[alancalverd]

Don't worry about the numbers - they are arbitrary human choices between parsecs and microns, how to divide a circle, and various types of second. Let's see the physics. If the dimensional analysis makes sense, you may have a viable theory.

Accelerated expansion makes some sense in terms of my "generalised two particle universe". The bits that are travelling slower than the fastest, are effectively inside a sphere which is expanding faster than their radial speed, so g is decreasing, for all but the most distant particle, faster than 1/r^3 and the kinetic energy of the slower particles is therefore increasing.

[timey (OP)]

When I get back to my laptop later I will post you some contracting scenario papers by professional physicists.

But if I make your 2 particle universe into a 30 particle universe and say that 3 groups of 10 particles start moving towards each other into 3 separate clumps, then g in the space that is occurring between the 3 separate clumping processes will be decreasing, and will be decreasing even if the overall 'sphere' or 'arena', in which we imagine the entire process to be occurring within, is also slowly shrinking as a result of the clumping.

Edit: This arrangement would result in a discrepancy between what physics calls 'galaxy cluster recessional speeds' and 'CMB recessional speeds', as 'is' observed.

[alancalverd]

Well folks, that's astrophysics sorted and the 3-body problem solved. Anything else we can help with?

[timey (OP)]

For sure! I was wondering if I might look in your mouth before asking you for the name of your dentist?

[timey (OP)]

@alancalverd
Investigation into the concept of a contracting universe has been explored under various premise:

By Christof Wetterich
https://arxiv.org/abs/1303.6878

Here in the form of a pre-big bang contraction by Thorsten Battefeld, Robert Brandenberger
https://arxiv.org/abs/hep-th/0406180

And more recently here with regards to black holes by Jerome Quintin, Robert H. Brandenberger
https://arxiv.org/abs/1609.02556

In case, as a latecomer, you have not realised, I was asking about the mathematical consideration b/c I am, following both @Colin2B and @jeffreyH advice, currently improving on my paper that I am trying to submit with arXiv scientific journal.

[timey (OP)]

But going back to post 861...

https://www.space.com/38496-hunt-for-hubble-constant-standard-model.html?utm_source=notification
quote link:
"Using the Hubble Space Telescope to measure the light from a number of type 1a supernovas, a 2001 study revealed an 8 percent discrepancy in the value for the Hubble constant when compared with the method using precise measurements of the CMB. In other words, the Hubble Space Telescope recorded a faster rate of universal expansion than CMB measurements did. For the Hubble constant to be a fundamental constant, it must be, well, constant, no matter how it's measured."

Of course this necessity for the observation to be a constant is the case for a universe that is supposed to be expanding, but is not the case for a universe that is contracting at an accelerated rate.

[alancalverd]

There's no "supposed to be", nor any a priori reason why it should be constant: it is an experimental value derived from measurements of what is actually happening - or at least what happened several zillion years ago - and is quite likely to vary according to how and where it is measured.

However, the term "constant" is somewhat of a misnomer, the Hubble constant H₀is the current value of the Hubble parameter H, which changes over time.

The only surprise would be if it turned out to be negative or oscillatory in the short term.

[timey (OP)]

@alancalverd
Huh?  You have CMB radiation receding at one speed, and galaxy clusters receding at a speed that is 8% faster. 
That is the observation and the measurement, and these measurements of observation are not as the expanding theory demands, as said in the article.
My model will result in the CMB having a lesser redshift than galaxy clusters do, as 'is' observed.
My model's interpretation of the redshift observation is different from the expanding theory, as it states all (edit correction: all of the CMB, and the major part of galaxy cluster) redshift observations as being due to gravitational shift of the light in the changing gravity field.

I am not here to debate a contracting universe versus an expanding universe.  In fact your posts are causing me some distress here Alan.  I have no wish to have to defend my right to create an alternative model of the universe, or to persuade you as to the importance of dicerning that a measurement based on an interpretation of an observation is not 'factual physics', and therefore the expanding universe is 'theoretical physics', a fact I thought we cleared up many posts ago.

