[Colin2B]

(Back on lap top now and can see much better what is going on, the phone is restricting)
....
I want to say that:distance R = radius of observable universe, travelled at speed c + the acceleration.
Then I want to subtract the distance travelled if travelling at c without the acceleration. ie: (ct) (where t is the age of the universe) from this c + the acceleration distance, leaving me with the distance travelled due to the acceleration.

Then I divide this distance by the distance (ct) and this will give me a small distance.

Ok, good you can see the formulae clearly.
First your last line, dividing a distance by a distance doesn’t leave you with a distance so that is out.*

So “I want to say that:distance R = radius of observable universe, travelled at speed c + the acceleration.”
Problem is that we know R=ct, so how can  R= ct+ dist due to acceleration ?

This leads me to believe that the question you are asking might not be the one you want answered. I wonder if you are really wanting to ask how you convert an observed expansion into a nonexpansion, presumably by using an adjustment to observed time?
Is it worth us following through how you get to the correction to the field equations first? Or do you want to try and work this through first?

As ive said before, and @alancalverd  seems to have the same objective, we only want to make sure your ideas are presented in the best possible way and if we allow mistakes like * to appear in the paper your readers will walk away at that point.
It’s a painful process, i know ive been there, but it’s worth it.

EDIT:  just noticed Alan modified his post while i was writing. What he says about Smolin’s acceleration now makes sense, something to work with. Out today, will look later.

[opportunity]

Apologies for doing this, but I'm using Ockham's Razor here.

Running a clock, any mechanism, to out-pace light from a defined source; maybe that's why light doesn't carry mass naturally, because the laws of space-time we're investigating disallow such? Nonetheless, to try that, carry mass at light speed, obviously the mass in question I'm thinking will try to be more light-like, and decay, "or" be bent from that trajectory of light its trying to out-pace? If any measuring instrument being used in that context is held as gold, no effect on its initial workings, I'm thinking maybe the experiment is already contaminated with the hyped-up process of natural decay of mass in play, interfering with the normal process of the designed atomic clock, slowing it?

Once again, layman at the helm here given the number of posts. But, if light is what it is without mass and we try to use mass as light will not nature intervene, a nature we haven't properly scientifically understood?

[timey (OP)]

OK, (feeling better now btw).  I think I see where the confusion is.

I am not thinking upon R as being inclusive of (a) for this equation.
The observation is c times t.
ct=R
So
a=c^2/R
(c+a)t=R+distance extra travelled due to acceleration.
And I am looking to then minus R and 'do stuff' with the extra distance travelled.

'Do stuff' like:
What percentage of R is this extra distance?
If I divide this extra distance by R? (Like one might divide 10 miles, by 2 miles and end up with 5 x 2 mile markers)
If I divide this extra distance by R and then c, and then t (age of universe)? (Like one might divide 10 miles by 2 mile markers, and end up with 5 x 2 mile markers, where it takes time t to travel 2 miles.)

Start figuring out how to say that 13.8 billion years ago as per our clock rate at this moment in time, time ran x percentage slower, and is universally speeding up as the clumping process continues, where this speeding up of time is associated with the given acceleration.

And then start looking at the discrepancy between the 'recessional velocity' of the CMB and the 'recessional velocity' of galaxy clusters. (I have highlighted 'recessional velocity' b/c in my model this is not a discrepancy between recessional velocities, but simply an anomaly between redshifts observations that is predicted by the model)

[alancalverd]

(c+a)t=R+distance extra travelled due to acceleration.

No. The "extra distance travelled" in a time interval  Δt is vΔt + a(Δt)²/2 where v is the initial velocity at time t.

The problem is that we don't have an expression for v that stands up to analysis at t=0, so we can't solve the equation theoretically*. So do we have any actual observed value for v_(now)?


*hence the pigs-ear integral I proposed yesterday!

