5) The redshift and the time (or distance) relationship.

5) The redshift and the time (or distance) relationship.

Since in the Shrinking Matter Theory there is not receding speed, there is no reason to determine the distance based in the standard model (expanding universe), which is necessary determine the apparent receding speed to infer the distance based in the Hubble constant.

In the Shrinking Matter Theory, the size of the atom decrease along the time, so the time should be defined by the rule of lost in volume per unit of time (LVL). The LVL can be mathematically defined as d_VL /d_t.. The LVL should vary along the time, according to the size of the atoms, and this variance could be proportional to the surface or to the volume of the atoms along the time.

This would let us to two hypotheses, A, and B.

The hypothesis A proposes the LVL variance could be proportional to the surface of the atoms.

The hypothesis B proposes the LVL variance could be proportional to the volume of the atoms.

Now we can develop the two hypotheses to analyze the possibility of choose the one which best fit to the observations. 

 

5.1)  Hypothesis A:

This hypothesis proposes the LVL (d_VL/dt) varies proportionally to the surface S_f of the atom, so we can write:

LVL/S_f = constsnt = K_s =>

(d_VL / d_t) / S_f  = K_{s    =>}

d_t  = d_VL / (K_s  S_f)          (I)

Solving this system we have:

D = t = K_z  (x^2/3-1)   (IV)

x = (1+Z)   

The full solving for the above function can be found here: 

https://app.box.com/s/lu5gmwwj5tfxzjrpu1y3kokdp7i5b0k6

                                   

D = Distance  (Gly)

t = Time        (Gyr)

Kz = Stretching factor of the function so that fitting it to the measured observations at low redshifts.

The redshift Z can now be expressed in function of the time t as follow:

Z = ((t+K_z)/K_z)^3/2-1      (For hypothesis A)

The farthest bodies newly observed present redshift of about Z =8, so we should limit our researches in in the range of Z from 0 to 8

The distance D in the standard model for Z= 8 is 13.436113 Gly, 

The Bohr radius in the shrinking model r_o and  r_f  are:

r_o = 5,291773 x 10^-11 m (for Z=0)

r_f  = 2,899617 x 10^-10 m (for Z=8)

r_o  = Bohr radius of the hydrogen in the ground state at the present, in our local frame (m).

r_f   = Bohr radius of the hydrogen in the ground state  in the past frame (m).

For the hypothesis A, the above equation (IV), is the basic to define all the relationships in the Shrinking Matter Theory.

Now we can determine the best value for the constant Kz, so that calibrating the equation to the observed distances. This calibration must be done at low redshift, where we can determine the distances by parallax. This mean the above function should give us the same value when the redshift is null (zero), and at low redshifts give us neglected differences. This mean the tangent of the above function (IV), at Z= 0, should have the same as the tangent in function of the standard model (expansion universe).

In the standard model, (expanding universe), the equation to define the distance is:

                     

D = t =  ((x²-1) c 3.26) / ((x² + 1) H_o 10⁶)     mpc   (VI)

c = light speed = 299792458 m/s

H₀ = Hubble constant = 71 km/s/mpc

When deriving and matching the distance equations of the shrinking model and the standard model, we have:

K_z = ( 3 c 3.26) / (2 H_o 10⁶)   =>

c = light speed = 299792458 m/s

H₀ = Hubble constant = 71 km/s/mpc

The exact value of the conversion factor “3.26” is (3.261 633 430 119 53), and it should be used for taking of accurate results.

The full solving for the K_z constant can be found here: 

https://app.box.com/s/lu5gmwwj5tfxzjrpu1y3kokdp7i5b0k6

Kz = 20.65802330515155      (best value for Kz, for hypothesis A, for H_o = 71)

5.1.1) Shrinking speed SHV along the time in function of the redshift

The shrinking speed SHV of the Bohr radius can be defined as dr/dt_.

The Bohr radius in the past is defined by the function: 

r_f  =  r_o x^2/3      =>              

t = K_z  (x^2/3-1)   (IV) =>

SHV  = r_o / ( K_z (31 556 926.08)  (10)⁹  )                       

SHV  =  8.117414  (10)^-29  m/s   =  constant (for hypothesis A)

The Shrinking speed is constant along the time, for hypothesis A. 

