[Colin2B]

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.

On page 6 of your video, second line down, you give c²/R = acceleration so I have just taken this as a in at²/2.

[timey (OP)]

Yes, Lee Smolin says that where R is wavelength on Rscale:
R/c = age of universe
c2/R = acceleration (equal to the acceleration that the 'expanding universe' expansion is thought to be accelerating at)

...so the maths "at2/2" where a is c2/R, says acceleration multiplied by time squared, divided by 2.
What is, or why 2?

[Colin2B]

What is, or why 2?

I’ll do a diagram

[timey (OP)]

What is, or why 2?

I’ll do a diagram

Ok, great!  Probably for the best (chuckle)

In the mean time, does this work?

R/c=t (age of universe)
ct=R (distance)
c2/R=a (acceleration = cosmological constant)

at2/2/R= tiny length distance
at2/2/c/t= tiny length time

[alancalverd]

...so the maths "at2/2" where a is c2/R, says acceleration multiplied by time squared, divided by 2.
What is, or why 2?

Welcome back to the asylum!

Acceleration is the change of velocity per unit time. If a body starts at rest and accelerates at a for time t, its final velocity is at. If we want to know how far it has travelled (s), we need to multiply its average velocity (at/2) by time t.

Generalising, for a body with initial velocity u and final velocity v

v = u + at

s = ut + ½at²    and for completeness

v² = u² + 2as.

Nothing clever about these equations - they just derive from the  definition of velocity and acceleration.

[Colin2B]

Ok, what Alan said, what i said earlier, plus piccies.

Pic 1
This shows constant speed for a time t, easy to understand because distance travelled in time t = u₁t

Pic 2
This shows a constant acceleration a starting at 0 and finishing at time t. Final speed u₂ is = at
However, we cannot use this final speed as with pic 1 because the speed varies over time, but we can use the average speed which is ½at, multiply this by time to get distance and we get ½at²

Pic 3
This just combines the effects of constant speed and acceleration and is used where the starting speed is not 0.


Speed graph resize.jpg (149.56 kB . 640x478 - viewed 2788 times)

As a little aside, you will notice that in each case the distance is the area under the graph - shaded area.

[timey (OP)]

Thank you @alancalverd for the welcome.

Yes between yourself and @Colin2B 's diagrams, I am understanding now that the notation I questioned is concerning the mean average...

So...on the basis that it is the extra distance travelled due to the acceleration that I wish to work with, you said Colin in post 839 that:

"So distance due to the acceleration = at2/2 so if a=c2/R
Then dist =c2t2/2R"

So just to check - the distance that =c2t2/2R, that is the extra distance travelled due to the acceleration?

[Colin2B]

So just to check - the distance that =c2t2/2R, that is the extra distance travelled due to the acceleration?

There are 2 situations
either universe is not expanding in which case light will travel distance ct
Or universe is expanding and accelerating so total distance due to accelerated expansion is c²t²/2R

If you want to find out the difference in distance between the 2 this
= c²t²/2R - ct
I’m assuming you are using t=age of universe. That’s a lot of seconds

[timey (OP)]

Yes it sure is a lot of seconds!
Ok, I think I have what I need now hopefully...

R/c=t (age of universe)
ct=R (distance)
c2/R=a (acceleration = cosmological constant)

c2t2/2R-ct/R= tiny length distance
c2t2/2R-ct/c/t= tiny length time

That tiny length of time should be just a tiny fraction of a second, if it isn't then I'm not doing the equation correctly.

(As an asside that would really help me visually, I don't suppose you would convert the length of c2t2/2R-ct into a percentage of ct for me?)

[Colin2B]

That tiny length of time should be just a tiny fraction of a second, if it isn't then I'm not doing the equation correctly.

Or the acceleration youve been given is wrong.

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).”
A little exercise for the brain cels

[timey (OP)]

The velocity of expansion is on as un-solid ground, regarding the discrepancy between galaxy recession and the CMB recession, as the rate of accelerated expansion is Colin, and why would Smolin print in his book an equation that is not the rate that the accelerated expansion is thought to be?

Are you saying that my equation of a tiny length of time is not resulting in a fraction of second?  Because if not then this will only be because I haven't finished the equation properly, in which case it's not about exercising brain cells, it's about needing some advice.

Edit: There is a chance that I might have dyslexic-ly given c2/R when it should be R/c2, and I will go back to the book and check it later. But with regards to the calculations, it will not work if I use your suggested method of calculation, b/c the whole point of using the Rscale observation is that the observation of the Rscale is relativistic. (Edit 3: besides - the acceleration has to be calculated for the entire length of the Rscale for the required tiny distance and the required tiny time to be proportional for the purpose I'm putting them to) - (Edit 2: By introducing numerical mph, etc, this renders the calculation as only valid for the observers reference frames clock rate. The calculations I seek will be valid from any reference frames clock) ...and I am 'not' going to be describing an expanding universe with the tiny length distance, and the tiny length time I wish to achieve with these calculations.

(Edit 4: I just checked the book and c2/R is the acceleration by which the rate of the universe is thought to be expanding - that is, the acceleration produced by the cosmological constant.)

