On the Observational constrains of shrinking matter theories

[caracal]

Hi all, I wanted to write new thread about this topic just because there is just too much text in the previous one. I also change the perspective and look directly to a important question: how cosmological observations constrains shrinking matter theories. I was thinking if this is repetition but i wasn't sure. If many of you think this is repetition maybe i then ask you to delete this thread.

So Here in this topic i look what kind of observational constrains there are for shrinking matter theory. 

First why do i still bother thinking shrinking matter theory?
---------
MRS Hawkings have published (2010) a result that quasars don't exhibit effects of time dilation. (https://arxiv.org/abs/1004.1824) This result is in fact the only good reason i still think shrinking matter model could be real. This result may be explained by that supermassive black holes do not shrink when ordinary matter shrinks.
Hawking has proposed some other explanations at the end of the paper. I don't actually know how astronomers think of this study and do they think it is for example reliable. 

IF there is just one thing i ask you to discuss about it is this study. How to explain this kind of result? The rest could actually be something i have already discussed with other members in this forum.

---------

I try to be as brief as possible.

I don't concider CMD - lambda model in different coordinates - that would just be exactly the same theory than CMD lambda model but in different kind of coordinates where matter shrinks relative to the coordinates.

There are two things what i concider that are different:
1)Shrinking depends on proper time (and of course the 'scale' of the matter)
2)Apparent expansion of space is only apparent and is observational illusion caused by shrinking of matter. Gravitation   however does pull matter together

On the scalability argument
----------

One main argument against shrinking matter theory was that standard model and gravitation should start to look very different if matter shrinks. However i think it is still possible that the whole standard model gravitation experiences just right kind of shift into smaller length scale when matter shrinks that it looks like in our perspective that nothing has changed in standard model or behaviour of matter. I don't however know what would be the underlying cause for this kind of shift. 

Another argument against SMT is that standard model should look different in distant object in cosmological distances that has been in the past. But actually the standard model can be different, if the behavior of matter looks exactly as if it has only changes that are equal to cosmological observations in expanding space model: Light signal coming from distant object has time dilation, red shift and has it looks like that matter has been closer together in the past.

That observation of cosmic photons actually demands three things - not only length but also the time rate and all energies of matter should change in the shrinking matter. Only that way the cosmic photon appears to as as it has just to have lost some of its momentum, while the real explanation of this would be that the photon already in the moment of emission has these properties. This is because the energy, wavelength and frequency of photon follows equation E = hf ,where h is universal constant.

 

Why shrinking matter theory is worth thinking? There are 3 reasons for that:

1)If the shrinking of matter depends on proper time, then black holes do not shrink and neutron stars shrink slower. This could suite together with MRS Hawkings result that quasars don't exhibit effects of time dilation. (https://arxiv.org/abs/1004.1824) This result is in fact the ONLY reason i still think shrinking matter model could be real.

2)The exiting part of the theory is that there should exist matter that has shrunk differently in the past and therefore has
different 'preferred length scale'. This matter is in places where matter has have relativistic time dilation for long time. However the differences between matter in different places in solar system are very small, just barely observable. For example differences of proton or electron in meteorite samples. (This kind of matter could even be candidate for dark matter. Universe may for example contain two or more generations of matter that lies in different scales, for example protons that belongs to 200 times larger length scale than ordinary protons )

3)There are two measurable modifications to stellar and interstellar/galactic dynamics 
 a) - "Distance expansion" R1/R0 = 1 + k(t1-t0)  = 1 + 6.93*10^-11 1/year [t1-t0] (about same as hubble constant)
 b) - delay effect correction to gravity g = -(1 + kc/r)(GM/r^2) (which is very small if the rate of shrinking is small)
 
 Distance expansion is not a force - therefore it is not cancelled by gravitation. "Distance expansion" is apparent growth
 of otherwise fixed distances if they are measured by shrinking observer. 

 The delay effect comes from that matter has been different in the past - including its gravitation field. But this delay
 effect is very small if the shrinking of matter is slow.

 

Observational problems

-------

There is a Problem with "distance expansion" in solar system that could falsify shrinking matter theory:
-Because of distance expansion, moon should receed from earth at least 2.6cm/year and earth should preceed from
 sun 10.4m/year. The observed values are 3.8cm/year and 10.4cm/year, later is 100 times too small and the former
 may be also too big but i dont know how much of this 3.8cm is coming from tidal decay. Is there a process
 that could cancel this 10.4m/year out? for example the influence of other planets? If there are no such processes, this
 would falsify shrinking matter theories.

On the observational constrains for shrinking matter theory:
--------------

What shrinking matter theory should do is the following
-Standard model and gravitation is measured not to change over cosmological time when doing local measurements
-Velocity of light is constant in empty space and space follows Lorentz covariance
-When observing distant galaxies in the past the light signal should have
 1)Redshift
 2)Time dilation
 3)The distant galaxy looks as if it has been closer in the past
 4)Photons lose momentum

Like i already wrote above, one main argument against shrinking matter theory is that standard model and gravitation should look very different if matter shrinks. However it is still possible that the whole standard model gravitation experiences just right kind of shift into smaller length scale when matter shrinks. 

Another argument against SMT is that standard model should look different in distant object in cosmological distances that has been in the past. But actually the standard model can be different, if the behavior of matter
looks exactly as if it has only changes that are equal to 1)-4) and nothing else.

1),2) and c=constant requires that the time of the matter must accelerate by inverse of its shrinking factor
4) requires, if the law E = hf still holds and h is universal constant, that the energy and momentum meter we
use, should shift that way that all energies, momentums and masses increases by same factor than the time accelerates.