The full solving for the SHV can be found here:

https://app.box.com/s/lu5gmwwj5tfxzjrpu1y3kokdp7i5b0k6

                                                                                                             

                        

5.1.2) Specific shrinking speed (SPV)

The specific shrinking speed is defined as  V_f  / r_f .

Vf : Shrinking speed in a reference frame SHV (IX).

r_f : Bohr radius  in a reference frame. r_f  (VIII).

So,     SPV = x ^-2/3/(K_z (31 556 926.08) 10⁹)       m/s /m  (X)

SPV = x ^-2/3 (3.085 677 581 492 37)(10)⁹ / (K_z  31 556 926.08)    Km/s /mpc   

The full solving for the SPV can be found here: 

https://app.box.com/s/lu5gmwwj5tfxzjrpu1y3kokdp7i5b0k6

For Z = 0  =>  x = 1  =>  SPV = 1.534 (10)^-18   m/s /m

The equatorial radius of the Earth is 6 378 136.3 m.

The shrinking speed of the Earth would be:

SHV = (6378136,3) (1.534) (10)^-18   =>

SHV = 9.7839 (10)^-12  m/s

1 year  = 31 556 926.08 seconds, so,

SHV =  (31 556 926.08) (9.7839)(10)^-12  m/year    =>

SHV = 3.0875 (10) ^-4   m / yr

SHV = 0.30875        mm / yr

SHV = 308.75             m / Myr

              

5.2) Hypothesis B:

This hypothesis proposes the LVL (d_VL/dt) variance is proportional to the volume VL_f  of the atom, so we can write:

LVL/VL_f = constsnt = K_v =>

(d_VL / d_t) / VL_f  = K_v     

d_t = d_VL / (K_v  VL_f)       (XI) =>

t = K_z ln(x)          (XIII)

The full solving for the above function can be found here: 

https://app.box.com/s/lu5gmwwj5tfxzjrpu1y3kokdp7i5b0k6

x = (1+Z)  =>     (t/K_z) = ln(x) =>     x = e^(t/Kz)   =>  1+Z = e^(t/Kz) =>    

Z = e^(t/Kz) -1        (For hypothesis B)    

e = 2.718 281 828 459 05

K_Z = see below resolution

t : (Gyr)

Now we can determine the best value to the constant Kz, so that calibrating the equation to the observed distances. This calibration must be done at low redshift, where we can determine the distances by parallax. This mean the above function should give us the same value when the redshift is null (zero), and at low redshifts give us neglected differences.

This mean the tangent of the above function at Z= 0, should be the same as the tangent in the respective function of the standard model (expansion universe).

In the standard model, (expanding universe), the equation to define the distance is:

                     

D = t =  ((x²-1) c 3.26) / ((x² + 1) H_o 10⁶)     mpc   (VI)

c = light speed = 299792458 m/s

H0 = Hubble constant = 71 km/s/mpc

When deriving and matching the distance equations of the shrinking model and the standard model, we have:

K_z = ( c 3.26) / ( H_o 10⁶)   =>

K_Z = 13.772 015 536 767 7  (best value for Kz in the function (XIII), hypothesis B, for H_o = 71)

c = light speed = 299792458 m/s

H₀ = Hubble constant = 71 km/s/mpc

The exact value of the conversion factor “3.26” is (3.261 633 430 119 53), and it should be used for taking of accurate results.

The full solving for the K_z constant can be found here: 

https://app.box.com/s/lu5gmwwj5tfxzjrpu1y3kokdp7i5b0k6

5.2.1) The Shrinking speed SHV along the time in function of the redshift

The shrinking speed SHV of the Bohr radius can be defined as dr/dt_.

