[alancalverd]

So let's put a clock at 2R. Now put one observer on earth and another on the moon. What do they see?

[timey (OP)]

The clock at 2r will be GR time dilated, so conventional relativity describes what the moon observer will see in relation to what the Earth observer will see - is the answer to your question.

The observation of the 3rd time dilation would be in that the clock without any energy input to maintain its position at 2r, would then be changing position from 2r back to Earth, where the increasingly shorter seconds of the g-field are increasing the speed the clock moves at through the g-field.

[GoC]

So let's put a clock at 2R. Now put one observer on earth and another on the moon. What do they see?

2R from the center of the Earth, from the surface of the Earth or from the atmosphere of the Earth?

The clock at 2r will be GR time dilated, so conventional relativity describes what the moon observer will see in relation to what the Earth observer will see - is the answer to your question.

The observation of the 3rd time dilation would be in that the clock without any energy input to maintain its position at 2r, would then be changing position from 2r back to Earth, where the increasingly shorter seconds of the g-field are increasing the speed the clock moves at through the g-field.

What does GR dilated mean in space. Where is the threshold of attraction for the difference in the inverse square of the distance? There is one for inside the parameter of mass and one for outside the parameter of mass.

[alancalverd]

R is always taken from the centre of gravity, provided that R > the radius at mean sea level. It's a lot easier than asking where the atmosphere ends, because it doesn't.

[timey (OP)]

So let's put a clock at 2R. Now put one observer on earth and another on the moon. What do they see?

The clock at 2r will be GR time dilated, so conventional relativity describes what the moon observer will see in relation to what the Earth observer will see - is the answer to your question.

The observation of the 3rd time dilation would be in that the clock without any energy input to maintain its position at 2r, would then be changing position from 2r back to Earth, where the increasingly shorter seconds of the g-field are increasing the speed the clock moves at through the g-field.

Any response?

[Mike Gale]

So let's put a clock at 2R. Now put one observer on earth and another on the moon. What do they see?

That's a tough one because the moon's gravity is not trivial and it's orbital speed is variable. The GPS scenario is similar and simpler because the satellite's gravity is trivial and it's orbital speed is effectively constant. A GEO satellite is even easier because it is stationary with respect to the Earth observer. In that case, GR says the satellite clock runs faster or slower by a factor of sqrt(1-2GM/c^2/R)/sqrt(1-2GM/c^2/r) and you can take that result to the bank. (https://en.wikipedia.org/wiki/Gravitational_time_dilation)

[timey (OP)]

Ok - so if we could imagine for the purpose of the calculation that a constant speed - never mind the cause of the movement or consideration of that which is moving - to be moving in the direction of r, away from M, would it be possible for you to calculate the acceleration that a constant speed would accelerate at if the speed were held relative to the faster seconds of each r between R and r?

Edit: This assuming that R is the closer radius, I've had a moment of doubt, but if I've got it wrong way round...

[Mike Gale]

R is indeed the shorter radius, but I've had my own 2nd thoughts. Even though the satellite is stationary with respect to the Earth observer, both are rotating within the SC coordinate system. It's not valid to assume that the SC coordinate system rotates with the Earth unless the satellite is replaced with a hovering rocket (co-rotating with the Earth observer) or another terrestrial observer at the top of a tall tower. Centripetal acceleration does not amount to the same thing because the satellite does not feel its own weight. We should revise our scenario accordingly to avoid that wrinkle. Constant linear velocity is even more complicated because you have to accelerate in a gravitational field in order to achieve that.

[GoC]

R is always taken from the centre of gravity, provided that R > the radius at mean sea level. It's a lot easier than asking where the atmosphere ends, because it doesn't.

Yes but the density of mass has a threshold where attraction to the Earth for your weight to the center of mass changes abruptly. Being basically weightless in space. There is an abrupt change in tick rate of your clock that is not linear to the center of mass. Basically insignificant change but a change non the less. This is where the gradient dilation changes its acceleration to the center of the Earth.

