Geocentric Belief

[AlexG]

The strong and weak nuclear forces are not scale invariant, so if the universe was shrinking they couldn't maintain the same value and atomic reactions wouldn't work.

 

[Schmelzer]

Which, assuming you accept the vacuum 'has structure' and is not the totally empty void of pre QFT, implies space also shrinks. How then does one have a theory any different conceptually to standard metric theories?

We do not have. We are talking here about an interpretation of GR, which is a standard metric theory.
By the way, my ether theory of gravity is different from GR, but also a standard metric theory.

Or, if the rulers are restricted to matter & energy, as I get the impression is so in your theory, is it not the case your interpretation would have objects subject to say a uniform gravitational potential wrt to some external observer (e.g. placed inside a spherical mass shell) - 'shrinking', but not the space between them? [There is a subtle GR issue in that particular situation, but let's go with 'shrinkage' as a generic standard prediction of metric theory] In which case you have a theory differing fundamentally from a usual metric theory.

This second understanding would be closer to my ether theory. There is a space, an absolute one, which exists independent of the matter content, and the fields of QFT, as well as the gravitational field, would describe the matter content. And the shrinking happens relative to this background.

An interpretation in terms of "shrinking" is not something one could name a standard prediction of a metric theory. "Shrinkage" has to be relative to something - to space. It presupposes some interpretation of what is space, and this interpretation may be not supported by the metric theory itself. So, in GR the "shrinking rulers" picture and the "expanding universe" picture are simply different interpretations of what is, from point of view of the equivalence principle, the same (or at least "equivalent", which means indistinguishable by observation) GR solution.

 

[Schmelzer]

I see this as somewhat of a joke Schmezer, how you continually avoid what I have put in bold, just so your ego does not have to admit I'm right.

Learn to read: I wrote already long ago "If this statement is what you want to focus about, we can finish this, I do not even object because this is IMHO completely irrelevant."

My ego has no problem at all with admitting that my position is not the mainstream position. Instead, my ego as a scientist would be much lower if I would not have reached interesting new results, results which are not mainstream, which distinguish me from the mainstream.

Also I would suggest with the fabricated shrinking interpretation, one would than need to question other shrinking properties like the known physics constants, Planck scale, the speed of light, etc.
If it didn't apply to the speed of light, as I suggested, we would see blue shifts.

To repeat it again: The interpretation applies to the whole solution, to all of its parts, to everything which can be used as a ruler. And the equations are exactly the same equations, thus, all the constants, c as well as the Planck constant, are the same too.

Again, that's not to say that sometimes the shrinking ruler/matter interpretation may not be a conveniant alternative to use in isolated situations. Just as though we know with 100% certainty that the Earth is round, we can still find a use for "flat Earth" around the garden for instance.

To repeat it again: The interpretation applies to the whole solution, to all of its parts, Not only to a small piece like your garden.

Also remember that we would also have inflation to explain with "shrinking rulers" which we need to address homogeneity, Isotropy and flatness.
Expansion quite obviously fits more naturally within the accepted cosmology picture we have today.

To repeat it again: The interpretation applies to the whole solution, to all of its parts, including the parts where inflation happens. The equations are exactly the same equations, thus, all the constants, including the cosmological constant and the constants which control inflation, are the same too.

We see the usual picture: Repetition of the same claims, again and again, now even boldfaced, combined with complete ignorance of the counterarguments. Counterarguments which are quite simple, simple enough to be understood even by a layman with only minor knowledge about GR.

The strong and weak nuclear forces are not scale invariant, so if the universe was shrinking they couldn't maintain the same value and atomic reactions wouldn't work.

They are not scale invariant if the metric is considered to be fixed. If everything is transformed appropriately, as required in GR, the equivalence principle requires that nothing changes.

Or, to express this in other words, the Planck length is something defined in terms of the local rulers, It shrinks together with the rulers.

 

[paddoboy]

Learn to read: I wrote already long ago "If this statement is what you want to focus about, we can finish this, I do not even object because this is IMHO completely irrelevant."

Oh I read it all right......Just another example of you skirting around the issue.
That is what it is all about, whether you like it or not.
What I said.......

The Universe has no center except the center of your personal observable universe.
The Universe is also said to be Isotropic and homegeneous, meaning looking the same in all directions, and being the same where ever you are in the Universe. These are views over macroscopic scales.

What you replied.......