The Bohr radius in the past is defined by the function:

r_f  =  r_o x^2/3      =>                      dr = 2 r_o x ^-1/3 / 3          

 t = K_z ln(x)   (XIII )       =>      dt =  K_z / x (XII) =>

SHV = dr/dt = 2 r_o x^2/3/(3 K_z)            m / Gyr          =>

SHV =  2 r_o x^2/3/(3 K_z (31 556 926.08) 10⁹ )   m/s  (XIV)

   

x = (1+Z)

The full solving for the SHV can be found here: 

https://app.box.com/s/lu5gmwwj5tfxzjrpu1y3kokdp7i5b0k6

5.2.2) Specific shrinking speed (SPV)

The specific shrinking speed SPV is defined as V_f  / r_f .

V_f  : Shrinking speed in a reference frame SHV (XIV).

r_f : Bohr radius  in a reference frame.

r_f  = r_o x^2/3    =>

SPV = 2 / (3 K_z (31 556 926.08) 10⁹)    m/s /m    (XV)

SPV = 1,5339 (10)^-18   m/s /m

SPV = 2 (3.085 677 581 492 37)(10)¹⁰ / (3 K_z  31 556 926.08 )  km/s /mpc

SPV = 47.333  km/s /mpc

                     

5.2.3) The Shrinking acceleration (SHA) along the time in function of the redshift

The shrinking acceleration SHA is defined as the variation of the speed in function of the time, so, it can be defined mathematically as:

SHA  = dv / dt  =>

V = SHV  (IX)      and      d_t = (VII)

SHA = 4 r_o x^2/3 / (9 (K_z)² (31 556 926.08) (10)⁹ )  m/s   /Gyr  =>

SHA = 4 r_o x^2/3 / (9 (K_z)² (31 556 926.08) (10)¹² )  m/s   /Myr    (XVI)

The full solving for the SHV can be found here: 

https://app.box.com/s/lu5gmwwj5tfxzjrpu1y3kokdp7i5b0k6

5.2.4) Specific shrinking acceleration (SPA) along the time in function of the redshift

The specific acceleration SPA is defined as the shrinking acceleration SHA per unit of length.

This means as bigger the length of a body, as bigger the SHA.

The SPA can be defined as:      SPA = SHA / r_f

SPA = 4 / (9 (K_z)² (31 556 926.08) (10)¹² )  m/s /m  /Myr  =>  (XVII)

For hypothesis B,  SPA = Constant = 7.4245 (10)^-23   m/s /m /Myr

SPA = 4(3.085 677 581 492 37)(10)⁷ / (9 (K_z)² (31 556 926.08) )  km/s /mpc  /Myr  =>

For hypothesis B,  SPA = Constant = 2.2909 (10)^-3     km/s /mpc /Myr

The Graphic 01 presents the comparative evolution of the distance (Gly) or time (Gyr), for the shrinking Model hypothesis A “Time shrM A”, the shrinking Model hypothesis B “Time shrM B”, and the standard Model “Time stdM”.

Graphic  01

THE SHRINKING MATTER THEORY

1) THE SHRINKING MATTER THEORY

This blog is not to disprove the big bang theory, but for those not yet brainwashed by the believers in such theory.

The first step of the Shrinking Matter Theory is a compact summary, but it contains all the basic mathematic to assume the universe as the reference frame.

The shrinking matter theory and the expansion universe theory are equivalent. If we make our world as the reference frame, the universe should expand. If we make the universe as the reference frame, the matter should shrink. The laws of physics work to both theories.

The main diference of the expansion universe and the shrinking matter theory is what is the cause of the longer wavelenght observed of the deep space objects.

The doppler shift (redshift) is well known in the expansion theory.

In the shrinking matter theory, the universe is the reference frame, so there is not expansion to cause redshift (except in the systemic local movements like rotation, orbits, binary systems, turbulence, ejection, gravitational effect and gravitational falling), so, the longer wavelenghts observed are actually longer emission lines due the bigger size of the atoms in the past.

If we assume the speed of the light is constant along the time, the Planck constant  “h” should grow by the factor of (1+Z)^(1/3) in the past. This mean the constant plank decrease along the time.

To simplify, we could call (1+Z)^(1/3)=Kh, so, h(f)=Kh x h(o).