There probably is no place in the universe where the tick rate remains the same so while we can be somewhat accurate we can never be precise. A mathematicians goal of precision in relativity is a moving target.

[timey (OP)]

R is indeed the shorter radius, but I've had my own 2nd thoughts. Even though the satellite is stationary with respect to the Earth observer, both are rotating within the SC coordinate system. It's not valid to assume that the SC coordinate system rotates with the Earth unless the satellite is replaced with a hovering rocket (co-rotating with the Earth observer) or another terrestrial observer at the top of a tall tower. Centripetal acceleration does not amount to the same thing because the satellite does not feel its own weight. We should revise our scenario accordingly to avoid that wrinkle. Constant linear velocity is even more complicated because you have to accelerate in a gravitational field in order to achieve that.

Even the top of tower will be rotating faster than the bottom of tower...
The only way, as you say, is to have a hovering rocket that when maintaining height above the Earth, also maintains the same speed of rotation, where the observer on the craft will observe the observer on the ground rotating away from the crafts position, and therefore the speed of both will remain the same.

And yes if we take the gravitational field into consideration this does complicate matters for a trajectory away from M...
However - this is why I said to just consider the calculation as a constant speed - no matter what is causing the motion, or consideration of that which is being moved - to remove gravitational and SR aspects from the calculation.
What I'm interested in is by how much GR time dilation would increase a constant speed between R and r if we held the speed relative to the shorter seconds at each h from M.
What I'm looking for is a m/s^2 acceleration - so having taken into consideration that the shorter seconds of GR time dilation have accelerated this constant speed, clearly the 'acceleration' part described by m/s^2 would then be being held relative to the rate of an 'Earth second' at R, or 'standard second' as per the physics remit of holding metres per second squared relative to the standard second.

Edit:  It would be pertinent to my intended direction as to the use of this calculation if you considered r to be 2 radii from centre of Earth...

[Mike Gale]

The point is to get both observers attached to the planet by gravity at different altitudes. That's the simplest case for the SC solution because the metric reduces to: dT/dt = sqrt(1 - 2GM/c²r). Anything else involves the addition of more variables, which only serve to obfuscate the result. This effect can be measured directly and is actually used to maintain the accuracy of the clocks that track universal time (during seismic events for example.) It can be interpreted as a change in light speed, but most people prefer to think of it as a change in time speed (i.e. time dilation.) The net effect is the same either way because clock speed depends on light speed as well as time speed. Note that acceleration due to gravity is GM/r².

[Mike Gale]

...just consider the calculation as a constant speed - no matter what is causing the motion, or consideration of that which is being moved - to remove gravitational and SR aspects from the calculation.

SR describes constant velocity in the absence of gravity. GR describes free fall in a gravitational field. It can be extrapolated to describe suspension in a gravitational field, but there is no exact GR solution for any other case, only numerical approximations.

What I'm interested in is by how much GR time dilation would increase a constant speed between R and r if we held the speed relative to the shorter seconds at each h from M.
What I'm looking for is a m/s^2 acceleration - so having taken into consideration that the shorter seconds of GR time dilation have accelerated this constant speed, clearly the 'acceleration' part described by m/s^2 would then be being held relative to the rate of an 'Earth second' at R, or 'standard second' as per the physics remit of holding metres per second squared relative to the standard second.

I think you're talking about free falling from the top of the tower. (Although that's accelerated motion, not constant velocity.) It's easy to compute time dilation for that case relative to an infinitely removed observer, but not so easy when the bystander is on the ground. The SC solution can cope with two free falling observers or two suspended observers, but not one of each. That's the GPS scenario and there is no consensus on the correct way to solve that problem.

[timey (OP)]

No you misunderstand my intention - I'm not referring to any 'actual' physical event in wanting to know by how much a constant speed would be accelerated by in m/s^2, if the constant speed were held relative to GR time dilation at every r, from R to r=2radii.

Excluding the other physical considerations, all I want to know is - if we reduce the length of a second, how much faster will the speed be?
At each and every r, from R to r=2radii, GR time dilated seconds get shorter. (or appear as if they do from the lower potential)
What would the acceleration be in m/s^2 if we held a constant speed relative to the shorter seconds at each radius.