To put these into simple math:

length unit:  l_new = L * l_old 
time unit :   t_new = L * t_old
mass unit:    m_new = (1/L) m_old
Energy unit:  E_new = (1/L) E_old

Where L = 1 + k(t_new-t_old) , which is only linear approximation that fits to Hubble's law. K would be actually slightly
greater than Hubble constant if you count that gravitation is sligthly pulling matter together.

this k > Hubble Constant, propably by few percents?.

For example the changes in photon that is emitted by same matter in the past and now are exactly same than effects in the picture in just looking or photon in cosmological distances in expanding space model. 

The change in all energies and masses is really DEMANDED by the observational fact that cosmic photon appears to lose momentum and energy. (Other possibility could be planck constant h is not constant in equation E = hf but i dont concider it here. I think it is an observed fact that h is universal constant also for cosmic photons.)

About dynamics
------------

Next question is, how do dynamical properties of matter change?

If newtons 2nd law is universal law, then F = ma for inner interactions

=> F_new/F_old = (1/L^2)
 
This does not apply to cross interactions (interaction between two differently shrunk particles)

The equation for cross interactions could be F_cross/F_old = 1/(L1*L2) (or is it?)

Since power P = E/t

=> P_new/P_old = (1/L^2)

Since acceleration is a = v/t

=> a_new/a_old = 1/L

About Friedmann equations
-----------------------------

What is the time dependency of scale factor? There are now two phenomena that has effect on scale factor:
- Distance expansion
- Gravitation

And it is possible that there is no "ordinary expansion" of the space present. 

In empty space or space with small amount of dust there is only distance expansion. But how does distance expansion
vary over cosmological time scales? A good guess could be that it is exponential in the viewpoint of shrinking observer:

a(t) = exp(k(t-t0))
a(t0) = 1

This looks similar than dust + cosmological constant - universe

What is the equation for a(t) if also gravitation is taken into account? I don't know...

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End

[caracal]

I found one research article that is related to this topic.

news article: https://www.hawaii.edu/news/2021/11/03/expansion-of-universe-black-hole-growth/

research article: https://arxiv.org/abs/2109.08146

"Cosmologically coupled compact objects: a single parameter model for LIGO--Virgo mass and redshift distributions"

This study tests hypothesis that Black hole growth could be coupled with cosmic expansion. It does not say anything
about shrinking matter theory. But it tries to have meaningful results for LIGO and Virgo data by hypothesing that black
holes grow when space is expanding by following single parameter equation and then simulating stellar evolution:

m(a)=m0(aai)k

,where a_i <= a and k is a parameter of the coupling.

quote:
"To investigate this hypothesis, the researchers simulated the birth, life, and death of millions of pairs of large stars. Any pairs where both stars died to form black holes were then linked to the size of the universe, starting at the time of their death. As the universe continued to grow, the masses of these black holes grew as they spiraled toward each other. The result was not only more massive black holes when they merged, but also many more mergers. When the researchers compared the LIGO--Virgo data to their predictions, they agreed reasonably well. “I have to say I didn't know what to think at first,'' said research co-author and University of Michigan Professor Gregory Tarlé. “It was a such a simple idea, I was surprised it worked so well."

...

In the shrinking matter theory where black holes do not shrink, close this kind of dependency exists but the equation is not exactly this. it is in dust only -no lambda universe same with k=1, but in matter+radiation-no lambda universe it would be:

m(a)=m0∗LL(a)=m0(aai)∗s(a)

,where k=1 and s(a) is a function that can be obtained by solving first Friedmann equation. s(a_i) is propably slightly more than 1, maybe by few percents - Shrinking of matter is more dominant than gravitation. By the way it means that universe is contracting, but because matter is shrinking even more, the shrinking observer sees that space appear to expand.

I am not sure of this new kind of friedmann equation. It can be expressed best with two equations:

atrue=a⋅exp(k(t−t0))  

(a˙a)2=(3πG8)(ρm,0a3+ρr,0a4)

,where [math]a_{true}[/math] is 'true' scale factor. The exponential comes from cosmological principle: i assume that the observed redshift/time unit that is coming from shrinking of matter observed by shrinking observer is same at every moment.

LL(t)=exp[1+k(t−t0)]

K is here a parameter that is likely close to Hubble constant, but is slightly greater than that.

 

There are lacking new terms in that equation: compact matter, relativistic matter and matter that belong to different scale. All of these shrink at different speed than ordinary matter. For example the density of black holes behaves almost like [math]\frac{\rho}{a^2}. Also small amount of matter becomes black holes and neutron stars or relativistic matter over time.

Above i considered only flat universe. When matter shrinks, shrinking observer would measure that the curvature radius appears to increase - as all distances appear to grow. This would mean that since CMB the curvature radius has increased by factor of 1000 or was it 2000. 

What happens to Kerr black hole ergosphere? It has time dilation factor by few percents. Does it stay unchanged or does it
shrink slightly? That goes to question what is actually shrinking when matter shrinks. Is it only matter that shrinks or can ergosphere of rotating BH shrink too? This is open question to me.

---

[Mordred]

You really don't have much here to show a shrinking matter theory. Trying to show shrinking matter and how it supposedly accounts for universe expansion measurements isn't at all viable. For starters if matter shrinks then the fine structure constant itself would vary along with numerous other coupling constants. There is zero evidence this ever occurs. You moon conjecture has absolutely zero relation as the orbitals mathematics as it applies to escape velocity and the conservation laws is sufficient to explain the moons orbit.

 The paper you posted examines cosmological redshift of quasars vs super nova and shows the two have different redshift relations due to various factors related to luminosity distance relations etc. Unfortunately the paper didn't really do a good job as it doesn't take into account the non linearity past the Hubble horizon of z.  However that's just my opinion. However regardless. The paper does nothing to support a shrinking matter case. (your first paper You already admit your second paper doesn't relate

 Lastly the very scales of change were talking about is like seeing a tiny change at one end to a massive change in the measurements.