Z : (observed redshift)               

h(f): Planck constant in the observed frame.

h(o): Planck constant of our local frame.

Constant dependence:

We must apply the constant Kh for all formulae and constants used in physics were the Planck constant “h” is used.

So that simplify the work, we can apply the constant Kh directly over the used values of our local frame, observing the right exponential use of the Planck constant as follow;

h(f)=Kh x h(o)                “Planck constant”  

λ(f)=(Kh)³ x λ(o)            “wavelenght emission lines”

r(f)=(Kh)² x r(o)             “Bohr radius”

E(f)= E(o) / (Kh)²           “energy of the emission line”

WDC(f)=(Kh) x WDC(o)   “Wien Displacement Constant”

K∞(f)=K∞(o) / (Kh)³       “Rydberg constant”

T(f)=T(o) / (Kh)²             “Temperature of the emission line (Wien)”

(f) observed frame in the past.

(o) our local frame at the presente

     2) Exemple of changing to a reference frame in the past

Suppose we search a galaxy and we detect the Lyα emission being three times greater than the Lyα in our world. The wavelenght is exactly 3647,07 Â.

The H Lyα in our frame is 1215,69 Â.

So, the apparent redshift Z(f) is Lyα(f)/Lyα(o)-1 = 2

The constant Kh is (1+Z(f))^(1/3) = (1+2)^(1/3) =1,44224957

So, Kh=1,44224957

Now we can determine the main constants of the reference frame in the past;

cst/vle              formula*             local frame(o)           past frame(f)

h(f)              h(o) x (Kh)        6,62606957E-34 Js      9,5564460E-34 Js

Lyα(f)      Lyα(o) x (Kh)³              1215,69                   3647,07 Â

r(f) “Bohr”       r(o) x (Kh)²             0,529                      1,1007 Â

E(f)             E(o) / (Kh)²               10,204 Ev                   4,906 Ev

WDC(f)    WDC(o) x (Kh)            0,0028978 mK             0,0041796 mK 

               

K∞(f)       K∞(o) / (Kh)³         10973730,68 m-¹          3657910,22 m-¹

T(f)             T(o) / (Kh)²              23836 ºK                    11459 °K

(f) observed frame in the past

(o) local frame at the present

 * simplified formula

If we consider Ho=71 km/s/mpc and assume it is enough to determine the distance, we have:

distance= 3380,3 mpc   = 11,02 GLY

time (past) = 11,02 Gyr

Ho= Hublle constant

3) The CMBs and the Shrinking Matter Theory   

The lack of bandwidth emissions pattern avoids us to determine exactly what actually the CMBs are. This could let us to various scenarios.

One is assuming the CMBs could be the first thermal emission lines. In this scenario, if we consider the CMBs are Lyman alpha emissions, we have:

Temperature: ______________56,15 K

Wavelength: ______________1,063214 mm

Energy: __________________0,024039 eV

WDC :____________________0,059703 mK

Z: _______________________8744,81

Another scenario is to assume the CMBs could be hydrogen fine structure emission lines. In this case, the redshift is negative (blue shift), and the radiation could be the remaining of the collapsed universe, which provided the energy to the emergence of the universe we know. In this case we have:

Temperature:_____________0,46721  K

Wavelength: ______________1,063214 mm

Energy: __________________2 x 10^-4  eV

WDC:__________________4,967462 x 10^-4 mK

Z (blueshift):_____________-0,99496253

The shrinking matter theory states that the Planck constant “h” varies along the time, so the energy of the emissions also varies with the time. In this scenario, there is a systematic error in our researches assuming that the observed waves, emitted in the past and detected in our devices have the same energy as the waves produced in our local frame. We shouldn’t forget that the waves with the same frequency can be added and give the impression that they are more energetic. The amount of energy of each wave could be determined by the receptor, but it may not represent the real emitted energy of the wave.