This is, by the way, an interesting point: The "expanding universe" picture suggests the existence of a center. The ballon picture has no center, but suggests another dimension - which is also a misleading suggestion, at least GR itself does not suggest such a thing.
The shrinking rulers picture does not have these problems. Dried up earth with cracks nicely illustrates how such a shrinking creates inhomogenity in an initially homogeneous universe - without any center, without any additional dimensions.

My ego has no problem at all with admitting that my position is not the mainstream position.

Thank you! At last!
I rest my case. [Although obviously this will create even more turmoil ]

 

[paddoboy]

We see the usual picture: Repetition of the same claims, again and again, now even boldfaced, combined with complete ignorance of the counterarguments. Counterarguments which are quite simple, simple enough to be understood even by a layman with only minor knowledge about GR.

You don't have counter arguments. You have unsupported anti mainstream excuses.

 

[Q-reeus]

We do not have. We are talking here about an interpretation of GR, which is a standard metric theory.
By the way, my ether theory of gravity is different from GR, but also a standard metric theory.

This second understanding would be closer to my ether theory. There is a space, an absolute one, which exists independent of the matter content, and the fields of QFT, as well as the gravitational field, would describe the matter content. And the shrinking happens relative to this background.

An interpretation in terms of "shrinking" is not something one could name a standard prediction of a metric theory. "Shrinkage" has to be relative to something - to space. It presupposes some interpretation of what is space, and this interpretation may be not supported by the metric theory itself. So, in GR the "shrinking rulers" picture and the "expanding universe" picture are simply different interpretations of what is, from point of view of the equivalence principle, the same (or at least "equivalent", which means indistinguishable by observation) GR solution.

OK so it seems clear your theory admits to not only an absolute space and time, but operationally defined ('radar ranging') space and time consistent with say GR metric interpretation. Fine then. Accept - to be anything more than purely metaphysical, such absolute space and time should admit to being defined in terms of current operationally defined values. So, can you offer functional definitions of T = f(t), X = f(x). Where T/t, X/x, refer to absolute/operationally-defined-time-and-space-mean-values-at-present-Hubble-time respectively. That is, as determined in an ideally homogeneous universe devoid of local matter concentrations that might spoil a useful standard reference. So our references are absolute vs idealized FLRW cosmology metric 'at present epoch'.
Example: My wrist-watch ticks at a given proper rate omega. What rate would that be in absolute time units? Similarly for a standard meter ruler.

 

[paddoboy]

Neil deGrasse Tyson: Is the Universe Expanding or Are We Shrinking?

 

[paddoboy]

[1]We would have blue shift which we don't see of distant galaxies:
[2]There is obviously a low limitation to how far something can be shrunk:
[3] It does not explain the gravitationally bound smaller regions of the Universe:
[4]And finally the shrinking ruler analogy makes no sense when applied with the fact that our Universe/spacetime had a beginning at the BB.
We cannot talk about shrinking rulers when the Universe started from a point.

Just adding to the Blue shift reality of point [1]
The Redshift we see with the accepted observed expansion model is a "Cosmological" Redshift.......While the Blue Shift we would observe If shrinking rulers/matter was valid, would be a Doppler shift.

 

[Schmelzer]

OK so it seems clear your theory admits to not only an absolute space and time, but operationally defined ('radar ranging') space and time consistent with say GR metric interpretation. Fine then. Accept - to be anything more than purely metaphysical, such absolute space and time should admit to being defined in terms of current operationally defined values. So, can you offer functional definitions of T = f(t), X = f(x).

Not sure what you mean with "functional", but, indeed, in my ether theory, as well as in the Lorentz ether interpretation of GR, there are functions T=T(x,t), X=X(x,t), and they have a well-defined evolution equation, which is the harmonic equation.

The difference between the two is that in my ether theory of gravity there are also additional terms in the basic equations: $$ G_{mn} = T_{mn} + F(T, X)$$
while in the pure ether interpretation this additional terms F(T, X) do not exist, so that it is impossible, even in principle, to identify the X,T by observation of matter or measurements with rulers and clocks.

Example: My wrist-watch ticks at a given proper rate omega. What rate would that be in absolute time units? Similarly for a standard meter ruler.

Let's start with coordinates for the flat FLRW universe: $$ ds^2= dt^2 - a^2(t) dx^2, \, X(x,t) = x, \, T(x,t) = T(t), \, dt = a^3(t)dT$$. So, if your wrist-watch is in rest to the CMB frame, it measures dt, with absolute time changing like dT. And rulers measure a(t) dX. Of course I have omitted for simplicity spatial indices.