Just to be absolutely clear:
When referring to a speed it is no mystery that a speed is defined as per a distance held relative to a time period.  In this case metres travelled per second, and it should be pretty obvious that metres per second are being held relative to the time period of a standard second measurement.
So on this basis we can now hold a constant speed relative to a series of increasingly shorter seconds found to be shorter at each and every r between R and r=2radii, and this will give us an acceleration.
It is the value of this mathematically contrived acceleration that I need to know.

At 2 radii from centre of Earth the acceleration of gravity is 4.25m/s^2, or thereabouts.
At near Earth it is around 9.807m/s^2.
At each and every r between R and r=2 radii, the acceleration decreases.

I want to examine the difference in value between the 'gravitational acceleration' of m/s^2 occurring between r=2radii and R, in relation to this mathematically contrived 'time dilation' acceleration between R and r=2radii - that I'm trying to get you to calculate the value of...

This is actually pertinent to the calculation of my model, where the 'acceleration' of gravity is 3rd time dilation related... In order to calculate my model, each component of the GR field equations must be dissembled and reassembled in an alternative arrangement.  Once I know the value of this 'mathematically contrived' acceleration, I'll be in a better position to proceed.

[Mike Gale]

Here's a cheat sheet I made for calculating GR time dilation with the Schwarzschild metric for cases that involve only radial motion. Of particular interest to this thread are the stationary and constant velocity cases, but I'm not entirely satisfied with those two results because they involve additional energy, beyond that which is available in the metric. I think that invalidates the interpretation of proper time as local time. (That's why GPS is so tricky for example.)
Note also that the validity of the Schwarzschild metric in the vicinity of the event horizon is questionable, as I pointed out in this thread: https://www.thenakedscientists.com/forum/index.php?topic=69764.0
If you accept my proposed correction to the metric, the scaling factor changes from (1-r_s/r) to (1-r_s/2r)².
I should also point out that my free fall solutions are only valid for escape velocity (i.e. when KE cancels PE.) Anything else exceeds the energy in the metric.

[Mike Gale]

Do you (Timey) think this is a fair assessment of your theory?
https://www.thenakedscientists.com/forum/index.php?topic=69882.msg510239#msg510239

[timey (OP)]

Do you (Timey) think this is a fair assessment of your theory?
https://www.thenakedscientists.com/forum/index.php?topic=69882.msg510239#msg510239

I think Timey is proposing that spacetime is intrinsically dilated and that's what determines the location and movement of objects in space and time. It's an anthropic argument (i.e. chicken vs. egg) so it's really a matter of philosophy, not physics. The same could be said of string theory of course, but physics is supposed to be about the observables. It seeks to explain how one observable changes in relation to another. An explanation is worthless if it invokes undefined concepts like photon-to-electron ratio, electron cycle, electron travel distance, and oscillating mass. You might as well be talking about gnomes and fairies (or strings.)
I expect you're eluding to wave-particle duality. If so, you are way off base because the amplitude of a matter wave is a distance in probability space, not conventional space. That is, matter wave power, which is proportional to amplitude squared, equates to a probability of finding a mass at a given location in space and time. GR and SR have nothing to say about any of that.
At the risk of adding to your confusion, I should add that probability space is only one possible interpretation of QM. There is a respectable theory that the waves are actually electromagnetic in nature. It's incomplete and far from mainstream, though.

Ok - Mike, bringing your post on GoC's thread back here, as I wouldn't want to clog up his thread with my posts, I have more respect...

Firstly, I'm sorry but I do not have access to a computer and am just conducting myself from a phone's operating system, whereby I can't view pdf's, so for the moment I haven't seen the info you posted in pdf format.

Secondly, I am still observing that you are having difficulty stepping outside of the view of conventional GR and SR.
Clearly the conventional view describes a universe that is presently expanding...
My model seeks to describe a universe that is presently contracting, a contraction that has been slowly accelerating from the point that my model's rendition of the universe's inflation period ceased.