The CMBs are the most populous microwaves in the universe, as well the hydrogen is the most abundant element in nature, so, for now we should suppose (and state), the CMBs are the hydrogen fine structure emission lines of the collapsed universe which provided the energy to the emergence of the universe we know. I know it is a hard exercise for the minds which are indoctrinated in assuming the BB as a fact, but I hope you can. We know the CMBs are the most distant emissions detected, among the unresolved CXRBs, so, in this scenario, the wavelength of the CMB, compared with the hydrogen fine structure emission in our reference frame (21 cm), the negative redshift (blue shift), could only be attributed to the remaining fine structure emissions of the hydrogen in its collapsed last phase of the cyclic universe.

     

In this scenario, as issued later, the redshift is negative (blue shift), and can be calculated as follow:

 Z= (1,063214/211,06114)-1   =>

 Z = -0,99496253

Kh = (1+Z)^(1/3) = ( 1 - 0,99496253)^(1/3) =>

Kh = 0,171 423 684

The constant Planck h(f) in this scenario would be:  h(f) = Kh x h(o) =>

h (f) = 0,171 423 684 x 6,626 069 57 x 10^-34 =>

h (f) = 1,135 865 258 x 10^-34 Js

When we replace the h(o) by the h(f) in the formulae, we have:

r(f) = 1,555 pm  (Bohr radius)

Lyα(f) = 6,123975 Â

E (Lyα(f)) =347,248 eV

E (n=1) = -463 eV

T (Lyα(f))= 811 150,06 K

WDC * = 4,967462 x 10^-4 mK

In this transition, (Lyα(f)), the fine structure emission lines can happens in the ground state and would be:

Temperature:_______________0,46721  K

Wavelength:_______________1,063214 mm

Energy:___________________2 x 10^-4  eV

WDC:____________________4,967462 x 10^-4 mK

The unexpected and most important result in this scenario is that the Lyα(f) falls surprisingly in the lower end band of the unresolved CXRB (Cosmic X-Ray Background). So, the shrinking matter theory (in this scenario) could solve the origin of the CMB and the unresolved CXRB as being remnants of the past collapsed universe, and the future of this universe. Of course this needs further resources, but it is a strong evidence of the consistence of this theory.

         4 ) The Fine-structure constant and the Shrinking Matter Theory

The fine-structure constant “α” is a dimensionless value, but it reflects the relationship between the electromagnetic coupling constant ‘e” and ”Ԑₒ”, “h”, and “c”.

e = (2 α Ԑₒ h c) ^ (1/2)   or   e² = 2 α Ԑₒ h c

As c is constant, result Ԑₒ is also constant, then α should vary with the inverse of the rate of h.

Rewriting the expression we have:

α = e² / (2 Ԑₒ c h), and

α(o) = e² / (2 Ԑₒ c h(o) ) =>

α(f) = e² / (2 Ԑₒ c h(f) ) =>

α(f) = e² / (2 Ԑₒ c h(o) (Kh))

Then α(f) = α(o) / Kh 

Or  α(f) = α(o)  / ( (1+Z)^(1/3) )

α(o)  =  0,007 297 352 5698(24)

(o): our local frame

(f): distant reference frame

Z : redshift

Kh: scaling factor of the constant Planck h as a function of Z

“However, if multiple coupling constants are allowed to vary simultaneously, not just α, then in fact almost all combinations of values support a form of stellar fusion.” https://en.wikipedia.org/wiki/Fine-structure_constant

The Fine-structure constant and the Shrinking Matter Theory

          4 ) The Fine-structure constant and the Shrinking Matter Theory

The fine-structure constant “α” is a dimensionless value, but it reflects the relationship between the electromagnetic coupling constant ‘e” and ”Ԑₒ”, “h”, and “c”.

e = (2 α Ԑₒ h c) ^ (1/2)   or   e² = 2 α Ԑₒ h c

As c is constant, result Ԑₒ is also constant, then α should vary with the inverse of the rate of h.