I am here asking for advice with my mathematical method in describing a contracting universe, and advice on the layout of the paper that I am busy writing. I would be most delighted if you helped me in this venture, but cannot and will not engage with you in arguments about whether the universe is 'supposed to be' expanding.
I provided you with 3 links to papers by professional theoretical physicists who have put forward contracting scenarios, and General Relativity can describe a contracting universe just as soon as it describes an expanding one.
Enough already!

[timey (OP)]

@Colin2B
I have posted the maths again as they had got lost back there somewhere...

OK, so my calculations (for better or worse) make that tiny distance 0.5 of a metre, and that tiny time 0.5 of a second.

If I try 0.5 seconds squared divided by 0.5 metres I get 0.5

Or if I try 0.5 metres divided by 0.5 seconds I get 1.

Not really sure about the construct of my method to say so, still running it through, and in all honesty could use some advice really.
(Edit: Actually my calculations may well be wrong b/c to get away from the big numbers I used:
c2x10 second2/2ct-ct/ct=0.5metre
And:
c2x10second2/2ct-ct/c/t=0.5second
Where it may be that c2x10second2/2ct is not proportional to c2x age of universe2/2R?)

The idea is that I want to attribute a magnitude to a change of time that will result in a change of acceleration to a constant speed travelling within a specific distance.
And that this change in distance constituting a change in position in the gravity potential, comes with changes in time that I'm attibututing to changes in acceleration, where the magnitude of distance (tiny length distance) relates to the magnitude (tiny length time) of changes in time, and the consequent changes in acceleration, via proportionality with the cosmological constant.
----------------------------
Next post:
Yes had already tried the big numbers, they fried my brain b/c I didn't know what I was looking at with the 'powers of' and 'e' notations, therefore I could not assess if I had done it correctly.

-------------------------------
Next post:
Ok, I have since worked out that the results of my 10second calculation will indeed, (unless I am very much mistaken), be the same as the 'age of the universe' calculation.
 At first I thought that b/c the speed of light squared was being multiplied by a smaller number of seconds squared, that this would throw the proportions off.  But (of course), the result is then divided by 2 times the smaller distance that is the consequence of the reduced number of seconds.  So the resulting tiny distance and tiny time from either calculation should be the same. (Please, please, please someone correct me if I am wrong)
Edit correction: Please, please, please someone tell me if I am right.

[alancalverd]

It's difficult to understand your equations. If you don't have access to superscripts,  please clarify by using the convention a^2 to indicate a², and plenty of brackets so that  p/(p + q) is clearly different from (p/p) + q, rather than the ambiguous p/p+q.

[timey (OP)]

Hmmm yes, I see my sloppiness now.  Hope this has fixed it...

c2^x10 second2^/2(ct)-(ct)/(ct)=0.5metre
And:
c2^x10second2^/2(ct)-(ct)/c/t=0.5second

Where it may be that c2^x10second2^/2(ct) is not proportional to c2^x age of universe2^/2R, where R is radius of observable universe.

Except that I now think that the reduced measurement calculation 'is' propotional to the big number calculation, and that the 0.5 metre, 0.5 second result will be the same for both the big number and the reduced measurement calculation, but would like to confirm that this is actually the case.

[Colin2B]

@timey  I think you mean:

c^2x10 second^2/2(ct)-(ct)/(ct)=0.5metre
And:
c^2x10second^2/2(ct)-(ct)/c/t=0.5second

So the resulting tiny distance and tiny time from either calculation should be the same. (Please, please, please someone correct me if I am wrong)
Edit correction: Please, please, please someone tell me if I am right.

Just to be clear, none of what I have said or will say is aimed at whether your overall ideas are right or wrong. My only objective is to clarify what you are saying and give your ideas the best chance of being understood. With that in mind:

I’m trying to understand what you have done and why. Can you explain step by step. It looks as though you substituted for R in the 1st part of the equation, but why did you divide by ct in the 2nd part. Also i don't see how the 1st equation can give metres and the 2nd seconds. Please explain.

However, this may be irrelevant if i interpret this correctly

The idea is that I want to attribute a magnitude to a change of time that will result in a change of acceleration to a constant speed travelling within a specific distance.
And that this change in distance constituting a change in position in the gravity potential, comes with changes in time that I'm attibututing to changes in acceleration, where the magnitude of distance (tiny length distance) relates to the magnitude (tiny length time) of changes in time, and the consequent changes in acceleration, via proportionality with the cosmological constant.