This involves a completely different rendition of GR and SR principles, therefore what I am attempting to describe 'will be' different.
However, the differences that my model makes are an alternative means of describing experimentally confirmed observations, without the necessity for an inclusion of Dark matter, or Dark Energy.

I now know more or less exactly how my model can be calculated, bar not having the required value of the information that I was requesting from you...
And what I am seeking is someone well versed in manipulating mathematics, who can can let go of their conventional relativity/quantum preconceptions in order to take specific instructions as how GR and SR and quantum principles can be very subtly changed in order to describe how my model is put together.
Nothing philosophical about it what-so-ever...

With regards to what you surmise about my model, the closest you come is in regarding probability space.  My model includes a time dilation factor to the quantum region of physics that adds probability space before the fact rather than after, where my model states that the concept of probability space is born of the fact of current physics not taking into account that where frequency is a timing function of energy, +energy = shorter seconds.

My model is based on a theory of time which renders time itself as a reactive phenomenon caused within and as part of the mechanics of the universe, where the rate of time anywhere is a reaction to energy, and different rates of timing are occurring simultaneously as a reaction to their energy state.
As opposed to the current view where time is 'only' a measurement of sequential events, as observed by an observer.

Because your relativistic correction to the SC metric includes holding the speed of light relative to GR time dilation, I had thought that it wouldn't be too much trouble to transpose the amount by which the speed of light would be accelerated by these increases in the rate of time into a m/s^2 value... (between EarthR and r=2radii)
This is all I'm asking...

[timey (OP)]

OK, I stand corrected. You are proposing a new twist on the aether theory. I assume you are aware that aether was the prevailing view before Einstein. You should be intimidated by the fact that he was able to sway so many of the greatest minds of the modern era, but even if you are not, you should study his arguments. Chances are he has already debunked your theory. For starters, you need to account for the Michelson-Morley result.

My model does account for the Michelson-Morley result in that it makes an additional axiom that the speed of light cannot exceed the local rate of time.  As I have said before.

https://en.m.wikipedia.org/wiki/Hubble's_law

After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant, which he had designed to modify his equations of general relativity to allow them to produce a static solution, which he thought was the correct state of the universe. The Einstein equations in their simplest form model generally either an expanding or contracting universe, so Einstein's cosmological constant was artificially created to counter the expansion or contraction to get a perfect static and flat universe.[41] After Hubble's discovery that the Universe was, in fact, expanding, Einstein called his faulty assumption that the Universe is static his "biggest mistake".[41] On its own, general relativity could predict the expansion of the Universe, which (through observations such as the bending of light by large masses, or the precession of the orbit of Mercury) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.

Here we can see that the Einstein equations will describe an expanding universe or a contracting universe.

If Hubble's red shift velocities are re-interpreted as being due to slower time in space, then the aether type scenario is that motion is affected by slower time in space.

It's a logical proposition for a contracting universe of the cyclic type that my model describes. 

[Mike Gale]

My bias towards mainstream physics is irrelevant. I'm not trying to debunk your theory. (At least not yet.) I'm only trying to identify how it differs from mainstream. Because you are unable to provide a formal derivation, our only recourse is to juxtapose predictions. You obviously have the constant velocity scenario worked out in your mind, but GR can't solve that one without generating controversy. The approach I'm advocating is to define a scenario which is unambiguous in GR and then ask what your theory has to say about it.

[Mike Gale]

I noted earlier that the expanding universe hypothesis comes from the Friedmann solution, not the Schwarzschild solution. Although both are consistent with GR principles, they are distinctly different. Friedmann dilation is exclusively temporal so it is the same for all points in space. Schwarzschild dilation may or may not be temporal, but it most definitely has a spatial dependency.

[Mike Gale]

I cannot lay claim to the variable speed of light (VSL) hypothesis. Einstein floated that idea for several years before he conceded the dilation view. Although VSL has fallen out of favour, neither view is free of controversy.