Rewriting the expression we have:

α = e² / (2 Ԑₒ c h), and

α(o) = e² / (2 Ԑₒ c h(o) ) =>

α(f) = e² / (2 Ԑₒ c h(f) ) =>

α(f) = e² / (2 Ԑₒ c h(o) (Kh))

Then α(f) = α(o) / Kh 

Or  α(f) = α(o)  / ( (1+Z)^(1/3) )

α(o)  =  0,007 297 352 5698(24)

(o): our local frame

(f): distant reference frame

Z : redshift

Kh: scaling factor of the constant Planck h as a function of Z

“However, if multiple coupling constants are allowed to vary simultaneously, not just α, then in fact almost all combinations of values support a form of stellar fusion.” https://en.wikipedia.org/wiki/Fine-structure_constant

3) The CMBs and the Shrinking Matter Theory

The lack of bandwidth emissions pattern avoids us to determine exactly what actually the CMBs are. This could let us to various scenarios.

One is assuming the CMBs could be the first thermal emission lines. In this scenario, if we consider the CMBs are Lyman alpha emissions, we have:

Temperature: ______________56,15 K

Wavelength: ______________1,063214 mm

Energy: __________________0,024039 eV

WDC :____________________0,059703 mK

Z: _______________________8744,81

Another scenario is to assume the CMBs could be hydrogen fine structure emission lines. In this case, the redshift is negative (blue shift), and the radiation could be the remaining of the collapsed universe, which provided the energy to the emergence of the universe we know. In this case we have:

Temperature:_____________0,46721  K

Wavelength: ______________1,063214 mm

Energy: __________________2 x 10~-4  eV

WDC:__________________4,967462 x 10^-4 mK

Z (blueshift):_____________-0,99496253

The shrinking matter theory states that the constant Planck “h” varies along the time, so the energy of the emissions also varies with the time. In this scenario, there is a systematic error in our researches assuming that the observed waves, emitted in the past and detected in our devices have the same energy as the waves produced in our local frame. We shouldn’t forget that the waves with the same frequency can be added and give the impression that they are more energetic. The amount of energy of each wave could be determined by the receptor, but it may not represent the real emitted energy of the wave.

The CMBs are the most populous microwaves in the universe, as well the hydrogen is the most abundant element in nature, so, for now we should suppose (and state), the CMBs are the hydrogen fine structure emission lines of the collapsed universe which provided the energy to the emergence of the universe we know. I know it is a hard exercise for the minds which are indoctrinated in assuming the BB as a fact, but I hope you can. We know the CMBs are the most distant emissions detected, among the unresolved CXRBs, so, in this scenario, the wavelength of the CMB, compared with the hydrogen fine structure emission in our reference frame (21 cm), the negative redshift (blue shift), could only be attributed to the remaining fine structure emissions of the hydrogen in its collapsed last phase of the cyclic universe.

     

In this scenario, as issued later, the redshift is negative (blue shift), and can be calculated as follow:

 Z= (1,063214/211,06114)-1   =>

 Z = -0,99496253

Kh = (1+Z)^(1/3) = ( 1 - 0,99496253)^(1/3) =>

Kh = 0,171 423 684

The constant Planck h(f) in this scenario would be:  h(f) = Kh x h(o) =>

h (f) = 0,171 423 684 x 6,626 069 57 x 10^-34 =>

h (f) = 1,135 865 258 x 10^-34 Js

When we replace the h(o) by the h(f) in the formulae, we have:

r(f) = 1,555 pm  (Bohr radius)

Lyα(f) = 6,123975 Â

E (Lyα(f)) =347,248 eV

E (n=1) = -463 eV

T (Lyα(f))= 811 150,06 K

WDC * = 4,967462 x 10^-4 mK

In this transition, (Lyα(f)), the fine structure emission lines can happens in the ground state and would be:

Temperature:_______________0,46721  K

Wavelength:_______________1,063214 mm

Energy:___________________2 x 10^-4  eV

WDC:____________________4,967462 x 10^-4 mK

The unexpected and most important result in this scenario is that the Lyα(f) falls surprisingly in the lower end band of the unresolved CXRB (Cosmic X-Ray Background). So, the shrinking matter theory (in this scenario) could solve the origin of the CMB and the unresolved CXRB as being remnants of the past collapsed universe, and the future of this universe. Of course this needs further resources, but it is a strong evidence of the consistence of this theory.