[alancalverd]

PS if there really was a primal big bang that resulted in the dispersal of mass from a huge black hole, then time certainly did run slower in the infant universe - isn't that the consequence of everyday relativity?

[Colin2B]

The problem is that we don't have an expression for v that stands up to analysis at t=0, so we can't solve the equation theoretically*. So do we have any actual observed value for v_(now)?
*hence the pigs-ear integral I proposed yesterday!

I did post a value some time back https://www.thenakedscientists.com/forum/index.php?topic=69800.msg532208#msg532208

Why not use something like this from measurements in 2012
“expanding at a rate of 74.3 plus or minus 2.1 kilometers (46.2 plus or minus 1.3 miles) per second per megaparsec (a megaparsec is roughly 3 million light-years).”

PS, I didn't think the integral was too pig eared (I assumed dt) and looked like a good starter. Question might be whether variation of v is constant over time, Also @timey is suggesting light red/blue shift is affected by path through g anomalies. Probably best to start with a simple assumption and see if magnitude is approx ok.

[alancalverd]

You have put your finger on part of the problem. If, by observation, we know that the expansion is accelerating now, then our best guess is that v has not been constant over time past!

So let's take the current rate of expansion v = 28 km/sec per million lightyears and multiply by the current value of R, say 14 000 000 000 lightyears, gives v at the periphery of the observable universe as 28 000 x 14 000 = 392 000 000 m/s which, sadly, is faster than c. This does not make sense: it implies that there is an infinite amount of energy available to accelerate every particle that we can't see!

Time for some beer and rugby.

[Colin2B]

Time for some beer and rugby.

Are you participating in rugby or watching? I can guess for the beer.
Raining here so excellent rugby weather, enjoy 

[timey (OP)]

You guys are still trying to fit expanding theory to my request for help with an equation for a contracting model.

There is no integral expanding velocity in my model. Everything already expanded in my model's inflation period, and has been contracting at a=c^2/R for 13.8 billion years. (By the rate of our clock at this moment in time)

There has never been a time=0 in my model.
Time will be running slow at end of inflation period where mass (in particle form) and energy are at maximum dispersement.
Time will be running at it's fastest just before inflation period when all mass and energy (in black hole form) are at minimum dispersement.
And time will be running at it's slowest in the open spaces between galaxy clusters, that are made up of galaxies. Galaxies that are converging inwards upon each other.

This is why my model makes the prediction, that while clocks in elevation to mass will tick faster than clocks at lesser elevation, that if placing 2 clocks in different locations at same longitude (to equalise centripetal speed), and same height from centre of earth, (so that both clocks are equal), but the locations are of know significant difference in geological density - that contrary to general relativity my model predicts that the clock in the denser location will tick faster.
This is a doable experiment when NIST get their portable clocks up and running.

The narrative out there on the theoretical physics circuit is that no existing theories of everything can make testable predictions for anything different. And that observations like the discrepancy between CMB and galaxy clusters 'recessional velocity' cannot be explained by any existing theory.
My model and theory of everything does both...

So no - time=0 doesn't exist in the equation, so nothing to be theoretically unexplained there.  And introducing recessional velocity is an 'expanding theory' consideration that will not apply to a contracting model.

Hope this clears up the points that you both have made.

[Colin2B]

You guys are still trying to fit expanding theory to my request for help with an equation for a contracting model.

No, just looking at the fact your model still has to result in what is currently observed, accepting that your interpretation of what is observed will be different.

Thanks for the clarification of which stage your universe is at currently, i hadn’t picked that out before.

So, if you dont want us looking at the expansion, what do you mean by “extra distance travelled”. Please clarify in terms of the contracting model you have just outlined.
In your contracting model we could take t=0 as being 13.8bn yrs ago, this would be start point for the contraction, which i assume is accelerating from 0 velocity at the turnaround point.

I don’t think the formulae we have been using will work if time is not constant over the period. Do you have a model for how time varies between start of deflation and current time?

