need to be clear which one of the variables you are taking the derivative with respect to. This not clear from the graphs - the assumption would be wrt x as time is the dependant variable to x, however, derivative of t wrt x is not speed, neither is the partial differential of t divided by x an acceleration.
As it's the first time you use a derivative is page 2 diagrams 4 & 5, you might like to expand on what you mean and also how you arrive at eg deceleration = longer seconds.
Again, you know what you are trying to say and the editing is up to you, as long as you are clear how you are using the terminology.

But going back to page 6, this being my main concern, if you can find the time at some point Colin to help me properly formalise that R scale consideration with the appropriate mathematical notation, that would be really great. 

In equations of motion distance s=vt+at²/2
vt is the distance travelled if there were no acceleration, in this case =ct
So distance due to the acceleration = at²/2 so if a=c²/R
Then dist =c²t²/2R

So if you want to compare extra distance travelled to distance without acceleration you divide the extra dist by ct
so ratio = ct/2R

@jeffreyH can you think of any other ways of presenting this?

[timey (OP)]

Thanks for the feedback Colin.
On the basis of your previous comments I had actually included in my 'latest" re-write an explanation as to my usage of the partial dirivative term as part of a prelude introduction to the worksheets.
On the basis of your most recent comments I've added again to that prelude - posted below, and I am hoping that my explanation is sufficient that I am not miss-understood?  This is a very different way of describing the familiar phenomenon of gravitational acceleration and attraction, and other types of motions taking place within the gravity potential, where magnitude is attributed via the magnitude of the gravitational mass...
...And I ask you to hold the thought that in General Relativity, mass tells space how to bend, and space tells mass how to move.

I am mulling over your page 6 postings.  This will take me some time, as I tranpose the meaning of your maths at 'baby steps' rate into words, shapes, and back to maths again in order to understand.  I'll get back when I've understood it.

-------------------------------

Introducing An Additional Time Dilation Phenomenon:

These following worksheets illustrate how the geometric curvature of spacetime can be attributed to an additional temporal phenomenon, and how by adding this temporal phenomenon, this constitutes a renormalisation term to the GR distortion of the metric, resulting in Euclidean geometry.

The descriptions below will ask you to consider that there are not 2 but 3 time dilation phenomenons.
Time dilation 1 being caused by motion, both centripetal and other.
Time dilation 2 being caused by postion of height in the gravity potential of M.
Note that this model states that time dilation 1 and time dilation 2 are for where m doesn't equal zero.
This model introduces an additional time dilation - time dilation 3 - this being for where m does equal zero. ie: for particles m=0, and for the open spaces or 'background space' between masses.

The considerations below are based on a simple idea that if an object is travelling in a background space that is inherent with it's own rate of time - a rate of time that the object must travel through - an object travelling at a constant speed over distances where seconds get progressively shorter, will be accelerated. And an object travelling at constant speed over distances where seconds get progressively longer, will be decelerated.

I have described in the worksheets below, (perhaps unusually, hence the explanation), the 'up' 'down' changes of each time dilation phenomenon as 'partial dirivatives' of that time dilation.  As well as signifying the plus minus changes in time, this notation is indicative of directional orientation in the gravitational gradient.  These 'up' 'down' dirivatives also become useful notation when a consideration of changes in acceleration contains both a plus and a minus of the same time dilation phenomenon.
The time changes in each of the 3 time dilations are then each considered as a partial dirivative of changes in acceleration, where when added together in the mannner suggested, these 3 partial dirivatives of changes in acceleration become the changes in acceleration that are proportional to changes in gravity potential.

-------------------------------------

[jeffreyH]

@Colin2B I need to review the following first.
https://en.m.wikipedia.org/wiki/Modified_Newtonian_dynamics

[jeffreyH]

@Colin2B I have read through the wikipedia article and I am unconvinced by MOND.

[Colin2B]

@Colin2B I have read through the wikipedia article and I am unconvinced by MOND.

I agree, it seems to put forward a solution which has no evidence to suggest it might be the way to go.

@timey you say “Note that this model states that time dilation 1 and time dilation 2 are for where m doesn't equal zero.”
SR is motion related and is defined for where gravity = 0, or a very close approximation ie flat spacetime. Does time dilation 1 include SR?

[timey (OP)]

I'm not really sure where MOND applies in the page 6 Rscale consideration other than via the cosmological constant.  What interests me is that Milgrom's simple mathematical variant can describe galaxy rotation without dark matter.

quote wiki:
"By itself, Milgrom's law is not a complete and self-contained physical theory, but rather an ad-hoc empirically motivated variant of one of the several equations that constitute classical mechanics. Its status within a coherent non-relativistic theory of MOND is akin to Kepler's Third Law within Newtonian mechanics; it provides a succinct description of observational facts, but must itself be explained by more fundamental concepts situated within the underlying theory."
Unquote

Special relativity is a motion related calculation that can only be applied where gravity can be negated, ie: flat spacetime.
Yes time dilation 1 is a special relativity related consideration, where I am asking the question "Does the fact that clocks all tick 'potentially' at the same rate at sea level of any elevation of the equatorial bulge on Earth, mean that a clock ticking at sea level is both a general relativity, and a special relativity consideration?"

And yes, it is important that special relativity is calculated in flat space time, because adding the addition time phenomenon 3 for background space means that curvature is a temporal phenomenon and the spatial geometry of space is 'not' curved by a gravitational mass.

[Colin2B]

@timey “I am mulling over your page 6 postings.  This will take me some time, as I tranpose the meaning of your maths at 'baby steps' rate into words, shapes, and back to maths again in order to understand.  I'll get back when I've understood it.”

I could do some diagrams of the motion equations if that would help.

[timey (OP)]

No it's ok, I think I am with you on your description below as to the outcome of extra distance travelled due to acceleration, but I do have some questions about the notation that I shall get into in a mo.
-----------------------
quote Colin:
"In equations of motion distance s=vt+at2/2
vt is the distance travelled if there were no acceleration, in this case =ct
So distance due to the acceleration = at2/2 so if a=c2/R
Then dist =c2t2/2R

So if you want to compare extra distance travelled to distance without acceleration you divide the extra dist by ct
so ratio = ct/2R"
--------------------------
Yes I do want to compare the extra distance travelled with the acceleration, to the original distance (wavelength Rscale) without acceleration, but I think in order to get the small amount of distance I'm looking for I need to divide the extra distance by the distance of wavelength Rscale.  And in order to get the small amount of time I'm looking for I need to divide the extra distance by the speed of light. (Edit: Oh I don't think that is quite finished. Then perhaps divide this time by the age of the universe? Noting that all measurements are made via the observers clock.)  In this manner the small acceleration is proportional to the small distance and the small time.  Am I right?

Ok, I get your notation right up until you say divided by 2 and divided by 2R.  I'm assuming that R is the Rscale wavelength, but could benefit from some clarification as to this, and the use of 2.