The two do not equate.... 

You mentioned in your opening posts concerning constraints .

1) the effect on coupling constants

2) doesn't account for BB nucleosythesis

3) cosmological redhift is a logarithic exponential change  it isn't linear  

4) the temperature history corresponds to that redshift as being proportional to the scale factor.

5) the cosmic microwave background we can measure infalling and out flows of matter in terms of the corresponding sound wave modes E and B modes  why do we not see evidence of an expanded matter field in terms of c ?

That's a start

Edited January 6, 2023 by Mordred

[caracal]

Thank you for detailed answer!

i am able to answer to 1,2,3 and maybe 4 but i don't understand 5.

Actually the last paper considers black hole growth coupling with cosmic expansion and this shrinking matter theory
also predicts that black holes should appear to grow when they are observed by shrinking observer. 

The following is quite lengthy and slightly repetitious.

I think it is experimentally well established that:
1) If we do local observations, we see no change in standard model or gravitation over cosmological times.
2) If we do cosmological observations, we see 
-time dilation in signal
-red shift in light
-loss of photon momentum and energy
-expansion of the space

Also observations suggest that the velocity of light is constant, it does not accelerate. Light passes 299 800 km every second all the time. 

I basicly consider two things in this shrinking matter theory:

A) I consider that the standard model and gravitation has a shift into smaller length scale as a whole. That would cause that fine structure constant and any of the coupling constants do not change over time if we measure things nearby us. 

B) And i consider that certain kind of changes in matter, standard model and gravitation, not only shrinking but multiple changes simultaneously, produces same cosmological observations that i mentioned above. But all these observations are now caused by that matter has been bigger and behaved differently in past - not by stretching the signal on the way. Therefore it only looks like that the space is expanding.

these A) and B) gives that the effect of coupling constants remain the same except that the signal coming from distant place appear to have red shift and time dilation and space appear to expand. (and except that BH, neutron stars and relativistic matter behave differently) 

(It is possible that i did thinking error and The statement B) would not hold after all)

Why these kind of things happens in matter? i don't know, but they might have some common cause.

But what kind of changes are then happening in the behavior of matter?

By demanding
-that special relativity (for example factoral time dilation and factoral length contraction) holds 
-light velocity c = constant, 
-photon equation E = hf and 
-Heisenberg's uncertainty principle dp*dx = h/2pi 
with h being universal constant 

and demanding that all these three valid all the time and do not change, at least three changes should take place:

1)Matter shrinks (note that free photons do not shrink since they travel at light velocity)
2)time of the matter accelerates such a way that observation of light velocity stay constant
3)All energies, momentum and masses increase such a way that observation of photon coming from distant place appear to lose energy and momentum

s'/s = L [m]  all lengths
t'/t = L - duration of all events in the behavior of matter
E'/E = 1/L [J] energy of all events...
p'/p = 1/L [kg m/s] momentum of any object or particle
m'/m = 1/L [kg] mass of any object or particle

,where 0 < L < 1 is factor of the change

(What do i mean by 'accelerating time of matter'? it is the shortening of duration of every event happening in matter, for example spin rate of the nucleus of deuteron and half life of carbon-14 and so on.)

By doing dimensional analysis from the three statements 1),2),3) above, i also get following changes in dynamics of matter:

f'/f = 1/L frequency [1/s]
v'/v = 1 velocity [m/s]
a'/a = 1/L acceleration [m/s^2]
F'/F = 1/L^2 strength of local forces [kg m/s^2]
P'/P = 1/L^2 power [J/s]
T'/T = 1/L temperature [K]
f'/f = 1/L^4 luminosity [W/m^2]

where 0 < L < 1

(Note that any field like force field or potential would also shrink into smaller size)

When this kind of change in matter happens it gives theory that passes so called Tolman test states that in expanding universe, surface brightness should be inverse proportional to the fourth power of cosmological redshift. This model gives this result.  (except keeping in mind that compact objects shrink more slowly and black holes do not shrink at all)

f = A/(1+z)^4  where A is some constant 

These kind of changes also produces Robertson Walker Metrics in flat space - which is now only 'apparent' metric, not real metric.

ds^2 = c^2dt^2 - a(t)dr^2

There are important differences from expanding space theory.

The three differences are that 
1) expansion of distances is not a force - it is 'apparent growth' that can be seen as velocity vector. Also the Friedmann equations are different for the same reason. And 
2) compact,relativistic matter and matter in strong gravitation field shrinks more slowly and black holes do not shrink.

It is also now possible that 
3) there exist matter that belong to different scale or have shrunk differently in the past. 

The time dependency of scale factor a(t) IS NOT LINEAR in this theory. IF cosmological principle holds, the observed change in distances if gravitys effect is reduced and photon wavelength are all the time same during same time interval of time of the shrinking observer. This would give exponential law:

dL/dt = k*LL

LL(t) = e^[k(t-t0)] = a(t)

Note that L is now a function (of time of a shrinking observer t - not constant time t) and LL(t) > 1. it is not the same than L in the equations above. I used to mark this function as LL(t). 

But because gravity slightly pulls matter together, the real time evolution of scale factor is only nearly exponential, but
it will eventually come close to exponential since the effect of gravity becomes all the time smaller.

(this may be wrong pair of equations)

1)a(t) = a_f * e^[k(t-t0)]

2)((da_f/dt)/a_f)^2 = (3piG/8c^2)* rho(t)

(Note also that the equation 2) does not need cosmological constant to get accelerating apparent expansion.)

The rough linear approximation a(t) = 1 + H0(t-t0) i use only to get value for k that is close to H0 and to estimate how much distances should grow in solar system

dr(t)/dt = (roughly) r(t0)*H0

This equation (that radius vector r increases or 'appear to increase' should be taken then account in numerical simulations. It does
make escape velocity smaller like you said.