As with your use of partial derivative, I find parts of this confusing. Are you talking about changes in acceleration (see bold), or are you talking about changing an acceleration to a straight line - what you are calling “a constant speed travelling within a specific distance”?
If it is the latter then working out the “tiny distance and tiny time” won’t give you what you are looking for. To explain, imagine a car accelerating from rest. Say in the 1st 100m it takes 100s ie 1m/s. Later it covers 100m in say 10s = 10m/s so as it accelerates it covers fewer seconds for each 100m, so in your model to keep a straight line graph the spacing between seconds has to get longer as it accelerates, and it is this relationship you are looking for. You will remember early on I talked about log scales etc.
So we can use the equation for a straight line graph y=mx+c. In this case there is no constant c, so we use y=mx
So if distance s=at^2/2=c^2t^2/2R we can see that c^2/2R is a constant equivalent to m in y=mx. Then we call dilated time t_d =t^2 (x in y=mx) and we have a straight line graph s=c^2t_d/2R which gives you the relationship between distance and dilated time.

[timey (OP)]

Colin (chuckle), on my phone it took me a while to spot the difference.  Wrong placing of (^) noted

What you have posted is highly useful to me in my further description of page 5 and the consideration of 'vanishing' curvature and 'vanishing' SR distortions in length.  So thanks!

But to say so, the page 6 consideration of the Rscale equation is for a different purpose.
The reason I am looking for this 'tiny length distance' and 'tiny length time' is for the purpose of describing a 'value' or 'magnitude' to a description of the 'change' in time when a change occurs, and - on the basis that distortions of geometry have been 'vanished' as suggested page 1 through to 5 - a 'specific' tiny length of distance to which I can pin the 'changes' as occurring within.

My reason for doing so is based on the fact that a second is a quantised unit of an hour, where any further breakdown of these units of time can also be considered as quantised units. And my intention is quantising a 'tiny length time' as the magnitude of a change in time, where the magnitude of a change in time causes the changes in acceleration that occur in that specific 'tiny length' distance.*
The reason why it is important for my model to ascertain this particular measure of changes in acceleration has its basis in the fact that there are several factors causing acceleration in my model, where the values must be separately described.

(*The fact that the consideration is based on the 'observation' of the R scale observable universe means that the mathematical structure is 'background independent' and will be proportional from any reference frame)

[Colin2B]

Ok, but can you explain what you did to the original formulae in order to get what you believe is a small distance and small time? As i said before:
“I’m trying to understand what you have done and why. Can you explain step by step. It looks as though you substituted for R in the 1st part of the equation, but why did you divide by ct in the 2nd part. Also i don't see how the 1st equation can give metres and the 2nd seconds. Please explain.”

EDIT: I've read paras 3&4 in your last post a few times and I'm still not sure exactly what you are trying to do. Can you explain another way??
Also you are still talking about changes in acceleration. The formulae Alan & I gave you are for constant acceleration, changing speed so would not work directly with a changing acceleration.

[timey (OP)]

Just saw your edit which will have to wait till.later but:

OK, what I have done in order to make a reduced measurement calculation that 'should' be proportional to the 'required' calculation of
c^2xage of universe^2/2R
where R is the radius of observable universe

...is substitute the age of the universe with 10seconds, and substitute R with the distance that c travels in 10seconds, ie: (ct).

In the 'required' equation I then minus R like this:
c^2x age universe^2/2R-R

So in the reduced equation this is:
c^2x10second^2/2(ct)-(ct)
where t is 10second

So this action of minus the original distance has resulted in the distance travelled due to the acceleration, and now to arrive at the 0.5 metre result I continue the equation:
c^2x10second^2/2(ct)-(ct)/(ct)=0.5metre

And to arrive at the 0.5second result:
c^2x10second^2/2(ct)-(ct)/c/t=0.5seconds

Where b/c the reduced equation is proportional to the required equation (that is the intention anyway), that the required equation will calculate the same result, like this:
c^2xage of universe^2/2R-R/R=0.5metres?
And:
c^2xage of universe^2/2R-R/c/t=0.5seconds?
where t is the age of the universe.