The equation for a(t) would, in GR, not contain any terms relating to X,T, in my ether theory they would.

 

[Q-reeus]

Not sure what you mean with "functional"...

My bad - poor wording. I just meant 'defined as a function of', not a 'functional' in the strict mathematical sense.

, but, indeed, in my ether theory, as well as in the Lorentz ether interpretation of GR, there are functions T=T(x,t), X=X(x,t), and they have a well-defined evolution equation, which is the harmonic equation.
The difference between the two is that in my ether theory of gravity there are also additional terms in the basic equations: $$ G_{mn} = T_{mn} + F(T, X)$$
while in the pure ether interpretation this additional terms F(T, X) do not exist, so that it is impossible, even in principle, to identify the X,T by observation of matter or measurements with rulers and clocks.

Fine. Let's here ignore the additional terms which I believe involve adjustable parameters.

Let's start with coordinates for the flat FLRW universe: $$ ds^2= dt^2 - a^2(t) dx^2, \, X(x,t) = x, \, T(x,t) = T(t), \, dt = a^3(t)dT$$. So, if your wrist-watch is in rest to the CMB frame, it measures dt, with absolute time changing like dT. And rulers measure a(t) dX. Of course I have omitted for simplicity spatial indices.

The equation for a(t) would, in GR, not contain any terms relating to X,T, in my ether theory they would.

The way it reads there to me, you arbitrarily set current epoch (a = 1) as that defining a 1:1 correspondence. Surely that can't be right - if absolute space and time have a physical not arbitrarily gauged metaphysical existence? Wouldn't a 'natural' choice for 1:1 correspondence be somewhere way back at the BB epoch when a << a (current)?

 

[Schmelzer]

Neil deGrasse Tyson: Is the Universe Expanding or Are We Shrinking?

Please, don't cry. So, what this tells us? Hm, he has to think about this, he has to think. The rulers have to shrink with us. Of course.

The Redshift we see with the accepted observed expansion model is a "Cosmological" Redshift.......While the Blue Shift we would observe If shrinking rulers/matter was valid, would be a Doppler shift.

Again, we would not observe a blueshift, because the solution is exactly the same as in GR, simply because it is the GR solution, and the physical predictions in GR do not depend on the system of coordinates. Therefore we see a redshift. If you have a problem with obtaining the standard redshift prediction, learn GR based on any GR textbook of your choice.

 

[Schmelzer]

Let's here ignore the additional terms which I believe involve adjustable parameters.

Not only in your belief, in my theory too. It is one of this adjustable parameter, $$\Upsilon$$, where the choice >0 gives inflation and stable frozen stars but the choice <0 only an additional strange dark matter term which does not lead to any qualitative changes.

The way it reads there to me, you arbitrarily set current epoch (a = 1) as that defining a 1:1 correspondence. Surely that can't be right - if absolute space and time have a physical not arbitrarily gauged metaphysical existence? Wouldn't a 'natural' choice for 1:1 correspondence be somewhere way back at the BB epoch when a << a (current)?

Of course, the a(t) is defined modulo an arbitrary constant factor. Given that we cannot measure background distances anyway, there is also no standard measurement unit. For practical purposes, the distance at the time of origin of the CMBR would be natural, or, as you suggest, some inflation parameter. For $$\Upsilon>0$$ there would exist a minimal value of a(t) at the big bounce.

 

[Q-reeus]

Not only in your belief, in my theory too. It is one of this adjustable parameter, $$\Upsilon$$, where the choice >0 gives inflation and stable frozen stars but the choice <0 only an additional strange dark matter term which does not lead to any qualitative changes.

Of course, the a(t) is defined modulo an arbitrary constant factor. Given that we cannot measure background distances anyway, there is also no standard measurement unit. For practical purposes, the distance at the time of origin of the CMBR would be natural, or, as you suggest, some inflation parameter. For $$\Upsilon>0$$ there would exist a minimal value of a(t) at the big bounce.

OK, thanks for clearing up a few things. As you say, what ultimately matters is correspondence between theory and observation.

 

[paddoboy]

Please, don't cry. So, what this tells us? Hm, he has to think about this, he has to think. The rulers have to shrink with us. Of course.