---

I think nucleosynthesis and recombination are both possible in this shrinking matter theory and gives same results.
Also inflation is possible - now inflation may be a period where matter shrinks very fast during short period of time.

---

I hope this clarifies what i think of the possibility that certain kind of changes in matter, standard model and gravitation - simultaneously could give almost same cosmological observations than expanding space gives.

.

 

Edited January 12, 2023 by caracal

[Mordred]

2 hours ago, caracal said:

 

By doing dimensional analysis from the three statements 1),2),3) above, i also get following changes in dynamics of matter:

f'/f = 1/L frequency [1/s]
v'/v = 1 velocity [m/s]
a'/a = 1/L acceleration [m/s^2]
F'/F = 1/L^2 strength of local forces [kg m/s^2]
P'/P = 1/L^2 power [J/s]
T'/T = 1/L temperature [K]
f'/f = 1/L^4 luminosity [W/m^2]

You might want to revisit your dimensional analysis.... You have in the above units units of length on the right hand side of your equations However no corresponding units of length on the left hand side in several of the above such as temperature, power, and luminosity secondly many of the above has non linear rates of change where you have linear.

assuming you are dividing the primed value with the unprimed value then you have dimensionless quantities on the LHS. So the RHS definitely does not match in every case in the above.

My point 5 is an example of a very distant set of measurements that can be examined using spectrographic evidence. Google Rydberg lines for what that entails. However when you account for redshift the lines show the same distance in the atomic orbitals. No you have not adequately accounted for that as your equations are too linear to handle the nonlinearity of redshift.

this is what I am referring to on the nonlinearity note how Z as well as temperature suddenly spikes. Where distance now hits the x axis is the time now... previous to that is the past while to the right is the future using current cosmological parameters. You will also find that the expansion rate ie Hubble parameter is also non linear. In point of detail the above shows logarithmic rates of change. Zero on th x axis corresponds to z= 1100 CMB

http://web.mit.edu/2.25/www/pdf/DA_unified.pdf

use this and recheck all your equations under proper dimensional analysis 

Edited January 12, 2023 by Mordred

[caracal]

About Rydberg emission lines:

(This following may be unnecessary to write:)

The Rydberg emission lines of hydrogen in distant universe should be similar than in expanding space theory. But now the light had red shift already when it was left from the matter in past.

-atomic orbitals of matter have just been bigger in the past by factor (1+z), and the time needed for emission from exited state has been (1+z) times longer. The binding energy of electron would have been 1/(1+z) times less. But the velocity of light and velocity of electron have been exactly same. Planck constant has been exactly same also.

it would be difficult to distinguish whether red shift is coming from expansion of space or from matter that has been bigger in the past. It is also difficult to distinguish whether red shift is coming from matter that is bigger or from Doppler effect. 

---

About non-linearity:

You mean non-linearity = rapid spike up in the early universe in the redshift and temperature evolution curve? 

Both of the following are possible: 
1 that there is ordinary expansion of space besides that gravity pulls matter together and matter shrink. 
2 There is no ordinary expansion, only gravitation pulls universe back together and matter shrink.

If 1 is true then i think the theory have almost similar non-linearity in very early universe than benchmark model. The difference is just slightly different Friedmann equations and their solutions.

But if 2 is true i am not sure of that. In this case, non-lireaty can be achieved if the function LL(t') that might be something else than exponential, has been greater than exponential in early universe. But if not, then i think universe and CMB both should have been much older than about 13.7 Billion years. And that could have a problem or disagreement with current observations of early universe. I don't know which observations.

If there were no gravitation present and 2 is true, the shrinking matter universe would be similar than de-sitter universe.
(That is so if i assume that the factoral rate of apparent expansion is same all the time: dLL(t')/dt' = H_0 LL(t'). This assumption may be wrong.) 

In both cases 1 and 2 the universe would be asymptotically close to De Sitter universe in distant future.

---

About equations of change:

I think all equations of the change are correct, but i marked them in unclear manner.

for example notation

F'/F = 1/L^2 [kg m/s^2]

means that when matter and its behavior changes, the ratio (new force/old force) is multiplied by factor 1/L^2 and what is in the bracket [] is just remainder that the dimension of force is kg m/s^2. The brackets is not a factor in equation.

I could write the equation like this:

new force = old force * 1/L^2  [remind that unit of the force is kg m/s^2]

But it is a little more convenient to divide both sides by old force:

new force/old force = 1/L^2

How do i calculate these equations? I start with these

$t'/t = L$
$s'/s = L$
$m'/m = E'/E = 1/L$

I can end up to equation for force starting with:

F'/F = (m'/m)(v'/v)/(t'/t) and i know already that

m'/m = 1/L
v'/v = 1
t'/t = L

=> F'/F = 1/L^2

and for example equation of change for power i start with

P'/P = (E'/E)/(t'/t)

and knowing

E'/E = 1/L
t'/t = L

gives me that

P'/P = 1/L^2

and equation of change for acceleration

a'/a = (v'/v)/(t'/t)

and knowing

v'/v = 1
t'/t = 1

it gives

=> a'/a = 1/L

-----
Actually (i forgot this statement earlier) if matter is shrinking continuously and the time is accelerating (duration of all
events is all the time getting shorter) then equation

t'/t = L

holds only when t' and t are very short. The equation for elapsing time in this situation would be

t(t') = definite integral(t1->t2) (1/L(t')) dt'

(But who measures this kind of time t if all observers are shrinking?)

-----
I earlier noted already that when i talk about apparent expansion of space observed by shrinking observer, i use function LL(t') that is not same as L. LL is a function that describes factoral change in photon wavelength or expansion of space if it was solely coming from the shrinking of matter - if they were observed by shrinking observer. LL is also expressed as function of the elapsing time of shrinking observer. I could mark this time as t'.