[alancalverd]

if placing 2 clocks in different locations at same longitude (to equalise centripetal speed), and same height from centre of earth, (so that both clocks are equal), but the locations are of know significant difference in geological density - that contrary to general relativity my model predicts that the clock in the denser location will tick faster.

What does the clock know about its environment? Only g

[timey (OP)]

OK, to start with it will be useful at all times to remember that 'observation' is relativistic.
(This being what makes these considerations 'background independent'. An important feature in a theory of everything)

The 'observation' is c times t. (where t is somewhat dubiously based on parallax and standard candles)
There is no consideration here where t=0 has any actual physical meaning with regards to the equation.

The velocity of the contraction of the entire universe starts from 0 at c^2/R.
(And this measurement of acceleration will be proportional from any location in the universe, and also at any point in the history of the universe, because c is 299 792 458 metres per second of the rate of time at that point in history.)
But the contraction mechanism is the gravitational clumping process, so light arriving at our location as a phenomenon that is part and parcel of the universes clumping process cannot be associated with any t=0 concept.

Yes I can tell you the process by which time changes.
At start of contraction (clumping process) time is slow but more or less uniformish across entire universe, matching the more or less uniformish distribution of particles and energy.
Where there is more density in the slight un-uniformity, time runs a bit faster than in the less dense areas...
By a process in which particles that are satellite to a greater mass are increased in their internal timing, they are electro magnetically drawn in the direction of the greater mass, and the faster rates of time surrounding the greater mass accelerate this gravitational attraction. ie: gravity @alancalverd.
(My modification to general relativity is adding this third aspect of time dilation to describe gravitational acceleration, and adding these 2 axioms: "+energy = shorter seconds" and "The speed of light cannot exceed the local rate of time")

My model states the universal contraction process proceeds from 0 clumping, and accelerates at c^2/R.

The extra distance 'could' be used to describe by how much the universe has contracted.  But not until it is know (I have figured out) by how much the universal rate of time has increased.
This being where the observations of redshifts anomaly between CMB and galaxy clusters at 8% difference will come in useful.

[Colin2B]

There is no consideration here where t=0 has any actual physical meaning with regards to the equation.

But there is. t in " c times t" is the elapsed time from t=0, the start of the contraction

The velocity of the contraction of the entire universe starts from 0 at c^2/R.

Problem with this is that  c^2/R is from Smolin's view of an expanding universe. what makes you think it is now contracting at that rate?

The extra distance 'could' be used to describe by how much the universe has contracted.  But not until it is know (I have figured out) by how much the universal rate of time has increased.

It should really be a reduced distance if the universe is contracting.

EDIT: PS
You are saying that the outer edge of universe has been contracting for 13.8bn yrs, and is now at a distance of 13.8bn yrs, so it must have gone out to 27.6 bn yrs. How have you calculated that?

[timey (OP)]

c times t is not the start time of the contraction though.
c times t is our 'current' observation of a universe that has already contracted by a certain degree.

c^2/R matches the acceleration that is thought to occur as per 'observation' of redshifts.
It is the interpretation of those redshifts that results in expansion, (that GR descibes) and more recently, accelerated expansion. (That GR plus a=c^2/R describes)
My model's interpretation of the observation of redshifts is a contraction (that GR can describe) plus an acceleration (that a contracting GR plus a=c^2/R describes)

Yes, the distance R that we observe as (ct), 'is' the reduced measurement for this equation. The idea is to work out how much bigger it was.
(8% maybe? But suspect more complicated, still thinking on)
Where the rate of universal changes in rate of time, (as opposed to individual masses differing rates of time changing in the gravity potential, and the inverse changes to the rates of time (that I added) in the background spaces between masses - where both will also be increasing at this rate), is also accelerating at a rate associated with c^2/R.
(Where our 'working with' value of c^2/R, is as per our present time clock rate, and current observation of R)

In reply to your edit:
That would be the case, apart from the fact we are calculating in 'our' years, and I am saying that time has been speeding up at a rate associated with c^2/R. So in slower time, as per comparison to the rate of our clock now, c would not cover 'as much distance as we would associate with 27.6 bn yrs', in these ever increasingly slower rates of time as we go back in the history.
However it is worth me stating at this point that my model will calculate the universe as being a hell of a lot older that 13.8 billion years, when it is considered how these slower rates of time convert into an equivalent number of years as per our current rate of time.