Don't cry?? You now sound like rajesh, and his ego and fabricated maths was also deflated and invalidated.
Take note of what he said at the 30 sec mark
"It's the Universe itself that is expanding, not the things within it"
While the shrinking ruler interprets mass as shrinking...Like I said, a very limited analogy at best..

Again, we would not observe a blueshift, because the solution is exactly the same as in GR, simply because it is the GR solution, and the physical predictions in GR do not depend on the system of coordinates. Therefore we see a redshift. If you have a problem with obtaining the standard redshift prediction, learn GR based on any GR textbook of your choice.

So you keep saying......
The Redshift we see with the accepted observed expansion model is a "Cosmological" Redshift.......While the Blue Shift we would observe If shrinking rulers/matter was valid, would be a Doppler shift.
Again.....
The best that can ever be said for the "shrinking ruler" analogy, is that it is an "alternative perspective" albeit faulty, on the accepted standard cosmological model, rather than an "alternative model"
When you can bring yourself around to admitting that, you will have finally made some headway.
The shrinking ruler analogy is an alternative to the accepted model [universal expansion] that is on the odd occasions used for sake of convenience.
It only plays a very minor role in cosmology interpretations against the far more accepted expanding Universe/BB model.

 

[Schmelzer]

Don't cry??

A standard internet reaction to excessive use of big fonts, bold or uppercase letters, exclamation marks, and similar things. Educated people seldom use them, and if they use them, then only one (say, or underscoring, or italic, or bold) and only to a few words to be emphasized. These are elementary rules of civilized behaviour.

Take note of what he said at the 30 sec mark
"It's the Universe itself that is expanding, not the things within it"

Oh, he said it. And he is Authority or so, so I have to accept this? No, it simply means that he describes the expanding universe picture in these words.

Boring repetitions of things answered many times deleted.

 

[paddoboy]

A standard internet reaction to excessive use of big fonts, bold or uppercase letters, exclamation marks, and similar things. Educated people seldom use them, and if they use them, then only one (say, or underscoring, or italic, or bold) and only to a few words to be emphasized. These are elementary rules of civilized behaviour.

No, just the fabricated made up nonsense you have come up with of late.
As I have noted many times...excuses, and you and your constant wriggling in getting out from under.
Do better.

Oh, he said it. And he is Authority or so, so I have to accept this? No, it simply means that he describes the expanding universe picture in these words.

What you accept is neither here nor there. You are the maverick...you are the renegade. You are the one who is wrong and avoiding confirming my simple relevant statement for all your worth. And of course Neil in one short sentence has invalidated your maverick anti mainstream approach.
Here is that statement again.......
The shrinking ruler analogy is an alternative to the accepted model [universal expansion] that is on the odd occasions used for sake of convenience.
It only plays a very minor role in cosmology interpretations against the far more accepted expanding Universe/BB model.

Boring repetitions of things answered many times deleted.

Interpretation:
"The above bold type is true but I cannot confirm it as it would invalidate my anti mainstream stance and confirm paddoboy is correct"

 

[paddoboy]

Some more food for thought to invalidate this archaic unrealistic hypothesis/ limited analogy of shrinking rulers/matter.
[1]How big was all our rulers and matter at the BB?
[2]How big were our sub atomic particles?
[3] The binding forces holding quarks together only act over tiny distances and are limited in range, how can they manage to hold a proton together before it started to shrink?
[4] How big were our stars before they started to shrink?
[5] And how are S/N possible if matter/rulers are shrinking?
[6] Consider that in that first Planck instant after the BB, it was impossible for matter to exist, so how was the rulers/matter in this analogy created?
[7]How big were electron orbitals when these rulers/matter were created?
[8]What we call hot is atomic and molecular motion. As something gets hotter it expands: how can it expand if it is shrinking?
[9] How did shrinking operate during the Inflation epoch?
And don't forget the inevitable Poof! It's gone finally. I forgot, Schmelzer swept that under the carpet..
Sound crazy? Yep, just as Bigfoots, ghosts, goblins, Anal probing aliens, and believing in conspiracies are crazy, but that didn't stop MR from still fabricating nonsense to continue validating that which is stupid. Likewise it appears Schmelzer operates the same way.

NB: I'll probably get another lecture now about how the use of big fonts, using bold print, Capital letters, exclamation marks, are seldom used by "educated people" and how it is all just elementary civilised behaviour, in the extreme world that Schmelzer seems to inhabit.