LL(t') = e^[k(t'-t0')]
LL(t0) = 1

If there were no gravity, a(t') would be just same as LL(t'). In this situation a(t') behaves exactly like in de sitter space.

---

Edited January 15, 2023 by caracal

[Mordred]

No I posted the graphs showing non linearity. The curves themselves are not linear. I'm sure you have heard the equation y=mx+b for linear graphs? A nonlinear function is a function whose graph is NOT a straight line. Its graph can be any curve other than a straight line. Does that help

You still haven't fixed your dimensions in your equations they are still invalid as a result. Convert each unit to SI units on both the LHS and RHS of the equal sign. Follow the procedure in that link I provided 

lets take an example \[\frac{\acute{t}}{t}=L\] so \[\frac{s}{s}= metres\] wrong does not equal the seconds are on the LHS it doesn't have units of length which are on the RHS.

Edited January 15, 2023 by Mordred

[Mordred]

lets take this equation ask yourself what units is z ? (cosmological redshift equation)

\[z = \frac{\lambda_r}{\lambda_e} - 1\] now this equation is only approximtely accurate when z<1 however it will diverge into a non linear curve. The other detail to note is that -1 included. 

lets look at your luminosity

f'/f = 1/L^4 luminosity [W/m^2] is f the flux ? even then how did you derive that given the luminosity to distance is

\[D_L=\sqrt{\frac{L}{4\pi F}}\] 

course the one that I find truly mysterious is how you get a length from temperature. Seems to me that you've assumed each of the values are going to have the same ratio of change with the scale factor and that is not the case.

 

Edited January 16, 2023 by Mordred

[caracal]

About nonlinearity:

yes i know linear function is y=ax+b that is a straight line in xy-plane.

This theory ,if there were only shrinking of matter present and universe is static, and assuming exponential apparent expansion, is similar than de sitter space and gives the age of CMB to be about 100 Byrs which is 7.5 times longer than current cosmological model gives. 

*** How i calculate the age of the universe in static + shrinking matter only universe:

For age of CMB i solve following equation by assuming k = H0 = 0.0693 [1/Byrs]

e^(H0(t'-t_now')) = 1/1100 => (t'-tnow')= Ln[1/1100]/(0.0693) = 100 Byrs (that is 7.54 times greater than in lamda-CDM model.)

(I don't know can some observation verify that universe is 13.7 Byrs old, or is that extrapolation based on cosmological
benchmark model. )

***

In that moment when universe is young i think some observables can go up but in this case they have gone long way. But they are nonlinear nevertheless.

(I don't know which observations actually tells how old CMB and universe are or is it just extrapolation based on the benchmark model. I know that oldest known globular cluster stars are about 12Byrs old based on at least HR-diagram mainsequence cut-off.)

If i add some amount of matter to this kind of space, it just pulls universe together and the observed apparent expansion is slower. (In principle gravitation could win the apparent expansion if matter is added to this universe more.)

But if there were matter, radiation and 'ordinary expansion' but not cosmological constant and shrinking present in the universe the model gives somewhat similar age than benchmark model does. In this case the shrinking of matter would be substitute to cosmological constant. But the Friedmann equations are slightly different.

Therefore i guess just in basis of the similarity with benchmark model - in this case all behavior of observables in early universe can go up when looking backward in time just the same way than in benchmark model.

---
About the equations of change:

I remind that L describes the factor of the shrinking - it is not directly scale factor (it is that only in the 'shrinking matter' + static universe). In order to get scale factor you need to solve friedmann equation. There is gravitation and may be ordinary expansion present in universe besides of the shrinking of the matter that also have effect on the time evolution of scale factor.

LHS is dimensionless and L is dimensionless, also RHS is dimensionless. I think the correct way to write the equations with units marked in each quantity is:

Equation for lengths : (s'[m])/(s [m]) = L

Equation for duration of any event : (t')/(t) = L

Equation for energies: (E'[J])/(E[J]) = 1/L

Equation for masses: (m'[kg]/m[kg]) = 1/L

and for example:

Equation for forces: (F'[kg m/s^2] / F [kg m/s^2]) = 1/L^2

Equation for accelerations: a'[m/s^2]/a[m/s^2] = 1/L

Equation for powers: (P'[J/s]/P[J/s]) = 1/L^2

m = meter
s = second
J = kg m^2/s^2 = Joule
kg = kilogram

---
About luminosity:

You ask how does luminosity of distant star $$ L = F * 4\pi D_{L}^2 $$ appear to shrinking observer?

-First In the viewpoint of shrinking observer, distant star has been bigger in past and has had 'expansion' by factor L>1

The light that was radiated by the star red shifted and the flux is time dilated which makes power go down like 1/L^2.

1) the power of that star is 1/L^2 times weaker

Also since the meter unit of the observer has shrunk, the distance to that star is greater by factor L.

2) distance to that star is L times greater

These two changes 1,2 makes luminosity of distant star to be 1/L^4 times weaker if it is observed by shrinking observer.

Now if the universe was static, this 1/L would be exactly red shift:

1/L = proportional red shift  ( in static universe, only shrinking of matter present in the universe )

---
About Temperature

To get equation of change for temperature, i can look all the equations that connects energy,power,flux or wavelength to temperature.