[alancalverd]

The 'observation' is c times t.

No. Light travels at c, so the the distance of any object you can see must be cτ where τ is the time it took for the light to travel from there to here. If the universe has a finite age t then the farthest observable object is at R = ct,the Schwarzchild radius.

R is important as long as c is the limiting speed for the propagation of gravity, which seems to be the case.Nothing outside of R can affect anything inside. Or can it?

Imagine a static universe. If there is a massive body at R + ΔR, it will have a gravitational effect at R such that photons emitted towards us from a body at R will appear to have come from a more massive body and thus be redshifted.Which is what we observe!

[timey (OP)]

But 'time' is dynamical and changing in relativity Alan.

... And in each reference frame of gravity potential light is measured as being 299 792 458 metres per 'second', and the 'far away' clock will confirm that there is a rate of time difference between 1 reference frame's clock compared to another reference frame's clock.

Therefore the speed of light when in one reference frame of gravity potential is travelling at a different proportion of speed per second, due to the 'length' of the second there, than it is in the next reference frame of gravity potential that has a different length of second.

...and as a result c times t in the gravity potential is complicated.

R is what we can see, where it is accepted physics theory that there is more universe that we can't see.
It is part and parcel of accepted physics theory that this is the 'observable universe' and the fact of Hubbles constant and the expansion theory requires that the outer edges of the 'observable universe' are expanding at an accelerated rate that exceeds the speed of light.  Where c is held relative to our 'length' of second.
(Experiment: Make c relative to a longer second than ours, compare it to a measurement of c as per our second with regards to distance travelled.)

"Imagine a static universe"...
Yes, that is correct... and if masses were starting out smaller and becoming bigger, then redshift is what we would observe.

How are they getting bigger?
Via the clumping process.
What drives the clumping process?
Gravity
What is gravity?
GR answer:
Space tells mass how to move and mass tells space how to bend (as a spacial distortion of geometry)
My model's answer:
Mass tells space what it's rates of time are. Mass also tells satelite masses what their rates of time are.  And these changes in both rates of time that ocurr as seperate issues, but concurrently with each other, cause mass to move the way they do in the gravity potential of the greater mass.

Why do we observe accelerated redshifts?
GR+positive cosmological constant answer:
Because the universes expansion (described by GR without cosmological constant) is accelerating at c^2/R.
My model + negative cosmological constant answer:Because the universes clumping process is causing a contraction, (that can be described by GR without cosmological constant), that is accelerating at c^2/R.

[alancalverd]

Whatever the complication, R = c∫dt where the integral of time is from the birth of the universe to now. It may well be that the Schwarzchild "radius" is actually a bit bumpy, but space seems to be mostly empty and the universe sufficiently isotropic that the observation limit can be considered a sphere for all practical purposes.

 

And in each reference frame of gravity potential light is measured as being 299 792 458 metres per 'second'

No. The second is defined everywhere by an atomic transition and the metre is defined everywhere as 1/299 792 458 of the distance light travels in a second.

Mass tells space what it's rates of time are.

But we know by (very precise) experiment that it is the combination of mass and distance, i.e. gravitational potential,  that determines relative clock rates.

[timey (OP)]

The description you put forward hasn't defined what the birth of the universe is, and if you say Big Bang, this is not a defined mechanism in currently held physics theories.
Further more, space seems to be mostly empty, but the description doesn't give the mechanics of 'why' it is empty, other than an unknown event caused an inflation period of unknown mechanics that slowed down, and then speeded up again as accelerated expansion for an unknown reason, while the universe developed into what we see today with regards to mass clumping.