PS:
And last but certainly not least, I have claimed that with the fanaticism that Schmelzer is pushing this shrinking ruler/matter concept, that he must have an agenda.
I thought that this agenda may have been his original highly speculative paper he so often falls back on. I was wrong. He has another speculative paper which has languished since 1998, which requires "shrinking rulers"
So this may be what causes the erational support and refusal to acknowledge what I correctly claimed re shrinking rulers.
In the paper towards the end he says.......
Note that in this ansatz the universe does not really expand, the observable expansion is an effect of shrinking rulers. Below we nonetheless use standard relativistic language. Using some matter with p = kε we obtain the equations (8πG = c = 1):
http://arxiv.org/pdf/gr-qc/9811033.pdf

 

[Schmelzer]

It only plays a very minor role in cosmology interpretations against the far more accepted expanding Universe/BB model.
Interpretation:
"The above bold type is true but I cannot confirm it as it would invalidate my anti mainstream stance and confirm paddoboy is correct"

Yet another repetition, and obviously you cannot read, because it has been repeated already:

Learn to read: ... I do not even object ..."

But, ok, if you get an ..... from this, I can even reformulate: In this particular case, paddoboy is correct. I hope this will at least stop these boring repetitions of something I have never objected to.

Of course, this invalidates nothing. Else, I would have objected long ago, given that this irrelevant claim has been repeated already perceived 423 times.

Some more food for thought to invalidate this archaic unrealistic hypothesis/ limited analogy of shrinking rulers/matter.
[1]How big was all our rulers and matter at the BB?

Depends on which moment you name BB. The singularity itself is not part of the GR solution, thus, does not matter. For some arbitrary other time, compute
$$a(t_{BB}/a(t_{now}$$ and you get the factor. Don't forget that near the BB an additional element appears: The rulers will be in a physical environment of very high pressure. The deformation related with this very high pressure has to be taken into account additionally.
But this does not change the formula - for the same ruler, at the same pressure as common at that time, you would obtain the formula $$a(t_{BB}/a(t_{now}$$.

[2]How big were our sub atomic particles?

Given that sub-atomic particles may be used as rulers, the same answer.

[3] The binding forces holding quarks together only act over tiny distances and are limited in range, how can they manage to hold a proton together before it started to shrink?

Their range of action can be used as another (even if quite exotic) ruler, thus, similarly decreases.

[4] How big were our stars before they started to shrink?

The size of stars can also be used as a ruler, thus, the same rule $$a(t_{BB}/a(t_{now}$$. Of course, only up to the moment where all stars are so big that they touch each other. Before this, this has to be corrected, taking into account that the matter of this star is under higher pressure, so that the formula applies only relative to star material under the same high pressure.

[5] And how are S/N possible if matter/rulers are shrinking?

I don't understand this question, https://en.wiktionary.org/wiki/S/N ???

[6] Consider that in that first Planck instant after the BB, it was impossible for matter to exist, so how was the rulers/matter in this analogy created?

I do not know any instant where it is impossible for matter to exist. There may have been instances of very high pressure, but matter would certainly exist. If you think not, this certainly goes beyond GR, so that it is irrelevant, because we discuss here interpretations of solutions of GR.

[7]How big were electron orbitals when these rulers/matter were created?

The same factor $$a(t_{BB}/a(t_{now}$$ applies to them too. Starting with the moment where pressure is so high that it no longer makes sense to talk about them.

[8]What we call hot is atomic and molecular motion. As something gets hotter it expands: how can it expand if it is shrinking?

These are independent physical effects. The shriking which is relevant here is caused by the influence of the gravitational field. It has to be distinguished from expansion and shrinking caused by the variation of temperature and pressure.

A given peace of material can freely increase (if we go back in time) only as long as there is empty space around it. If everything is full with other pieces of the same material, it can no longer increase its size. As a consequence, pressure will increase so that the increase in size caused by gravity is compensated by the shrinking caused by the increase of pressure.

[9] How did shrinking operate during the Inflation epoch?

In the same way as without inflation. Inflation is simply a different function a(t), one with a''(t)>0. Given that the same GR solution is interpreted, this does not change at all.
At the time of inflation, the universe was nearly homogeneous, so that instead of shrinking rulers we would have decreasing pressure.

And don't forget the inevitable Poof!

I know that namecalling against me from your side is inevitable, and I don't care if you name me poof. Whatever you call me is irrelevant.