For example for black body radiation, Wien displacement law is  lambda = b/T . I know that b must be universal constant and i get

T'/T = b/(lambda'/lambda) = 1/L

Or i can look Stefan-Boltzmann law  flux = rho*T^4. Rho must be universal constant. Therefore i get

(T'/T)^4 = flux'/flux = (power'/power)^2/(cross section area'/cross section area)^2

=> T'/T = 1/L

(Example: If sun would shrink by factor L=0.5, its mass gets 2 times greater, its temperature gets 2 times hotter and its flux becomes 16 times greater and total luminosity 4 times greater. However the nuclear reactions get only 2 times faster - all atom nuclei also change by certain ways: their interacting forces,radiating powers, masses, coulomb walls and binding energies changes also. But actually the star would behave as if light coming from it just have time dilation, redshift and that the star appears to been closer, in other words, the star just appears to behave as if the space was expanding and changing the picture and signal on the way)

 

Edited January 18, 2023 by caracal

[Mordred]

Thank you for clarifying that L is a dimensional less parameter, your age calculations are off. Unfortunately the calculations involve the density of matter, radiation, Lambda as well as the curvature term K. You also have to factor in how each expansion contributor evolves over time.

the generic formula for the age of the universe is as follows (will vary depending on the applied cosmological parameters.)

\[dt=\frac{da}{aH_o}\frac{1}{[\Omega_r(\frac{a_o}{a})^4 \Omega_m(\frac{a_o}{a})^3 \Omega_k(\frac{a_o}{a})^2 \Omega_\Lambda(\frac{a_o}{a})]^2}\]

for our universe with K=0 and being Lambda dominant today this simplifies to

\[t_o=\frac{2}{3}\frac{1}{H_O}\sqrt{\Omega_\Lambda}\sinh^{-1}\sqrt{\frac{\Omega_\Lambda}{1-\Omega_\Lambda}(\frac{a}{a^3})^3}\]

How to determine the decoupling time for the CMB is a lengthy process involving the Saha equation however for out universe without going into all the required decoupling chains etc the solution simplifies to

\[t_{dec}=\frac{2}{3H_O (1+z_{dec})^{3/2}}\]

quite frankly the only way to truly test your theory out is to see if you can generate the same curves that the FLRW metric does You can't afford to guess at those ratios of change as the expansion history and subsequently how each factor above evolves will depend on the evolution of each of the contributors above. The Cosmological calculator in my signature will greatly help generate a dataset for you using whichever cosmological parameters you choose. Unless you can produce each curve then your theory still requires significant work. It does anyways as you still need to prove it can prove how the universe seems to expand. You also haven't recognize that we don't rely on redshift and luminosity distance. We also use methods such as intergalactic parallax. 

 

 

Edited January 19, 2023 by Mordred

[Mordred]

I would like you to consider the following in terms of Luminosity distance. You can see from the equations above in my previous post that the evolution of matter, radiation and Lambda has significance in distance measurements as well as expansion rates. Furthermore the common formulas you often see for redshift, luminosity, universe age etc do not include those details. example above.

here is how luminosity distance relates with the evolution of the above.

the energy flux being the measured energy per unit time per unit area of the detector. the luminosity distance is then defined on the radius of the sphere centered on the source in which the absolute luminosity would give the observed flux.

\[\mathcal{F}=\frac{\mathcal{L}}{4\pi d^2_L}\] as light travels on null geodesic ds^2=0 

\[ds^2=dt^2-at^2[\frac{dr^2}{1-k r^2}+r^2(d\theta^2+sin^2\theta d\phi^2)]\]

with k=0 and the various contributions above this gives

\[\frac{dr}{1+a_o^2H_o^2 r^2\Omega_k}=\frac{1}{a_o^2H_o^2}\frac{dz}{(1+dz)^2(1+dz\Omega_M)-z(2+z)\Omega_\Lambda}\]

which determines the coordinate distance (not proper distance) as a function of redshift for 

\[r=r(z,H_0,\Omega+M\Omega_\Lambda)\]

energy becomes

\[E_O=\frac{E}{1+z}\]

rate of photon arrival will be time delayed via

\[dt_o=(1+z)dt\]

\[\mathcal{F}=\frac{\mathcal{L}}{4\pi a^2_Or^2(z)}=\frac{\mathcal{L}}{4\pi d^2_L}\]

gives luminosity distance as a function of redshift

\[H_O d_L=(1+z)|\Omega_k|^{-1/2}sinn[|\Omega_k|^{-1/2}\int^z_0\frac{d\acute{z}}{\sqrt{(1+\acute{z}^2)(1+\acute{z}\Omega_M)-\acute{z}(2+\acute{z})\Omega_\Lambda}}]\]

where sinn(x)=x k=o,sin(x) if k=1, sinh(x) if k=_1

leads to

\[H_Od_L=z+\frac{1}{2}(1-\frac{\Omega_M}{2}+\Omega_\Lambda)z^2+\mathcal{O}(z^3)\]

where H evolves as

\[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\]

temperature as a function of redshift gives

\[T=T_O(1+z)\]

the above is a methodology by Juan Garcıa-Bellido in his numerous papers, though you can find similar solutions in Bunn and Hoggs (distance measures) and Lineweaver and Davies.

Here is the Hogg paper

Distance measures in cosmology

https://arxiv.org/pdf/astro-ph/9905116.pdf

in this paper you can see similar a similar treatment using E(z) equation 14. The paper further covers angular diameter distance which further relates to luminosity distance.

One of the details you should note in the last paper is that many of these factors do not have identical rates of change. see the graphs in the paper above for an example. Those should further highlight the non linearity logarithmic rates of change.

 

 

 

Edited January 21, 2023 by Mordred

[caracal]

Thank you for those formulas and equations. I have to think about them for some time. (I hope the following math i represent does not disturb them.)

I think this theory produces FLRW metric. But it is 'pseudo' metric or apparent metric, not real metric. (but only if all matter were shrinking similar way everywhere.) Actually the observed metric is combination of pseudo metric and real metric. 

But the Friedmann equation is slightly different.

Since the metric is FLRW, solving the new Friedmann equation is i think quite simple. You just insert or substitute 

$$ a = a_{obs}/LL(t) = a_{obs}*e^{-k(t-t0)} $$

$$ \frac{da/dt}{a} = H = H_{obs} + k $$ 

to any kind of Friedmann equation or other equation or formula you have that describe expanding universe. 

k [1/s] is a parameter. I earlier guessed that k is a little higher than H0 but it could be something else as well.