[timey (OP)]

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 c2xage 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.

[alancalverd]

R/c=t (age of universe)
ct=R (distance)
c2/R=a (acceleration = cosmological constant)

For the benefit of latecomers, what is R? Looks like the Schwarzchild radius but I'd like to be sure.

Then a= c²/R admittedly has the dimensions of an acceleration but it is an assertion, not an obvious consequence of physics: acceleration of what?  How derived from observation or known physics?

The assertion (or conclusion if it is such) that ∂²R/∂t² = c²/R means that the expansion of the universe is slowing down, which is apparently counterfactual to the point of being interesting.

[Colin2B]

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.

The formulae i quoted are standard for accelleration, velocity, speed, time relationships, but they are dependent on the input data in order to give correct answers.
The reason i said “or the acceleration you’ve been given is wrong” is that i have no knowledge of how c²/R has been derived and under what circumstances it is valid. I dont for example understand how it can equal the cosmological constant.
The reason i suggested you use the 2012 data is that this is a direct observation. My understanding was that your theory would confirm all current observations but give a different interpretation of, say, red shift and expansion, due to your inverse dilation effects.

[timey (OP)]

@alancalverd
R is the radius of
the observable universe.  And yes you are correct that I am changing the outlook on the expanding universe, but this is not to say that the expansion of the universe is slowing, but that the contraction of the universe is speeding up by the rate of that acceleration, noting that in my model the universe contracts from the moment that inflation ceases.

@Colin2B
I think that the circumstances of c2/R are the observation of R, where dividing c2 by R gives an acceleration that matches that of the acceleration that the universe is thought to be expanding at, where this rate of acceleration is now thought to be associated with the cosmological constant that Einstein retracted from GR.

Yes I understood your idea of reducing the measurement which is what led me to using a 10second time and subsequent distance, (hoping this would be proportional).
But using a measurement that incorporates a redshift consideration based on recessional speed will not work for my calculations.

Yes my model will give a different mathematical description of redshift observations, but this current calculation, although linked, is not the equation that describes this alternative interpretation of the redshift observation.

[Colin2B]

to get away from the big numbers I used

R is the radius of the observable universe.

It's probably worth plugging in the real numbers to see what happens.
I've got limited access to WiFi for a while, be interested to see what you've got when I'm back.

[timey (OP)]

@Colin2B lol, I did try plugging in the big numbers and it fried my brain.
I didn't know what I was looking at with the 'powers of' and (e) notations, and subsequently couldn't assess if I'd done it correctly.

[alancalverd]

If we consider a simple universe consisting of just two massive particles, and for simplicity give them both the same mass m, then the only way the universe can begin with a big bang and not collapse thereafter is if the particles move apart at greater than their mutual escape speed v_e.

Having no other source of kinetic energy they will slow down asymptotically to a constant speed v_∞ > v_e.

We can generalise this by symmetry to the case of a very large number of particles expanding away from an origin in 3 dimensions.

If the universe is fairly mature, we are moving at or close to v_∞ away from the point of origin, so the bits of the universe closest to us will be moving on near-parallel paths with a relative speed of near-zero, and those furthest from us will be on antiparallel paths with a relative speed of 2v_∞. All of which seems fairly consistent with observation.

[timey (OP)]

All of which seems fairly consistent with 'interpretation' of observation.  Please do not forget that the expanding universe and accelerated expansion are not 'factual' physics, but 'theoretical physics' as they cannot be tested experimentally.
Yes, you are describing an existing model of the universe, all of which seems fairly consistent with observation, (as it should do considering how the theory was created to explain these 'interpretations' of observation), except for the fact that the theory doesn't describe the mechanics, and contains many documented problems.

So... I am describing a different model that will also be consistent with observation.

Back to the maths:
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)
 

[timey (OP)]

As an asside, until I hear back about the maths...
My model does bounce, but it doesn't bounce like the animation on this link...

https://www.quantamagazine.org/big-bounce-models-reignite-big-bang-debate-20180131/?utm_content=bufferd6943&utm_medium=social&utm_source=twitter.com&utm_campaign=buffer

In my model the outward trajectory would occur in a flash (miniscule fraction of 1 of our seconds), leaving a slightly anistropically distibuted sea of energy and individual particles, that start the clumping process as the outward trajectory stops (fizzles out), this being due to explosion finished.
 
And then the inward trajectory would occur imperceptably slowly, accelerating, as the clumping progress escalates, at the same rate that the universe is supposed to be accelerating in it's expansion at under the remit of the Big Bang theory...
... And this contraction wouldn't necessarily be ending everything up back in the same spot everything left from, like the animation from the link shows.

My model's contraction mechanism is occurring in front of our faces at this moment, as our observations of black holes merging, and galaxies of galaxy clusters colliding. This being the ongoing continuation of the clumping process.

That continues until 'everything' is clumped into one mass, (a singular black hole) which explodes, ejecting everything (via jets), leaving a slightly anistropically distributed sea of energy and individual particles - and on it goes...