I'll probably get another lecture now about how the use of big fonts, using bold print, Capital letters, exclamation marks, are seldom used by "educated people" and how it is all just elementary civilised behaviour, in the extreme world that Schmelzer seems to inhabit.

Why? I know very well that repetitions will not help. Or you are willing to accept such rules, then repetition is not necessary, or you are unwilling, then it will have no effect. So, repetitions may be useful and have an effect for accidental other readers, so, from time to time it may be useful - else such accidental readers could think that such behaviour is acceptable and start to behave similarly.

And last but certainly not least, I have claimed that with the fanaticism that Schmelzer is pushing this shrinking ruler/matter concept, that he must have an agenda.

Yes, having an "agenda" is something horrible in paddoboys view.

 

[paddoboy]

Depends on which moment you name BB.

I'll only answer a few pertinent things here, ignoring the fabricated word salad parts. The rest is done and dusted from my point anyway.

I do not know any instant where it is impossible for matter to exist. There may have been instances of very high pressure, but matter would certainly exist. If you think not, this certainly goes beyond GR, so that it is irrelevant, because we discuss here interpretations of solutions of GR.

Let this lowly lay person inform you then.
According to the standard BB model, [Not Schmelzer's interpretation[the BB was an evolution of space and time. During the very early Universe after the BB, temperatures and pressures were so high, matter particles could not exist.
Yes, the limitation parameter of GR is at t+10-43 seconds. That does not mean that in line with data we do have, that we are not able to logically speculate back to the prime event.
That alone with the other objections and facts I have raised, support my view.
https://en.wikipedia.org/wiki/Chronology_of_the_universe
In the first phase, the very earliest universe was so hot, or energetic, that initially no matter particles existed or could exist perhaps only fleetingly. According to prevailing scientific theories, at this time the distinct forces we see around us today were joinedin one unified force. Space-time itself expanded during an inflationary epoch due to the immensity of the energies involved

These are independent physical effects. The shriking which is relevant here is caused by the influence of the gravitational field. It has to be distinguished from expansion and shrinking caused by the variation of temperature and pressure.

So gravity now caused this so called fabricated shrinking effect?

I know that name calling against me from your side is inevitable, and I don't care if you name me poof. Whatever you call me is irrelevant.

I was not referring to you. Please read it again.
I'm referring to the fact that depending on the size of mass and rulers in the beginning, once shrinking starts, a time a point is reached where the rulers and matter just go Poof! out of existence.
I have used it in this crazy debate with you a few times and now you just happen to notice and misinterprete it?

So, repetitions may be useful and have an effect for accidental other readers, so, from time to time it may be useful - else such accidental readers could think that such behaviour is acceptable and start to behave similarly.

And you are here to attempt to educate the forum to forum behaviour?

Yes, having an "agenda" is something horrible in paddoboys view.

Only when it blinds one or inhibits one to the accepted view and why it is accepted.
But Like I said, this matter is now done and dusted.

 

[Schmelzer]

According to the standard BB model, [Not Schmelzer's interpretation[the BB was an evolution of space and time. During the very early Universe after the BB, temperatures and pressures were so high, matter particles could not exist.

Matter existed, in a possibly different form.

Yes, the limitation parameter of GR is at t+10-43 seconds.
That does not mean that in line with data we do have, that we are not able to logically speculate back to the prime event.

Feel free to speculate, I was talking about interpretations of GR solutions.

So gravity now caused this so called fabricated shrinking effect?

We are talking about the interpretation of solutions of a theory of gravity, if you have not forgotten. Thus, about things caused by gravity.

I was not referring to you. Please read it again.
I'm referring to the fact that depending on the size of mass and rulers in the beginning, once shrinking starts, a time a point is reached where the rulers and matter just go Poof! out of existence.

And this makes not sense for me. Given that the shrinking factor is $$a(t)/a(t_{now})$$, and a(t) is defined for all times, a nontrivial shrinking factor is defined for all times too.

Of course, if you use an ether theory, with some critical atomic size, and this atomic size is constant, then the shrinking will have some nontrivial finish. But this is not what we are talking about now. What we talk about now it an interpretation of the FLRW solutions of classical GR.

I have used it in this crazy debate with you a few times and now you just happen to notice and misinterprete it?

I often ignore things which make IMHO no sense.

And you are here to attempt to educate the forum to forum behaviour?

I simply think about how one should behave, what would be reasonable behaviour and what would be unreasonable. Behaviour which could, possibly, educate other people seems at least not unreasonable to me.