(But you have to assume that all matter is shrinking at equal rate in universe and the amount of black holes neutron stars and relativistic particles is negligible, and that there exist negligible amount of matter that belongs to different preferred scale - it would have different shrinking rate which causes that its gravitational influence and field changes relative to shrinking observer. All these matter would have different density components that depend differently from scale factor than ordinary matter)

---

An example to solve Friedmann equation:

I don't use here in this example Lamda-CDM what you did above - but old model where is no cosmological constant and i add shrinking of matter to it.

Now i am considering situation where space is flat and there is ordinary expansion + gravitation + shrinking matter present in universe, but there is no cosmological constant - shrinking of matter is here a substitute for cosmological constant:

$$ ds^2 = c^2dt^2 - a_{obs}^2(t)dr^2 $$ 

$$ a_{obs} = a_{real}a_{apparent} $$
$$ a_{apparent} = e^{k(t-t_0)} $$
$$ a_{obs0} = a_{real0} = a_{apparent0} = 1 $$

(Here i assume that apparent expansion that is coming from shrinking of matter is exponential)

i mark: 

$$ a_{real} = a $$ in the following:

$$ (\frac{\dot{a}}{a})^2 = (\frac{8\pi G}{3})(\frac{\rho_{m0}}{a^3} + \frac{\rho_{rad}}{a^4}) $$

First i get the ordinary Friedmann equation solution to solve a 

$$\frac{\dot{a} }{a} = H_0\sqrt{\Omega_{m0}(\frac{1}{a^3})+\Omega_{r0}(\frac{1}{a^4})}$$
$$\Rightarrow  t = \frac{1}{H_0}\int_{0}^{a}\frac{xdx}{\sqrt{\Omega_{m0}x+\Omega_{r0}}} $$

(formula is taken from www.universeinproblems.com and modified by setting a/a_0 = a and a_0 = 1)

Next step is just to insert to equation above the following:  $$  a =  \frac{a_{obs}}{e^{k(t-t_0)}} $$

With computer it might be quite easy to solve the inverse relation $ a_{obs}(t) $ numerically and then get other
quantities and their curves (from 2nd friedmann eq and eq of state (?))

My guess is that all curves are just slightly different from benchmark model that has cosmological constant.
(or are they?)

---

About differences between this shrinking matter theory and expanding space theory:

There are some significant differences in this shrinking matter theory. Some of them are in the range of observations.

The differences of this shrinking matter theory from expanding space theory are:
1. Different kind of Friedmann equation - scale factor solution from 1FE is afterwards multiplied by LL-function that could be exponential LL = e^(k(t-t0)) , where k is parameter
2. Apparent expansion is velocity component - not a force - therefore it is not cancelled in solar system and milky way: R = R0*e^(k(t-t0))
3. Black holes do not shrink
4. Neutron stars shrink less and old neutron stars start to have matter that has shrunk less than ordinary matter.
5. Relativistic matter shrink less
6. Gravitation of ordinary matter has very small delay effect by factor e^{kr/c}
7. There exist matter that prefers different length,time and energy scales. (I invented term 'scale difference' to describe the difference between two kind of matter that prefer different scales: There is matter that has scale difference) 
8. Cosmological redshift - the apparent part - is now 'illusion' that comes from changes in shrinking observers meterstick,clock rate and energy units. However there may be ordinary expansion/contraction of universe present.
9. Universe can be contracting and at the same time it can look to be expanding in the viewpoint of shrinking observer.
----

2,3,4,5 might be just barely in the range of observations
7 it may be possible to weight proton from meteorite sample - it is in range of measurements to see if it has more mass
7 may be difficult to observe from spectral lines since it is difficult to distinguish from doppler effect

One problem with 2 : earth - sun distance should increase but it is observed that it does that only 10-15cm/year. 

---

Edited January 22, 2023 by caracal

[Mordred]

Careful the overdot on the scale factor is a time derivative for velocity. Will look over the rest later on.

Here

https://en.m.wikipedia.org/wiki/Time_derivative

I don't believe your intention is to modify the fluid equations above The fluid equations directly derive from the thermodynamic laws via the effective equations of state (cosmology).

I'm not clear on this statement of yours

\[a_{obs0} = a_{real0} = a_{apparent0} = 1\]

the scale factor is simply a constant of proportionality as I'm sure your aware the scale factor today is set at 1. the scale factor at some point in the past is simply the ratio of radius of the observable universe then as opposed to today. For example a scale factor of 0.5 the radius of the observable universe would be half what it is today. So I do not know where your getting the extra scale factor terms such as apparent. Nor the need to normalize the above terms as that would remove the usefulness. However the equations above wouldn't work. As I mentioned the overdot is the velocity term of the scale factor in the equation above. 

If your goal is to match observational data you will also need the full Friedmann equation with the cosmological term. You will still have nonlinearity in point of detail until the Lambda dominant  era the universe expansion was slowing down until the Lambda term became dominant a close examination of this will show this occurs roughly at the universe age of 7 Gyrs. The value will vary according the the cosmological parameter dataset used. Via the lookback time equation you have above which is similar enough to the one I posted earlier.

None of this still addresses numerous other problems such as the nucleosynthesis, electroweak symmetry breaking, which both rely on thermal equilibrium relations and expansion not to mention the fine structure constant and other related coupling constants which have relations involving radius for their effective strength.

 Nor have you mentioned any particular cause for shrinking matter and how the rates of the shrinking will correspond to a varying rate of change in expansion rates. The rates of shrinkage would have to correspondently shrink. I fail to think of any viable mechanism as to how that could possibly work. That includes via gravity or any of the fundamental forces.