The second is defined everywhere by an atomic transition.
But the atomic transition of the 'far away clock' will tell you that the atomic transitions in one observed reference frame are not only different from it's own, but that another reference frame close to, but at a different gravity potential to the first reference frame, has different atomic transitions to the first reference frame.

And to reply to your edit:
I said:
"Mass tells space what it's rates of time are."
You said
"But we know by (very precise) experiment that it is the combination of mass and distance, i.e. gravitational potential,  that determines relative clock rates."
Yes, that is gravitational mass telling satellite mass what it's time is. (in my model)
'Mass telling space what it's rates of time are' is me referring to my models added time for space between masses.  The changes of which are inversely proportional to the changes in the rate of time for clocks held at different elevations from mass.
And this added time phenomenon occurs concurrently with the timing of clocks in the gravity potential, and can describe a physical reason for gravitational acceleration of objects falling towards gravitational mass.

[alancalverd]

The description you put forward hasn't defined what the birth of the universe is, and if you say Big Bang, this is not a defined mechanism in currently held physics theories.

It doesn't matter! If any or all stuff has been moving away from you for time t, the furthest stuff you can see is at ct.

Further more, space seems to be mostly empty, but the description doesn't give the mechanics of 'why' it is empty,

It is mostly empty because there is more space than stuff, and stuff tends to coalesce in clumps as a result of gravitation.

[timey (OP)]

Quote Alan:
"If any or all stuff has been moving away from you for time t, the furthest stuff you can see is at ct."

But in my model stuff has not been moving away from us for time t.
Small bits of stuff have been moving towards other small bits of stuff, making bigger bits of stuff, for more years than the galaxies that emit the light we observe have existed for. And c times t is a measure of the observation of galaxies that are formed already, and are estimated to be x distance away from us.

The light is coming from galaxies of galaxy clusters, where the galaxies of those clusters are converging.
The galaxies of our galaxy cluster are moving away from other galaxy clusters, and closer to other galaxies of our galaxy cluster.  Other galaxies of other galaxy clusters are moving closer to the other galaxies of their own galaxy clusters.
But this is a type of back reaction recessional value, and there is no need to say that everything is moving apart, just that what is there is being drawn together, by gravity, at an accelerating rate.

Quote Alan:
" It is mostly empty because there is more space than stuff, and stuff tends to coalesce in clumps as a result of gravitation."

You have not described why there is more space than stuff, nor why stuff coalesces into clumps as a result of gravitation.

It's all about 'initial conditions' Alan.
My initial conditions for a contraction are a more or less uniform sea of energy and particles.  Spaces in between masses are caused by particles vacating their former positions in this sea to the clumping process called gravitation that is described in my model as the changes in rate of time for masses in the gravity potential, and the changes in the rates of time my model adds for the spaces between masses.

In any case I know that for my model the equations that I am seeking are valid, and that c times t can only be an observation of light from a galaxy x distance away, and that the age of the universe is based, in part, on redshifts observations and Hubble's constant, so despite the fact that my model will calculate that the universe is much older, I can still use the current theory age to calculate an observation of ct.
In physical cosmology, the age of the universe is the time elapsed since the Big Bang.
In my model the age of the universe is also the time elapsed since the Big Bang.  Except that  in my model the Big Bang and Inflation period occurred really quickly, and the contraction period kicked in after inflation by the physics of gravitational clumping, where the overall contraction of the universe occurs at an acceleration of c^2/R.

My model makes a better description of observations. It also makes a falsifiable prediction for something different to current theory, which is what all other theories of everything fail to do.
So is there any chance I could get a hand with formally describing the equation that will describe (ca)t-(ct)=extra distance travelled, and how to work out what percentage of (ct) this extra distance is?