[alancalverd]

Ltet's unravel

c2^x10 second2^/2(ct)-(ct)/(ct)=0.5metre

Assuming you mean (c² x 10²/2ct ) - ct/ct

ct/ct = 1 so we have ((c² x 100)/2ct) - 1 = (50c/t) - 1 so it all depends on the value you have chosen for t, except that c/t is a length and 1 is dimensionless, so the equation is meaningless.

The radius of the observable universe is R= ct if t is the age of the universe, so what exactly are you trying to calculate?

[timey (OP)]

@alancalverd
quote alan:
"Assuming you mean (c2 x 102/2ct ) - ct/ct"

No, I think I meant (c^2x10seconds^2/2(ct) - (ct)/(ct)
In words:
The speed of light squared times ten seconds squared, divided by two times the speed of light times ten seconds, minus the speed of light times ten seconds, divided by the speed of light times ten seconds. 

quote alan:
"The radius of the observable universe is R= ct if t is the age of the universe, so what exactly are you trying to calculate?"

Does c^2xage of universe^2/2R-R/R=0.5metres? Where R is the radius of the ovservable universe.

Does c^2xage of universe^2/2R-R/c/t=0.5seconds?
where t is the age of the universe.

(I can write these above 2 equations in words too if it helps)

I will explain how and why I want to use these resulting distance and time in the next post as a clarification requested by Colin.  But Alan, you do realise that Colin has watched my YouTube lecture?

[timey (OP)]

EDIT: I've read paras 3&4 in your last post a few times and I'm still not sure exactly what you are trying to do. Can you explain another way??
Also you are still talking about changes in acceleration. The formulae Alan & I gave you are for constant acceleration, changing speed so would not work directly with a changing acceleration.

@Colin2B  Are you familiar with the set of 10 equations in Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy?

B/c it occurs to me that if you are, although it is simpler for me to think in terms of how I think about the considerations that I am making, that it would be a damn sight simpler for me to take you through these existing equations that distort the geometry (via DrPhysicsA's YouTube lecture "Einstein's Field Equations fo Beginners"), and describe my correction at source, than it would for me to explain to you the route that I am attempting.
Perhaps more interesting for you, and not so irritating for Alan, if we are on famiiar ground maybe?

But I do very much want to know if I'm right in thinking that the R scale equations* I am talking about do result in 0.5 metres and 0.5 seconds, so that I can carry on with my thinking in my own terms. (*Hope the walk through in post 874/876 clarified)
Alan quoted a comment earlier, that Hubble's constant changes over time.  In my model time changes over time, and the information I am seeking is associated (in part) with considering this factor.

[alancalverd]

Does c^2xage of universe^2/2R-R/R=0.5metres? Where R is the radius of the ovservable universe.

This now looks like c²t²/(2R-R)/R, which we can rearrange more conventionally as Rc²t²/R = c²t² = R² since R = ct. Since R² has dimensions of square meters (an area), it cannot equal 0.5 meters or any other distance.

Does c^2xage of universe^2/2R-R/c/t=0.5seconds?

Conventionally written as c²t²/(2R-R)/c/t, or rearranged as cR²/Rt or  cR/t, this has dimensions L x T^-1 x L x T^-1, i.e. (meters/second)² - the square of a speed - and therefore cannot equal 0.5 seconds.

It doesn't matter if t is 10 seconds or the age of the universe: the numbers will change but the dimensions won't.

[timey (OP)]

Not c^2t^2/(2R-R)/R

(you are dividing c^2t^2 by (2R-R), which mathematically breaks down to (1R) and as such the term (2R-R) is nonsensical)

Please excuse my lack of brackets in my last post, it's:

c^2t^2/(2R)-R/R
and
c^2t^2/(2R)-R/c/t

In words:
The speed of light squared times the age of the universe squared, divided by 2 times the radius of the universe, minus the radius of the universe, divided by the radius of the universe.
and
The speed of light squared times the age of the universe squared, divided by 2 times the radius of the universe, minus the radius of the universe, divided by the speed of light, divided by the age of the universe.