However my feelings as to your model viability is secondary. The point of detail is that you are making the effort to properly model and in that regard I will still assist as one learns from correctly modelling even when the model is wrong. LOL truth be told a good theorist physicist will do everything in their power to prove their own models wrong. That's how they become robust to begin with. One other thing to keep in mind. Even if you fully get the mathematics to work and match the curves I mentioned (they correspond to actual datasets otherwise the theory wouldn't be viable to begin with).

 You will still need to figure out the cause of shrinkage and what controls that states behavior over time. As well as the cause of its history of variations. That will also need to be mathematically modelled.

Edited January 23, 2023 by Mordred

[caracal]

About Friedmann equation and distance expansion:

I couldn't manage to write correct equations. But i decided to write anyway what i am thinking about.

My calculations were wrong. i cant multiply a with apparent a to get something like

$$a_{obs} * a_{apparent}*a_{real}$$

this is wrong.

I should start with stating that because matter is shrinking, all distances appear to grow by

$$ r(t) = r_0 e^{k(t-t_0)} $$

This is the only thing i add to cosmological model at first. K is here a parameter. Besides the ordinary expansion of space, all distances just 'magically' appear to grow like this. (well not all - stars and planets do not expand)

Maybe the law for planetary motion when matter is shrinking is then:

$$ r_x(t) = r*e^{k(t-t_0)} $$
$$ a(t) = -\frac{GM}{r_x^2}$$
=>
$$ a(t) = -\frac{GM}{r^2}*e^{-2k(t-t_0)}$$

(?)

IF thinking increments the orbital elements of the planet should be continuously changing such that the radial vector increases but velocity vector remains same. For this reason, the planet should gradually migrate away from the sun. I don't know does the eccentricity increase if you start with circular orbit. I know i could do numerical calculations by adding following increments:

1. Planet travels along Keplerian orbit a small increment

2.The radius vector gets increment but the velocity remain same - the planet is now in different orbit that is slightly further from sum but it has still exactly same velocity.

I could look that situation on other perspective: as seen by non-shrinking observer. In this perspective the gravitation field of sun becomes different and shrinks. In Newtonian inverse square law gravitation, the observed change in gravitation is a' = La , 0 < L < 1. But what is L(t)? I know that L(t') = 1/LL(t') = e^{k(t-t_0)} and that t' = integral 0->t L(t) dt.

Second question is - How to derive Friedmann equation from this new equation of planetary motion? I know that for Newtonian gravitation the first Friedmann equation in flat space becomes (Newtonian derivation of FE):

$$ (\frac{\dot a}{a})^2 = \frac{8\pi G}{3}*\rho $$

 

On the other hand i suggested that in empty space the apparent expansion of scale factor is 

$$ a(t)= e^{k(t-t_0)} $$

Which is similar than in cosmological constant-only universe 

Could i from this correspondence just add A*k^2 to RHS of Friedmann equation?

$$ (\frac{\dot a}{a})^2 = \frac{8\pi G}{3}*(\rho + Ak^2) $$

where A is certain constant (that i didnt manage to find from internet)?

In this case the A*k^2 would be substitute to cosmological constant.

I would need some kind of reference to make correct planetary motion equation and Friedmann equation that i failed to find for now.

---
About the cause of shrinking
(this is more open speculation but i write here some thoughts)

I don't know the mechanism or process what would make matter to shrink. But i can describe how it could do that.

It could be that if something happens to spacetime, for example the flow of time was accelerating could be the cause. Space or matter could be coupled with or stuck with flow of time that way, that it experiences shrinking when time accelerates. But what makes time to accelerate, i don't know. Maybe empty space differentiates but matter for some reason stay intact and shrinks. 

Space-time could be entity that is very dynamic in very small scales - i think that is what is needed. It could be full of continuously occurring events in a small scale. 

But not knowing this i can still describe something about possibility on shrinking of matter. What kind of principles hold. I selected to keep Lorentz covariance, constant light velocity, Heisenberg uncertainty principle, Photon energy law E=hf, De Broglie equation lambda = h/p and constant Planck constant.

(Newton didn't know what causes gravitation but he knew how it works. He wrote mathematical description for it - the Newtons law of gravitation F = G M1M2/r^2. Now we know that gravitation field is not a force field, it is curvature of space-time. Newton's gravitation law is weak field approximation. And there is gravitational time dilation what newton didn't know also present in weak gravitational field)

---

About curves

I think if this theory gives almost similar Friedmann equation and time evolution of scale factor, then i think all other curves behaves also close to same way than in Lamda-CDM model. It will also give almost similar answer to nucleosynthesis. 
 

Edited January 29, 2023 by caracal

[caracal]

This is a recent study that has observed that supermassive black hole growth
could be coupled with cosmic expansion. This study seems to have gained much attention and also critizism.

news article:
https://www.ralspace.stfc.ac.uk/Pages/first-evidence-black-holes-source-of-dark-energy.aspx
"Scientists find first evidence that black holes are the source of dark energy"

research paper:
https://iopscience.iop.org/article/10.3847/2041-8213/acb704
"Observational Evidence for Cosmological Coupling of Black Holes and its Implications for an Astrophysical Source of Dark Energy"

(Published 2023 February 15)

Shrinking matter theory explains this cosmological coupling by that when matter shrinks, the shrinking depends on proper time and black holes do not shrink since they have infinite time dilation. Therefore black holes appear to grow.

There are some mistakes in my previous post regarding derivation of Friedmann equation and modification to stellar dynamics. The task is i think quite simple. i just have to somehow contribute both stellar dynamics and scale factor time evolution that all distances appear to grow by

$$ r_(t) = r_0 e^{k(t-t_0)} $$

where k is parameter.

There is still a problem with this theory: Earth-sun distance should appear to grow but it is observed to do that only 15cm/year.